0s autopkgtest [20:22:21]: starting date and time: 2024-03-16 20:22:21+0000 0s autopkgtest [20:22:21]: git checkout: b506e79c ssh-setup/nova: fix ARCH having two lines of data 0s autopkgtest [20:22:21]: host juju-7f2275-prod-proposed-migration-environment-3; command line: /home/ubuntu/autopkgtest/runner/autopkgtest --output-dir /tmp/autopkgtest-work.u1gljowl/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=src:r-base,src:curl,src:glib2.0,src:libpng1.6,src:libpsl,src:libtirpc,src:libxt,src:openssl,src:orthanc-python,src:readline,src:wp2latex --apt-upgrade r-cran-systemfit --timeout-short=300 --timeout-copy=20000 --timeout-build=20000 '--env=ADT_TEST_TRIGGERS=r-base/4.3.3-2build1 curl/8.5.0-2ubuntu7 glib2.0/2.79.3-3ubuntu5 libpng1.6/1.6.43-3 libpsl/0.21.2-1.1 libtirpc/1.3.4+ds-1.1 libxt/1:1.2.1-1.2 openssl/3.0.13-0ubuntu1 orthanc-python/4.1+ds-2build3 readline/8.2-3.1 wp2latex/4.4~ds-1build1' -- ssh -s /home/ubuntu/autopkgtest/ssh-setup/nova -- --flavor autopkgtest --security-groups autopkgtest-juju-7f2275-prod-proposed-migration-environment-3@bos03-arm64-20.secgroup --name adt-noble-arm64-r-cran-systemfit-20240316-202221-juju-7f2275-prod-proposed-migration-environment-3 --image adt/ubuntu-noble-arm64-server --keyname testbed-juju-7f2275-prod-proposed-migration-environment-3 --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/ 82s autopkgtest [20:23:43]: testbed dpkg architecture: arm64 82s autopkgtest [20:23:43]: testbed apt version: 2.7.12 82s autopkgtest [20:23:43]: @@@@@@@@@@@@@@@@@@@@ test bed setup 83s Get:1 http://ftpmaster.internal/ubuntu noble-proposed InRelease [117 kB] 83s Get:2 http://ftpmaster.internal/ubuntu noble-proposed/restricted Sources [6540 B] 83s Get:3 http://ftpmaster.internal/ubuntu noble-proposed/universe Sources [3704 kB] 84s Get:4 http://ftpmaster.internal/ubuntu noble-proposed/multiverse Sources [51.4 kB] 84s Get:5 http://ftpmaster.internal/ubuntu noble-proposed/main Sources [474 kB] 84s Get:6 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 Packages [646 kB] 84s Get:7 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 c-n-f Metadata [3144 B] 84s Get:8 http://ftpmaster.internal/ubuntu noble-proposed/restricted arm64 Packages [33.6 kB] 84s Get:9 http://ftpmaster.internal/ubuntu noble-proposed/restricted arm64 c-n-f Metadata [116 B] 84s Get:10 http://ftpmaster.internal/ubuntu noble-proposed/universe arm64 Packages [4012 kB] 84s Get:11 http://ftpmaster.internal/ubuntu noble-proposed/universe arm64 c-n-f Metadata [8528 B] 84s Get:12 http://ftpmaster.internal/ubuntu noble-proposed/multiverse arm64 Packages [55.5 kB] 84s Get:13 http://ftpmaster.internal/ubuntu noble-proposed/multiverse arm64 c-n-f Metadata [116 B] 86s Fetched 9112 kB in 2s (5243 kB/s) 86s Reading package lists... 89s Reading package lists... 89s Building dependency tree... 89s Reading state information... 89s Calculating upgrade... 90s The following packages will be REMOVED: 90s libglib2.0-0 libssl3 90s The following NEW packages will be installed: 90s libglib2.0-0t64 libssl3t64 xdg-user-dirs 90s The following packages have been kept back: 90s curl 90s The following packages will be upgraded: 90s gir1.2-glib-2.0 libglib2.0-data libtirpc-common openssl readline-common 90s ubuntu-minimal ubuntu-standard 90s 7 upgraded, 3 newly installed, 2 to remove and 1 not upgraded. 90s Need to get 4613 kB of archives. 90s After this operation, 211 kB of additional disk space will be used. 90s Get:1 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 gir1.2-glib-2.0 arm64 2.79.3-3ubuntu5 [182 kB] 91s Get:2 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libglib2.0-0t64 arm64 2.79.3-3ubuntu5 [1527 kB] 91s Get:3 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 openssl arm64 3.0.13-0ubuntu1 [983 kB] 91s Get:4 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libssl3t64 arm64 3.0.13-0ubuntu1 [1770 kB] 91s Get:5 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libglib2.0-data all 2.79.3-3ubuntu5 [46.6 kB] 91s Get:6 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 libtirpc-common all 1.3.4+ds-1.1 [8018 B] 91s Get:7 http://ftpmaster.internal/ubuntu noble-proposed/main arm64 readline-common all 8.2-3.1 [56.4 kB] 91s Get:8 http://ftpmaster.internal/ubuntu noble/main arm64 ubuntu-minimal arm64 1.536 [10.7 kB] 91s Get:9 http://ftpmaster.internal/ubuntu noble/main arm64 xdg-user-dirs arm64 0.18-1 [18.1 kB] 91s Get:10 http://ftpmaster.internal/ubuntu noble/main arm64 ubuntu-standard arm64 1.536 [10.7 kB] 92s Fetched 4613 kB in 1s (4913 kB/s) 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 ... 74758 files and directories currently installed.) 92s Preparing to unpack .../gir1.2-glib-2.0_2.79.3-3ubuntu5_arm64.deb ... 92s Unpacking gir1.2-glib-2.0:arm64 (2.79.3-3ubuntu5) over (2.79.2-1~ubuntu1) ... 92s dpkg: libglib2.0-0:arm64: dependency problems, but removing anyway as you requested: 92s udisks2 depends on libglib2.0-0 (>= 2.77.0). 92s shared-mime-info depends on libglib2.0-0 (>= 2.75.3). 92s python3-gi depends on libglib2.0-0 (>= 2.77.0). 92s python3-dbus depends on libglib2.0-0 (>= 2.16.0). 92s netplan.io depends on libglib2.0-0 (>= 2.70.0). 92s netplan-generator depends on libglib2.0-0 (>= 2.70.0). 92s libxmlb2:arm64 depends on libglib2.0-0 (>= 2.54.0). 92s libvolume-key1:arm64 depends on libglib2.0-0 (>= 2.18.0). 92s libudisks2-0:arm64 depends on libglib2.0-0 (>= 2.75.3). 92s libqrtr-glib0:arm64 depends on libglib2.0-0 (>= 2.56). 92s libqmi-proxy depends on libglib2.0-0 (>= 2.30.0). 92s libqmi-glib5:arm64 depends on libglib2.0-0 (>= 2.54.0). 92s libpolkit-gobject-1-0:arm64 depends on libglib2.0-0 (>= 2.38.0). 92s libpolkit-agent-1-0:arm64 depends on libglib2.0-0 (>= 2.38.0). 92s libnetplan0:arm64 depends on libglib2.0-0 (>= 2.75.3). 92s libmm-glib0:arm64 depends on libglib2.0-0 (>= 2.62.0). 92s libmbim-proxy depends on libglib2.0-0 (>= 2.56). 92s libmbim-glib4:arm64 depends on libglib2.0-0 (>= 2.56). 92s libjson-glib-1.0-0:arm64 depends on libglib2.0-0 (>= 2.75.3). 92s libjcat1:arm64 depends on libglib2.0-0 (>= 2.75.3). 92s libgusb2:arm64 depends on libglib2.0-0 (>= 2.75.3). 92s libgudev-1.0-0:arm64 depends on libglib2.0-0 (>= 2.38.0). 92s libgirepository-1.0-1:arm64 depends on libglib2.0-0 (>= 2.79.0). 92s libfwupd2:arm64 depends on libglib2.0-0 (>= 2.79.0). 92s libblockdev3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s libblockdev-utils3:arm64 depends on libglib2.0-0 (>= 2.75.3). 92s libblockdev-swap3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s libblockdev-part3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s libblockdev-nvme3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s libblockdev-mdraid3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s libblockdev-loop3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s libblockdev-fs3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s libblockdev-crypto3:arm64 depends on libglib2.0-0 (>= 2.42.2). 92s fwupd depends on libglib2.0-0 (>= 2.79.0). 92s bolt depends on libglib2.0-0 (>= 2.56.0). 92s 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 ... 74758 files and directories currently installed.) 92s Removing libglib2.0-0:arm64 (2.79.2-1~ubuntu1) ... 92s Selecting previously unselected package libglib2.0-0t64:arm64. 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 ... 74733 files and directories currently installed.) 92s Preparing to unpack .../libglib2.0-0t64_2.79.3-3ubuntu5_arm64.deb ... 92s libglib2.0-0t64.preinst: Removing /var/lib/dpkg/info/libglib2.0-0:arm64.postrm to avoid loss of /usr/share/glib-2.0/schemas/gschemas.compiled... 92s removed '/var/lib/dpkg/info/libglib2.0-0:arm64.postrm' 92s Unpacking libglib2.0-0t64:arm64 (2.79.3-3ubuntu5) ... 92s Preparing to unpack .../openssl_3.0.13-0ubuntu1_arm64.deb ... 92s Unpacking openssl (3.0.13-0ubuntu1) over (3.0.10-1ubuntu4) ... 93s dpkg: libssl3:arm64: dependency problems, but removing anyway as you requested: 93s wget depends on libssl3 (>= 3.0.0). 93s u-boot-tools depends on libssl3 (>= 3.0.0). 93s tnftp depends on libssl3 (>= 3.0.0). 93s tcpdump depends on libssl3 (>= 3.0.0). 93s systemd-resolved depends on libssl3 (>= 3.0.0). 93s systemd depends on libssl3 (>= 3.0.0). 93s sudo depends on libssl3 (>= 3.0.0). 93s sbsigntool depends on libssl3 (>= 3.0.0). 93s rsync depends on libssl3 (>= 3.0.0). 93s python3-cryptography depends on libssl3 (>= 3.0.0). 93s openssh-server depends on libssl3 (>= 3.0.10). 93s openssh-client depends on libssl3 (>= 3.0.10). 93s mtd-utils depends on libssl3 (>= 3.0.0). 93s mokutil depends on libssl3 (>= 3.0.0). 93s linux-headers-6.8.0-11-generic depends on libssl3 (>= 3.0.0). 93s libsystemd-shared:arm64 depends on libssl3 (>= 3.0.0). 93s libssh-4:arm64 depends on libssl3 (>= 3.0.0). 93s libsasl2-modules:arm64 depends on libssl3 (>= 3.0.0). 93s libsasl2-2:arm64 depends on libssl3 (>= 3.0.0). 93s libpython3.12-minimal:arm64 depends on libssl3 (>= 3.0.0). 93s libnvme1 depends on libssl3 (>= 3.0.0). 93s libkrb5-3:arm64 depends on libssl3 (>= 3.0.0). 93s libkmod2:arm64 depends on libssl3 (>= 3.0.0). 93s libfido2-1:arm64 depends on libssl3 (>= 3.0.0). 93s libcurl4:arm64 depends on libssl3 (>= 3.0.0). 93s libcryptsetup12:arm64 depends on libssl3 (>= 3.0.0). 93s kmod depends on libssl3 (>= 3.0.0). 93s dhcpcd-base depends on libssl3 (>= 3.0.0). 93s bind9-libs:arm64 depends on libssl3 (>= 3.0.0). 93s 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 ... 74758 files and directories currently installed.) 93s Removing libssl3:arm64 (3.0.10-1ubuntu4) ... 93s Selecting previously unselected package libssl3t64:arm64. 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 ... 74747 files and directories currently installed.) 93s Preparing to unpack .../0-libssl3t64_3.0.13-0ubuntu1_arm64.deb ... 93s Unpacking libssl3t64:arm64 (3.0.13-0ubuntu1) ... 93s Preparing to unpack .../1-libglib2.0-data_2.79.3-3ubuntu5_all.deb ... 93s Unpacking libglib2.0-data (2.79.3-3ubuntu5) over (2.79.2-1~ubuntu1) ... 93s Preparing to unpack .../2-libtirpc-common_1.3.4+ds-1.1_all.deb ... 93s Unpacking libtirpc-common (1.3.4+ds-1.1) over (1.3.4+ds-1build1) ... 93s Preparing to unpack .../3-readline-common_8.2-3.1_all.deb ... 93s Unpacking readline-common (8.2-3.1) over (8.2-3) ... 93s Preparing to unpack .../4-ubuntu-minimal_1.536_arm64.deb ... 93s Unpacking ubuntu-minimal (1.536) over (1.535) ... 93s Selecting previously unselected package xdg-user-dirs. 93s Preparing to unpack .../5-xdg-user-dirs_0.18-1_arm64.deb ... 93s Unpacking xdg-user-dirs (0.18-1) ... 93s Preparing to unpack .../6-ubuntu-standard_1.536_arm64.deb ... 93s Unpacking ubuntu-standard (1.536) over (1.535) ... 93s Setting up ubuntu-minimal (1.536) ... 93s Setting up xdg-user-dirs (0.18-1) ... 93s Setting up libssl3t64:arm64 (3.0.13-0ubuntu1) ... 93s Setting up libtirpc-common (1.3.4+ds-1.1) ... 93s Setting up ubuntu-standard (1.536) ... 93s Setting up libglib2.0-0t64:arm64 (2.79.3-3ubuntu5) ... 94s No schema files found: doing nothing. 94s Setting up libglib2.0-data (2.79.3-3ubuntu5) ... 94s Setting up gir1.2-glib-2.0:arm64 (2.79.3-3ubuntu5) ... 94s Setting up openssl (3.0.13-0ubuntu1) ... 94s Setting up readline-common (8.2-3.1) ... 94s Processing triggers for man-db (2.12.0-3) ... 95s Processing triggers for install-info (7.1-3) ... 95s Processing triggers for libc-bin (2.39-0ubuntu2) ... 95s Reading package lists... 96s Building dependency tree... 96s Reading state information... 97s 0 upgraded, 0 newly installed, 0 to remove and 1 not upgraded. 98s sh: Attempting to set up Debian/Ubuntu apt sources automatically 98s sh: Distribution appears to be Ubuntu 99s Reading package lists... 99s Building dependency tree... 99s Reading state information... 100s eatmydata is already the newest version (131-1). 100s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 100s Reading package lists... 100s Building dependency tree... 100s Reading state information... 101s dbus is already the newest version (1.14.10-4ubuntu1). 101s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 101s Reading package lists... 102s Building dependency tree... 102s Reading state information... 103s rng-tools-debian is already the newest version (2.4). 103s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 103s Reading package lists... 104s Building dependency tree... 104s Reading state information... 105s The following packages will be REMOVED: 105s cloud-init* python3-configobj* python3-debconf* 105s 0 upgraded, 0 newly installed, 3 to remove and 0 not upgraded. 105s After this operation, 3252 kB disk space will be freed. 105s (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 ... 74774 files and directories currently installed.) 105s Removing cloud-init (24.1.1-0ubuntu1) ... 106s Removing python3-configobj (5.0.8-3) ... 106s Removing python3-debconf (1.5.86) ... 106s Processing triggers for man-db (2.12.0-3) ... 107s (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 ... 74385 files and directories currently installed.) 107s Purging configuration files for cloud-init (24.1.1-0ubuntu1) ... 108s dpkg: warning: while removing cloud-init, directory '/etc/cloud/cloud.cfg.d' not empty so not removed 108s Processing triggers for rsyslog (8.2312.0-3ubuntu3) ... 108s invoke-rc.d: policy-rc.d denied execution of try-restart. 108s Reading package lists... 108s Building dependency tree... 108s Reading state information... 109s linux-generic is already the newest version (6.8.0-11.11+1). 109s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 110s Hit:1 http://ftpmaster.internal/ubuntu noble InRelease 110s Hit:2 http://ftpmaster.internal/ubuntu noble-updates InRelease 110s Hit:3 http://ftpmaster.internal/ubuntu noble-security InRelease 112s Reading package lists... 113s Reading package lists... 113s Building dependency tree... 113s Reading state information... 113s Calculating upgrade... 113s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 114s Reading package lists... 114s Building dependency tree... 114s Reading state information... 114s 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 115s autopkgtest [20:24:16]: rebooting testbed after setup commands that affected boot 152s autopkgtest-virt-ssh: WARNING: ssh connection failed. Retrying in 3 seconds... 159s autopkgtest [20:25:00]: testbed running kernel: Linux 6.8.0-11-generic #11-Ubuntu SMP PREEMPT_DYNAMIC Wed Feb 14 02:53:31 UTC 2024 162s autopkgtest [20:25:03]: @@@@@@@@@@@@@@@@@@@@ apt-source r-cran-systemfit 165s Get:1 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (dsc) [2203 B] 165s Get:2 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (tar) [1040 kB] 165s Get:3 http://ftpmaster.internal/ubuntu noble/universe r-cran-systemfit 1.1-30-1 (diff) [2516 B] 165s gpgv: Signature made Wed Jun 28 12:43:54 2023 UTC 165s gpgv: using RSA key F1F007320A035541F0A663CA578A0494D1C646D1 165s gpgv: issuer "tille@debian.org" 165s gpgv: Can't check signature: No public key 165s dpkg-source: warning: cannot verify inline signature for ./r-cran-systemfit_1.1-30-1.dsc: no acceptable signature found 165s autopkgtest [20:25:06]: testing package r-cran-systemfit version 1.1-30-1 166s autopkgtest [20:25:07]: build not needed 167s autopkgtest [20:25:08]: test run-unit-test: preparing testbed 168s Reading package lists... 168s Building dependency tree... 168s Reading state information... 169s Starting pkgProblemResolver with broken count: 0 169s Starting 2 pkgProblemResolver with broken count: 0 169s Done 169s The following additional packages will be installed: 169s fontconfig fontconfig-config fonts-dejavu-core fonts-dejavu-mono 169s fonts-glyphicons-halflings fonts-mathjax libblas3 libcairo2 libdatrie1 169s libdeflate0 libfontconfig1 libgfortran5 libgomp1 libgraphite2-3 169s libharfbuzz0b libice6 libjbig0 libjpeg-turbo8 libjpeg8 libjs-bootstrap 169s libjs-highlight.js libjs-jquery libjs-jquery-datatables libjs-mathjax 169s liblapack3 liblerc4 libnlopt0 libpango-1.0-0 libpangocairo-1.0-0 169s libpangoft2-1.0-0 libpaper-utils libpaper1 libpixman-1-0 libsharpyuv0 libsm6 169s libtcl8.6 libthai-data libthai0 libtiff6 libtk8.6 libwebp7 libxcb-render0 169s libxcb-shm0 libxft2 libxrender1 libxss1 libxt6 littler node-normalize.css 169s r-base-core r-cran-abind r-cran-backports r-cran-bdsmatrix r-cran-bit 169s r-cran-bit64 r-cran-boot r-cran-brio r-cran-broom r-cran-callr r-cran-car 169s r-cran-cardata r-cran-caret r-cran-cellranger r-cran-class r-cran-cli 169s r-cran-clipr r-cran-clock r-cran-codetools r-cran-collapse r-cran-colorspace 169s r-cran-conquer r-cran-cpp11 r-cran-crayon r-cran-curl r-cran-data.table 169s r-cran-desc r-cran-diagram r-cran-diffobj r-cran-digest r-cran-dplyr 169s r-cran-e1071 r-cran-ellipsis r-cran-evaluate r-cran-fansi r-cran-farver 169s r-cran-forcats r-cran-foreach r-cran-foreign r-cran-formula r-cran-fs 169s r-cran-future r-cran-future.apply r-cran-generics r-cran-ggplot2 169s r-cran-globals r-cran-glue r-cran-gower r-cran-gtable r-cran-hardhat 169s r-cran-haven r-cran-highr r-cran-hms r-cran-ipred r-cran-isoband 169s r-cran-iterators r-cran-jsonlite r-cran-kernsmooth r-cran-knitr 169s r-cran-labeling r-cran-lattice r-cran-lava r-cran-lifecycle r-cran-listenv 169s r-cran-littler r-cran-lme4 r-cran-lmtest r-cran-lubridate r-cran-magrittr 169s r-cran-maptools r-cran-mass r-cran-matrix r-cran-matrixmodels 169s r-cran-matrixstats r-cran-maxlik r-cran-mgcv r-cran-minqa r-cran-misctools 169s r-cran-modelmetrics r-cran-munsell r-cran-nlme r-cran-nloptr r-cran-nnet 169s r-cran-numderiv r-cran-openxlsx r-cran-parallelly r-cran-pbkrtest 169s r-cran-pillar r-cran-pkgbuild r-cran-pkgconfig r-cran-pkgkitten 169s r-cran-pkgload r-cran-plm r-cran-plyr r-cran-praise r-cran-prettyunits 169s r-cran-proc r-cran-processx r-cran-prodlim r-cran-progress r-cran-progressr 169s r-cran-proxy r-cran-ps r-cran-purrr r-cran-quantreg r-cran-r.methodss3 169s r-cran-r.oo r-cran-r.utils r-cran-r6 r-cran-rbibutils r-cran-rcolorbrewer 169s r-cran-rcpp r-cran-rcpparmadillo r-cran-rcppeigen r-cran-rdpack r-cran-readr 169s r-cran-readxl r-cran-recipes r-cran-rematch r-cran-rematch2 r-cran-reshape2 169s r-cran-rio r-cran-rlang r-cran-rpart r-cran-rprojroot r-cran-sandwich 169s r-cran-scales r-cran-shape r-cran-sp r-cran-sparsem r-cran-squarem 169s r-cran-statmod r-cran-stringi r-cran-stringr r-cran-survival 169s r-cran-systemfit r-cran-testthat r-cran-tibble r-cran-tidyr 169s r-cran-tidyselect r-cran-timechange r-cran-timedate r-cran-tzdb r-cran-utf8 169s r-cran-vctrs r-cran-viridislite r-cran-vroom r-cran-waldo r-cran-withr 169s r-cran-writexl r-cran-xfun r-cran-yaml r-cran-zip r-cran-zoo unzip 169s x11-common xdg-utils zip 169s Suggested packages: 169s fonts-mathjax-extras fonts-stix libjs-mathjax-doc tcl8.6 tk8.6 169s libjs-html5shiv elpa-ess r-doc-info | r-doc-pdf r-mathlib r-base-html 169s r-cran-roxygen2 r-cran-rmarkdown r-cran-ff r-cran-aer r-cran-bbmle 169s r-cran-cluster r-cran-cmprsk r-cran-coda r-cran-covr r-cran-emmeans 169s r-cran-epir r-cran-gam r-cran-gee r-cran-geepack r-cran-glmnet r-cran-gmm 169s r-cran-hmisc r-cran-irlba r-cran-interp r-cran-ks r-cran-lavaan r-cran-leaps 169s r-cran-lsmeans r-cran-maps r-cran-mclust r-cran-metafor r-cran-modeldata 169s r-cran-multcomp r-cran-network r-cran-ordinal r-cran-psych r-cran-robust 169s r-cran-robustbase r-cran-rsample r-cran-spdep r-cran-spatialreg 169s r-cran-spelling r-cran-survey r-cran-tseries r-cran-bradleyterry2 169s r-cran-ellipse r-cran-mlbench r-cran-party r-cran-pls r-cran-randomforest 169s r-cran-rann r-cran-rstudioapi r-cran-slider r-cran-kernlab r-cran-mvtnorm 169s r-cran-vcd r-cran-shiny r-cran-shinyjs r-cran-png r-cran-jpeg r-cran-viridis 169s r-cran-tinytest r-cran-markdown r-cran-th.data r-cran-magick r-cran-sf 169s r-cran-getopt r-cran-rgeos r-cran-spatstat.geom r-cran-raster 169s r-cran-polyclip r-cran-plotrix r-cran-spatstat.linnet r-cran-spatstat.utils 169s r-cran-spatstat r-cran-clue r-cran-dbi r-cran-formattable r-cran-nanotime 169s r-cran-palmerpenguins r-cran-units r-cran-vdiffr r-cran-inline r-cran-sem 169s r-cran-bench r-cran-blob r-cran-here r-cran-htmltools r-cran-runit 169s Recommended packages: 169s javascript-common r-recommended r-base-dev r-doc-html r-cran-covr 169s r-cran-cliapp r-cran-mockery r-cran-earth r-cran-mda r-cran-mlmetrics 169s r-cran-fastica r-cran-kernlab r-cran-themis r-cran-htmltools 169s r-cran-htmlwidgets r-cran-rmarkdown r-cran-rstudioapi r-cran-whoami 169s r-cran-xts r-cran-bench r-cran-decor r-cran-lobstr r-cran-spelling 169s r-cran-later r-cran-httpuv r-cran-webutils r-cran-nanotime r-cran-gh 169s r-cran-dbi r-cran-dbplyr r-cran-rmysql r-cran-rpostgresql r-cran-rsqlite 169s r-cran-unitizer r-cran-rhpcblasctl r-cran-r.rsp r-cran-markdown 169s r-cran-hexbin r-cran-hmisc r-cran-mapproj r-cran-maps r-cran-multcomp 169s r-cran-profvis r-cran-ragg r-cran-sf r-cran-svglite r-cran-vdiffr 169s r-cran-xml2 r-cran-devtools r-cran-modeldata r-cran-roxygen2 r-cran-usethis 169s r-cran-testit r-cran-mlbench r-cran-httr r-cran-bslib r-cran-formatr 169s r-cran-gridsvg r-cran-jpeg r-cran-magick r-cran-png r-cran-reticulate 169s r-cran-rgl r-cran-sass r-cran-tikzdevice r-cran-tinytex r-cran-webshot 169s node-highlight.js r-cran-ellipse r-cran-fields r-cran-geepack r-bioc-graph 169s r-cran-bookdown r-cran-igraph r-cran-lavasearch2 r-cran-mets r-cran-optimx 169s r-cran-polycor r-cran-lintr r-cran-tidyverse r-cran-base64enc 169s r-cran-r.devices r-cran-runit r-cran-bitops r-cran-mathjaxr r-cran-mockr 169s r-cran-remotes r-cran-aer r-cran-spdep r-cran-urca r-cran-doparallel 169s r-cran-itertools r-cran-logcondens r-cran-webfakes r-cran-pbmcapply 169s r-cran-furrr r-cran-shiny r-cran-commonmark r-cran-cba r-cran-pingr 169s r-cran-gbrd r-cran-ddalpha r-cran-dials r-cran-rann r-cran-rcpproll 169s r-cran-rsample r-cran-rspectra r-cran-splines2 r-cran-dichromat r-cran-gstat 169s r-cran-deldir r-cran-terra r-cran-raster r-cran-setrng r-cran-formattable 169s r-cran-pkgdown r-cran-zeallot r-cran-mime r-cran-renv libfile-mimeinfo-perl 169s libnet-dbus-perl libx11-protocol-perl x11-utils x11-xserver-utils 170s The following NEW packages will be installed: 170s autopkgtest-satdep fontconfig fontconfig-config fonts-dejavu-core 170s fonts-dejavu-mono fonts-glyphicons-halflings fonts-mathjax libblas3 170s libcairo2 libdatrie1 libdeflate0 libfontconfig1 libgfortran5 libgomp1 170s libgraphite2-3 libharfbuzz0b libice6 libjbig0 libjpeg-turbo8 libjpeg8 170s libjs-bootstrap libjs-highlight.js libjs-jquery libjs-jquery-datatables 170s libjs-mathjax liblapack3 liblerc4 libnlopt0 libpango-1.0-0 170s libpangocairo-1.0-0 libpangoft2-1.0-0 libpaper-utils libpaper1 libpixman-1-0 170s libsharpyuv0 libsm6 libtcl8.6 libthai-data libthai0 libtiff6 libtk8.6 170s libwebp7 libxcb-render0 libxcb-shm0 libxft2 libxrender1 libxss1 libxt6 170s littler node-normalize.css r-base-core r-cran-abind r-cran-backports 170s r-cran-bdsmatrix r-cran-bit r-cran-bit64 r-cran-boot r-cran-brio 170s r-cran-broom r-cran-callr r-cran-car r-cran-cardata r-cran-caret 170s r-cran-cellranger r-cran-class r-cran-cli r-cran-clipr r-cran-clock 170s r-cran-codetools r-cran-collapse r-cran-colorspace r-cran-conquer 170s r-cran-cpp11 r-cran-crayon r-cran-curl r-cran-data.table r-cran-desc 170s r-cran-diagram r-cran-diffobj r-cran-digest r-cran-dplyr r-cran-e1071 170s r-cran-ellipsis r-cran-evaluate r-cran-fansi r-cran-farver r-cran-forcats 170s r-cran-foreach r-cran-foreign r-cran-formula r-cran-fs r-cran-future 170s r-cran-future.apply r-cran-generics r-cran-ggplot2 r-cran-globals 170s r-cran-glue r-cran-gower r-cran-gtable r-cran-hardhat r-cran-haven 170s r-cran-highr r-cran-hms r-cran-ipred r-cran-isoband r-cran-iterators 170s r-cran-jsonlite r-cran-kernsmooth r-cran-knitr r-cran-labeling 170s r-cran-lattice r-cran-lava r-cran-lifecycle r-cran-listenv r-cran-littler 170s r-cran-lme4 r-cran-lmtest r-cran-lubridate r-cran-magrittr r-cran-maptools 170s r-cran-mass r-cran-matrix r-cran-matrixmodels r-cran-matrixstats 170s r-cran-maxlik r-cran-mgcv r-cran-minqa r-cran-misctools r-cran-modelmetrics 170s r-cran-munsell r-cran-nlme r-cran-nloptr r-cran-nnet r-cran-numderiv 170s r-cran-openxlsx r-cran-parallelly r-cran-pbkrtest r-cran-pillar 170s r-cran-pkgbuild r-cran-pkgconfig r-cran-pkgkitten r-cran-pkgload r-cran-plm 170s r-cran-plyr r-cran-praise r-cran-prettyunits r-cran-proc r-cran-processx 170s r-cran-prodlim r-cran-progress r-cran-progressr r-cran-proxy r-cran-ps 170s r-cran-purrr r-cran-quantreg r-cran-r.methodss3 r-cran-r.oo r-cran-r.utils 170s r-cran-r6 r-cran-rbibutils r-cran-rcolorbrewer r-cran-rcpp 170s r-cran-rcpparmadillo r-cran-rcppeigen r-cran-rdpack r-cran-readr 170s r-cran-readxl r-cran-recipes r-cran-rematch r-cran-rematch2 r-cran-reshape2 170s r-cran-rio r-cran-rlang r-cran-rpart r-cran-rprojroot r-cran-sandwich 170s r-cran-scales r-cran-shape r-cran-sp r-cran-sparsem r-cran-squarem 170s r-cran-statmod r-cran-stringi r-cran-stringr r-cran-survival 170s r-cran-systemfit r-cran-testthat r-cran-tibble r-cran-tidyr 170s r-cran-tidyselect r-cran-timechange r-cran-timedate r-cran-tzdb r-cran-utf8 170s r-cran-vctrs r-cran-viridislite r-cran-vroom r-cran-waldo r-cran-withr 170s r-cran-writexl r-cran-xfun r-cran-yaml r-cran-zip r-cran-zoo unzip 170s x11-common xdg-utils zip 170s 0 upgraded, 208 newly installed, 0 to remove and 0 not upgraded. 170s Need to get 161 MB/161 MB of archives. 170s After this operation, 333 MB of additional disk space will be used. 170s Get:1 /tmp/autopkgtest.34lrrc/1-autopkgtest-satdep.deb autopkgtest-satdep arm64 0 [716 B] 170s Get:2 http://ftpmaster.internal/ubuntu noble/main arm64 fonts-dejavu-mono all 2.37-8 [502 kB] 170s Get:3 http://ftpmaster.internal/ubuntu noble/main arm64 fonts-dejavu-core all 2.37-8 [835 kB] 170s Get:4 http://ftpmaster.internal/ubuntu noble/main arm64 fontconfig-config arm64 2.15.0-1ubuntu1 [37.0 kB] 170s Get:5 http://ftpmaster.internal/ubuntu noble/main arm64 libfontconfig1 arm64 2.15.0-1ubuntu1 [142 kB] 170s Get:6 http://ftpmaster.internal/ubuntu noble/main arm64 fontconfig arm64 2.15.0-1ubuntu1 [190 kB] 170s Get:7 http://ftpmaster.internal/ubuntu noble/universe arm64 fonts-glyphicons-halflings all 1.009~3.4.1+dfsg-3 [118 kB] 170s Get:8 http://ftpmaster.internal/ubuntu noble/main arm64 fonts-mathjax all 2.7.9+dfsg-1 [2208 kB] 170s Get:9 http://ftpmaster.internal/ubuntu noble/main arm64 libblas3 arm64 3.12.0-3 [143 kB] 170s Get:10 http://ftpmaster.internal/ubuntu noble/main arm64 libpixman-1-0 arm64 0.42.2-1 [193 kB] 170s Get:11 http://ftpmaster.internal/ubuntu noble/main arm64 libxcb-render0 arm64 1.15-1 [16.1 kB] 170s Get:12 http://ftpmaster.internal/ubuntu noble/main arm64 libxcb-shm0 arm64 1.15-1 [5780 B] 170s Get:13 http://ftpmaster.internal/ubuntu noble/main arm64 libxrender1 arm64 1:0.9.10-1.1 [19.1 kB] 170s Get:14 http://ftpmaster.internal/ubuntu noble/main arm64 libcairo2 arm64 1.18.0-1 [550 kB] 170s Get:15 http://ftpmaster.internal/ubuntu noble/main arm64 libdatrie1 arm64 0.2.13-3 [21.7 kB] 170s Get:16 http://ftpmaster.internal/ubuntu noble/main arm64 libdeflate0 arm64 1.19-1 [43.4 kB] 170s Get:17 http://ftpmaster.internal/ubuntu noble/main arm64 libgfortran5 arm64 14-20240303-1ubuntu1 [444 kB] 170s Get:18 http://ftpmaster.internal/ubuntu noble/main arm64 libgomp1 arm64 14-20240303-1ubuntu1 [144 kB] 170s Get:19 http://ftpmaster.internal/ubuntu noble/main arm64 libgraphite2-3 arm64 1.3.14-2 [81.5 kB] 170s Get:20 http://ftpmaster.internal/ubuntu noble/main arm64 libharfbuzz0b arm64 8.3.0-2 [463 kB] 170s Get:21 http://ftpmaster.internal/ubuntu noble/main arm64 x11-common all 1:7.7+23ubuntu2 [23.4 kB] 170s Get:22 http://ftpmaster.internal/ubuntu noble/main arm64 libice6 arm64 2:1.0.10-1build2 [41.7 kB] 170s Get:23 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg-turbo8 arm64 2.1.5-2ubuntu1 [160 kB] 170s Get:24 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg8 arm64 8c-2ubuntu11 [2148 B] 170s Get:25 http://ftpmaster.internal/ubuntu noble/universe arm64 libjs-bootstrap all 3.4.1+dfsg-3 [129 kB] 170s Get:26 http://ftpmaster.internal/ubuntu noble/universe arm64 libjs-highlight.js all 9.18.5+dfsg1-2 [385 kB] 170s Get:27 http://ftpmaster.internal/ubuntu noble/main arm64 libjs-jquery all 3.6.1+dfsg+~3.5.14-1 [328 kB] 170s Get:28 http://ftpmaster.internal/ubuntu noble/universe arm64 libjs-jquery-datatables all 1.11.5+dfsg-2 [146 kB] 170s Get:29 http://ftpmaster.internal/ubuntu noble/main arm64 liblapack3 arm64 3.12.0-3 [2241 kB] 171s Get:30 http://ftpmaster.internal/ubuntu noble/main arm64 liblerc4 arm64 4.0.0+ds-4ubuntu1 [153 kB] 171s Get:31 http://ftpmaster.internal/ubuntu noble/main arm64 libthai-data all 0.1.29-2 [158 kB] 171s Get:32 http://ftpmaster.internal/ubuntu noble/main arm64 libthai0 arm64 0.1.29-2 [18.1 kB] 171s Get:33 http://ftpmaster.internal/ubuntu noble/main arm64 libpango-1.0-0 arm64 1.51.0+ds-4 [226 kB] 171s Get:34 http://ftpmaster.internal/ubuntu noble/main arm64 libpangoft2-1.0-0 arm64 1.51.0+ds-4 [41.2 kB] 171s Get:35 http://ftpmaster.internal/ubuntu noble/main arm64 libpangocairo-1.0-0 arm64 1.51.0+ds-4 [27.6 kB] 171s Get:36 http://ftpmaster.internal/ubuntu noble/main arm64 libpaper1 arm64 1.1.29 [13.1 kB] 171s Get:37 http://ftpmaster.internal/ubuntu noble/main arm64 libpaper-utils arm64 1.1.29 [8480 B] 171s Get:38 http://ftpmaster.internal/ubuntu noble/main arm64 libsharpyuv0 arm64 1.3.2-0.4 [14.4 kB] 171s Get:39 http://ftpmaster.internal/ubuntu noble/main arm64 libsm6 arm64 2:1.2.3-1build2 [16.1 kB] 171s Get:40 http://ftpmaster.internal/ubuntu noble/main arm64 libtcl8.6 arm64 8.6.13+dfsg-2 [980 kB] 171s Get:41 http://ftpmaster.internal/ubuntu noble/main arm64 libjbig0 arm64 2.1-6.1ubuntu1 [28.9 kB] 171s Get:42 http://ftpmaster.internal/ubuntu noble/main arm64 libwebp7 arm64 1.3.2-0.4 [191 kB] 171s Get:43 http://ftpmaster.internal/ubuntu noble/main arm64 libtiff6 arm64 4.5.1+git230720-3ubuntu1 [226 kB] 171s Get:44 http://ftpmaster.internal/ubuntu noble/main arm64 libxft2 arm64 2.3.6-1 [43.3 kB] 171s Get:45 http://ftpmaster.internal/ubuntu noble/main arm64 libxss1 arm64 1:1.2.3-1build2 [8252 B] 171s Get:46 http://ftpmaster.internal/ubuntu noble/main arm64 libtk8.6 arm64 8.6.13-2 [760 kB] 171s Get:47 http://ftpmaster.internal/ubuntu noble/main arm64 libxt6 arm64 1:1.2.1-1.1 [167 kB] 171s Get:48 http://ftpmaster.internal/ubuntu noble/main arm64 zip arm64 3.0-13 [172 kB] 171s Get:49 http://ftpmaster.internal/ubuntu noble/main arm64 unzip arm64 6.0-28ubuntu3 [171 kB] 171s Get:50 http://ftpmaster.internal/ubuntu noble/main arm64 xdg-utils all 1.1.3-4.1ubuntu3 [62.0 kB] 171s Get:51 http://ftpmaster.internal/ubuntu noble/universe arm64 r-base-core arm64 4.3.2-1build1 [26.8 MB] 171s Get:52 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-littler arm64 0.3.19-1 [93.4 kB] 171s Get:53 http://ftpmaster.internal/ubuntu noble/universe arm64 littler all 0.3.19-1 [2472 B] 171s Get:54 http://ftpmaster.internal/ubuntu noble/universe arm64 node-normalize.css all 8.0.1-5 [10.8 kB] 171s Get:55 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-abind all 1.4-5-2 [63.6 kB] 171s Get:56 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-backports arm64 1.4.1-1 [101 kB] 171s Get:57 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-bdsmatrix arm64 1.3-6-1 [292 kB] 171s Get:58 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-bit arm64 4.0.5-1 [1057 kB] 171s Get:59 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-bit64 arm64 4.0.5-1 [467 kB] 171s Get:60 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-boot all 1.3-30-1 [619 kB] 171s Get:61 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-brio arm64 1.1.4-1 [37.7 kB] 171s Get:62 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-cli arm64 3.6.2-1 [1377 kB] 171s Get:63 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-generics all 0.1.3-1 [81.3 kB] 171s Get:64 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-glue arm64 1.7.0-1 [154 kB] 171s Get:65 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rlang arm64 1.1.3-1 [1663 kB] 172s Get:66 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-lifecycle all 1.0.4+dfsg-1 [110 kB] 172s Get:67 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-magrittr arm64 2.0.3-1 [154 kB] 172s Get:68 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-fansi arm64 1.0.5-1 [616 kB] 172s Get:69 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-utf8 arm64 1.2.4-1 [140 kB] 172s Get:70 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-vctrs arm64 0.6.5-1 [1327 kB] 172s Get:71 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-pillar all 1.9.0+dfsg-1 [464 kB] 172s Get:72 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-r6 all 2.5.1-1 [99.0 kB] 172s Get:73 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-pkgconfig all 2.0.3-2build1 [19.7 kB] 172s Get:74 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-tibble arm64 3.2.1+dfsg-2 [415 kB] 172s Get:75 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-withr all 2.5.0-1 [225 kB] 172s Get:76 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-tidyselect arm64 1.2.0+dfsg-1 [218 kB] 172s Get:77 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-dplyr arm64 1.1.4-1 [1513 kB] 172s Get:78 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-ellipsis arm64 0.3.2-2 [35.5 kB] 172s Get:79 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-purrr arm64 1.0.2-1 [501 kB] 172s Get:80 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-stringi arm64 1.8.3-1 [869 kB] 172s Get:81 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-stringr all 1.5.1-1 [290 kB] 172s Get:82 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-cpp11 all 0.4.7-1 [266 kB] 172s Get:83 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-tidyr arm64 1.3.1-1 [1154 kB] 172s Get:84 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-broom all 1.0.5+dfsg-1 [1729 kB] 172s Get:85 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-ps arm64 1.7.6-1 [313 kB] 172s Get:86 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-processx arm64 3.8.3-1 [345 kB] 172s Get:87 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-callr all 3.7.3-2 [425 kB] 172s Get:88 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-cardata all 3.0.5-1 [1819 kB] 172s Get:89 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-mass arm64 7.3-60.0.1-1 [1119 kB] 172s Get:90 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-lattice arm64 0.22-5-1 [1342 kB] 172s Get:91 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-nlme arm64 3.1.164-1 [2259 kB] 172s Get:92 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-matrix arm64 1.6-5-1 [3776 kB] 172s Get:93 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-mgcv arm64 1.9-1-1 [3248 kB] 172s Get:94 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-nnet arm64 7.3-19-2 [111 kB] 172s Get:95 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-pkgkitten all 0.2.3-1 [25.1 kB] 172s Get:96 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rcpp arm64 1.0.12-1 [1971 kB] 172s Get:97 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-minqa arm64 1.2.6-1 [107 kB] 172s Get:98 http://ftpmaster.internal/ubuntu noble/universe arm64 libnlopt0 arm64 2.7.1-5build2 [174 kB] 172s Get:99 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-desc all 1.4.3-1 [359 kB] 172s Get:100 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-digest arm64 0.6.34-1 [182 kB] 172s Get:101 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-evaluate all 0.23-1 [90.2 kB] 172s Get:102 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-jsonlite arm64 1.8.8+dfsg-1 [441 kB] 172s Get:103 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-crayon all 1.5.2-1 [164 kB] 173s Get:104 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-fs arm64 1.6.3+dfsg-1 [227 kB] 173s Get:105 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-pkgbuild all 1.4.3-1 [209 kB] 173s Get:106 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rprojroot all 2.0.4-1 [124 kB] 173s Get:107 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-pkgload all 1.3.4-1 [207 kB] 173s Get:108 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-praise all 1.0.0-4build1 [20.3 kB] 173s Get:109 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-diffobj arm64 0.3.5-1 [1116 kB] 173s Get:110 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rematch2 all 2.1.2-2build1 [46.5 kB] 173s Get:111 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-waldo all 0.5.2-1build1 [120 kB] 173s Get:112 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-testthat arm64 3.2.1-1 [1678 kB] 173s Get:113 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-nloptr arm64 2.0.3-1 [375 kB] 173s Get:114 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rcppeigen arm64 0.3.3.9.4-1 [1180 kB] 173s Get:115 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-statmod arm64 1.5.0-1 [294 kB] 173s Get:116 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-lme4 arm64 1.1-35.1-4 [4116 kB] 173s Get:117 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-numderiv all 2016.8-1.1-3 [115 kB] 173s Get:118 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-xfun arm64 0.41+dfsg-1 [415 kB] 173s Get:119 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-highr all 0.10+dfsg-1 [38.3 kB] 173s Get:120 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-yaml arm64 2.3.8-1 [107 kB] 173s Get:121 http://ftpmaster.internal/ubuntu noble/main arm64 libjs-mathjax all 2.7.9+dfsg-1 [5665 kB] 173s Get:122 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-knitr all 1.45+dfsg-1 [917 kB] 173s Get:123 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-pbkrtest all 0.5.2-2 [182 kB] 173s Get:124 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-sparsem arm64 1.81-1 [902 kB] 173s Get:125 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-matrixmodels all 0.5-3-1 [361 kB] 173s Get:126 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-survival arm64 3.5-8-1 [6116 kB] 174s Get:127 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-matrixstats arm64 1.2.0-1 [475 kB] 174s Get:128 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rcpparmadillo arm64 0.12.8.0.0-1 [859 kB] 174s Get:129 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-gtable all 0.3.4+dfsg-1 [191 kB] 174s Get:130 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-isoband arm64 0.2.7-1 [1481 kB] 174s Get:131 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-farver arm64 2.1.1-1 [1336 kB] 174s Get:132 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-labeling all 0.4.3-1 [62.1 kB] 174s Get:133 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-colorspace arm64 2.1-0+dfsg-1 [1540 kB] 174s Get:134 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-munsell all 0.5.0-2build1 [208 kB] 174s Get:135 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rcolorbrewer all 1.1-3-1build1 [55.4 kB] 174s Get:136 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-viridislite all 0.4.2-2 [1088 kB] 174s Get:137 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-scales all 1.3.0-1 [603 kB] 174s Get:138 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-ggplot2 all 3.4.4+dfsg-1 [3411 kB] 174s Get:139 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-class arm64 7.3-22-2 [88.2 kB] 174s Get:140 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-proxy arm64 0.4-27-1 [181 kB] 174s Get:141 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-e1071 arm64 1.7-14-1 [556 kB] 174s Get:142 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-codetools all 0.2-19-1 [90.5 kB] 174s Get:143 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-iterators all 1.0.14-1 [336 kB] 174s Get:144 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-foreach all 1.5.2-1 [124 kB] 174s Get:145 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-data.table arm64 1.14.10+dfsg-1 [1844 kB] 174s Get:146 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-modelmetrics arm64 1.2.2.2-1build1 [121 kB] 174s Get:147 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-plyr arm64 1.8.9-1 [831 kB] 174s Get:148 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-proc arm64 1.18.5-1 [963 kB] 174s Get:149 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-tzdb arm64 0.4.0-2 [512 kB] 174s Get:150 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-clock arm64 0.7.0-1.1 [1736 kB] 174s Get:151 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-gower arm64 1.0.1-1 [206 kB] 174s Get:152 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-hardhat all 1.3.1+dfsg-1 [554 kB] 174s Get:153 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rpart arm64 4.1.23-1 [660 kB] 174s Get:154 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-shape all 1.4.6-1 [770 kB] 174s Get:155 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-diagram all 1.6.5-2 [656 kB] 174s Get:156 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-kernsmooth arm64 2.23-22-1 [91.1 kB] 174s Get:157 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-globals all 0.16.2-1 [117 kB] 174s Get:158 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-listenv all 0.9.1+dfsg-1 [112 kB] 174s Get:159 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-parallelly arm64 1.37.1-1 [364 kB] 174s Get:160 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-future all 1.33.1+dfsg-1 [634 kB] 174s Get:161 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-future.apply all 1.11.1+dfsg-1 [171 kB] 174s Get:162 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-progressr all 0.14.0-1 [338 kB] 174s Get:163 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-squarem all 2021.1-1 [179 kB] 174s Get:164 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-lava all 1.7.3+dfsg-1 [2166 kB] 174s Get:165 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-prodlim arm64 2023.08.28-1 [407 kB] 175s Get:166 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-ipred arm64 0.9-14-1 [383 kB] 175s Get:167 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-timechange arm64 0.3.0-1 [172 kB] 175s Get:168 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-lubridate arm64 1.9.3+dfsg-1 [1010 kB] 175s Get:169 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-timedate arm64 4032.109-1 [1229 kB] 175s Get:170 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-recipes all 1.0.9+dfsg-1 [1964 kB] 175s Get:171 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-reshape2 arm64 1.4.4-2build1 [110 kB] 175s Get:172 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-caret arm64 6.0-94+dfsg-1 [3434 kB] 175s Get:173 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-conquer arm64 1.3.3-1 [440 kB] 175s Get:174 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-quantreg arm64 5.97-1 [1527 kB] 175s Get:175 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-sp arm64 1:2.1-2+dfsg-1 [1448 kB] 175s Get:176 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-foreign arm64 0.8.86-1 [240 kB] 175s Get:177 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-maptools arm64 1:1.1-8+dfsg-1 [1365 kB] 175s Get:178 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-forcats all 1.0.0-1 [369 kB] 175s Get:179 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-hms all 1.1.3-1 [96.5 kB] 175s Get:180 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-clipr all 0.8.0-1 [53.5 kB] 175s Get:181 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-prettyunits all 1.2.0-1 [162 kB] 175s Get:182 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-progress all 1.2.3-1 [91.9 kB] 175s Get:183 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-vroom arm64 1.6.5-1 [832 kB] 175s Get:184 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-readr arm64 2.1.5-1 [756 kB] 175s Get:185 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-haven arm64 2.5.4-1 [338 kB] 175s Get:186 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-curl arm64 5.2.0+dfsg-1 [189 kB] 175s Get:187 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rematch all 2.0.0-1 [18.3 kB] 175s Get:188 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-cellranger all 1.1.0-3 [102 kB] 175s Get:189 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-readxl arm64 1.4.3-1 [726 kB] 175s Get:190 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-writexl arm64 1.5.0-1 [157 kB] 175s Get:191 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-r.methodss3 all 1.8.2-1 [84.0 kB] 175s Get:192 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-r.oo all 1.26.0-1 [955 kB] 175s Get:193 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-r.utils all 2.12.3-1 [1386 kB] 175s Get:194 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-zip arm64 2.3.1-1 [125 kB] 175s Get:195 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-openxlsx arm64 4.2.5.2-1 [1925 kB] 175s Get:196 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rio all 1.0.1-1 [529 kB] 175s Get:197 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-car all 3.1-2-2 [1692 kB] 175s Get:198 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-collapse arm64 2.0.10-1 [3033 kB] 175s Get:199 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-formula all 1.2-5-1 [158 kB] 175s Get:200 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-zoo arm64 1.8-12-2 [984 kB] 175s Get:201 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-lmtest arm64 0.9.40-1 [396 kB] 175s Get:202 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-misctools all 0.6-28-1 [99.9 kB] 175s Get:203 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-sandwich all 3.1-0-1 [1484 kB] 176s Get:204 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-maxlik all 1.5-2-1 [1550 kB] 176s Get:205 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rbibutils arm64 2.2.16-1 [748 kB] 176s Get:206 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-rdpack all 2.6-1 [742 kB] 176s Get:207 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-plm all 2.6-3-1 [2141 kB] 176s Get:208 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-systemfit all 1.1-30-1 [1174 kB] 177s Preconfiguring packages ... 177s Fetched 161 MB in 7s (23.8 MB/s) 177s Selecting previously unselected package fonts-dejavu-mono. 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 ... 74330 files and directories currently installed.) 178s Preparing to unpack .../000-fonts-dejavu-mono_2.37-8_all.deb ... 178s Unpacking fonts-dejavu-mono (2.37-8) ... 178s Selecting previously unselected package fonts-dejavu-core. 178s Preparing to unpack .../001-fonts-dejavu-core_2.37-8_all.deb ... 178s Unpacking fonts-dejavu-core (2.37-8) ... 178s Selecting previously unselected package fontconfig-config. 178s Preparing to unpack .../002-fontconfig-config_2.15.0-1ubuntu1_arm64.deb ... 178s Unpacking fontconfig-config (2.15.0-1ubuntu1) ... 178s Selecting previously unselected package libfontconfig1:arm64. 178s Preparing to unpack .../003-libfontconfig1_2.15.0-1ubuntu1_arm64.deb ... 178s Unpacking libfontconfig1:arm64 (2.15.0-1ubuntu1) ... 178s Selecting previously unselected package fontconfig. 178s Preparing to unpack .../004-fontconfig_2.15.0-1ubuntu1_arm64.deb ... 178s Unpacking fontconfig (2.15.0-1ubuntu1) ... 178s Selecting previously unselected package fonts-glyphicons-halflings. 178s Preparing to unpack .../005-fonts-glyphicons-halflings_1.009~3.4.1+dfsg-3_all.deb ... 178s Unpacking fonts-glyphicons-halflings (1.009~3.4.1+dfsg-3) ... 178s Selecting previously unselected package fonts-mathjax. 178s Preparing to unpack .../006-fonts-mathjax_2.7.9+dfsg-1_all.deb ... 178s Unpacking fonts-mathjax (2.7.9+dfsg-1) ... 178s Selecting previously unselected package libblas3:arm64. 178s Preparing to unpack .../007-libblas3_3.12.0-3_arm64.deb ... 178s Unpacking libblas3:arm64 (3.12.0-3) ... 178s Selecting previously unselected package libpixman-1-0:arm64. 178s Preparing to unpack .../008-libpixman-1-0_0.42.2-1_arm64.deb ... 178s Unpacking libpixman-1-0:arm64 (0.42.2-1) ... 178s Selecting previously unselected package libxcb-render0:arm64. 178s Preparing to unpack .../009-libxcb-render0_1.15-1_arm64.deb ... 178s Unpacking libxcb-render0:arm64 (1.15-1) ... 178s Selecting previously unselected package libxcb-shm0:arm64. 178s Preparing to unpack .../010-libxcb-shm0_1.15-1_arm64.deb ... 178s Unpacking libxcb-shm0:arm64 (1.15-1) ... 178s Selecting previously unselected package libxrender1:arm64. 178s Preparing to unpack .../011-libxrender1_1%3a0.9.10-1.1_arm64.deb ... 178s Unpacking libxrender1:arm64 (1:0.9.10-1.1) ... 178s Selecting previously unselected package libcairo2:arm64. 178s Preparing to unpack .../012-libcairo2_1.18.0-1_arm64.deb ... 178s Unpacking libcairo2:arm64 (1.18.0-1) ... 178s Selecting previously unselected package libdatrie1:arm64. 178s Preparing to unpack .../013-libdatrie1_0.2.13-3_arm64.deb ... 178s Unpacking libdatrie1:arm64 (0.2.13-3) ... 178s Selecting previously unselected package libdeflate0:arm64. 178s Preparing to unpack .../014-libdeflate0_1.19-1_arm64.deb ... 178s Unpacking libdeflate0:arm64 (1.19-1) ... 179s Selecting previously unselected package libgfortran5:arm64. 179s Preparing to unpack .../015-libgfortran5_14-20240303-1ubuntu1_arm64.deb ... 179s Unpacking libgfortran5:arm64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libgomp1:arm64. 179s Preparing to unpack .../016-libgomp1_14-20240303-1ubuntu1_arm64.deb ... 179s Unpacking libgomp1:arm64 (14-20240303-1ubuntu1) ... 179s Selecting previously unselected package libgraphite2-3:arm64. 179s Preparing to unpack .../017-libgraphite2-3_1.3.14-2_arm64.deb ... 179s Unpacking libgraphite2-3:arm64 (1.3.14-2) ... 179s Selecting previously unselected package libharfbuzz0b:arm64. 179s Preparing to unpack .../018-libharfbuzz0b_8.3.0-2_arm64.deb ... 179s Unpacking libharfbuzz0b:arm64 (8.3.0-2) ... 179s Selecting previously unselected package x11-common. 179s Preparing to unpack .../019-x11-common_1%3a7.7+23ubuntu2_all.deb ... 179s Unpacking x11-common (1:7.7+23ubuntu2) ... 179s Selecting previously unselected package libice6:arm64. 179s Preparing to unpack .../020-libice6_2%3a1.0.10-1build2_arm64.deb ... 179s Unpacking libice6:arm64 (2:1.0.10-1build2) ... 179s Selecting previously unselected package libjpeg-turbo8:arm64. 179s Preparing to unpack .../021-libjpeg-turbo8_2.1.5-2ubuntu1_arm64.deb ... 179s Unpacking libjpeg-turbo8:arm64 (2.1.5-2ubuntu1) ... 179s Selecting previously unselected package libjpeg8:arm64. 179s Preparing to unpack .../022-libjpeg8_8c-2ubuntu11_arm64.deb ... 179s Unpacking libjpeg8:arm64 (8c-2ubuntu11) ... 179s Selecting previously unselected package libjs-bootstrap. 179s Preparing to unpack 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.../028-liblerc4_4.0.0+ds-4ubuntu1_arm64.deb ... 179s Unpacking liblerc4:arm64 (4.0.0+ds-4ubuntu1) ... 179s Selecting previously unselected package libthai-data. 179s Preparing to unpack .../029-libthai-data_0.1.29-2_all.deb ... 179s Unpacking libthai-data (0.1.29-2) ... 179s Selecting previously unselected package libthai0:arm64. 179s Preparing to unpack .../030-libthai0_0.1.29-2_arm64.deb ... 179s Unpacking libthai0:arm64 (0.1.29-2) ... 179s Selecting previously unselected package libpango-1.0-0:arm64. 179s Preparing to unpack .../031-libpango-1.0-0_1.51.0+ds-4_arm64.deb ... 179s Unpacking libpango-1.0-0:arm64 (1.51.0+ds-4) ... 179s Selecting previously unselected package libpangoft2-1.0-0:arm64. 179s Preparing to unpack .../032-libpangoft2-1.0-0_1.51.0+ds-4_arm64.deb ... 179s Unpacking libpangoft2-1.0-0:arm64 (1.51.0+ds-4) ... 179s Selecting previously unselected package libpangocairo-1.0-0:arm64. 179s Preparing to unpack .../033-libpangocairo-1.0-0_1.51.0+ds-4_arm64.deb ... 179s Unpacking libpangocairo-1.0-0:arm64 (1.51.0+ds-4) ... 179s Selecting previously unselected package libpaper1:arm64. 179s Preparing to unpack .../034-libpaper1_1.1.29_arm64.deb ... 179s Unpacking libpaper1:arm64 (1.1.29) ... 179s Selecting previously unselected package libpaper-utils. 179s Preparing to unpack .../035-libpaper-utils_1.1.29_arm64.deb ... 179s Unpacking libpaper-utils (1.1.29) ... 179s Selecting previously unselected package libsharpyuv0:arm64. 179s Preparing to unpack .../036-libsharpyuv0_1.3.2-0.4_arm64.deb ... 179s Unpacking libsharpyuv0:arm64 (1.3.2-0.4) ... 179s Selecting previously unselected package libsm6:arm64. 179s Preparing to unpack .../037-libsm6_2%3a1.2.3-1build2_arm64.deb ... 179s Unpacking libsm6:arm64 (2:1.2.3-1build2) ... 179s Selecting previously unselected package libtcl8.6:arm64. 179s Preparing to unpack .../038-libtcl8.6_8.6.13+dfsg-2_arm64.deb ... 179s Unpacking libtcl8.6:arm64 (8.6.13+dfsg-2) ... 180s Selecting previously unselected package libjbig0:arm64. 180s Preparing to unpack .../039-libjbig0_2.1-6.1ubuntu1_arm64.deb ... 180s Unpacking libjbig0:arm64 (2.1-6.1ubuntu1) ... 180s Selecting previously unselected package libwebp7:arm64. 180s Preparing to unpack .../040-libwebp7_1.3.2-0.4_arm64.deb ... 180s Unpacking libwebp7:arm64 (1.3.2-0.4) ... 180s Selecting previously unselected package libtiff6:arm64. 180s Preparing to unpack .../041-libtiff6_4.5.1+git230720-3ubuntu1_arm64.deb ... 180s Unpacking libtiff6:arm64 (4.5.1+git230720-3ubuntu1) ... 180s Selecting previously unselected package libxft2:arm64. 180s Preparing to unpack .../042-libxft2_2.3.6-1_arm64.deb ... 180s Unpacking libxft2:arm64 (2.3.6-1) ... 180s Selecting previously unselected package libxss1:arm64. 180s Preparing to unpack .../043-libxss1_1%3a1.2.3-1build2_arm64.deb ... 180s Unpacking libxss1:arm64 (1:1.2.3-1build2) ... 180s Selecting previously unselected package libtk8.6:arm64. 180s Preparing to unpack .../044-libtk8.6_8.6.13-2_arm64.deb ... 180s Unpacking libtk8.6:arm64 (8.6.13-2) ... 180s Selecting previously unselected package libxt6:arm64. 180s Preparing to unpack .../045-libxt6_1%3a1.2.1-1.1_arm64.deb ... 180s Unpacking libxt6:arm64 (1:1.2.1-1.1) ... 180s Selecting previously unselected package zip. 180s Preparing to unpack .../046-zip_3.0-13_arm64.deb ... 180s Unpacking zip (3.0-13) ... 180s Selecting previously unselected package unzip. 180s Preparing to unpack .../047-unzip_6.0-28ubuntu3_arm64.deb ... 180s Unpacking unzip (6.0-28ubuntu3) ... 180s Selecting previously unselected package xdg-utils. 180s Preparing to unpack .../048-xdg-utils_1.1.3-4.1ubuntu3_all.deb ... 180s Unpacking xdg-utils (1.1.3-4.1ubuntu3) ... 180s Selecting previously unselected package r-base-core. 180s Preparing to unpack .../049-r-base-core_4.3.2-1build1_arm64.deb ... 180s Unpacking r-base-core (4.3.2-1build1) ... 181s Selecting previously unselected package r-cran-littler. 181s Preparing to unpack .../050-r-cran-littler_0.3.19-1_arm64.deb ... 181s Unpacking r-cran-littler (0.3.19-1) ... 181s Selecting previously unselected package littler. 181s Preparing to unpack .../051-littler_0.3.19-1_all.deb ... 181s Unpacking littler (0.3.19-1) ... 181s Selecting previously unselected package node-normalize.css. 181s Preparing to unpack .../052-node-normalize.css_8.0.1-5_all.deb ... 181s Unpacking node-normalize.css (8.0.1-5) ... 181s Selecting previously unselected package r-cran-abind. 181s Preparing to unpack .../053-r-cran-abind_1.4-5-2_all.deb ... 181s Unpacking r-cran-abind (1.4-5-2) ... 181s Selecting previously unselected package r-cran-backports. 181s Preparing to unpack .../054-r-cran-backports_1.4.1-1_arm64.deb ... 181s Unpacking r-cran-backports (1.4.1-1) ... 181s Selecting previously unselected package r-cran-bdsmatrix. 181s Preparing to unpack .../055-r-cran-bdsmatrix_1.3-6-1_arm64.deb ... 181s Unpacking r-cran-bdsmatrix (1.3-6-1) ... 181s Selecting previously unselected package r-cran-bit. 181s Preparing to unpack .../056-r-cran-bit_4.0.5-1_arm64.deb ... 181s Unpacking r-cran-bit (4.0.5-1) ... 181s Selecting previously unselected package r-cran-bit64. 181s Preparing to unpack .../057-r-cran-bit64_4.0.5-1_arm64.deb ... 181s Unpacking r-cran-bit64 (4.0.5-1) ... 181s Selecting previously unselected package r-cran-boot. 181s Preparing to unpack .../058-r-cran-boot_1.3-30-1_all.deb ... 181s Unpacking r-cran-boot (1.3-30-1) ... 181s Selecting previously unselected package r-cran-brio. 181s Preparing to unpack .../059-r-cran-brio_1.1.4-1_arm64.deb ... 181s Unpacking r-cran-brio (1.1.4-1) ... 182s Selecting previously unselected package r-cran-cli. 182s Preparing to unpack .../060-r-cran-cli_3.6.2-1_arm64.deb ... 182s Unpacking r-cran-cli (3.6.2-1) ... 182s Selecting previously unselected package r-cran-generics. 182s Preparing to unpack .../061-r-cran-generics_0.1.3-1_all.deb ... 182s Unpacking r-cran-generics (0.1.3-1) ... 182s Selecting previously unselected package r-cran-glue. 182s Preparing to unpack .../062-r-cran-glue_1.7.0-1_arm64.deb ... 182s Unpacking r-cran-glue (1.7.0-1) ... 182s Selecting previously unselected package r-cran-rlang. 182s Preparing to unpack .../063-r-cran-rlang_1.1.3-1_arm64.deb ... 182s Unpacking r-cran-rlang (1.1.3-1) ... 182s Selecting previously unselected package r-cran-lifecycle. 182s Preparing to unpack .../064-r-cran-lifecycle_1.0.4+dfsg-1_all.deb ... 182s Unpacking r-cran-lifecycle (1.0.4+dfsg-1) ... 182s Selecting previously unselected package r-cran-magrittr. 182s Preparing to unpack .../065-r-cran-magrittr_2.0.3-1_arm64.deb ... 182s Unpacking r-cran-magrittr (2.0.3-1) ... 182s Selecting previously unselected package r-cran-fansi. 182s Preparing to unpack .../066-r-cran-fansi_1.0.5-1_arm64.deb ... 182s Unpacking r-cran-fansi (1.0.5-1) ... 182s Selecting previously unselected package r-cran-utf8. 182s Preparing to unpack .../067-r-cran-utf8_1.2.4-1_arm64.deb ... 182s Unpacking r-cran-utf8 (1.2.4-1) ... 182s Selecting previously unselected package r-cran-vctrs. 182s Preparing to unpack .../068-r-cran-vctrs_0.6.5-1_arm64.deb ... 182s Unpacking r-cran-vctrs (0.6.5-1) ... 182s Selecting previously unselected package r-cran-pillar. 182s Preparing to unpack .../069-r-cran-pillar_1.9.0+dfsg-1_all.deb ... 182s Unpacking r-cran-pillar (1.9.0+dfsg-1) ... 182s Selecting previously unselected package r-cran-r6. 182s Preparing to unpack .../070-r-cran-r6_2.5.1-1_all.deb ... 182s Unpacking r-cran-r6 (2.5.1-1) ... 182s Selecting previously unselected package r-cran-pkgconfig. 182s Preparing to unpack .../071-r-cran-pkgconfig_2.0.3-2build1_all.deb ... 182s Unpacking r-cran-pkgconfig (2.0.3-2build1) ... 182s Selecting previously unselected package r-cran-tibble. 182s Preparing to unpack .../072-r-cran-tibble_3.2.1+dfsg-2_arm64.deb ... 182s Unpacking r-cran-tibble (3.2.1+dfsg-2) ... 182s Selecting previously unselected package r-cran-withr. 182s Preparing to unpack .../073-r-cran-withr_2.5.0-1_all.deb ... 182s Unpacking r-cran-withr (2.5.0-1) ... 182s Selecting previously unselected package r-cran-tidyselect. 182s Preparing to unpack .../074-r-cran-tidyselect_1.2.0+dfsg-1_arm64.deb ... 182s Unpacking r-cran-tidyselect (1.2.0+dfsg-1) ... 182s Selecting previously unselected package r-cran-dplyr. 182s Preparing to unpack .../075-r-cran-dplyr_1.1.4-1_arm64.deb ... 182s Unpacking r-cran-dplyr (1.1.4-1) ... 182s Selecting previously unselected package r-cran-ellipsis. 182s Preparing to unpack .../076-r-cran-ellipsis_0.3.2-2_arm64.deb ... 182s Unpacking r-cran-ellipsis (0.3.2-2) ... 183s Selecting previously unselected package r-cran-purrr. 183s Preparing to unpack .../077-r-cran-purrr_1.0.2-1_arm64.deb ... 183s Unpacking r-cran-purrr (1.0.2-1) ... 183s Selecting previously unselected package r-cran-stringi. 183s Preparing to unpack .../078-r-cran-stringi_1.8.3-1_arm64.deb ... 183s Unpacking r-cran-stringi (1.8.3-1) ... 183s Selecting previously unselected package r-cran-stringr. 183s Preparing to unpack .../079-r-cran-stringr_1.5.1-1_all.deb ... 183s Unpacking r-cran-stringr (1.5.1-1) ... 183s Selecting previously unselected package r-cran-cpp11. 183s Preparing to unpack .../080-r-cran-cpp11_0.4.7-1_all.deb ... 183s Unpacking r-cran-cpp11 (0.4.7-1) ... 183s Selecting previously unselected package r-cran-tidyr. 183s Preparing to unpack .../081-r-cran-tidyr_1.3.1-1_arm64.deb ... 183s Unpacking r-cran-tidyr (1.3.1-1) ... 183s Selecting previously unselected package r-cran-broom. 183s Preparing to unpack .../082-r-cran-broom_1.0.5+dfsg-1_all.deb ... 183s Unpacking r-cran-broom (1.0.5+dfsg-1) ... 183s Selecting previously unselected package r-cran-ps. 183s Preparing to unpack .../083-r-cran-ps_1.7.6-1_arm64.deb ... 183s Unpacking r-cran-ps (1.7.6-1) ... 183s Selecting previously unselected package r-cran-processx. 183s Preparing to unpack .../084-r-cran-processx_3.8.3-1_arm64.deb ... 183s Unpacking r-cran-processx (3.8.3-1) ... 183s Selecting previously unselected package r-cran-callr. 183s Preparing to unpack .../085-r-cran-callr_3.7.3-2_all.deb ... 183s Unpacking r-cran-callr (3.7.3-2) ... 183s Selecting previously unselected package r-cran-cardata. 183s Preparing to unpack .../086-r-cran-cardata_3.0.5-1_all.deb ... 183s Unpacking r-cran-cardata (3.0.5-1) ... 183s Selecting previously unselected package r-cran-mass. 183s Preparing to unpack .../087-r-cran-mass_7.3-60.0.1-1_arm64.deb ... 183s Unpacking r-cran-mass (7.3-60.0.1-1) ... 183s Selecting previously unselected package r-cran-lattice. 183s Preparing to unpack .../088-r-cran-lattice_0.22-5-1_arm64.deb ... 183s Unpacking r-cran-lattice (0.22-5-1) ... 183s Selecting previously unselected package r-cran-nlme. 183s Preparing to unpack .../089-r-cran-nlme_3.1.164-1_arm64.deb ... 183s Unpacking r-cran-nlme (3.1.164-1) ... 183s Selecting previously unselected package r-cran-matrix. 183s Preparing to unpack .../090-r-cran-matrix_1.6-5-1_arm64.deb ... 183s Unpacking r-cran-matrix (1.6-5-1) ... 183s Selecting previously unselected package r-cran-mgcv. 183s Preparing to unpack .../091-r-cran-mgcv_1.9-1-1_arm64.deb ... 183s Unpacking r-cran-mgcv (1.9-1-1) ... 183s Selecting previously unselected package r-cran-nnet. 183s Preparing to unpack .../092-r-cran-nnet_7.3-19-2_arm64.deb ... 183s Unpacking r-cran-nnet (7.3-19-2) ... 183s Selecting previously unselected package r-cran-pkgkitten. 183s Preparing to unpack .../093-r-cran-pkgkitten_0.2.3-1_all.deb ... 183s Unpacking r-cran-pkgkitten (0.2.3-1) ... 183s Selecting previously unselected package r-cran-rcpp. 183s Preparing to unpack .../094-r-cran-rcpp_1.0.12-1_arm64.deb ... 183s Unpacking r-cran-rcpp (1.0.12-1) ... 183s Selecting previously unselected package r-cran-minqa. 184s Preparing to unpack .../095-r-cran-minqa_1.2.6-1_arm64.deb ... 184s Unpacking r-cran-minqa (1.2.6-1) ... 184s Selecting previously unselected package libnlopt0:arm64. 184s Preparing to unpack .../096-libnlopt0_2.7.1-5build2_arm64.deb ... 184s Unpacking libnlopt0:arm64 (2.7.1-5build2) ... 184s Selecting previously unselected package r-cran-desc. 184s Preparing to unpack .../097-r-cran-desc_1.4.3-1_all.deb ... 184s Unpacking r-cran-desc (1.4.3-1) ... 184s Selecting previously unselected package r-cran-digest. 184s Preparing to unpack .../098-r-cran-digest_0.6.34-1_arm64.deb ... 184s Unpacking r-cran-digest (0.6.34-1) ... 184s Selecting previously unselected package r-cran-evaluate. 184s Preparing to unpack .../099-r-cran-evaluate_0.23-1_all.deb ... 184s Unpacking r-cran-evaluate (0.23-1) ... 184s Selecting previously unselected package r-cran-jsonlite. 184s Preparing to unpack .../100-r-cran-jsonlite_1.8.8+dfsg-1_arm64.deb ... 184s Unpacking r-cran-jsonlite (1.8.8+dfsg-1) ... 184s Selecting previously unselected package r-cran-crayon. 184s Preparing to unpack .../101-r-cran-crayon_1.5.2-1_all.deb ... 184s Unpacking r-cran-crayon (1.5.2-1) ... 184s Selecting previously unselected package r-cran-fs. 184s Preparing to unpack .../102-r-cran-fs_1.6.3+dfsg-1_arm64.deb ... 184s Unpacking r-cran-fs (1.6.3+dfsg-1) ... 184s Selecting previously unselected package r-cran-pkgbuild. 184s Preparing to unpack .../103-r-cran-pkgbuild_1.4.3-1_all.deb ... 184s Unpacking r-cran-pkgbuild (1.4.3-1) ... 184s Selecting previously unselected package r-cran-rprojroot. 185s Preparing to unpack .../104-r-cran-rprojroot_2.0.4-1_all.deb ... 185s Unpacking r-cran-rprojroot (2.0.4-1) ... 185s Selecting previously unselected package r-cran-pkgload. 185s Preparing to unpack .../105-r-cran-pkgload_1.3.4-1_all.deb ... 185s Unpacking r-cran-pkgload (1.3.4-1) ... 185s Selecting previously unselected package r-cran-praise. 185s Preparing to unpack .../106-r-cran-praise_1.0.0-4build1_all.deb ... 185s Unpacking r-cran-praise (1.0.0-4build1) ... 185s Selecting previously unselected package r-cran-diffobj. 185s Preparing to unpack .../107-r-cran-diffobj_0.3.5-1_arm64.deb ... 185s Unpacking r-cran-diffobj (0.3.5-1) ... 185s Selecting previously unselected package r-cran-rematch2. 185s Preparing to unpack .../108-r-cran-rematch2_2.1.2-2build1_all.deb ... 185s Unpacking r-cran-rematch2 (2.1.2-2build1) ... 185s Selecting previously unselected package r-cran-waldo. 185s Preparing to unpack .../109-r-cran-waldo_0.5.2-1build1_all.deb ... 185s Unpacking r-cran-waldo (0.5.2-1build1) ... 185s Selecting previously unselected package r-cran-testthat. 185s Preparing to unpack .../110-r-cran-testthat_3.2.1-1_arm64.deb ... 185s Unpacking r-cran-testthat (3.2.1-1) ... 185s Selecting previously unselected package r-cran-nloptr. 185s Preparing to unpack .../111-r-cran-nloptr_2.0.3-1_arm64.deb ... 185s Unpacking r-cran-nloptr (2.0.3-1) ... 185s Selecting previously unselected package r-cran-rcppeigen. 185s Preparing to unpack .../112-r-cran-rcppeigen_0.3.3.9.4-1_arm64.deb ... 185s Unpacking r-cran-rcppeigen (0.3.3.9.4-1) ... 185s Selecting previously unselected package r-cran-statmod. 185s Preparing to unpack .../113-r-cran-statmod_1.5.0-1_arm64.deb ... 185s Unpacking r-cran-statmod (1.5.0-1) ... 185s Selecting previously unselected package r-cran-lme4. 185s Preparing to unpack .../114-r-cran-lme4_1.1-35.1-4_arm64.deb ... 185s Unpacking r-cran-lme4 (1.1-35.1-4) ... 185s Selecting previously unselected package r-cran-numderiv. 185s Preparing to unpack .../115-r-cran-numderiv_2016.8-1.1-3_all.deb ... 185s Unpacking r-cran-numderiv (2016.8-1.1-3) ... 185s Selecting previously unselected package r-cran-xfun. 185s Preparing to unpack .../116-r-cran-xfun_0.41+dfsg-1_arm64.deb ... 185s Unpacking r-cran-xfun (0.41+dfsg-1) ... 185s Selecting previously unselected package r-cran-highr. 185s Preparing to unpack .../117-r-cran-highr_0.10+dfsg-1_all.deb ... 185s Unpacking r-cran-highr (0.10+dfsg-1) ... 185s Selecting previously unselected package r-cran-yaml. 185s Preparing to unpack .../118-r-cran-yaml_2.3.8-1_arm64.deb ... 185s Unpacking r-cran-yaml (2.3.8-1) ... 185s Selecting previously unselected package libjs-mathjax. 185s Preparing to unpack .../119-libjs-mathjax_2.7.9+dfsg-1_all.deb ... 185s Unpacking libjs-mathjax (2.7.9+dfsg-1) ... 185s Selecting previously unselected package r-cran-knitr. 186s Preparing to unpack .../120-r-cran-knitr_1.45+dfsg-1_all.deb ... 186s Unpacking r-cran-knitr (1.45+dfsg-1) ... 186s Selecting previously unselected package r-cran-pbkrtest. 186s Preparing to unpack .../121-r-cran-pbkrtest_0.5.2-2_all.deb ... 186s Unpacking r-cran-pbkrtest (0.5.2-2) ... 186s Selecting previously unselected package r-cran-sparsem. 186s Preparing to unpack .../122-r-cran-sparsem_1.81-1_arm64.deb ... 186s Unpacking r-cran-sparsem (1.81-1) ... 186s Selecting previously unselected package r-cran-matrixmodels. 186s Preparing to unpack .../123-r-cran-matrixmodels_0.5-3-1_all.deb ... 186s Unpacking r-cran-matrixmodels (0.5-3-1) ... 186s Selecting previously unselected package r-cran-survival. 186s Preparing to unpack .../124-r-cran-survival_3.5-8-1_arm64.deb ... 186s Unpacking r-cran-survival (3.5-8-1) ... 186s Selecting previously unselected package r-cran-matrixstats. 186s Preparing to unpack .../125-r-cran-matrixstats_1.2.0-1_arm64.deb ... 186s Unpacking r-cran-matrixstats (1.2.0-1) ... 186s Selecting previously unselected package r-cran-rcpparmadillo. 186s Preparing to unpack .../126-r-cran-rcpparmadillo_0.12.8.0.0-1_arm64.deb ... 186s Unpacking r-cran-rcpparmadillo (0.12.8.0.0-1) ... 186s Selecting previously unselected package r-cran-gtable. 186s Preparing to unpack .../127-r-cran-gtable_0.3.4+dfsg-1_all.deb ... 186s Unpacking r-cran-gtable (0.3.4+dfsg-1) ... 186s Selecting previously unselected package r-cran-isoband. 186s Preparing to unpack .../128-r-cran-isoband_0.2.7-1_arm64.deb ... 186s Unpacking r-cran-isoband (0.2.7-1) ... 186s Selecting previously unselected package r-cran-farver. 186s Preparing to unpack .../129-r-cran-farver_2.1.1-1_arm64.deb ... 186s Unpacking r-cran-farver (2.1.1-1) ... 186s Selecting previously unselected package r-cran-labeling. 186s Preparing to unpack .../130-r-cran-labeling_0.4.3-1_all.deb ... 186s Unpacking r-cran-labeling (0.4.3-1) ... 186s Selecting previously unselected package r-cran-colorspace. 186s Preparing to unpack .../131-r-cran-colorspace_2.1-0+dfsg-1_arm64.deb ... 186s Unpacking r-cran-colorspace (2.1-0+dfsg-1) ... 186s Selecting previously unselected package r-cran-munsell. 186s Preparing to unpack .../132-r-cran-munsell_0.5.0-2build1_all.deb ... 186s Unpacking r-cran-munsell (0.5.0-2build1) ... 186s Selecting previously unselected package r-cran-rcolorbrewer. 186s Preparing to unpack .../133-r-cran-rcolorbrewer_1.1-3-1build1_all.deb ... 186s Unpacking r-cran-rcolorbrewer (1.1-3-1build1) ... 186s Selecting previously unselected package r-cran-viridislite. 186s Preparing to unpack .../134-r-cran-viridislite_0.4.2-2_all.deb ... 186s Unpacking r-cran-viridislite (0.4.2-2) ... 186s Selecting previously unselected package r-cran-scales. 186s Preparing to unpack .../135-r-cran-scales_1.3.0-1_all.deb ... 186s Unpacking r-cran-scales (1.3.0-1) ... 186s Selecting previously unselected package r-cran-ggplot2. 186s Preparing to unpack .../136-r-cran-ggplot2_3.4.4+dfsg-1_all.deb ... 186s Unpacking r-cran-ggplot2 (3.4.4+dfsg-1) ... 187s Selecting previously unselected package r-cran-class. 187s Preparing to unpack .../137-r-cran-class_7.3-22-2_arm64.deb ... 187s Unpacking r-cran-class (7.3-22-2) ... 187s Selecting previously unselected package r-cran-proxy. 187s Preparing to unpack .../138-r-cran-proxy_0.4-27-1_arm64.deb ... 187s Unpacking r-cran-proxy (0.4-27-1) ... 187s Selecting previously unselected package r-cran-e1071. 187s Preparing to unpack .../139-r-cran-e1071_1.7-14-1_arm64.deb ... 187s Unpacking r-cran-e1071 (1.7-14-1) ... 187s Selecting previously unselected package r-cran-codetools. 187s Preparing to unpack .../140-r-cran-codetools_0.2-19-1_all.deb ... 187s Unpacking r-cran-codetools (0.2-19-1) ... 187s Selecting previously unselected package r-cran-iterators. 187s Preparing to unpack .../141-r-cran-iterators_1.0.14-1_all.deb ... 187s Unpacking r-cran-iterators (1.0.14-1) ... 187s Selecting previously unselected package r-cran-foreach. 187s Preparing to unpack .../142-r-cran-foreach_1.5.2-1_all.deb ... 187s Unpacking r-cran-foreach (1.5.2-1) ... 187s Selecting previously unselected package r-cran-data.table. 187s Preparing to unpack .../143-r-cran-data.table_1.14.10+dfsg-1_arm64.deb ... 187s Unpacking r-cran-data.table (1.14.10+dfsg-1) ... 187s Selecting previously unselected package r-cran-modelmetrics. 187s Preparing to unpack .../144-r-cran-modelmetrics_1.2.2.2-1build1_arm64.deb ... 187s Unpacking r-cran-modelmetrics (1.2.2.2-1build1) ... 187s Selecting previously unselected package r-cran-plyr. 187s Preparing to unpack .../145-r-cran-plyr_1.8.9-1_arm64.deb ... 187s Unpacking r-cran-plyr (1.8.9-1) ... 187s Selecting previously unselected package r-cran-proc. 187s Preparing to unpack .../146-r-cran-proc_1.18.5-1_arm64.deb ... 187s Unpacking r-cran-proc (1.18.5-1) ... 187s Selecting previously unselected package r-cran-tzdb. 187s Preparing to unpack .../147-r-cran-tzdb_0.4.0-2_arm64.deb ... 187s Unpacking r-cran-tzdb (0.4.0-2) ... 187s Selecting previously unselected package r-cran-clock. 187s Preparing to unpack .../148-r-cran-clock_0.7.0-1.1_arm64.deb ... 187s Unpacking r-cran-clock (0.7.0-1.1) ... 187s Selecting previously unselected package r-cran-gower. 187s Preparing to unpack .../149-r-cran-gower_1.0.1-1_arm64.deb ... 187s Unpacking r-cran-gower (1.0.1-1) ... 187s Selecting previously unselected package r-cran-hardhat. 187s Preparing to unpack .../150-r-cran-hardhat_1.3.1+dfsg-1_all.deb ... 187s Unpacking r-cran-hardhat (1.3.1+dfsg-1) ... 187s Selecting previously unselected package r-cran-rpart. 188s Preparing to unpack .../151-r-cran-rpart_4.1.23-1_arm64.deb ... 188s Unpacking r-cran-rpart (4.1.23-1) ... 188s Selecting previously unselected package r-cran-shape. 188s Preparing to unpack .../152-r-cran-shape_1.4.6-1_all.deb ... 188s Unpacking r-cran-shape (1.4.6-1) ... 188s Selecting previously unselected package r-cran-diagram. 188s Preparing to unpack .../153-r-cran-diagram_1.6.5-2_all.deb ... 188s Unpacking r-cran-diagram (1.6.5-2) ... 188s Selecting previously unselected package r-cran-kernsmooth. 188s Preparing to unpack .../154-r-cran-kernsmooth_2.23-22-1_arm64.deb ... 188s Unpacking r-cran-kernsmooth (2.23-22-1) ... 188s Selecting previously unselected package r-cran-globals. 188s Preparing to unpack .../155-r-cran-globals_0.16.2-1_all.deb ... 188s Unpacking r-cran-globals (0.16.2-1) ... 188s Selecting previously unselected package r-cran-listenv. 188s Preparing to unpack .../156-r-cran-listenv_0.9.1+dfsg-1_all.deb ... 188s Unpacking r-cran-listenv (0.9.1+dfsg-1) ... 188s Selecting previously unselected package r-cran-parallelly. 188s Preparing to unpack .../157-r-cran-parallelly_1.37.1-1_arm64.deb ... 188s Unpacking r-cran-parallelly (1.37.1-1) ... 188s Selecting previously unselected package r-cran-future. 188s Preparing to unpack .../158-r-cran-future_1.33.1+dfsg-1_all.deb ... 188s Unpacking r-cran-future (1.33.1+dfsg-1) ... 188s Selecting previously unselected package r-cran-future.apply. 188s Preparing to unpack .../159-r-cran-future.apply_1.11.1+dfsg-1_all.deb ... 188s Unpacking r-cran-future.apply (1.11.1+dfsg-1) ... 188s Selecting previously unselected package r-cran-progressr. 188s Preparing to unpack .../160-r-cran-progressr_0.14.0-1_all.deb ... 188s Unpacking r-cran-progressr (0.14.0-1) ... 188s Selecting previously unselected package r-cran-squarem. 188s Preparing to unpack .../161-r-cran-squarem_2021.1-1_all.deb ... 188s Unpacking r-cran-squarem (2021.1-1) ... 188s Selecting previously unselected package r-cran-lava. 188s Preparing to unpack .../162-r-cran-lava_1.7.3+dfsg-1_all.deb ... 188s Unpacking r-cran-lava (1.7.3+dfsg-1) ... 188s Selecting previously unselected package r-cran-prodlim. 188s Preparing to unpack .../163-r-cran-prodlim_2023.08.28-1_arm64.deb ... 188s Unpacking r-cran-prodlim (2023.08.28-1) ... 188s Selecting previously unselected package r-cran-ipred. 188s Preparing to unpack .../164-r-cran-ipred_0.9-14-1_arm64.deb ... 188s Unpacking r-cran-ipred (0.9-14-1) ... 188s Selecting previously unselected package r-cran-timechange. 189s Preparing to unpack .../165-r-cran-timechange_0.3.0-1_arm64.deb ... 189s Unpacking r-cran-timechange (0.3.0-1) ... 189s Selecting previously unselected package r-cran-lubridate. 189s Preparing to unpack .../166-r-cran-lubridate_1.9.3+dfsg-1_arm64.deb ... 189s Unpacking r-cran-lubridate (1.9.3+dfsg-1) ... 189s Selecting previously unselected package r-cran-timedate. 189s Preparing to unpack .../167-r-cran-timedate_4032.109-1_arm64.deb ... 189s Unpacking r-cran-timedate (4032.109-1) ... 189s Selecting previously unselected package r-cran-recipes. 189s Preparing to unpack .../168-r-cran-recipes_1.0.9+dfsg-1_all.deb ... 189s Unpacking r-cran-recipes (1.0.9+dfsg-1) ... 189s Selecting previously unselected package r-cran-reshape2. 189s Preparing to unpack .../169-r-cran-reshape2_1.4.4-2build1_arm64.deb ... 189s Unpacking r-cran-reshape2 (1.4.4-2build1) ... 189s Selecting previously unselected package r-cran-caret. 189s Preparing to unpack .../170-r-cran-caret_6.0-94+dfsg-1_arm64.deb ... 189s Unpacking r-cran-caret (6.0-94+dfsg-1) ... 189s Selecting previously unselected package r-cran-conquer. 189s Preparing to unpack .../171-r-cran-conquer_1.3.3-1_arm64.deb ... 189s Unpacking r-cran-conquer (1.3.3-1) ... 189s Selecting previously unselected package r-cran-quantreg. 189s Preparing to unpack .../172-r-cran-quantreg_5.97-1_arm64.deb ... 189s Unpacking r-cran-quantreg (5.97-1) ... 189s Selecting previously unselected package r-cran-sp. 189s Preparing to unpack .../173-r-cran-sp_1%3a2.1-2+dfsg-1_arm64.deb ... 189s Unpacking r-cran-sp (1:2.1-2+dfsg-1) ... 189s Selecting previously unselected package r-cran-foreign. 189s Preparing to unpack .../174-r-cran-foreign_0.8.86-1_arm64.deb ... 189s Unpacking r-cran-foreign (0.8.86-1) ... 189s Selecting previously unselected package r-cran-maptools. 189s Preparing to unpack .../175-r-cran-maptools_1%3a1.1-8+dfsg-1_arm64.deb ... 189s Unpacking r-cran-maptools (1:1.1-8+dfsg-1) ... 189s Selecting previously unselected package r-cran-forcats. 189s Preparing to unpack .../176-r-cran-forcats_1.0.0-1_all.deb ... 189s Unpacking r-cran-forcats (1.0.0-1) ... 189s Selecting previously unselected package r-cran-hms. 190s Preparing to unpack .../177-r-cran-hms_1.1.3-1_all.deb ... 190s Unpacking r-cran-hms (1.1.3-1) ... 190s Selecting previously unselected package r-cran-clipr. 190s Preparing to unpack .../178-r-cran-clipr_0.8.0-1_all.deb ... 190s Unpacking r-cran-clipr (0.8.0-1) ... 190s Selecting previously unselected package r-cran-prettyunits. 190s Preparing to unpack .../179-r-cran-prettyunits_1.2.0-1_all.deb ... 190s Unpacking r-cran-prettyunits (1.2.0-1) ... 190s Selecting previously unselected package r-cran-progress. 190s Preparing to unpack .../180-r-cran-progress_1.2.3-1_all.deb ... 190s Unpacking r-cran-progress (1.2.3-1) ... 190s Selecting previously unselected package r-cran-vroom. 190s Preparing to unpack .../181-r-cran-vroom_1.6.5-1_arm64.deb ... 190s Unpacking r-cran-vroom (1.6.5-1) ... 190s Selecting previously unselected package r-cran-readr. 190s Preparing to unpack .../182-r-cran-readr_2.1.5-1_arm64.deb ... 190s Unpacking r-cran-readr (2.1.5-1) ... 190s Selecting previously unselected package r-cran-haven. 190s Preparing to unpack .../183-r-cran-haven_2.5.4-1_arm64.deb ... 190s Unpacking r-cran-haven (2.5.4-1) ... 190s Selecting previously unselected package r-cran-curl. 190s Preparing to unpack .../184-r-cran-curl_5.2.0+dfsg-1_arm64.deb ... 190s Unpacking r-cran-curl (5.2.0+dfsg-1) ... 190s Selecting previously unselected package r-cran-rematch. 190s Preparing to unpack .../185-r-cran-rematch_2.0.0-1_all.deb ... 190s Unpacking r-cran-rematch (2.0.0-1) ... 190s Selecting previously unselected package r-cran-cellranger. 190s Preparing to unpack .../186-r-cran-cellranger_1.1.0-3_all.deb ... 190s Unpacking r-cran-cellranger (1.1.0-3) ... 190s Selecting previously unselected package r-cran-readxl. 190s Preparing to unpack .../187-r-cran-readxl_1.4.3-1_arm64.deb ... 190s Unpacking r-cran-readxl (1.4.3-1) ... 190s Selecting previously unselected package r-cran-writexl. 190s Preparing to unpack .../188-r-cran-writexl_1.5.0-1_arm64.deb ... 190s Unpacking r-cran-writexl (1.5.0-1) ... 190s Selecting previously unselected package r-cran-r.methodss3. 190s Preparing to unpack .../189-r-cran-r.methodss3_1.8.2-1_all.deb ... 190s Unpacking r-cran-r.methodss3 (1.8.2-1) ... 190s Selecting previously unselected package r-cran-r.oo. 190s Preparing to unpack .../190-r-cran-r.oo_1.26.0-1_all.deb ... 190s Unpacking r-cran-r.oo (1.26.0-1) ... 190s Selecting previously unselected package r-cran-r.utils. 190s Preparing to unpack .../191-r-cran-r.utils_2.12.3-1_all.deb ... 190s Unpacking r-cran-r.utils (2.12.3-1) ... 190s Selecting previously unselected package r-cran-zip. 190s Preparing to unpack .../192-r-cran-zip_2.3.1-1_arm64.deb ... 190s Unpacking r-cran-zip (2.3.1-1) ... 190s Selecting previously unselected package r-cran-openxlsx. 190s Preparing to unpack .../193-r-cran-openxlsx_4.2.5.2-1_arm64.deb ... 190s Unpacking r-cran-openxlsx (4.2.5.2-1) ... 190s Selecting previously unselected package r-cran-rio. 190s Preparing to unpack .../194-r-cran-rio_1.0.1-1_all.deb ... 190s Unpacking r-cran-rio (1.0.1-1) ... 190s Selecting previously unselected package r-cran-car. 190s Preparing to unpack .../195-r-cran-car_3.1-2-2_all.deb ... 190s Unpacking r-cran-car (3.1-2-2) ... 190s Selecting previously unselected package r-cran-collapse. 190s Preparing to unpack .../196-r-cran-collapse_2.0.10-1_arm64.deb ... 190s Unpacking r-cran-collapse (2.0.10-1) ... 190s Selecting previously unselected package r-cran-formula. 191s Preparing to unpack .../197-r-cran-formula_1.2-5-1_all.deb ... 191s Unpacking r-cran-formula (1.2-5-1) ... 191s Selecting previously unselected package r-cran-zoo. 191s Preparing to unpack .../198-r-cran-zoo_1.8-12-2_arm64.deb ... 191s Unpacking r-cran-zoo (1.8-12-2) ... 191s Selecting previously unselected package r-cran-lmtest. 191s Preparing to unpack .../199-r-cran-lmtest_0.9.40-1_arm64.deb ... 191s Unpacking r-cran-lmtest (0.9.40-1) ... 191s Selecting previously unselected package r-cran-misctools. 191s Preparing to unpack .../200-r-cran-misctools_0.6-28-1_all.deb ... 191s Unpacking r-cran-misctools (0.6-28-1) ... 191s Selecting previously unselected package r-cran-sandwich. 191s Preparing to unpack .../201-r-cran-sandwich_3.1-0-1_all.deb ... 191s Unpacking r-cran-sandwich (3.1-0-1) ... 191s Selecting previously unselected package r-cran-maxlik. 191s Preparing to unpack .../202-r-cran-maxlik_1.5-2-1_all.deb ... 191s Unpacking r-cran-maxlik (1.5-2-1) ... 191s Selecting previously unselected package r-cran-rbibutils. 191s Preparing to unpack .../203-r-cran-rbibutils_2.2.16-1_arm64.deb ... 191s Unpacking r-cran-rbibutils (2.2.16-1) ... 191s Selecting previously unselected package r-cran-rdpack. 191s Preparing to unpack .../204-r-cran-rdpack_2.6-1_all.deb ... 191s Unpacking r-cran-rdpack (2.6-1) ... 191s Selecting previously unselected package r-cran-plm. 191s Preparing to unpack .../205-r-cran-plm_2.6-3-1_all.deb ... 191s Unpacking r-cran-plm (2.6-3-1) ... 191s Selecting previously unselected package r-cran-systemfit. 191s Preparing to unpack .../206-r-cran-systemfit_1.1-30-1_all.deb ... 191s Unpacking r-cran-systemfit (1.1-30-1) ... 191s Selecting previously unselected package autopkgtest-satdep. 191s Preparing to unpack .../207-1-autopkgtest-satdep.deb ... 191s Unpacking autopkgtest-satdep (0) ... 191s Setting up libgraphite2-3:arm64 (1.3.14-2) ... 191s Setting up libpixman-1-0:arm64 (0.42.2-1) ... 191s Setting up libsharpyuv0:arm64 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and comes with ABSOLUTELY NO WARRANTY. 210s You are welcome to redistribute it under certain conditions. 210s Type 'license()' or 'licence()' for distribution details. 210s 210s R is a collaborative project with many contributors. 210s Type 'contributors()' for more information and 210s 'citation()' on how to cite R or R packages in publications. 210s 210s Type 'demo()' for some demos, 'help()' for on-line help, or 210s 'help.start()' for an HTML browser interface to help. 210s Type 'q()' to quit R. 210s 210s > library( "systemfit" ) 211s Loading required package: car 211s Loading required package: carData 211s Loading required package: lmtest 211s Loading required package: zoo 211s 211s Attaching package: ‘zoo’ 211s 211s The following objects are masked from ‘package:base’: 211s 211s as.Date, as.Date.numeric 211s 211s 211s Please cite the 'systemfit' package as: 211s 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/. 211s 211s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 211s https://r-forge.r-project.org/projects/systemfit/ 211s > library( "sandwich" ) 211s > options( warn = 1 ) 211s > options( digits = 3 ) 211s > 211s > data( "KleinI" ) 211s > eqConsump <- consump ~ corpProf + corpProfLag + wages 211s > eqInvest <- invest ~ corpProf + corpProfLag + capitalLag 211s > eqPrivWage <- privWage ~ gnp + gnpLag + trend 211s > inst <- ~ govExp + taxes + govWage + trend + capitalLag + corpProfLag + gnpLag 211s > system <- list( Consumption = eqConsump, Investment = eqInvest, 211s + PrivateWages = eqPrivWage ) 211s > restrict <- c( "Consumption_corpProf + Investment_capitalLag = 0" ) 211s > restrict2 <- c( restrict, "Consumption_corpProfLag - PrivateWages_trend = 0" ) 211s > 211s > for( dataNo in 1:5 ) { 211s + # set some values of some variables to NA 211s + if( dataNo == 2 ) { 211s + KleinI$gnpLag[ 7 ] <- NA 211s + } else if( dataNo == 3 ) { 211s + KleinI$wages[ 10 ] <- NA 211s + } else if( dataNo == 4 ) { 211s + KleinI$corpProf[ 13 ] <- NA 211s + } else if( dataNo == 5 ) { 211s + KleinI$invest[ 16 ] <- NA 211s + } 211s + 211s + # single-equation OLS 211s + lmConsump <- lm( eqConsump, data = KleinI ) 211s + lmInvest <- lm( eqInvest, data = KleinI ) 211s + lmPrivWage <- lm( eqPrivWage, data = KleinI ) 211s + 211s + for( methodNo in 1:5 ) { 211s + method <- c( "OLS", "2SLS", "SUR", "3SLS", "3SLS" )[ methodNo ] 211s + maxit <- ifelse( methodNo == 5, 500, 1 ) 211s + 211s + cat( "> \n> # ", ifelse( maxit == 1, "", "I" ), method, "\n", sep = "" ) 211s + if( method %in% c( "OLS", "WLS", "SUR" ) ) { 211s + kleinModel <- systemfit( system, method = method, data = KleinI, 211s + methodResidCov = ifelse( method == "OLS", "geomean", "noDfCor" ), 211s + maxit = maxit ) 211s + } else { 211s + kleinModel <- systemfit( system, method = method, data = KleinI, 211s + inst = inst, methodResidCov = "noDfCor", maxit = maxit ) 211s + } 211s + cat( "> summary\n" ) 211s + print( summary( kleinModel ) ) 211s + if( method == "OLS" ) { 211s + cat( "compare coef with single-equation OLS\n" ) 211s + print( all.equal( coef( kleinModel ), 211s + c( coef( lmConsump ), coef( lmInvest ), coef( lmPrivWage ) ), 211s + check.attributes = FALSE ) ) 211s + } 211s + cat( "> residuals\n" ) 211s + print( residuals( kleinModel ) ) 211s + cat( "> fitted\n" ) 211s + print( fitted( kleinModel ) ) 211s + cat( "> predict\n" ) 211s + print( predict( kleinModel, se.fit = TRUE, 211s + interval = ifelse( methodNo %in% c( 1, 4 ), "prediction", "confidence" ), 211s + useDfSys = methodNo %in% c( 1, 3, 5 ) ) ) 211s + cat( "> model.frame\n" ) 211s + if( methodNo == 1 ) { 211s + mfOls <- model.frame( kleinModel ) 211s + print( mfOls ) 211s + } else if( methodNo == 2 ) { 211s + mf2sls <- model.frame( kleinModel ) 211s + print( mf2sls ) 211s + cat( "> Frames of instrumental variables\n" ) 211s + for( i in 1:3 ){ 211s + print( kleinModel$eq[[ i ]]$modelInst ) 211s + } 211s + } else if( methodNo == 3 ) { 211s + print( all.equal( mfOls, model.frame( kleinModel ) ) ) 211s + } else { 211s + print( all.equal( mf2sls, model.frame( kleinModel ) ) ) 211s + } 211s + cat( "> model.matrix\n" ) 211s + if( methodNo == 1 ) { 211s + mmOls <- model.matrix( kleinModel ) 211s + print( mmOls ) 211s + } else { 211s + print( all.equal( mmOls, model.matrix( kleinModel ) ) ) 211s + } 211s + if( methodNo == 2 ) { 211s + cat( "> matrix of instrumental variables\n" ) 211s + print( model.matrix( kleinModel, which = "z" ) ) 211s + cat( "> matrix of fitted regressors\n" ) 211s + print( round( model.matrix( kleinModel, which = "xHat" ), digits = 7 ) ) 211s + } 211s + cat( "> nobs\n" ) 211s + print( nobs( kleinModel ) ) 211s + cat( "> linearHypothesis\n" ) 211s + print( linearHypothesis( kleinModel, restrict ) ) 211s + print( linearHypothesis( kleinModel, restrict, test = "F" ) ) 211s + print( linearHypothesis( kleinModel, restrict, test = "Chisq" ) ) 211s + print( linearHypothesis( kleinModel, restrict2 ) ) 211s + print( linearHypothesis( kleinModel, restrict2, test = "F" ) ) 211s + print( linearHypothesis( kleinModel, restrict2, test = "Chisq" ) ) 211s + cat( "> logLik\n" ) 211s + print( logLik( kleinModel ) ) 211s + print( logLik( kleinModel, residCovDiag = TRUE ) ) 211s + if( method == "OLS" ) { 211s + cat( "compare log likelihood value with single-equation OLS\n" ) 211s + print( all.equal( logLik( kleinModel, residCovDiag = TRUE ), 211s + logLik( lmConsump ) + logLik( lmInvest ) + logLik( lmPrivWage ), 211s + check.attributes = FALSE ) ) 211s + } 211s + 211s + cat( "Estimating function\n" ) 211s + print( round( estfun( kleinModel ), digits = 7 ) ) 211s + print( all.equal( colSums( estfun( kleinModel ) ), 211s + rep( 0, ncol( estfun( kleinModel ) ) ), check.attributes = FALSE ) ) 211s + 211s + cat( "> Bread\n" ) 211s + print( bread( kleinModel ) ) 211s + } 211s + } 211s > 211s > # OLS 211s > summary 211s 211s systemfit results 211s method: OLS 211s 211s N DF SSR detRCov OLS-R2 McElroy-R2 211s system 63 51 45.2 0.371 0.977 0.991 211s 211s N DF SSR MSE RMSE R2 Adj R2 211s Consumption 21 17 17.9 1.052 1.026 0.981 0.978 211s Investment 21 17 17.3 1.019 1.009 0.931 0.919 211s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 211s 211s The covariance matrix of the residuals 211s Consumption Investment PrivateWages 211s Consumption 1.0517 0.0611 -0.470 211s Investment 0.0611 1.0190 0.150 211s PrivateWages -0.4704 0.1497 0.589 211s 211s The correlations of the residuals 211s Consumption Investment PrivateWages 211s Consumption 1.0000 0.0591 -0.598 211s Investment 0.0591 1.0000 0.193 211s PrivateWages -0.5979 0.1933 1.000 211s 211s 211s OLS estimates for 'Consumption' (equation 1) 211s Model Formula: consump ~ corpProf + corpProfLag + wages 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 16.2366 1.3027 12.46 5.6e-10 *** 211s corpProf 0.1929 0.0912 2.12 0.049 * 211s corpProfLag 0.0899 0.0906 0.99 0.335 211s wages 0.7962 0.0399 19.93 3.2e-13 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.026 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 211s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 211s 211s 211s OLS estimates for 'Investment' (equation 2) 211s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 10.1258 5.4655 1.85 0.08137 . 211s corpProf 0.4796 0.0971 4.94 0.00012 *** 211s corpProfLag 0.3330 0.1009 3.30 0.00421 ** 211s capitalLag -0.1118 0.0267 -4.18 0.00062 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.009 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 211s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 211s 211s 211s OLS estimates for 'PrivateWages' (equation 3) 211s Model Formula: privWage ~ gnp + gnpLag + trend 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 1.4970 1.2700 1.18 0.25474 211s gnp 0.4395 0.0324 13.56 1.5e-10 *** 211s gnpLag 0.1461 0.0374 3.90 0.00114 ** 211s trend 0.1302 0.0319 4.08 0.00078 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 0.767 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 211s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 211s 211s compare coef with single-equation OLS 211s [1] TRUE 211s > residuals 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 -0.32389 -0.0668 -1.2942 211s 3 -1.25001 -0.0476 0.2957 211s 4 -1.56574 1.2467 1.1877 211s 5 -0.49350 -1.3512 -0.1358 211s 6 0.00761 0.4154 -0.4654 211s 7 0.86910 1.4923 -0.4838 211s 8 1.33848 0.7889 -0.7281 211s 9 1.05498 -0.6317 0.3392 211s 10 -0.58856 1.0830 1.1957 211s 11 0.28231 0.2791 -0.1508 211s 12 -0.22965 0.0369 0.5942 211s 13 -0.32213 0.3659 0.1027 211s 14 0.32228 0.2237 0.4503 211s 15 -0.05801 -0.1728 0.2816 211s 16 -0.03466 0.0101 0.0138 211s 17 1.61650 0.9719 -0.8508 211s 18 -0.43597 0.0516 0.9956 211s 19 0.21005 -2.5656 -0.4688 211s 20 0.98920 -0.6866 -0.3795 211s 21 0.78508 -0.7807 -1.0909 211s 22 -2.17345 -0.6623 0.5917 211s > fitted 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 42.2 -0.133 26.8 211s 3 46.3 1.948 29.0 211s 4 50.8 3.953 32.9 211s 5 51.1 4.351 34.0 211s 6 52.6 4.685 35.9 211s 7 54.2 4.108 37.9 211s 8 54.9 3.411 38.6 211s 9 56.2 3.632 38.9 211s 10 58.4 4.017 40.1 211s 11 54.7 0.721 38.1 211s 12 51.1 -3.437 33.9 211s 13 45.9 -6.566 28.9 211s 14 46.2 -5.324 28.0 211s 15 48.8 -2.827 30.3 211s 16 51.3 -1.310 33.2 211s 17 56.1 1.128 37.7 211s 18 59.1 1.948 40.0 211s 19 57.3 0.666 38.7 211s 20 60.6 1.987 42.0 211s 21 64.2 4.081 46.1 211s 22 71.9 5.562 52.7 211s > predict 211s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 211s 1 NA NA NA NA 211s 2 42.2 0.462 40.0 44.5 211s 3 46.3 0.518 43.9 48.6 211s 4 50.8 0.341 48.6 52.9 211s 5 51.1 0.396 48.9 53.3 211s 6 52.6 0.397 50.4 54.8 211s 7 54.2 0.359 52.0 56.4 211s 8 54.9 0.327 52.7 57.0 211s 9 56.2 0.350 54.1 58.4 211s 10 58.4 0.370 56.2 60.6 211s 11 54.7 0.606 52.3 57.1 211s 12 51.1 0.484 48.9 53.4 211s 13 45.9 0.629 43.5 48.3 211s 14 46.2 0.602 43.8 48.6 211s 15 48.8 0.374 46.6 50.9 211s 16 51.3 0.333 49.2 53.5 211s 17 56.1 0.366 53.9 58.3 211s 18 59.1 0.321 57.0 61.3 211s 19 57.3 0.371 55.1 59.5 211s 20 60.6 0.434 58.4 62.8 211s 21 64.2 0.425 62.0 66.4 211s 22 71.9 0.666 69.4 74.3 211s Investment.pred Investment.se.fit Investment.lwr Investment.upr 211s 1 NA NA NA NA 211s 2 -0.133 0.607 -2.498 2.231 211s 3 1.948 0.499 -0.313 4.208 211s 4 3.953 0.449 1.735 6.171 211s 5 4.351 0.371 2.192 6.510 211s 6 4.685 0.349 2.540 6.829 211s 7 4.108 0.329 1.976 6.239 211s 8 3.411 0.292 1.301 5.521 211s 9 3.632 0.389 1.460 5.804 211s 10 4.017 0.447 1.801 6.233 211s 11 0.721 0.601 -1.638 3.080 211s 12 -3.437 0.507 -5.704 -1.169 211s 13 -6.566 0.616 -8.940 -4.192 211s 14 -5.324 0.694 -7.783 -2.865 211s 15 -2.827 0.373 -4.988 -0.667 211s 16 -1.310 0.320 -3.436 0.816 211s 17 1.128 0.347 -1.015 3.271 211s 18 1.948 0.243 -0.136 4.033 211s 19 0.666 0.312 -1.456 2.787 211s 20 1.987 0.366 -0.169 4.143 211s 21 4.081 0.332 1.948 6.214 211s 22 5.562 0.461 3.334 7.790 211s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 211s 1 NA NA NA NA 211s 2 26.8 0.354 25.1 28.5 211s 3 29.0 0.355 27.3 30.7 211s 4 32.9 0.354 31.2 34.6 211s 5 34.0 0.269 32.4 35.7 211s 6 35.9 0.266 34.2 37.5 211s 7 37.9 0.266 36.3 39.5 211s 8 38.6 0.273 37.0 40.3 211s 9 38.9 0.261 37.2 40.5 211s 10 40.1 0.247 38.5 41.7 211s 11 38.1 0.354 36.4 39.7 211s 12 33.9 0.363 32.2 35.6 211s 13 28.9 0.429 27.1 30.7 211s 14 28.0 0.376 26.3 29.8 211s 15 30.3 0.371 28.6 32.0 211s 16 33.2 0.310 31.5 34.8 211s 17 37.7 0.305 36.0 39.3 211s 18 40.0 0.238 38.4 41.6 211s 19 38.7 0.357 37.0 40.4 211s 20 42.0 0.321 40.3 43.6 211s 21 46.1 0.335 44.4 47.8 211s 22 52.7 0.502 50.9 54.5 211s > model.frame 211s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 211s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 211s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 211s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 211s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 211s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 211s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 211s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 211s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 211s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 211s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 211s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 211s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 211s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 211s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 211s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 211s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 211s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 211s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 211s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 211s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 211s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 211s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 211s trend 211s 1 -11 211s 2 -10 211s 3 -9 211s 4 -8 211s 5 -7 211s 6 -6 211s 7 -5 211s 8 -4 211s 9 -3 211s 10 -2 211s 11 -1 211s 12 0 211s 13 1 211s 14 2 211s 15 3 211s 16 4 211s 17 5 211s 18 6 211s 19 7 211s 20 8 211s 21 9 211s 22 10 211s > model.matrix 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_2 1 12.4 211s Consumption_3 1 16.9 211s Consumption_4 1 18.4 211s Consumption_5 1 19.4 211s Consumption_6 1 20.1 211s Consumption_7 1 19.6 211s Consumption_8 1 19.8 211s Consumption_9 1 21.1 211s Consumption_10 1 21.7 211s Consumption_11 1 15.6 211s Consumption_12 1 11.4 211s Consumption_13 1 7.0 211s Consumption_14 1 11.2 211s Consumption_15 1 12.3 211s Consumption_16 1 14.0 211s Consumption_17 1 17.6 211s Consumption_18 1 17.3 211s Consumption_19 1 15.3 211s Consumption_20 1 19.0 211s Consumption_21 1 21.1 211s Consumption_22 1 23.5 211s Investment_2 0 0.0 211s Investment_3 0 0.0 211s Investment_4 0 0.0 211s Investment_5 0 0.0 211s Investment_6 0 0.0 211s Investment_7 0 0.0 211s Investment_8 0 0.0 211s Investment_9 0 0.0 211s Investment_10 0 0.0 211s Investment_11 0 0.0 211s Investment_12 0 0.0 211s Investment_13 0 0.0 211s Investment_14 0 0.0 211s Investment_15 0 0.0 211s Investment_16 0 0.0 211s Investment_17 0 0.0 211s Investment_18 0 0.0 211s Investment_19 0 0.0 211s Investment_20 0 0.0 211s Investment_21 0 0.0 211s Investment_22 0 0.0 211s PrivateWages_2 0 0.0 211s PrivateWages_3 0 0.0 211s PrivateWages_4 0 0.0 211s PrivateWages_5 0 0.0 211s PrivateWages_6 0 0.0 211s PrivateWages_7 0 0.0 211s PrivateWages_8 0 0.0 211s PrivateWages_9 0 0.0 211s PrivateWages_10 0 0.0 211s PrivateWages_11 0 0.0 211s PrivateWages_12 0 0.0 211s PrivateWages_13 0 0.0 211s PrivateWages_14 0 0.0 211s PrivateWages_15 0 0.0 211s PrivateWages_16 0 0.0 211s PrivateWages_17 0 0.0 211s PrivateWages_18 0 0.0 211s PrivateWages_19 0 0.0 211s PrivateWages_20 0 0.0 211s PrivateWages_21 0 0.0 211s PrivateWages_22 0 0.0 211s Consumption_corpProfLag Consumption_wages 211s Consumption_2 12.7 28.2 211s Consumption_3 12.4 32.2 211s Consumption_4 16.9 37.0 211s Consumption_5 18.4 37.0 211s Consumption_6 19.4 38.6 211s Consumption_7 20.1 40.7 211s Consumption_8 19.6 41.5 211s Consumption_9 19.8 42.9 211s Consumption_10 21.1 45.3 211s Consumption_11 21.7 42.1 211s Consumption_12 15.6 39.3 211s Consumption_13 11.4 34.3 211s Consumption_14 7.0 34.1 211s Consumption_15 11.2 36.6 211s Consumption_16 12.3 39.3 211s Consumption_17 14.0 44.2 211s Consumption_18 17.6 47.7 211s Consumption_19 17.3 45.9 211s Consumption_20 15.3 49.4 211s Consumption_21 19.0 53.0 211s Consumption_22 21.1 61.8 211s Investment_2 0.0 0.0 211s Investment_3 0.0 0.0 211s Investment_4 0.0 0.0 211s Investment_5 0.0 0.0 211s Investment_6 0.0 0.0 211s Investment_7 0.0 0.0 211s Investment_8 0.0 0.0 211s Investment_9 0.0 0.0 211s Investment_10 0.0 0.0 211s Investment_11 0.0 0.0 211s Investment_12 0.0 0.0 211s Investment_13 0.0 0.0 211s Investment_14 0.0 0.0 211s Investment_15 0.0 0.0 211s Investment_16 0.0 0.0 211s Investment_17 0.0 0.0 211s Investment_18 0.0 0.0 211s Investment_19 0.0 0.0 211s Investment_20 0.0 0.0 211s Investment_21 0.0 0.0 211s Investment_22 0.0 0.0 211s PrivateWages_2 0.0 0.0 211s PrivateWages_3 0.0 0.0 211s PrivateWages_4 0.0 0.0 211s PrivateWages_5 0.0 0.0 211s PrivateWages_6 0.0 0.0 211s PrivateWages_7 0.0 0.0 211s PrivateWages_8 0.0 0.0 211s PrivateWages_9 0.0 0.0 211s PrivateWages_10 0.0 0.0 211s PrivateWages_11 0.0 0.0 211s PrivateWages_12 0.0 0.0 211s PrivateWages_13 0.0 0.0 211s PrivateWages_14 0.0 0.0 211s PrivateWages_15 0.0 0.0 211s PrivateWages_16 0.0 0.0 211s PrivateWages_17 0.0 0.0 211s PrivateWages_18 0.0 0.0 211s PrivateWages_19 0.0 0.0 211s PrivateWages_20 0.0 0.0 211s PrivateWages_21 0.0 0.0 211s PrivateWages_22 0.0 0.0 211s Investment_(Intercept) Investment_corpProf 211s Consumption_2 0 0.0 211s Consumption_3 0 0.0 211s Consumption_4 0 0.0 211s Consumption_5 0 0.0 211s Consumption_6 0 0.0 211s Consumption_7 0 0.0 211s Consumption_8 0 0.0 211s Consumption_9 0 0.0 211s Consumption_10 0 0.0 211s Consumption_11 0 0.0 211s Consumption_12 0 0.0 211s Consumption_13 0 0.0 211s Consumption_14 0 0.0 211s Consumption_15 0 0.0 211s Consumption_16 0 0.0 211s Consumption_17 0 0.0 211s Consumption_18 0 0.0 211s Consumption_19 0 0.0 211s Consumption_20 0 0.0 211s Consumption_21 0 0.0 211s Consumption_22 0 0.0 211s Investment_2 1 12.4 211s Investment_3 1 16.9 211s Investment_4 1 18.4 211s Investment_5 1 19.4 211s Investment_6 1 20.1 211s Investment_7 1 19.6 211s Investment_8 1 19.8 211s Investment_9 1 21.1 211s Investment_10 1 21.7 211s Investment_11 1 15.6 211s Investment_12 1 11.4 211s Investment_13 1 7.0 211s Investment_14 1 11.2 211s Investment_15 1 12.3 211s Investment_16 1 14.0 211s Investment_17 1 17.6 211s Investment_18 1 17.3 211s Investment_19 1 15.3 211s Investment_20 1 19.0 211s Investment_21 1 21.1 211s Investment_22 1 23.5 211s PrivateWages_2 0 0.0 211s PrivateWages_3 0 0.0 211s PrivateWages_4 0 0.0 211s PrivateWages_5 0 0.0 211s PrivateWages_6 0 0.0 211s PrivateWages_7 0 0.0 211s PrivateWages_8 0 0.0 211s PrivateWages_9 0 0.0 211s PrivateWages_10 0 0.0 211s PrivateWages_11 0 0.0 211s PrivateWages_12 0 0.0 211s PrivateWages_13 0 0.0 211s PrivateWages_14 0 0.0 211s PrivateWages_15 0 0.0 211s PrivateWages_16 0 0.0 211s PrivateWages_17 0 0.0 211s PrivateWages_18 0 0.0 211s PrivateWages_19 0 0.0 211s PrivateWages_20 0 0.0 211s PrivateWages_21 0 0.0 211s PrivateWages_22 0 0.0 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_2 0.0 0 211s Consumption_3 0.0 0 211s Consumption_4 0.0 0 211s Consumption_5 0.0 0 211s Consumption_6 0.0 0 211s Consumption_7 0.0 0 211s Consumption_8 0.0 0 211s Consumption_9 0.0 0 211s Consumption_10 0.0 0 211s Consumption_11 0.0 0 211s Consumption_12 0.0 0 211s Consumption_13 0.0 0 211s Consumption_14 0.0 0 211s Consumption_15 0.0 0 211s Consumption_16 0.0 0 211s Consumption_17 0.0 0 211s Consumption_18 0.0 0 211s Consumption_19 0.0 0 211s Consumption_20 0.0 0 211s Consumption_21 0.0 0 211s Consumption_22 0.0 0 211s Investment_2 12.7 183 211s Investment_3 12.4 183 211s Investment_4 16.9 184 211s Investment_5 18.4 190 211s Investment_6 19.4 193 211s Investment_7 20.1 198 211s Investment_8 19.6 203 211s Investment_9 19.8 208 211s Investment_10 21.1 211 211s Investment_11 21.7 216 211s Investment_12 15.6 217 211s Investment_13 11.4 213 211s Investment_14 7.0 207 211s Investment_15 11.2 202 211s Investment_16 12.3 199 211s Investment_17 14.0 198 211s Investment_18 17.6 200 211s Investment_19 17.3 202 211s Investment_20 15.3 200 211s Investment_21 19.0 201 211s Investment_22 21.1 204 211s PrivateWages_2 0.0 0 211s PrivateWages_3 0.0 0 211s PrivateWages_4 0.0 0 211s PrivateWages_5 0.0 0 211s PrivateWages_6 0.0 0 211s PrivateWages_7 0.0 0 211s PrivateWages_8 0.0 0 211s PrivateWages_9 0.0 0 211s PrivateWages_10 0.0 0 211s PrivateWages_11 0.0 0 211s PrivateWages_12 0.0 0 211s PrivateWages_13 0.0 0 211s PrivateWages_14 0.0 0 211s PrivateWages_15 0.0 0 211s PrivateWages_16 0.0 0 211s PrivateWages_17 0.0 0 211s PrivateWages_18 0.0 0 211s PrivateWages_19 0.0 0 211s PrivateWages_20 0.0 0 211s PrivateWages_21 0.0 0 211s PrivateWages_22 0.0 0 211s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 211s Consumption_2 0 0.0 0.0 211s Consumption_3 0 0.0 0.0 211s Consumption_4 0 0.0 0.0 211s Consumption_5 0 0.0 0.0 211s Consumption_6 0 0.0 0.0 211s Consumption_7 0 0.0 0.0 211s Consumption_8 0 0.0 0.0 211s Consumption_9 0 0.0 0.0 211s Consumption_10 0 0.0 0.0 211s Consumption_11 0 0.0 0.0 211s Consumption_12 0 0.0 0.0 211s Consumption_13 0 0.0 0.0 211s Consumption_14 0 0.0 0.0 211s Consumption_15 0 0.0 0.0 211s Consumption_16 0 0.0 0.0 211s Consumption_17 0 0.0 0.0 211s Consumption_18 0 0.0 0.0 211s Consumption_19 0 0.0 0.0 211s Consumption_20 0 0.0 0.0 211s Consumption_21 0 0.0 0.0 211s Consumption_22 0 0.0 0.0 211s Investment_2 0 0.0 0.0 211s Investment_3 0 0.0 0.0 211s Investment_4 0 0.0 0.0 211s Investment_5 0 0.0 0.0 211s Investment_6 0 0.0 0.0 211s Investment_7 0 0.0 0.0 211s Investment_8 0 0.0 0.0 211s Investment_9 0 0.0 0.0 211s Investment_10 0 0.0 0.0 211s Investment_11 0 0.0 0.0 211s Investment_12 0 0.0 0.0 211s Investment_13 0 0.0 0.0 211s Investment_14 0 0.0 0.0 211s Investment_15 0 0.0 0.0 211s Investment_16 0 0.0 0.0 211s Investment_17 0 0.0 0.0 211s Investment_18 0 0.0 0.0 211s Investment_19 0 0.0 0.0 211s Investment_20 0 0.0 0.0 211s Investment_21 0 0.0 0.0 211s Investment_22 0 0.0 0.0 211s PrivateWages_2 1 45.6 44.9 211s PrivateWages_3 1 50.1 45.6 211s PrivateWages_4 1 57.2 50.1 211s PrivateWages_5 1 57.1 57.2 211s PrivateWages_6 1 61.0 57.1 211s PrivateWages_7 1 64.0 61.0 211s PrivateWages_8 1 64.4 64.0 211s PrivateWages_9 1 64.5 64.4 211s PrivateWages_10 1 67.0 64.5 211s PrivateWages_11 1 61.2 67.0 211s PrivateWages_12 1 53.4 61.2 211s PrivateWages_13 1 44.3 53.4 211s PrivateWages_14 1 45.1 44.3 211s PrivateWages_15 1 49.7 45.1 211s PrivateWages_16 1 54.4 49.7 211s PrivateWages_17 1 62.7 54.4 211s PrivateWages_18 1 65.0 62.7 211s PrivateWages_19 1 60.9 65.0 211s PrivateWages_20 1 69.5 60.9 211s PrivateWages_21 1 75.7 69.5 211s PrivateWages_22 1 88.4 75.7 211s PrivateWages_trend 211s Consumption_2 0 211s Consumption_3 0 211s Consumption_4 0 211s Consumption_5 0 211s Consumption_6 0 211s Consumption_7 0 211s Consumption_8 0 211s Consumption_9 0 211s Consumption_10 0 211s Consumption_11 0 211s Consumption_12 0 211s Consumption_13 0 211s Consumption_14 0 211s Consumption_15 0 211s Consumption_16 0 211s Consumption_17 0 211s Consumption_18 0 211s Consumption_19 0 211s Consumption_20 0 211s Consumption_21 0 211s Consumption_22 0 211s Investment_2 0 211s Investment_3 0 211s Investment_4 0 211s Investment_5 0 211s Investment_6 0 211s Investment_7 0 211s Investment_8 0 211s Investment_9 0 211s Investment_10 0 211s Investment_11 0 211s Investment_12 0 211s Investment_13 0 211s Investment_14 0 211s Investment_15 0 211s Investment_16 0 211s Investment_17 0 211s Investment_18 0 211s Investment_19 0 211s Investment_20 0 211s Investment_21 0 211s Investment_22 0 211s PrivateWages_2 -10 211s PrivateWages_3 -9 211s PrivateWages_4 -8 211s PrivateWages_5 -7 211s PrivateWages_6 -6 211s PrivateWages_7 -5 211s PrivateWages_8 -4 211s PrivateWages_9 -3 211s PrivateWages_10 -2 211s PrivateWages_11 -1 211s PrivateWages_12 0 211s PrivateWages_13 1 211s PrivateWages_14 2 211s PrivateWages_15 3 211s PrivateWages_16 4 211s PrivateWages_17 5 211s PrivateWages_18 6 211s PrivateWages_19 7 211s PrivateWages_20 8 211s PrivateWages_21 9 211s PrivateWages_22 10 211s > nobs 211s [1] 63 211s > linearHypothesis 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 0.82 0.37 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 0.73 0.4 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 52 211s 2 51 1 0.73 0.39 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.42 0.66 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.37 0.69 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 53 211s 2 51 2 0.74 0.69 211s > logLik 211s 'log Lik.' -72.3 (df=13) 211s 'log Lik.' -77.9 (df=13) 211s compare log likelihood value with single-equation OLS 211s [1] TRUE 211s Estimating function 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_2 -0.32389 -4.016 211s Consumption_3 -1.25001 -21.125 211s Consumption_4 -1.56574 -28.810 211s Consumption_5 -0.49350 -9.574 211s Consumption_6 0.00761 0.153 211s Consumption_7 0.86910 17.034 211s Consumption_8 1.33848 26.502 211s Consumption_9 1.05498 22.260 211s Consumption_10 -0.58856 -12.772 211s Consumption_11 0.28231 4.404 211s Consumption_12 -0.22965 -2.618 211s Consumption_13 -0.32213 -2.255 211s Consumption_14 0.32228 3.610 211s Consumption_15 -0.05801 -0.714 211s Consumption_16 -0.03466 -0.485 211s Consumption_17 1.61650 28.450 211s Consumption_18 -0.43597 -7.542 211s Consumption_19 0.21005 3.214 211s Consumption_20 0.98920 18.795 211s Consumption_21 0.78508 16.565 211s Consumption_22 -2.17345 -51.076 211s Investment_2 0.00000 0.000 211s Investment_3 0.00000 0.000 211s Investment_4 0.00000 0.000 211s Investment_5 0.00000 0.000 211s Investment_6 0.00000 0.000 211s Investment_7 0.00000 0.000 211s Investment_8 0.00000 0.000 211s Investment_9 0.00000 0.000 211s Investment_10 0.00000 0.000 211s Investment_11 0.00000 0.000 211s Investment_12 0.00000 0.000 211s Investment_13 0.00000 0.000 211s Investment_14 0.00000 0.000 211s Investment_15 0.00000 0.000 211s Investment_16 0.00000 0.000 211s Investment_17 0.00000 0.000 211s Investment_18 0.00000 0.000 211s Investment_19 0.00000 0.000 211s Investment_20 0.00000 0.000 211s Investment_21 0.00000 0.000 211s Investment_22 0.00000 0.000 211s PrivateWages_2 0.00000 0.000 211s PrivateWages_3 0.00000 0.000 211s PrivateWages_4 0.00000 0.000 211s PrivateWages_5 0.00000 0.000 211s PrivateWages_6 0.00000 0.000 211s PrivateWages_7 0.00000 0.000 211s PrivateWages_8 0.00000 0.000 211s PrivateWages_9 0.00000 0.000 211s PrivateWages_10 0.00000 0.000 211s PrivateWages_11 0.00000 0.000 211s PrivateWages_12 0.00000 0.000 211s PrivateWages_13 0.00000 0.000 211s PrivateWages_14 0.00000 0.000 211s PrivateWages_15 0.00000 0.000 211s PrivateWages_16 0.00000 0.000 211s PrivateWages_17 0.00000 0.000 211s PrivateWages_18 0.00000 0.000 211s PrivateWages_19 0.00000 0.000 211s PrivateWages_20 0.00000 0.000 211s PrivateWages_21 0.00000 0.000 211s PrivateWages_22 0.00000 0.000 211s Consumption_corpProfLag Consumption_wages 211s Consumption_2 -4.113 -9.134 211s Consumption_3 -15.500 -40.250 211s Consumption_4 -26.461 -57.932 211s Consumption_5 -9.080 -18.260 211s Consumption_6 0.148 0.294 211s Consumption_7 17.469 35.372 211s Consumption_8 26.234 55.547 211s Consumption_9 20.889 45.259 211s Consumption_10 -12.419 -26.662 211s Consumption_11 6.126 11.885 211s Consumption_12 -3.583 -9.025 211s Consumption_13 -3.672 -11.049 211s Consumption_14 2.256 10.990 211s Consumption_15 -0.650 -2.123 211s Consumption_16 -0.426 -1.362 211s Consumption_17 22.631 71.449 211s Consumption_18 -7.673 -20.796 211s Consumption_19 3.634 9.641 211s Consumption_20 15.135 48.867 211s Consumption_21 14.916 41.609 211s Consumption_22 -45.860 -134.319 211s Investment_2 0.000 0.000 211s Investment_3 0.000 0.000 211s Investment_4 0.000 0.000 211s Investment_5 0.000 0.000 211s Investment_6 0.000 0.000 211s Investment_7 0.000 0.000 211s Investment_8 0.000 0.000 211s Investment_9 0.000 0.000 211s Investment_10 0.000 0.000 211s Investment_11 0.000 0.000 211s Investment_12 0.000 0.000 211s Investment_13 0.000 0.000 211s Investment_14 0.000 0.000 211s Investment_15 0.000 0.000 211s Investment_16 0.000 0.000 211s Investment_17 0.000 0.000 211s Investment_18 0.000 0.000 211s Investment_19 0.000 0.000 211s Investment_20 0.000 0.000 211s Investment_21 0.000 0.000 211s Investment_22 0.000 0.000 211s PrivateWages_2 0.000 0.000 211s PrivateWages_3 0.000 0.000 211s PrivateWages_4 0.000 0.000 211s PrivateWages_5 0.000 0.000 211s PrivateWages_6 0.000 0.000 211s PrivateWages_7 0.000 0.000 211s PrivateWages_8 0.000 0.000 211s PrivateWages_9 0.000 0.000 211s PrivateWages_10 0.000 0.000 211s PrivateWages_11 0.000 0.000 211s PrivateWages_12 0.000 0.000 211s PrivateWages_13 0.000 0.000 211s PrivateWages_14 0.000 0.000 211s PrivateWages_15 0.000 0.000 211s PrivateWages_16 0.000 0.000 211s PrivateWages_17 0.000 0.000 211s PrivateWages_18 0.000 0.000 211s PrivateWages_19 0.000 0.000 211s PrivateWages_20 0.000 0.000 211s PrivateWages_21 0.000 0.000 211s PrivateWages_22 0.000 0.000 211s Investment_(Intercept) Investment_corpProf 211s Consumption_2 0.0000 0.000 211s Consumption_3 0.0000 0.000 211s Consumption_4 0.0000 0.000 211s Consumption_5 0.0000 0.000 211s Consumption_6 0.0000 0.000 211s Consumption_7 0.0000 0.000 211s Consumption_8 0.0000 0.000 211s Consumption_9 0.0000 0.000 211s Consumption_10 0.0000 0.000 211s Consumption_11 0.0000 0.000 211s Consumption_12 0.0000 0.000 211s Consumption_13 0.0000 0.000 211s Consumption_14 0.0000 0.000 211s Consumption_15 0.0000 0.000 211s Consumption_16 0.0000 0.000 211s Consumption_17 0.0000 0.000 211s Consumption_18 0.0000 0.000 211s Consumption_19 0.0000 0.000 211s Consumption_20 0.0000 0.000 211s Consumption_21 0.0000 0.000 211s Consumption_22 0.0000 0.000 211s Investment_2 -0.0668 -0.828 211s Investment_3 -0.0476 -0.804 211s Investment_4 1.2467 22.939 211s Investment_5 -1.3512 -26.213 211s Investment_6 0.4154 8.350 211s Investment_7 1.4923 29.248 211s Investment_8 0.7889 15.620 211s Investment_9 -0.6317 -13.329 211s Investment_10 1.0830 23.500 211s Investment_11 0.2791 4.353 211s Investment_12 0.0369 0.420 211s Investment_13 0.3659 2.561 211s Investment_14 0.2237 2.505 211s Investment_15 -0.1728 -2.126 211s Investment_16 0.0101 0.141 211s Investment_17 0.9719 17.105 211s Investment_18 0.0516 0.893 211s Investment_19 -2.5656 -39.254 211s Investment_20 -0.6866 -13.045 211s Investment_21 -0.7807 -16.474 211s Investment_22 -0.6623 -15.565 211s PrivateWages_2 0.0000 0.000 211s PrivateWages_3 0.0000 0.000 211s PrivateWages_4 0.0000 0.000 211s PrivateWages_5 0.0000 0.000 211s PrivateWages_6 0.0000 0.000 211s PrivateWages_7 0.0000 0.000 211s PrivateWages_8 0.0000 0.000 211s PrivateWages_9 0.0000 0.000 211s PrivateWages_10 0.0000 0.000 211s PrivateWages_11 0.0000 0.000 211s PrivateWages_12 0.0000 0.000 211s PrivateWages_13 0.0000 0.000 211s PrivateWages_14 0.0000 0.000 211s PrivateWages_15 0.0000 0.000 211s PrivateWages_16 0.0000 0.000 211s PrivateWages_17 0.0000 0.000 211s PrivateWages_18 0.0000 0.000 211s PrivateWages_19 0.0000 0.000 211s PrivateWages_20 0.0000 0.000 211s PrivateWages_21 0.0000 0.000 211s PrivateWages_22 0.0000 0.000 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_2 0.000 0.00 211s Consumption_3 0.000 0.00 211s Consumption_4 0.000 0.00 211s Consumption_5 0.000 0.00 211s Consumption_6 0.000 0.00 211s Consumption_7 0.000 0.00 211s Consumption_8 0.000 0.00 211s Consumption_9 0.000 0.00 211s Consumption_10 0.000 0.00 211s Consumption_11 0.000 0.00 211s Consumption_12 0.000 0.00 211s Consumption_13 0.000 0.00 211s Consumption_14 0.000 0.00 211s Consumption_15 0.000 0.00 211s Consumption_16 0.000 0.00 211s Consumption_17 0.000 0.00 211s Consumption_18 0.000 0.00 211s Consumption_19 0.000 0.00 211s Consumption_20 0.000 0.00 211s Consumption_21 0.000 0.00 211s Consumption_22 0.000 0.00 211s Investment_2 -0.848 -12.21 211s Investment_3 -0.590 -8.69 211s Investment_4 21.069 230.01 211s Investment_5 -24.862 -256.32 211s Investment_6 8.059 80.05 211s Investment_7 29.994 295.17 211s Investment_8 15.463 160.46 211s Investment_9 -12.507 -131.14 211s Investment_10 22.850 228.07 211s Investment_11 6.056 60.20 211s Investment_12 0.575 7.99 211s Investment_13 4.172 78.05 211s Investment_14 1.566 46.33 211s Investment_15 -1.936 -34.91 211s Investment_16 0.124 2.01 211s Investment_17 13.606 192.14 211s Investment_18 0.908 10.31 211s Investment_19 -44.385 -517.74 211s Investment_20 -10.505 -137.25 211s Investment_21 -14.834 -157.09 211s Investment_22 -13.975 -135.45 211s PrivateWages_2 0.000 0.00 211s PrivateWages_3 0.000 0.00 211s PrivateWages_4 0.000 0.00 211s PrivateWages_5 0.000 0.00 211s PrivateWages_6 0.000 0.00 211s PrivateWages_7 0.000 0.00 211s PrivateWages_8 0.000 0.00 211s PrivateWages_9 0.000 0.00 211s PrivateWages_10 0.000 0.00 211s PrivateWages_11 0.000 0.00 211s PrivateWages_12 0.000 0.00 211s PrivateWages_13 0.000 0.00 211s PrivateWages_14 0.000 0.00 211s PrivateWages_15 0.000 0.00 211s PrivateWages_16 0.000 0.00 211s PrivateWages_17 0.000 0.00 211s PrivateWages_18 0.000 0.00 211s PrivateWages_19 0.000 0.00 211s PrivateWages_20 0.000 0.00 211s PrivateWages_21 0.000 0.00 211s PrivateWages_22 0.000 0.00 211s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 211s Consumption_2 0.0000 0.000 0.000 211s Consumption_3 0.0000 0.000 0.000 211s Consumption_4 0.0000 0.000 0.000 211s Consumption_5 0.0000 0.000 0.000 211s Consumption_6 0.0000 0.000 0.000 211s Consumption_7 0.0000 0.000 0.000 211s Consumption_8 0.0000 0.000 0.000 211s Consumption_9 0.0000 0.000 0.000 211s Consumption_10 0.0000 0.000 0.000 211s Consumption_11 0.0000 0.000 0.000 211s Consumption_12 0.0000 0.000 0.000 211s Consumption_13 0.0000 0.000 0.000 211s Consumption_14 0.0000 0.000 0.000 211s Consumption_15 0.0000 0.000 0.000 211s Consumption_16 0.0000 0.000 0.000 211s Consumption_17 0.0000 0.000 0.000 211s Consumption_18 0.0000 0.000 0.000 211s Consumption_19 0.0000 0.000 0.000 211s Consumption_20 0.0000 0.000 0.000 211s Consumption_21 0.0000 0.000 0.000 211s Consumption_22 0.0000 0.000 0.000 211s Investment_2 0.0000 0.000 0.000 211s Investment_3 0.0000 0.000 0.000 211s Investment_4 0.0000 0.000 0.000 211s Investment_5 0.0000 0.000 0.000 211s Investment_6 0.0000 0.000 0.000 211s Investment_7 0.0000 0.000 0.000 211s Investment_8 0.0000 0.000 0.000 211s Investment_9 0.0000 0.000 0.000 211s Investment_10 0.0000 0.000 0.000 211s Investment_11 0.0000 0.000 0.000 211s Investment_12 0.0000 0.000 0.000 211s Investment_13 0.0000 0.000 0.000 211s Investment_14 0.0000 0.000 0.000 211s Investment_15 0.0000 0.000 0.000 211s Investment_16 0.0000 0.000 0.000 211s Investment_17 0.0000 0.000 0.000 211s Investment_18 0.0000 0.000 0.000 211s Investment_19 0.0000 0.000 0.000 211s Investment_20 0.0000 0.000 0.000 211s Investment_21 0.0000 0.000 0.000 211s Investment_22 0.0000 0.000 0.000 211s PrivateWages_2 -1.2942 -59.015 -58.109 211s PrivateWages_3 0.2957 14.813 13.482 211s PrivateWages_4 1.1877 67.938 59.505 211s PrivateWages_5 -0.1358 -7.755 -7.768 211s PrivateWages_6 -0.4654 -28.390 -26.575 211s PrivateWages_7 -0.4838 -30.965 -29.514 211s PrivateWages_8 -0.7281 -46.892 -46.601 211s PrivateWages_9 0.3392 21.881 21.847 211s PrivateWages_10 1.1957 80.111 77.122 211s PrivateWages_11 -0.1508 -9.230 -10.105 211s PrivateWages_12 0.5942 31.729 36.364 211s PrivateWages_13 0.1027 4.549 5.483 211s PrivateWages_14 0.4503 20.307 19.947 211s PrivateWages_15 0.2816 13.993 12.698 211s PrivateWages_16 0.0138 0.748 0.684 211s PrivateWages_17 -0.8508 -53.343 -46.282 211s PrivateWages_18 0.9956 64.717 62.427 211s PrivateWages_19 -0.4688 -28.547 -30.469 211s PrivateWages_20 -0.3795 -26.378 -23.114 211s PrivateWages_21 -1.0909 -82.582 -75.818 211s PrivateWages_22 0.5917 52.309 44.794 211s PrivateWages_trend 211s Consumption_2 0.000 211s Consumption_3 0.000 211s Consumption_4 0.000 211s Consumption_5 0.000 211s Consumption_6 0.000 211s Consumption_7 0.000 211s Consumption_8 0.000 211s Consumption_9 0.000 211s Consumption_10 0.000 211s Consumption_11 0.000 211s Consumption_12 0.000 211s Consumption_13 0.000 211s Consumption_14 0.000 211s Consumption_15 0.000 211s Consumption_16 0.000 211s Consumption_17 0.000 211s Consumption_18 0.000 211s Consumption_19 0.000 211s Consumption_20 0.000 211s Consumption_21 0.000 211s Consumption_22 0.000 211s Investment_2 0.000 211s Investment_3 0.000 211s Investment_4 0.000 211s Investment_5 0.000 211s Investment_6 0.000 211s Investment_7 0.000 211s Investment_8 0.000 211s Investment_9 0.000 211s Investment_10 0.000 211s Investment_11 0.000 211s Investment_12 0.000 211s Investment_13 0.000 211s Investment_14 0.000 211s Investment_15 0.000 211s Investment_16 0.000 211s Investment_17 0.000 211s Investment_18 0.000 211s Investment_19 0.000 211s Investment_20 0.000 211s Investment_21 0.000 211s Investment_22 0.000 211s PrivateWages_2 12.942 211s PrivateWages_3 -2.661 211s PrivateWages_4 -9.502 211s PrivateWages_5 0.951 211s PrivateWages_6 2.792 211s PrivateWages_7 2.419 211s PrivateWages_8 2.913 211s PrivateWages_9 -1.018 211s PrivateWages_10 -2.391 211s PrivateWages_11 0.151 211s PrivateWages_12 0.000 211s PrivateWages_13 0.103 211s PrivateWages_14 0.901 211s PrivateWages_15 0.845 211s PrivateWages_16 0.055 211s PrivateWages_17 -4.254 211s PrivateWages_18 5.974 211s PrivateWages_19 -3.281 211s PrivateWages_20 -3.036 211s PrivateWages_21 -9.818 211s PrivateWages_22 5.917 211s [1] TRUE 211s > Bread 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_(Intercept) 101.65 0.030 211s Consumption_corpProf 0.03 0.498 211s Consumption_corpProfLag -1.06 -0.316 211s Consumption_wages -1.97 -0.079 211s Investment_(Intercept) 0.00 0.000 211s Investment_corpProf 0.00 0.000 211s Investment_corpProfLag 0.00 0.000 211s Investment_capitalLag 0.00 0.000 211s PrivateWages_(Intercept) 0.00 0.000 211s PrivateWages_gnp 0.00 0.000 211s PrivateWages_gnpLag 0.00 0.000 211s PrivateWages_trend 0.00 0.000 211s Consumption_corpProfLag Consumption_wages 211s Consumption_(Intercept) -1.0607 -1.9718 211s Consumption_corpProf -0.3157 -0.0790 211s Consumption_corpProfLag 0.4922 -0.0402 211s Consumption_wages -0.0402 0.0956 211s Investment_(Intercept) 0.0000 0.0000 211s Investment_corpProf 0.0000 0.0000 211s Investment_corpProfLag 0.0000 0.0000 211s Investment_capitalLag 0.0000 0.0000 211s PrivateWages_(Intercept) 0.0000 0.0000 211s PrivateWages_gnp 0.0000 0.0000 211s PrivateWages_gnpLag 0.0000 0.0000 211s PrivateWages_trend 0.0000 0.0000 211s Investment_(Intercept) Investment_corpProf 211s Consumption_(Intercept) 0.00 0.0000 211s Consumption_corpProf 0.00 0.0000 211s Consumption_corpProfLag 0.00 0.0000 211s Consumption_wages 0.00 0.0000 211s Investment_(Intercept) 1846.89 -17.9709 211s Investment_corpProf -17.97 0.5831 211s Investment_corpProfLag 14.67 -0.5008 211s Investment_capitalLag -8.88 0.0814 211s PrivateWages_(Intercept) 0.00 0.0000 211s PrivateWages_gnp 0.00 0.0000 211s PrivateWages_gnpLag 0.00 0.0000 211s PrivateWages_trend 0.00 0.0000 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_(Intercept) 0.0000 0.0000 211s Consumption_corpProf 0.0000 0.0000 211s Consumption_corpProfLag 0.0000 0.0000 211s Consumption_wages 0.0000 0.0000 211s Investment_(Intercept) 14.6742 -8.8813 211s Investment_corpProf -0.5008 0.0814 211s Investment_corpProfLag 0.6289 -0.0824 211s Investment_capitalLag -0.0824 0.0442 211s PrivateWages_(Intercept) 0.0000 0.0000 211s PrivateWages_gnp 0.0000 0.0000 211s PrivateWages_gnpLag 0.0000 0.0000 211s PrivateWages_trend 0.0000 0.0000 211s PrivateWages_(Intercept) PrivateWages_gnp 211s Consumption_(Intercept) 0.000 0.0000 211s Consumption_corpProf 0.000 0.0000 211s Consumption_corpProfLag 0.000 0.0000 211s Consumption_wages 0.000 0.0000 211s Investment_(Intercept) 0.000 0.0000 211s Investment_corpProf 0.000 0.0000 211s Investment_corpProfLag 0.000 0.0000 211s Investment_capitalLag 0.000 0.0000 211s PrivateWages_(Intercept) 172.668 -0.5919 211s PrivateWages_gnp -0.592 0.1124 211s PrivateWages_gnpLag -2.313 -0.1062 211s PrivateWages_trend 1.993 -0.0274 211s PrivateWages_gnpLag PrivateWages_trend 211s Consumption_(Intercept) 0.00000 0.00000 211s Consumption_corpProf 0.00000 0.00000 211s Consumption_corpProfLag 0.00000 0.00000 211s Consumption_wages 0.00000 0.00000 211s Investment_(Intercept) 0.00000 0.00000 211s Investment_corpProf 0.00000 0.00000 211s Investment_corpProfLag 0.00000 0.00000 211s Investment_capitalLag 0.00000 0.00000 211s PrivateWages_(Intercept) -2.31299 1.99284 211s PrivateWages_gnp -0.10624 -0.02738 211s PrivateWages_gnpLag 0.14992 -0.00601 211s PrivateWages_trend -0.00601 0.10900 211s > 211s > # 2SLS 211s > summary 211s 211s systemfit results 211s method: 2SLS 211s 211s N DF SSR detRCov OLS-R2 McElroy-R2 211s system 63 51 61 0.288 0.969 0.992 211s 211s N DF SSR MSE RMSE R2 Adj R2 211s Consumption 21 17 21.9 1.290 1.136 0.977 0.973 211s Investment 21 17 29.0 1.709 1.307 0.885 0.865 211s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 211s 211s The covariance matrix of the residuals 211s Consumption Investment PrivateWages 211s Consumption 1.044 0.438 -0.385 211s Investment 0.438 1.383 0.193 211s PrivateWages -0.385 0.193 0.476 211s 211s The correlations of the residuals 211s Consumption Investment PrivateWages 211s Consumption 1.000 0.364 -0.546 211s Investment 0.364 1.000 0.237 211s PrivateWages -0.546 0.237 1.000 211s 211s 211s 2SLS estimates for 'Consumption' (equation 1) 211s Model Formula: consump ~ corpProf + corpProfLag + wages 211s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 211s gnpLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 16.5548 1.3208 12.53 5.2e-10 *** 211s corpProf 0.0173 0.1180 0.15 0.89 211s corpProfLag 0.2162 0.1073 2.02 0.06 . 211s wages 0.8102 0.0402 20.13 2.7e-13 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.136 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 21.925 MSE: 1.29 Root MSE: 1.136 211s Multiple R-Squared: 0.977 Adjusted R-Squared: 0.973 211s 211s 211s 2SLS estimates for 'Investment' (equation 2) 211s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 211s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 211s gnpLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 20.2782 7.5427 2.69 0.01555 * 211s corpProf 0.1502 0.1732 0.87 0.39792 211s corpProfLag 0.6159 0.1628 3.78 0.00148 ** 211s capitalLag -0.1578 0.0361 -4.37 0.00042 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.307 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 29.047 MSE: 1.709 Root MSE: 1.307 211s Multiple R-Squared: 0.885 Adjusted R-Squared: 0.865 211s 211s 211s 2SLS estimates for 'PrivateWages' (equation 3) 211s Model Formula: privWage ~ gnp + gnpLag + trend 211s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 211s gnpLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 1.5003 1.1478 1.31 0.20857 211s gnp 0.4389 0.0356 12.32 6.8e-10 *** 211s gnpLag 0.1467 0.0388 3.78 0.00150 ** 211s trend 0.1304 0.0291 4.47 0.00033 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 0.767 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 211s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 211s 211s > residuals 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 -0.46263 -1.320 -1.2940 211s 3 -0.61635 0.257 0.2981 211s 4 -1.30423 0.860 1.1918 211s 5 -0.24588 -1.594 -0.1361 211s 6 0.22948 0.259 -0.4634 211s 7 0.88538 1.207 -0.4824 211s 8 1.44189 0.969 -0.7284 211s 9 1.34190 0.113 0.3387 211s 10 -0.39403 1.796 1.1965 211s 11 -0.62564 -0.953 -0.1552 211s 12 -1.06543 -0.807 0.5882 211s 13 -1.33021 -0.895 0.0955 211s 14 0.61059 1.306 0.4487 211s 15 -0.14208 -0.151 0.2822 211s 16 0.00315 0.142 0.0145 211s 17 2.00337 1.749 -0.8478 211s 18 -0.60552 -0.192 0.9950 211s 19 -0.24771 -3.291 -0.4734 211s 20 1.38510 0.285 -0.3766 211s 21 1.03204 -0.104 -1.0893 211s 22 -1.89319 0.363 0.5974 211s > fitted 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 42.4 1.120 26.8 211s 3 45.6 1.643 29.0 211s 4 50.5 4.340 32.9 211s 5 50.8 4.594 34.0 211s 6 52.4 4.841 35.9 211s 7 54.2 4.393 37.9 211s 8 54.8 3.231 38.6 211s 9 56.0 2.887 38.9 211s 10 58.2 3.304 40.1 211s 11 55.6 1.953 38.1 211s 12 52.0 -2.593 33.9 211s 13 46.9 -5.305 28.9 211s 14 45.9 -6.406 28.1 211s 15 48.8 -2.849 30.3 211s 16 51.3 -1.442 33.2 211s 17 55.7 0.351 37.6 211s 18 59.3 2.192 40.0 211s 19 57.7 1.391 38.7 211s 20 60.2 1.015 42.0 211s 21 64.0 3.404 46.1 211s 22 71.6 4.537 52.7 211s > predict 211s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 211s 1 NA NA NA NA 211s 2 42.4 0.471 41.4 43.4 211s 3 45.6 0.577 44.4 46.8 211s 4 50.5 0.354 49.8 51.3 211s 5 50.8 0.405 50.0 51.7 211s 6 52.4 0.404 51.5 53.2 211s 7 54.2 0.359 53.5 55.0 211s 8 54.8 0.328 54.1 55.4 211s 9 56.0 0.368 55.2 56.7 211s 10 58.2 0.377 57.4 59.0 211s 11 55.6 0.728 54.1 57.2 211s 12 52.0 0.604 50.7 53.2 211s 13 46.9 0.765 45.3 48.5 211s 14 45.9 0.615 44.6 47.2 211s 15 48.8 0.374 48.1 49.6 211s 16 51.3 0.333 50.6 52.0 211s 17 55.7 0.409 54.8 56.6 211s 18 59.3 0.326 58.6 60.0 211s 19 57.7 0.414 56.9 58.6 211s 20 60.2 0.478 59.2 61.2 211s 21 64.0 0.446 63.0 64.9 211s 22 71.6 0.689 70.1 73.0 211s Investment.pred Investment.se.fit Investment.lwr Investment.upr 211s 1 NA NA NA NA 211s 2 1.120 0.865 -0.706 2.946 211s 3 1.643 0.594 0.390 2.895 211s 4 4.340 0.545 3.190 5.490 211s 5 4.594 0.443 3.660 5.527 211s 6 4.841 0.411 3.973 5.709 211s 7 4.393 0.399 3.550 5.235 211s 8 3.231 0.348 2.497 3.965 211s 9 2.887 0.542 1.744 4.030 211s 10 3.304 0.593 2.054 4.555 211s 11 1.953 0.855 0.148 3.757 211s 12 -2.593 0.679 -4.026 -1.160 211s 13 -5.305 0.876 -7.152 -3.457 211s 14 -6.406 0.916 -8.338 -4.473 211s 15 -2.849 0.435 -3.765 -1.932 211s 16 -1.442 0.376 -2.236 -0.649 211s 17 0.351 0.510 -0.724 1.426 211s 18 2.192 0.299 1.560 2.823 211s 19 1.391 0.464 0.411 2.371 211s 20 1.015 0.576 -0.201 2.230 211s 21 3.404 0.471 2.410 4.398 211s 22 4.537 0.675 3.114 5.961 211s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 211s 1 NA NA NA NA 211s 2 26.8 0.318 26.1 27.5 211s 3 29.0 0.330 28.3 29.7 211s 4 32.9 0.346 32.2 33.6 211s 5 34.0 0.242 33.5 34.5 211s 6 35.9 0.248 35.3 36.4 211s 7 37.9 0.244 37.4 38.4 211s 8 38.6 0.246 38.1 39.1 211s 9 38.9 0.235 38.4 39.4 211s 10 40.1 0.224 39.6 40.6 211s 11 38.1 0.350 37.3 38.8 211s 12 33.9 0.382 33.1 34.7 211s 13 28.9 0.454 27.9 29.9 211s 14 28.1 0.342 27.3 28.8 211s 15 30.3 0.335 29.6 31.0 211s 16 33.2 0.280 32.6 33.8 211s 17 37.6 0.291 37.0 38.3 211s 18 40.0 0.215 39.6 40.5 211s 19 38.7 0.356 37.9 39.4 211s 20 42.0 0.304 41.3 42.6 211s 21 46.1 0.306 45.4 46.7 211s 22 52.7 0.489 51.7 53.7 211s > model.frame 211s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 211s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 211s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 211s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 211s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 211s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 211s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 211s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 211s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 211s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 211s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 211s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 211s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 211s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 211s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 211s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 211s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 211s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 211s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 211s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 211s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 211s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 211s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 211s trend 211s 1 -11 211s 2 -10 211s 3 -9 211s 4 -8 211s 5 -7 211s 6 -6 211s 7 -5 211s 8 -4 211s 9 -3 211s 10 -2 211s 11 -1 211s 12 0 211s 13 1 211s 14 2 211s 15 3 211s 16 4 211s 17 5 211s 18 6 211s 19 7 211s 20 8 211s 21 9 211s 22 10 211s > Frames of instrumental variables 211s govExp taxes govWage trend capitalLag corpProfLag gnpLag 211s 1 2.4 3.4 2.2 -11 180 NA NA 211s 2 3.9 7.7 2.7 -10 183 12.7 44.9 211s 3 3.2 3.9 2.9 -9 183 12.4 45.6 211s 4 2.8 4.7 2.9 -8 184 16.9 50.1 211s 5 3.5 3.8 3.1 -7 190 18.4 57.2 211s 6 3.3 5.5 3.2 -6 193 19.4 57.1 211s 7 3.3 7.0 3.3 -5 198 20.1 61.0 211s 8 4.0 6.7 3.6 -4 203 19.6 64.0 211s 9 4.2 4.2 3.7 -3 208 19.8 64.4 211s 10 4.1 4.0 4.0 -2 211 21.1 64.5 211s 11 5.2 7.7 4.2 -1 216 21.7 67.0 211s 12 5.9 7.5 4.8 0 217 15.6 61.2 211s 13 4.9 8.3 5.3 1 213 11.4 53.4 211s 14 3.7 5.4 5.6 2 207 7.0 44.3 211s 15 4.0 6.8 6.0 3 202 11.2 45.1 211s 16 4.4 7.2 6.1 4 199 12.3 49.7 211s 17 2.9 8.3 7.4 5 198 14.0 54.4 211s 18 4.3 6.7 6.7 6 200 17.6 62.7 211s 19 5.3 7.4 7.7 7 202 17.3 65.0 211s 20 6.6 8.9 7.8 8 200 15.3 60.9 211s 21 7.4 9.6 8.0 9 201 19.0 69.5 211s 22 13.8 11.6 8.5 10 204 21.1 75.7 211s govExp taxes govWage trend capitalLag corpProfLag gnpLag 211s 1 2.4 3.4 2.2 -11 180 NA NA 211s 2 3.9 7.7 2.7 -10 183 12.7 44.9 211s 3 3.2 3.9 2.9 -9 183 12.4 45.6 211s 4 2.8 4.7 2.9 -8 184 16.9 50.1 211s 5 3.5 3.8 3.1 -7 190 18.4 57.2 211s 6 3.3 5.5 3.2 -6 193 19.4 57.1 211s 7 3.3 7.0 3.3 -5 198 20.1 61.0 211s 8 4.0 6.7 3.6 -4 203 19.6 64.0 211s 9 4.2 4.2 3.7 -3 208 19.8 64.4 211s 10 4.1 4.0 4.0 -2 211 21.1 64.5 211s 11 5.2 7.7 4.2 -1 216 21.7 67.0 211s 12 5.9 7.5 4.8 0 217 15.6 61.2 211s 13 4.9 8.3 5.3 1 213 11.4 53.4 211s 14 3.7 5.4 5.6 2 207 7.0 44.3 211s 15 4.0 6.8 6.0 3 202 11.2 45.1 211s 16 4.4 7.2 6.1 4 199 12.3 49.7 211s 17 2.9 8.3 7.4 5 198 14.0 54.4 211s 18 4.3 6.7 6.7 6 200 17.6 62.7 211s 19 5.3 7.4 7.7 7 202 17.3 65.0 211s 20 6.6 8.9 7.8 8 200 15.3 60.9 211s 21 7.4 9.6 8.0 9 201 19.0 69.5 211s 22 13.8 11.6 8.5 10 204 21.1 75.7 211s govExp taxes govWage trend capitalLag corpProfLag gnpLag 211s 1 2.4 3.4 2.2 -11 180 NA NA 211s 2 3.9 7.7 2.7 -10 183 12.7 44.9 211s 3 3.2 3.9 2.9 -9 183 12.4 45.6 211s 4 2.8 4.7 2.9 -8 184 16.9 50.1 211s 5 3.5 3.8 3.1 -7 190 18.4 57.2 211s 6 3.3 5.5 3.2 -6 193 19.4 57.1 211s 7 3.3 7.0 3.3 -5 198 20.1 61.0 211s 8 4.0 6.7 3.6 -4 203 19.6 64.0 211s 9 4.2 4.2 3.7 -3 208 19.8 64.4 211s 10 4.1 4.0 4.0 -2 211 21.1 64.5 211s 11 5.2 7.7 4.2 -1 216 21.7 67.0 211s 12 5.9 7.5 4.8 0 217 15.6 61.2 211s 13 4.9 8.3 5.3 1 213 11.4 53.4 211s 14 3.7 5.4 5.6 2 207 7.0 44.3 211s 15 4.0 6.8 6.0 3 202 11.2 45.1 211s 16 4.4 7.2 6.1 4 199 12.3 49.7 211s 17 2.9 8.3 7.4 5 198 14.0 54.4 211s 18 4.3 6.7 6.7 6 200 17.6 62.7 211s 19 5.3 7.4 7.7 7 202 17.3 65.0 211s 20 6.6 8.9 7.8 8 200 15.3 60.9 211s 21 7.4 9.6 8.0 9 201 19.0 69.5 211s 22 13.8 11.6 8.5 10 204 21.1 75.7 211s > model.matrix 211s [1] TRUE 211s > matrix of instrumental variables 211s Consumption_(Intercept) Consumption_govExp Consumption_taxes 211s Consumption_2 1 3.9 7.7 211s Consumption_3 1 3.2 3.9 211s Consumption_4 1 2.8 4.7 211s Consumption_5 1 3.5 3.8 211s Consumption_6 1 3.3 5.5 211s Consumption_7 1 3.3 7.0 211s Consumption_8 1 4.0 6.7 211s Consumption_9 1 4.2 4.2 211s Consumption_10 1 4.1 4.0 211s Consumption_11 1 5.2 7.7 211s Consumption_12 1 5.9 7.5 211s Consumption_13 1 4.9 8.3 211s Consumption_14 1 3.7 5.4 211s Consumption_15 1 4.0 6.8 211s Consumption_16 1 4.4 7.2 211s Consumption_17 1 2.9 8.3 211s Consumption_18 1 4.3 6.7 211s Consumption_19 1 5.3 7.4 211s Consumption_20 1 6.6 8.9 211s Consumption_21 1 7.4 9.6 211s Consumption_22 1 13.8 11.6 211s Investment_2 0 0.0 0.0 211s Investment_3 0 0.0 0.0 211s Investment_4 0 0.0 0.0 211s Investment_5 0 0.0 0.0 211s Investment_6 0 0.0 0.0 211s Investment_7 0 0.0 0.0 211s Investment_8 0 0.0 0.0 211s Investment_9 0 0.0 0.0 211s Investment_10 0 0.0 0.0 211s Investment_11 0 0.0 0.0 211s Investment_12 0 0.0 0.0 211s Investment_13 0 0.0 0.0 211s Investment_14 0 0.0 0.0 211s Investment_15 0 0.0 0.0 211s Investment_16 0 0.0 0.0 211s Investment_17 0 0.0 0.0 211s Investment_18 0 0.0 0.0 211s Investment_19 0 0.0 0.0 211s Investment_20 0 0.0 0.0 211s Investment_21 0 0.0 0.0 211s Investment_22 0 0.0 0.0 211s PrivateWages_2 0 0.0 0.0 211s PrivateWages_3 0 0.0 0.0 211s PrivateWages_4 0 0.0 0.0 211s PrivateWages_5 0 0.0 0.0 211s PrivateWages_6 0 0.0 0.0 211s PrivateWages_7 0 0.0 0.0 211s PrivateWages_8 0 0.0 0.0 211s PrivateWages_9 0 0.0 0.0 211s PrivateWages_10 0 0.0 0.0 211s PrivateWages_11 0 0.0 0.0 211s PrivateWages_12 0 0.0 0.0 211s PrivateWages_13 0 0.0 0.0 211s PrivateWages_14 0 0.0 0.0 211s PrivateWages_15 0 0.0 0.0 211s PrivateWages_16 0 0.0 0.0 211s PrivateWages_17 0 0.0 0.0 211s PrivateWages_18 0 0.0 0.0 211s PrivateWages_19 0 0.0 0.0 211s PrivateWages_20 0 0.0 0.0 211s PrivateWages_21 0 0.0 0.0 211s PrivateWages_22 0 0.0 0.0 211s Consumption_govWage Consumption_trend Consumption_capitalLag 211s Consumption_2 2.7 -10 183 211s Consumption_3 2.9 -9 183 211s Consumption_4 2.9 -8 184 211s Consumption_5 3.1 -7 190 211s Consumption_6 3.2 -6 193 211s Consumption_7 3.3 -5 198 211s Consumption_8 3.6 -4 203 211s Consumption_9 3.7 -3 208 211s Consumption_10 4.0 -2 211 211s Consumption_11 4.2 -1 216 211s Consumption_12 4.8 0 217 211s Consumption_13 5.3 1 213 211s Consumption_14 5.6 2 207 211s Consumption_15 6.0 3 202 211s Consumption_16 6.1 4 199 211s Consumption_17 7.4 5 198 211s Consumption_18 6.7 6 200 211s Consumption_19 7.7 7 202 211s Consumption_20 7.8 8 200 211s Consumption_21 8.0 9 201 211s Consumption_22 8.5 10 204 211s Investment_2 0.0 0 0 211s Investment_3 0.0 0 0 211s Investment_4 0.0 0 0 211s Investment_5 0.0 0 0 211s Investment_6 0.0 0 0 211s Investment_7 0.0 0 0 211s Investment_8 0.0 0 0 211s Investment_9 0.0 0 0 211s Investment_10 0.0 0 0 211s Investment_11 0.0 0 0 211s Investment_12 0.0 0 0 211s Investment_13 0.0 0 0 211s Investment_14 0.0 0 0 211s Investment_15 0.0 0 0 211s Investment_16 0.0 0 0 211s Investment_17 0.0 0 0 211s Investment_18 0.0 0 0 211s Investment_19 0.0 0 0 211s Investment_20 0.0 0 0 211s Investment_21 0.0 0 0 211s Investment_22 0.0 0 0 211s PrivateWages_2 0.0 0 0 211s PrivateWages_3 0.0 0 0 211s PrivateWages_4 0.0 0 0 211s PrivateWages_5 0.0 0 0 211s PrivateWages_6 0.0 0 0 211s PrivateWages_7 0.0 0 0 211s PrivateWages_8 0.0 0 0 211s PrivateWages_9 0.0 0 0 211s PrivateWages_10 0.0 0 0 211s PrivateWages_11 0.0 0 0 211s PrivateWages_12 0.0 0 0 211s PrivateWages_13 0.0 0 0 211s PrivateWages_14 0.0 0 0 211s PrivateWages_15 0.0 0 0 211s PrivateWages_16 0.0 0 0 211s PrivateWages_17 0.0 0 0 211s PrivateWages_18 0.0 0 0 211s PrivateWages_19 0.0 0 0 211s PrivateWages_20 0.0 0 0 211s PrivateWages_21 0.0 0 0 211s PrivateWages_22 0.0 0 0 211s Consumption_corpProfLag Consumption_gnpLag 211s Consumption_2 12.7 44.9 211s Consumption_3 12.4 45.6 211s Consumption_4 16.9 50.1 211s Consumption_5 18.4 57.2 211s Consumption_6 19.4 57.1 211s Consumption_7 20.1 61.0 211s Consumption_8 19.6 64.0 211s Consumption_9 19.8 64.4 211s Consumption_10 21.1 64.5 211s Consumption_11 21.7 67.0 211s Consumption_12 15.6 61.2 211s Consumption_13 11.4 53.4 211s Consumption_14 7.0 44.3 211s Consumption_15 11.2 45.1 211s Consumption_16 12.3 49.7 211s Consumption_17 14.0 54.4 211s Consumption_18 17.6 62.7 211s Consumption_19 17.3 65.0 211s Consumption_20 15.3 60.9 211s Consumption_21 19.0 69.5 211s Consumption_22 21.1 75.7 211s Investment_2 0.0 0.0 211s Investment_3 0.0 0.0 211s Investment_4 0.0 0.0 211s Investment_5 0.0 0.0 211s Investment_6 0.0 0.0 211s Investment_7 0.0 0.0 211s Investment_8 0.0 0.0 211s Investment_9 0.0 0.0 211s Investment_10 0.0 0.0 211s Investment_11 0.0 0.0 211s Investment_12 0.0 0.0 211s Investment_13 0.0 0.0 211s Investment_14 0.0 0.0 211s Investment_15 0.0 0.0 211s Investment_16 0.0 0.0 211s Investment_17 0.0 0.0 211s Investment_18 0.0 0.0 211s Investment_19 0.0 0.0 211s Investment_20 0.0 0.0 211s Investment_21 0.0 0.0 211s Investment_22 0.0 0.0 211s PrivateWages_2 0.0 0.0 211s PrivateWages_3 0.0 0.0 211s PrivateWages_4 0.0 0.0 211s PrivateWages_5 0.0 0.0 211s PrivateWages_6 0.0 0.0 211s PrivateWages_7 0.0 0.0 211s PrivateWages_8 0.0 0.0 211s PrivateWages_9 0.0 0.0 211s PrivateWages_10 0.0 0.0 211s PrivateWages_11 0.0 0.0 211s PrivateWages_12 0.0 0.0 211s PrivateWages_13 0.0 0.0 211s PrivateWages_14 0.0 0.0 211s PrivateWages_15 0.0 0.0 211s PrivateWages_16 0.0 0.0 211s PrivateWages_17 0.0 0.0 211s PrivateWages_18 0.0 0.0 211s PrivateWages_19 0.0 0.0 211s PrivateWages_20 0.0 0.0 211s PrivateWages_21 0.0 0.0 211s PrivateWages_22 0.0 0.0 211s Investment_(Intercept) Investment_govExp Investment_taxes 211s Consumption_2 0 0.0 0.0 211s Consumption_3 0 0.0 0.0 211s Consumption_4 0 0.0 0.0 211s Consumption_5 0 0.0 0.0 211s Consumption_6 0 0.0 0.0 211s Consumption_7 0 0.0 0.0 211s Consumption_8 0 0.0 0.0 211s Consumption_9 0 0.0 0.0 211s Consumption_10 0 0.0 0.0 211s Consumption_11 0 0.0 0.0 211s Consumption_12 0 0.0 0.0 211s Consumption_13 0 0.0 0.0 211s Consumption_14 0 0.0 0.0 211s Consumption_15 0 0.0 0.0 211s Consumption_16 0 0.0 0.0 211s Consumption_17 0 0.0 0.0 211s Consumption_18 0 0.0 0.0 211s Consumption_19 0 0.0 0.0 211s Consumption_20 0 0.0 0.0 211s Consumption_21 0 0.0 0.0 211s Consumption_22 0 0.0 0.0 211s Investment_2 1 3.9 7.7 211s Investment_3 1 3.2 3.9 211s Investment_4 1 2.8 4.7 211s Investment_5 1 3.5 3.8 211s Investment_6 1 3.3 5.5 211s Investment_7 1 3.3 7.0 211s Investment_8 1 4.0 6.7 211s Investment_9 1 4.2 4.2 211s Investment_10 1 4.1 4.0 211s Investment_11 1 5.2 7.7 211s Investment_12 1 5.9 7.5 211s Investment_13 1 4.9 8.3 211s Investment_14 1 3.7 5.4 211s Investment_15 1 4.0 6.8 211s Investment_16 1 4.4 7.2 211s Investment_17 1 2.9 8.3 211s Investment_18 1 4.3 6.7 211s Investment_19 1 5.3 7.4 211s Investment_20 1 6.6 8.9 211s Investment_21 1 7.4 9.6 211s Investment_22 1 13.8 11.6 211s PrivateWages_2 0 0.0 0.0 211s PrivateWages_3 0 0.0 0.0 211s PrivateWages_4 0 0.0 0.0 211s PrivateWages_5 0 0.0 0.0 211s PrivateWages_6 0 0.0 0.0 211s PrivateWages_7 0 0.0 0.0 211s PrivateWages_8 0 0.0 0.0 211s PrivateWages_9 0 0.0 0.0 211s PrivateWages_10 0 0.0 0.0 211s PrivateWages_11 0 0.0 0.0 211s PrivateWages_12 0 0.0 0.0 211s PrivateWages_13 0 0.0 0.0 211s PrivateWages_14 0 0.0 0.0 211s PrivateWages_15 0 0.0 0.0 211s PrivateWages_16 0 0.0 0.0 211s PrivateWages_17 0 0.0 0.0 211s PrivateWages_18 0 0.0 0.0 211s PrivateWages_19 0 0.0 0.0 211s PrivateWages_20 0 0.0 0.0 211s PrivateWages_21 0 0.0 0.0 211s PrivateWages_22 0 0.0 0.0 211s Investment_govWage Investment_trend Investment_capitalLag 211s Consumption_2 0.0 0 0 211s Consumption_3 0.0 0 0 211s Consumption_4 0.0 0 0 211s Consumption_5 0.0 0 0 211s Consumption_6 0.0 0 0 211s Consumption_7 0.0 0 0 211s Consumption_8 0.0 0 0 211s Consumption_9 0.0 0 0 211s Consumption_10 0.0 0 0 211s Consumption_11 0.0 0 0 211s Consumption_12 0.0 0 0 211s Consumption_13 0.0 0 0 211s Consumption_14 0.0 0 0 211s Consumption_15 0.0 0 0 211s Consumption_16 0.0 0 0 211s Consumption_17 0.0 0 0 211s Consumption_18 0.0 0 0 211s Consumption_19 0.0 0 0 211s Consumption_20 0.0 0 0 211s Consumption_21 0.0 0 0 211s Consumption_22 0.0 0 0 211s Investment_2 2.7 -10 183 211s Investment_3 2.9 -9 183 211s Investment_4 2.9 -8 184 211s Investment_5 3.1 -7 190 211s Investment_6 3.2 -6 193 211s Investment_7 3.3 -5 198 211s Investment_8 3.6 -4 203 211s Investment_9 3.7 -3 208 211s Investment_10 4.0 -2 211 211s Investment_11 4.2 -1 216 211s Investment_12 4.8 0 217 211s Investment_13 5.3 1 213 211s Investment_14 5.6 2 207 211s Investment_15 6.0 3 202 211s Investment_16 6.1 4 199 211s Investment_17 7.4 5 198 211s Investment_18 6.7 6 200 211s Investment_19 7.7 7 202 211s Investment_20 7.8 8 200 211s Investment_21 8.0 9 201 211s Investment_22 8.5 10 204 211s PrivateWages_2 0.0 0 0 211s PrivateWages_3 0.0 0 0 211s PrivateWages_4 0.0 0 0 211s PrivateWages_5 0.0 0 0 211s PrivateWages_6 0.0 0 0 211s PrivateWages_7 0.0 0 0 211s PrivateWages_8 0.0 0 0 211s PrivateWages_9 0.0 0 0 211s PrivateWages_10 0.0 0 0 211s PrivateWages_11 0.0 0 0 211s PrivateWages_12 0.0 0 0 211s PrivateWages_13 0.0 0 0 211s PrivateWages_14 0.0 0 0 211s PrivateWages_15 0.0 0 0 211s PrivateWages_16 0.0 0 0 211s PrivateWages_17 0.0 0 0 211s PrivateWages_18 0.0 0 0 211s PrivateWages_19 0.0 0 0 211s PrivateWages_20 0.0 0 0 211s PrivateWages_21 0.0 0 0 211s PrivateWages_22 0.0 0 0 211s Investment_corpProfLag Investment_gnpLag 211s Consumption_2 0.0 0.0 211s Consumption_3 0.0 0.0 211s Consumption_4 0.0 0.0 211s Consumption_5 0.0 0.0 211s Consumption_6 0.0 0.0 211s Consumption_7 0.0 0.0 211s Consumption_8 0.0 0.0 211s Consumption_9 0.0 0.0 211s Consumption_10 0.0 0.0 211s Consumption_11 0.0 0.0 211s Consumption_12 0.0 0.0 211s Consumption_13 0.0 0.0 211s Consumption_14 0.0 0.0 211s Consumption_15 0.0 0.0 211s Consumption_16 0.0 0.0 211s Consumption_17 0.0 0.0 211s Consumption_18 0.0 0.0 211s Consumption_19 0.0 0.0 211s Consumption_20 0.0 0.0 211s Consumption_21 0.0 0.0 211s Consumption_22 0.0 0.0 211s Investment_2 12.7 44.9 211s Investment_3 12.4 45.6 211s Investment_4 16.9 50.1 211s Investment_5 18.4 57.2 211s Investment_6 19.4 57.1 211s Investment_7 20.1 61.0 211s Investment_8 19.6 64.0 211s Investment_9 19.8 64.4 211s Investment_10 21.1 64.5 211s Investment_11 21.7 67.0 211s Investment_12 15.6 61.2 211s Investment_13 11.4 53.4 211s Investment_14 7.0 44.3 211s Investment_15 11.2 45.1 211s Investment_16 12.3 49.7 211s Investment_17 14.0 54.4 211s Investment_18 17.6 62.7 211s Investment_19 17.3 65.0 211s Investment_20 15.3 60.9 211s Investment_21 19.0 69.5 211s Investment_22 21.1 75.7 211s PrivateWages_2 0.0 0.0 211s PrivateWages_3 0.0 0.0 211s PrivateWages_4 0.0 0.0 211s PrivateWages_5 0.0 0.0 211s PrivateWages_6 0.0 0.0 211s PrivateWages_7 0.0 0.0 211s PrivateWages_8 0.0 0.0 211s PrivateWages_9 0.0 0.0 211s PrivateWages_10 0.0 0.0 211s PrivateWages_11 0.0 0.0 211s PrivateWages_12 0.0 0.0 211s PrivateWages_13 0.0 0.0 211s PrivateWages_14 0.0 0.0 211s PrivateWages_15 0.0 0.0 211s PrivateWages_16 0.0 0.0 211s PrivateWages_17 0.0 0.0 211s PrivateWages_18 0.0 0.0 211s PrivateWages_19 0.0 0.0 211s PrivateWages_20 0.0 0.0 211s PrivateWages_21 0.0 0.0 211s PrivateWages_22 0.0 0.0 211s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 211s Consumption_2 0 0.0 0.0 211s Consumption_3 0 0.0 0.0 211s Consumption_4 0 0.0 0.0 211s Consumption_5 0 0.0 0.0 211s Consumption_6 0 0.0 0.0 211s Consumption_7 0 0.0 0.0 211s Consumption_8 0 0.0 0.0 211s Consumption_9 0 0.0 0.0 211s Consumption_10 0 0.0 0.0 211s Consumption_11 0 0.0 0.0 211s Consumption_12 0 0.0 0.0 211s Consumption_13 0 0.0 0.0 211s Consumption_14 0 0.0 0.0 211s Consumption_15 0 0.0 0.0 211s Consumption_16 0 0.0 0.0 211s Consumption_17 0 0.0 0.0 211s Consumption_18 0 0.0 0.0 211s Consumption_19 0 0.0 0.0 211s Consumption_20 0 0.0 0.0 211s Consumption_21 0 0.0 0.0 211s Consumption_22 0 0.0 0.0 211s Investment_2 0 0.0 0.0 211s Investment_3 0 0.0 0.0 211s Investment_4 0 0.0 0.0 211s Investment_5 0 0.0 0.0 211s Investment_6 0 0.0 0.0 211s Investment_7 0 0.0 0.0 211s Investment_8 0 0.0 0.0 211s Investment_9 0 0.0 0.0 211s Investment_10 0 0.0 0.0 211s Investment_11 0 0.0 0.0 211s Investment_12 0 0.0 0.0 211s Investment_13 0 0.0 0.0 211s Investment_14 0 0.0 0.0 211s Investment_15 0 0.0 0.0 211s Investment_16 0 0.0 0.0 211s Investment_17 0 0.0 0.0 211s Investment_18 0 0.0 0.0 211s Investment_19 0 0.0 0.0 211s Investment_20 0 0.0 0.0 211s Investment_21 0 0.0 0.0 211s Investment_22 0 0.0 0.0 211s PrivateWages_2 1 3.9 7.7 211s PrivateWages_3 1 3.2 3.9 211s PrivateWages_4 1 2.8 4.7 211s PrivateWages_5 1 3.5 3.8 211s PrivateWages_6 1 3.3 5.5 211s PrivateWages_7 1 3.3 7.0 211s PrivateWages_8 1 4.0 6.7 211s PrivateWages_9 1 4.2 4.2 211s PrivateWages_10 1 4.1 4.0 211s PrivateWages_11 1 5.2 7.7 211s PrivateWages_12 1 5.9 7.5 211s PrivateWages_13 1 4.9 8.3 211s PrivateWages_14 1 3.7 5.4 211s PrivateWages_15 1 4.0 6.8 211s PrivateWages_16 1 4.4 7.2 211s PrivateWages_17 1 2.9 8.3 211s PrivateWages_18 1 4.3 6.7 211s PrivateWages_19 1 5.3 7.4 211s PrivateWages_20 1 6.6 8.9 211s PrivateWages_21 1 7.4 9.6 211s PrivateWages_22 1 13.8 11.6 211s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 211s Consumption_2 0.0 0 0 211s Consumption_3 0.0 0 0 211s Consumption_4 0.0 0 0 211s Consumption_5 0.0 0 0 211s Consumption_6 0.0 0 0 211s Consumption_7 0.0 0 0 211s Consumption_8 0.0 0 0 211s Consumption_9 0.0 0 0 211s Consumption_10 0.0 0 0 211s Consumption_11 0.0 0 0 211s Consumption_12 0.0 0 0 211s Consumption_13 0.0 0 0 211s Consumption_14 0.0 0 0 211s Consumption_15 0.0 0 0 211s Consumption_16 0.0 0 0 211s Consumption_17 0.0 0 0 211s Consumption_18 0.0 0 0 211s Consumption_19 0.0 0 0 211s Consumption_20 0.0 0 0 211s Consumption_21 0.0 0 0 211s Consumption_22 0.0 0 0 211s Investment_2 0.0 0 0 211s Investment_3 0.0 0 0 211s Investment_4 0.0 0 0 211s Investment_5 0.0 0 0 211s Investment_6 0.0 0 0 211s Investment_7 0.0 0 0 211s Investment_8 0.0 0 0 211s Investment_9 0.0 0 0 211s Investment_10 0.0 0 0 211s Investment_11 0.0 0 0 211s Investment_12 0.0 0 0 211s Investment_13 0.0 0 0 211s Investment_14 0.0 0 0 211s Investment_15 0.0 0 0 211s Investment_16 0.0 0 0 211s Investment_17 0.0 0 0 211s Investment_18 0.0 0 0 211s Investment_19 0.0 0 0 211s Investment_20 0.0 0 0 211s Investment_21 0.0 0 0 211s Investment_22 0.0 0 0 211s PrivateWages_2 2.7 -10 183 211s PrivateWages_3 2.9 -9 183 211s PrivateWages_4 2.9 -8 184 211s PrivateWages_5 3.1 -7 190 211s PrivateWages_6 3.2 -6 193 211s PrivateWages_7 3.3 -5 198 211s PrivateWages_8 3.6 -4 203 211s PrivateWages_9 3.7 -3 208 211s PrivateWages_10 4.0 -2 211 211s PrivateWages_11 4.2 -1 216 211s PrivateWages_12 4.8 0 217 211s PrivateWages_13 5.3 1 213 211s PrivateWages_14 5.6 2 207 211s PrivateWages_15 6.0 3 202 211s PrivateWages_16 6.1 4 199 211s PrivateWages_17 7.4 5 198 211s PrivateWages_18 6.7 6 200 211s PrivateWages_19 7.7 7 202 211s PrivateWages_20 7.8 8 200 211s PrivateWages_21 8.0 9 201 211s PrivateWages_22 8.5 10 204 211s PrivateWages_corpProfLag PrivateWages_gnpLag 211s Consumption_2 0.0 0.0 211s Consumption_3 0.0 0.0 211s Consumption_4 0.0 0.0 211s Consumption_5 0.0 0.0 211s Consumption_6 0.0 0.0 211s Consumption_7 0.0 0.0 211s Consumption_8 0.0 0.0 211s Consumption_9 0.0 0.0 211s Consumption_10 0.0 0.0 211s Consumption_11 0.0 0.0 211s Consumption_12 0.0 0.0 211s Consumption_13 0.0 0.0 211s Consumption_14 0.0 0.0 211s Consumption_15 0.0 0.0 211s Consumption_16 0.0 0.0 211s Consumption_17 0.0 0.0 211s Consumption_18 0.0 0.0 211s Consumption_19 0.0 0.0 211s Consumption_20 0.0 0.0 211s Consumption_21 0.0 0.0 211s Consumption_22 0.0 0.0 211s Investment_2 0.0 0.0 211s Investment_3 0.0 0.0 211s Investment_4 0.0 0.0 211s Investment_5 0.0 0.0 211s Investment_6 0.0 0.0 211s Investment_7 0.0 0.0 211s Investment_8 0.0 0.0 211s Investment_9 0.0 0.0 211s Investment_10 0.0 0.0 211s Investment_11 0.0 0.0 211s Investment_12 0.0 0.0 211s Investment_13 0.0 0.0 211s Investment_14 0.0 0.0 211s Investment_15 0.0 0.0 211s Investment_16 0.0 0.0 211s Investment_17 0.0 0.0 211s Investment_18 0.0 0.0 211s Investment_19 0.0 0.0 211s Investment_20 0.0 0.0 211s Investment_21 0.0 0.0 211s Investment_22 0.0 0.0 211s PrivateWages_2 12.7 44.9 211s PrivateWages_3 12.4 45.6 211s PrivateWages_4 16.9 50.1 211s PrivateWages_5 18.4 57.2 211s PrivateWages_6 19.4 57.1 211s PrivateWages_7 20.1 61.0 211s PrivateWages_8 19.6 64.0 211s PrivateWages_9 19.8 64.4 211s PrivateWages_10 21.1 64.5 211s PrivateWages_11 21.7 67.0 211s PrivateWages_12 15.6 61.2 211s PrivateWages_13 11.4 53.4 211s PrivateWages_14 7.0 44.3 211s PrivateWages_15 11.2 45.1 211s PrivateWages_16 12.3 49.7 211s PrivateWages_17 14.0 54.4 211s PrivateWages_18 17.6 62.7 211s PrivateWages_19 17.3 65.0 211s PrivateWages_20 15.3 60.9 211s PrivateWages_21 19.0 69.5 211s PrivateWages_22 21.1 75.7 211s > matrix of fitted regressors 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_2 1 13.26 211s Consumption_3 1 16.58 211s Consumption_4 1 19.28 211s Consumption_5 1 20.96 211s Consumption_6 1 19.77 211s Consumption_7 1 18.24 211s Consumption_8 1 17.57 211s Consumption_9 1 19.54 211s Consumption_10 1 20.38 211s Consumption_11 1 17.18 211s Consumption_12 1 12.71 211s Consumption_13 1 9.00 211s Consumption_14 1 9.05 211s Consumption_15 1 12.67 211s Consumption_16 1 14.42 211s Consumption_17 1 14.71 211s Consumption_18 1 19.80 211s Consumption_19 1 19.21 211s Consumption_20 1 17.42 211s Consumption_21 1 20.31 211s Consumption_22 1 22.66 211s Investment_2 0 0.00 211s Investment_3 0 0.00 211s Investment_4 0 0.00 211s Investment_5 0 0.00 211s Investment_6 0 0.00 211s Investment_7 0 0.00 211s Investment_8 0 0.00 211s Investment_9 0 0.00 211s Investment_10 0 0.00 211s Investment_11 0 0.00 211s Investment_12 0 0.00 211s Investment_13 0 0.00 211s Investment_14 0 0.00 211s Investment_15 0 0.00 211s Investment_16 0 0.00 211s Investment_17 0 0.00 211s Investment_18 0 0.00 211s Investment_19 0 0.00 211s Investment_20 0 0.00 211s Investment_21 0 0.00 211s Investment_22 0 0.00 211s PrivateWages_2 0 0.00 211s PrivateWages_3 0 0.00 211s PrivateWages_4 0 0.00 211s PrivateWages_5 0 0.00 211s PrivateWages_6 0 0.00 211s PrivateWages_7 0 0.00 211s PrivateWages_8 0 0.00 211s PrivateWages_9 0 0.00 211s PrivateWages_10 0 0.00 211s PrivateWages_11 0 0.00 211s PrivateWages_12 0 0.00 211s PrivateWages_13 0 0.00 211s PrivateWages_14 0 0.00 211s PrivateWages_15 0 0.00 211s PrivateWages_16 0 0.00 211s PrivateWages_17 0 0.00 211s PrivateWages_18 0 0.00 211s PrivateWages_19 0 0.00 211s PrivateWages_20 0 0.00 211s PrivateWages_21 0 0.00 211s PrivateWages_22 0 0.00 211s Consumption_corpProfLag Consumption_wages 211s Consumption_2 12.7 29.4 211s Consumption_3 12.4 31.8 211s Consumption_4 16.9 35.8 211s Consumption_5 18.4 39.1 211s Consumption_6 19.4 39.1 211s Consumption_7 20.1 39.4 211s Consumption_8 19.6 40.2 211s Consumption_9 19.8 42.3 211s Consumption_10 21.1 44.0 211s Consumption_11 21.7 43.7 211s Consumption_12 15.6 39.5 211s Consumption_13 11.4 35.1 211s Consumption_14 7.0 32.8 211s Consumption_15 11.2 37.5 211s Consumption_16 12.3 40.1 211s Consumption_17 14.0 41.7 211s Consumption_18 17.6 47.9 211s Consumption_19 17.3 49.3 211s Consumption_20 15.3 48.4 211s Consumption_21 19.0 53.4 211s Consumption_22 21.1 60.7 211s Investment_2 0.0 0.0 211s Investment_3 0.0 0.0 211s Investment_4 0.0 0.0 211s Investment_5 0.0 0.0 211s Investment_6 0.0 0.0 211s Investment_7 0.0 0.0 211s Investment_8 0.0 0.0 211s Investment_9 0.0 0.0 211s Investment_10 0.0 0.0 211s Investment_11 0.0 0.0 211s Investment_12 0.0 0.0 211s Investment_13 0.0 0.0 211s Investment_14 0.0 0.0 211s Investment_15 0.0 0.0 211s Investment_16 0.0 0.0 211s Investment_17 0.0 0.0 211s Investment_18 0.0 0.0 211s Investment_19 0.0 0.0 211s Investment_20 0.0 0.0 211s Investment_21 0.0 0.0 211s Investment_22 0.0 0.0 211s PrivateWages_2 0.0 0.0 211s PrivateWages_3 0.0 0.0 211s PrivateWages_4 0.0 0.0 211s PrivateWages_5 0.0 0.0 211s PrivateWages_6 0.0 0.0 211s PrivateWages_7 0.0 0.0 211s PrivateWages_8 0.0 0.0 211s PrivateWages_9 0.0 0.0 211s PrivateWages_10 0.0 0.0 211s PrivateWages_11 0.0 0.0 211s PrivateWages_12 0.0 0.0 211s PrivateWages_13 0.0 0.0 211s PrivateWages_14 0.0 0.0 211s PrivateWages_15 0.0 0.0 211s PrivateWages_16 0.0 0.0 211s PrivateWages_17 0.0 0.0 211s PrivateWages_18 0.0 0.0 211s PrivateWages_19 0.0 0.0 211s PrivateWages_20 0.0 0.0 211s PrivateWages_21 0.0 0.0 211s PrivateWages_22 0.0 0.0 211s Investment_(Intercept) Investment_corpProf 211s Consumption_2 0 0.00 211s Consumption_3 0 0.00 211s Consumption_4 0 0.00 211s Consumption_5 0 0.00 211s Consumption_6 0 0.00 211s Consumption_7 0 0.00 211s Consumption_8 0 0.00 211s Consumption_9 0 0.00 211s Consumption_10 0 0.00 211s Consumption_11 0 0.00 211s Consumption_12 0 0.00 211s Consumption_13 0 0.00 211s Consumption_14 0 0.00 211s Consumption_15 0 0.00 211s Consumption_16 0 0.00 211s Consumption_17 0 0.00 211s Consumption_18 0 0.00 211s Consumption_19 0 0.00 211s Consumption_20 0 0.00 211s Consumption_21 0 0.00 211s Consumption_22 0 0.00 211s Investment_2 1 13.26 211s Investment_3 1 16.58 211s Investment_4 1 19.28 211s Investment_5 1 20.96 211s Investment_6 1 19.77 211s Investment_7 1 18.24 211s Investment_8 1 17.57 211s Investment_9 1 19.54 211s Investment_10 1 20.38 211s Investment_11 1 17.18 211s Investment_12 1 12.71 211s Investment_13 1 9.00 211s Investment_14 1 9.05 211s Investment_15 1 12.67 211s Investment_16 1 14.42 211s Investment_17 1 14.71 211s Investment_18 1 19.80 211s Investment_19 1 19.21 211s Investment_20 1 17.42 211s Investment_21 1 20.31 211s Investment_22 1 22.66 211s PrivateWages_2 0 0.00 211s PrivateWages_3 0 0.00 211s PrivateWages_4 0 0.00 211s PrivateWages_5 0 0.00 211s PrivateWages_6 0 0.00 211s PrivateWages_7 0 0.00 211s PrivateWages_8 0 0.00 211s PrivateWages_9 0 0.00 211s PrivateWages_10 0 0.00 211s PrivateWages_11 0 0.00 211s PrivateWages_12 0 0.00 211s PrivateWages_13 0 0.00 211s PrivateWages_14 0 0.00 211s PrivateWages_15 0 0.00 211s PrivateWages_16 0 0.00 211s PrivateWages_17 0 0.00 211s PrivateWages_18 0 0.00 211s PrivateWages_19 0 0.00 211s PrivateWages_20 0 0.00 211s PrivateWages_21 0 0.00 211s PrivateWages_22 0 0.00 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_2 0.0 0 211s Consumption_3 0.0 0 211s Consumption_4 0.0 0 211s Consumption_5 0.0 0 211s Consumption_6 0.0 0 211s Consumption_7 0.0 0 211s Consumption_8 0.0 0 211s Consumption_9 0.0 0 211s Consumption_10 0.0 0 211s Consumption_11 0.0 0 211s Consumption_12 0.0 0 211s Consumption_13 0.0 0 211s Consumption_14 0.0 0 211s Consumption_15 0.0 0 211s Consumption_16 0.0 0 211s Consumption_17 0.0 0 211s Consumption_18 0.0 0 211s Consumption_19 0.0 0 211s Consumption_20 0.0 0 211s Consumption_21 0.0 0 211s Consumption_22 0.0 0 211s Investment_2 12.7 183 211s Investment_3 12.4 183 211s Investment_4 16.9 184 211s Investment_5 18.4 190 211s Investment_6 19.4 193 211s Investment_7 20.1 198 211s Investment_8 19.6 203 211s Investment_9 19.8 208 211s Investment_10 21.1 211 211s Investment_11 21.7 216 211s Investment_12 15.6 217 211s Investment_13 11.4 213 211s Investment_14 7.0 207 211s Investment_15 11.2 202 211s Investment_16 12.3 199 211s Investment_17 14.0 198 211s Investment_18 17.6 200 211s Investment_19 17.3 202 211s Investment_20 15.3 200 211s Investment_21 19.0 201 211s Investment_22 21.1 204 211s PrivateWages_2 0.0 0 211s PrivateWages_3 0.0 0 211s PrivateWages_4 0.0 0 211s PrivateWages_5 0.0 0 211s PrivateWages_6 0.0 0 211s PrivateWages_7 0.0 0 211s PrivateWages_8 0.0 0 211s PrivateWages_9 0.0 0 211s PrivateWages_10 0.0 0 211s PrivateWages_11 0.0 0 211s PrivateWages_12 0.0 0 211s PrivateWages_13 0.0 0 211s PrivateWages_14 0.0 0 211s PrivateWages_15 0.0 0 211s PrivateWages_16 0.0 0 211s PrivateWages_17 0.0 0 211s PrivateWages_18 0.0 0 211s PrivateWages_19 0.0 0 211s PrivateWages_20 0.0 0 211s PrivateWages_21 0.0 0 211s PrivateWages_22 0.0 0 211s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 211s Consumption_2 0 0.0 0.0 211s Consumption_3 0 0.0 0.0 211s Consumption_4 0 0.0 0.0 211s Consumption_5 0 0.0 0.0 211s Consumption_6 0 0.0 0.0 211s Consumption_7 0 0.0 0.0 211s Consumption_8 0 0.0 0.0 211s Consumption_9 0 0.0 0.0 211s Consumption_10 0 0.0 0.0 211s Consumption_11 0 0.0 0.0 211s Consumption_12 0 0.0 0.0 211s Consumption_13 0 0.0 0.0 211s Consumption_14 0 0.0 0.0 211s Consumption_15 0 0.0 0.0 211s Consumption_16 0 0.0 0.0 211s Consumption_17 0 0.0 0.0 211s Consumption_18 0 0.0 0.0 211s Consumption_19 0 0.0 0.0 211s Consumption_20 0 0.0 0.0 211s Consumption_21 0 0.0 0.0 211s Consumption_22 0 0.0 0.0 211s Investment_2 0 0.0 0.0 211s Investment_3 0 0.0 0.0 211s Investment_4 0 0.0 0.0 211s Investment_5 0 0.0 0.0 211s Investment_6 0 0.0 0.0 211s Investment_7 0 0.0 0.0 211s Investment_8 0 0.0 0.0 211s Investment_9 0 0.0 0.0 211s Investment_10 0 0.0 0.0 211s Investment_11 0 0.0 0.0 211s Investment_12 0 0.0 0.0 211s Investment_13 0 0.0 0.0 211s Investment_14 0 0.0 0.0 211s Investment_15 0 0.0 0.0 211s Investment_16 0 0.0 0.0 211s Investment_17 0 0.0 0.0 211s Investment_18 0 0.0 0.0 211s Investment_19 0 0.0 0.0 211s Investment_20 0 0.0 0.0 211s Investment_21 0 0.0 0.0 211s Investment_22 0 0.0 0.0 211s PrivateWages_2 1 47.7 44.9 211s PrivateWages_3 1 49.3 45.6 211s PrivateWages_4 1 56.8 50.1 211s PrivateWages_5 1 60.7 57.2 211s PrivateWages_6 1 61.2 57.1 211s PrivateWages_7 1 61.3 61.0 211s PrivateWages_8 1 60.9 64.0 211s PrivateWages_9 1 62.4 64.4 211s PrivateWages_10 1 64.4 64.5 211s PrivateWages_11 1 64.4 67.0 211s PrivateWages_12 1 54.9 61.2 211s PrivateWages_13 1 47.1 53.4 211s PrivateWages_14 1 41.6 44.3 211s PrivateWages_15 1 51.0 45.1 211s PrivateWages_16 1 55.7 49.7 211s PrivateWages_17 1 57.3 54.4 211s PrivateWages_18 1 67.7 62.7 211s PrivateWages_19 1 68.2 65.0 211s PrivateWages_20 1 66.9 60.9 211s PrivateWages_21 1 75.3 69.5 211s PrivateWages_22 1 86.5 75.7 211s PrivateWages_trend 211s Consumption_2 0 211s Consumption_3 0 211s Consumption_4 0 211s Consumption_5 0 211s Consumption_6 0 211s Consumption_7 0 211s Consumption_8 0 211s Consumption_9 0 211s Consumption_10 0 211s Consumption_11 0 211s Consumption_12 0 211s Consumption_13 0 211s Consumption_14 0 211s Consumption_15 0 211s Consumption_16 0 211s Consumption_17 0 211s Consumption_18 0 211s Consumption_19 0 211s Consumption_20 0 211s Consumption_21 0 211s Consumption_22 0 211s Investment_2 0 211s Investment_3 0 211s Investment_4 0 211s Investment_5 0 211s Investment_6 0 211s Investment_7 0 211s Investment_8 0 211s Investment_9 0 211s Investment_10 0 211s Investment_11 0 211s Investment_12 0 211s Investment_13 0 211s Investment_14 0 211s Investment_15 0 211s Investment_16 0 211s Investment_17 0 211s Investment_18 0 211s Investment_19 0 211s Investment_20 0 211s Investment_21 0 211s Investment_22 0 211s PrivateWages_2 -10 211s PrivateWages_3 -9 211s PrivateWages_4 -8 211s PrivateWages_5 -7 211s PrivateWages_6 -6 211s PrivateWages_7 -5 211s PrivateWages_8 -4 211s PrivateWages_9 -3 211s PrivateWages_10 -2 211s PrivateWages_11 -1 211s PrivateWages_12 0 211s PrivateWages_13 1 211s PrivateWages_14 2 211s PrivateWages_15 3 211s PrivateWages_16 4 211s PrivateWages_17 5 211s PrivateWages_18 6 211s PrivateWages_19 7 211s PrivateWages_20 8 211s PrivateWages_21 9 211s PrivateWages_22 10 211s > nobs 211s [1] 63 211s > linearHypothesis 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 1.08 0.3 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 1.29 0.26 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 52 211s 2 51 1 1.29 0.26 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.54 0.58 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.65 0.53 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 53 211s 2 51 2 1.3 0.52 211s > logLik 211s 'log Lik.' -76.3 (df=13) 211s 'log Lik.' -85.5 (df=13) 211s Estimating function 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_2 -1.455 -19.28 211s Consumption_3 -0.246 -4.08 211s Consumption_4 -0.309 -5.96 211s Consumption_5 -1.952 -40.92 211s Consumption_6 -0.199 -3.93 211s Consumption_7 2.000 36.47 211s Consumption_8 2.547 44.76 211s Consumption_9 1.829 35.74 211s Consumption_10 0.665 13.55 211s Consumption_11 -1.947 -33.46 211s Consumption_12 -1.232 -15.65 211s Consumption_13 -2.039 -18.35 211s Consumption_14 1.714 15.52 211s Consumption_15 -0.877 -11.11 211s Consumption_16 -0.684 -9.87 211s Consumption_17 4.077 59.98 211s Consumption_18 -0.793 -15.70 211s Consumption_19 -3.072 -59.01 211s Consumption_20 2.230 38.84 211s Consumption_21 0.744 15.11 211s Consumption_22 -1.000 -22.66 211s Investment_2 0.000 0.00 211s Investment_3 0.000 0.00 211s Investment_4 0.000 0.00 211s Investment_5 0.000 0.00 211s Investment_6 0.000 0.00 211s Investment_7 0.000 0.00 211s Investment_8 0.000 0.00 211s Investment_9 0.000 0.00 211s Investment_10 0.000 0.00 211s Investment_11 0.000 0.00 211s Investment_12 0.000 0.00 211s Investment_13 0.000 0.00 211s Investment_14 0.000 0.00 211s Investment_15 0.000 0.00 211s Investment_16 0.000 0.00 211s Investment_17 0.000 0.00 211s Investment_18 0.000 0.00 211s Investment_19 0.000 0.00 211s Investment_20 0.000 0.00 211s Investment_21 0.000 0.00 211s Investment_22 0.000 0.00 211s PrivateWages_2 0.000 0.00 211s PrivateWages_3 0.000 0.00 211s PrivateWages_4 0.000 0.00 211s PrivateWages_5 0.000 0.00 211s PrivateWages_6 0.000 0.00 211s PrivateWages_7 0.000 0.00 211s PrivateWages_8 0.000 0.00 211s PrivateWages_9 0.000 0.00 211s PrivateWages_10 0.000 0.00 211s PrivateWages_11 0.000 0.00 211s PrivateWages_12 0.000 0.00 211s PrivateWages_13 0.000 0.00 211s PrivateWages_14 0.000 0.00 211s PrivateWages_15 0.000 0.00 211s PrivateWages_16 0.000 0.00 211s PrivateWages_17 0.000 0.00 211s PrivateWages_18 0.000 0.00 211s PrivateWages_19 0.000 0.00 211s PrivateWages_20 0.000 0.00 211s PrivateWages_21 0.000 0.00 211s PrivateWages_22 0.000 0.00 211s Consumption_corpProfLag Consumption_wages 211s Consumption_2 -18.47 -42.77 211s Consumption_3 -3.05 -7.82 211s Consumption_4 -5.22 -11.05 211s Consumption_5 -35.93 -76.29 211s Consumption_6 -3.85 -7.77 211s Consumption_7 40.20 78.70 211s Consumption_8 49.93 102.36 211s Consumption_9 36.21 77.42 211s Consumption_10 14.03 29.28 211s Consumption_11 -42.26 -85.10 211s Consumption_12 -19.22 -48.63 211s Consumption_13 -23.25 -71.64 211s Consumption_14 12.00 56.20 211s Consumption_15 -9.82 -32.89 211s Consumption_16 -8.42 -27.47 211s Consumption_17 57.07 170.01 211s Consumption_18 -13.96 -37.97 211s Consumption_19 -53.15 -151.48 211s Consumption_20 34.12 107.90 211s Consumption_21 14.14 39.73 211s Consumption_22 -21.10 -60.72 211s Investment_2 0.00 0.00 211s Investment_3 0.00 0.00 211s Investment_4 0.00 0.00 211s Investment_5 0.00 0.00 211s Investment_6 0.00 0.00 211s Investment_7 0.00 0.00 211s Investment_8 0.00 0.00 211s Investment_9 0.00 0.00 211s Investment_10 0.00 0.00 211s Investment_11 0.00 0.00 211s Investment_12 0.00 0.00 211s Investment_13 0.00 0.00 211s Investment_14 0.00 0.00 211s Investment_15 0.00 0.00 211s Investment_16 0.00 0.00 211s Investment_17 0.00 0.00 211s Investment_18 0.00 0.00 211s Investment_19 0.00 0.00 211s Investment_20 0.00 0.00 211s Investment_21 0.00 0.00 211s Investment_22 0.00 0.00 211s PrivateWages_2 0.00 0.00 211s PrivateWages_3 0.00 0.00 211s PrivateWages_4 0.00 0.00 211s PrivateWages_5 0.00 0.00 211s PrivateWages_6 0.00 0.00 211s PrivateWages_7 0.00 0.00 211s PrivateWages_8 0.00 0.00 211s PrivateWages_9 0.00 0.00 211s PrivateWages_10 0.00 0.00 211s PrivateWages_11 0.00 0.00 211s PrivateWages_12 0.00 0.00 211s PrivateWages_13 0.00 0.00 211s PrivateWages_14 0.00 0.00 211s PrivateWages_15 0.00 0.00 211s PrivateWages_16 0.00 0.00 211s PrivateWages_17 0.00 0.00 211s PrivateWages_18 0.00 0.00 211s PrivateWages_19 0.00 0.00 211s PrivateWages_20 0.00 0.00 211s PrivateWages_21 0.00 0.00 211s PrivateWages_22 0.00 0.00 211s Investment_(Intercept) Investment_corpProf 211s Consumption_2 0.0000 0.000 211s Consumption_3 0.0000 0.000 211s Consumption_4 0.0000 0.000 211s Consumption_5 0.0000 0.000 211s Consumption_6 0.0000 0.000 211s Consumption_7 0.0000 0.000 211s Consumption_8 0.0000 0.000 211s Consumption_9 0.0000 0.000 211s Consumption_10 0.0000 0.000 211s Consumption_11 0.0000 0.000 211s Consumption_12 0.0000 0.000 211s Consumption_13 0.0000 0.000 211s Consumption_14 0.0000 0.000 211s Consumption_15 0.0000 0.000 211s Consumption_16 0.0000 0.000 211s Consumption_17 0.0000 0.000 211s Consumption_18 0.0000 0.000 211s Consumption_19 0.0000 0.000 211s Consumption_20 0.0000 0.000 211s Consumption_21 0.0000 0.000 211s Consumption_22 0.0000 0.000 211s Investment_2 -1.4484 -19.199 211s Investment_3 0.3058 5.070 211s Investment_4 0.7275 14.029 211s Investment_5 -1.8279 -38.314 211s Investment_6 0.3088 6.104 211s Investment_7 1.4119 25.751 211s Investment_8 1.3034 22.906 211s Investment_9 0.3472 6.785 211s Investment_10 1.9947 40.642 211s Investment_11 -1.1903 -20.449 211s Investment_12 -1.0029 -12.742 211s Investment_13 -1.1958 -10.762 211s Investment_14 1.6279 14.739 211s Investment_15 -0.2072 -2.625 211s Investment_16 0.0790 1.140 211s Investment_17 2.1831 32.118 211s Investment_18 -0.5667 -11.219 211s Investment_19 -3.8778 -74.479 211s Investment_20 0.5228 9.107 211s Investment_21 0.0154 0.312 211s Investment_22 0.4893 11.087 211s PrivateWages_2 0.0000 0.000 211s PrivateWages_3 0.0000 0.000 211s PrivateWages_4 0.0000 0.000 211s PrivateWages_5 0.0000 0.000 211s PrivateWages_6 0.0000 0.000 211s PrivateWages_7 0.0000 0.000 211s PrivateWages_8 0.0000 0.000 211s PrivateWages_9 0.0000 0.000 211s PrivateWages_10 0.0000 0.000 211s PrivateWages_11 0.0000 0.000 211s PrivateWages_12 0.0000 0.000 211s PrivateWages_13 0.0000 0.000 211s PrivateWages_14 0.0000 0.000 211s PrivateWages_15 0.0000 0.000 211s PrivateWages_16 0.0000 0.000 211s PrivateWages_17 0.0000 0.000 211s PrivateWages_18 0.0000 0.000 211s PrivateWages_19 0.0000 0.000 211s PrivateWages_20 0.0000 0.000 211s PrivateWages_21 0.0000 0.000 211s PrivateWages_22 0.0000 0.000 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_2 0.000 0.0 211s Consumption_3 0.000 0.0 211s Consumption_4 0.000 0.0 211s Consumption_5 0.000 0.0 211s Consumption_6 0.000 0.0 211s Consumption_7 0.000 0.0 211s Consumption_8 0.000 0.0 211s Consumption_9 0.000 0.0 211s Consumption_10 0.000 0.0 211s Consumption_11 0.000 0.0 211s Consumption_12 0.000 0.0 211s Consumption_13 0.000 0.0 211s Consumption_14 0.000 0.0 211s Consumption_15 0.000 0.0 211s Consumption_16 0.000 0.0 211s Consumption_17 0.000 0.0 211s Consumption_18 0.000 0.0 211s Consumption_19 0.000 0.0 211s Consumption_20 0.000 0.0 211s Consumption_21 0.000 0.0 211s Consumption_22 0.000 0.0 211s Investment_2 -18.395 -264.8 211s Investment_3 3.792 55.8 211s Investment_4 12.295 134.2 211s Investment_5 -33.634 -346.8 211s Investment_6 5.991 59.5 211s Investment_7 28.378 279.3 211s Investment_8 25.548 265.1 211s Investment_9 6.875 72.1 211s Investment_10 42.088 420.1 211s Investment_11 -25.829 -256.7 211s Investment_12 -15.646 -217.3 211s Investment_13 -13.632 -255.1 211s Investment_14 11.395 337.1 211s Investment_15 -2.320 -41.8 211s Investment_16 0.972 15.7 211s Investment_17 30.564 431.6 211s Investment_18 -9.974 -113.2 211s Investment_19 -67.085 -782.5 211s Investment_20 7.999 104.5 211s Investment_21 0.292 3.1 211s Investment_22 10.325 100.1 211s PrivateWages_2 0.000 0.0 211s PrivateWages_3 0.000 0.0 211s PrivateWages_4 0.000 0.0 211s PrivateWages_5 0.000 0.0 211s PrivateWages_6 0.000 0.0 211s PrivateWages_7 0.000 0.0 211s PrivateWages_8 0.000 0.0 211s PrivateWages_9 0.000 0.0 211s PrivateWages_10 0.000 0.0 211s PrivateWages_11 0.000 0.0 211s PrivateWages_12 0.000 0.0 211s PrivateWages_13 0.000 0.0 211s PrivateWages_14 0.000 0.0 211s PrivateWages_15 0.000 0.0 211s PrivateWages_16 0.000 0.0 211s PrivateWages_17 0.000 0.0 211s PrivateWages_18 0.000 0.0 211s PrivateWages_19 0.000 0.0 211s PrivateWages_20 0.000 0.0 211s PrivateWages_21 0.000 0.0 211s PrivateWages_22 0.000 0.0 211s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 211s Consumption_2 0.0000 0.00 0.00 211s Consumption_3 0.0000 0.00 0.00 211s Consumption_4 0.0000 0.00 0.00 211s Consumption_5 0.0000 0.00 0.00 211s Consumption_6 0.0000 0.00 0.00 211s Consumption_7 0.0000 0.00 0.00 211s Consumption_8 0.0000 0.00 0.00 211s Consumption_9 0.0000 0.00 0.00 211s Consumption_10 0.0000 0.00 0.00 211s Consumption_11 0.0000 0.00 0.00 211s Consumption_12 0.0000 0.00 0.00 211s Consumption_13 0.0000 0.00 0.00 211s Consumption_14 0.0000 0.00 0.00 211s Consumption_15 0.0000 0.00 0.00 211s Consumption_16 0.0000 0.00 0.00 211s Consumption_17 0.0000 0.00 0.00 211s Consumption_18 0.0000 0.00 0.00 211s Consumption_19 0.0000 0.00 0.00 211s Consumption_20 0.0000 0.00 0.00 211s Consumption_21 0.0000 0.00 0.00 211s Consumption_22 0.0000 0.00 0.00 211s Investment_2 0.0000 0.00 0.00 211s Investment_3 0.0000 0.00 0.00 211s Investment_4 0.0000 0.00 0.00 211s Investment_5 0.0000 0.00 0.00 211s Investment_6 0.0000 0.00 0.00 211s Investment_7 0.0000 0.00 0.00 211s Investment_8 0.0000 0.00 0.00 211s Investment_9 0.0000 0.00 0.00 211s Investment_10 0.0000 0.00 0.00 211s Investment_11 0.0000 0.00 0.00 211s Investment_12 0.0000 0.00 0.00 211s Investment_13 0.0000 0.00 0.00 211s Investment_14 0.0000 0.00 0.00 211s Investment_15 0.0000 0.00 0.00 211s Investment_16 0.0000 0.00 0.00 211s Investment_17 0.0000 0.00 0.00 211s Investment_18 0.0000 0.00 0.00 211s Investment_19 0.0000 0.00 0.00 211s Investment_20 0.0000 0.00 0.00 211s Investment_21 0.0000 0.00 0.00 211s Investment_22 0.0000 0.00 0.00 211s PrivateWages_2 -2.1987 -104.79 -98.72 211s PrivateWages_3 0.6372 31.43 29.06 211s PrivateWages_4 1.3519 76.84 67.73 211s PrivateWages_5 -1.7306 -105.10 -98.99 211s PrivateWages_6 -0.5521 -33.79 -31.52 211s PrivateWages_7 0.7059 43.27 43.06 211s PrivateWages_8 0.8269 50.32 52.92 211s PrivateWages_9 1.2718 79.33 81.90 211s PrivateWages_10 2.3392 150.64 150.88 211s PrivateWages_11 -1.5500 -99.78 -103.85 211s PrivateWages_12 -0.0625 -3.43 -3.82 211s PrivateWages_13 -1.1474 -54.08 -61.27 211s PrivateWages_14 1.9682 81.95 87.19 211s PrivateWages_15 -0.2753 -14.03 -12.42 211s PrivateWages_16 -0.5389 -30.00 -26.78 211s PrivateWages_17 1.5156 86.87 82.45 211s PrivateWages_18 -0.1787 -12.09 -11.21 211s PrivateWages_19 -3.6814 -251.10 -239.29 211s PrivateWages_20 0.7597 50.83 46.27 211s PrivateWages_21 -0.9040 -68.05 -62.83 211s PrivateWages_22 1.4431 124.79 109.24 211s PrivateWages_trend 211s Consumption_2 0.000 211s Consumption_3 0.000 211s Consumption_4 0.000 211s Consumption_5 0.000 211s Consumption_6 0.000 211s Consumption_7 0.000 211s Consumption_8 0.000 211s Consumption_9 0.000 211s Consumption_10 0.000 211s Consumption_11 0.000 211s Consumption_12 0.000 211s Consumption_13 0.000 211s Consumption_14 0.000 211s Consumption_15 0.000 211s Consumption_16 0.000 211s Consumption_17 0.000 211s Consumption_18 0.000 211s Consumption_19 0.000 211s Consumption_20 0.000 211s Consumption_21 0.000 211s Consumption_22 0.000 211s Investment_2 0.000 211s Investment_3 0.000 211s Investment_4 0.000 211s Investment_5 0.000 211s Investment_6 0.000 211s Investment_7 0.000 211s Investment_8 0.000 211s Investment_9 0.000 211s Investment_10 0.000 211s Investment_11 0.000 211s Investment_12 0.000 211s Investment_13 0.000 211s Investment_14 0.000 211s Investment_15 0.000 211s Investment_16 0.000 211s Investment_17 0.000 211s Investment_18 0.000 211s Investment_19 0.000 211s Investment_20 0.000 211s Investment_21 0.000 211s Investment_22 0.000 211s PrivateWages_2 21.987 211s PrivateWages_3 -5.735 211s PrivateWages_4 -10.815 211s PrivateWages_5 12.114 211s PrivateWages_6 3.312 211s PrivateWages_7 -3.529 211s PrivateWages_8 -3.307 211s PrivateWages_9 -3.815 211s PrivateWages_10 -4.678 211s PrivateWages_11 1.550 211s PrivateWages_12 0.000 211s PrivateWages_13 -1.147 211s PrivateWages_14 3.936 211s PrivateWages_15 -0.826 211s PrivateWages_16 -2.156 211s PrivateWages_17 7.578 211s PrivateWages_18 -1.072 211s PrivateWages_19 -25.769 211s PrivateWages_20 6.078 211s PrivateWages_21 -8.136 211s PrivateWages_22 14.431 211s [1] TRUE 211s > Bread 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_(Intercept) 105.265 -0.9259 211s Consumption_corpProf -0.926 0.8409 211s Consumption_corpProfLag -0.287 -0.5775 211s Consumption_wages -1.975 -0.0921 211s Investment_(Intercept) 0.000 0.0000 211s Investment_corpProf 0.000 0.0000 211s Investment_corpProfLag 0.000 0.0000 211s Investment_capitalLag 0.000 0.0000 211s PrivateWages_(Intercept) 0.000 0.0000 211s PrivateWages_gnp 0.000 0.0000 211s PrivateWages_gnpLag 0.000 0.0000 211s PrivateWages_trend 0.000 0.0000 211s Consumption_corpProfLag Consumption_wages 211s Consumption_(Intercept) -0.287 -1.9751 211s Consumption_corpProf -0.578 -0.0921 211s Consumption_corpProfLag 0.694 -0.0320 211s Consumption_wages -0.032 0.0978 211s Investment_(Intercept) 0.000 0.0000 211s Investment_corpProf 0.000 0.0000 211s Investment_corpProfLag 0.000 0.0000 211s Investment_capitalLag 0.000 0.0000 211s PrivateWages_(Intercept) 0.000 0.0000 211s PrivateWages_gnp 0.000 0.0000 211s PrivateWages_gnpLag 0.000 0.0000 211s PrivateWages_trend 0.000 0.0000 211s Investment_(Intercept) Investment_corpProf 211s Consumption_(Intercept) 0.0 0.000 211s Consumption_corpProf 0.0 0.000 211s Consumption_corpProfLag 0.0 0.000 211s Consumption_wages 0.0 0.000 211s Investment_(Intercept) 2591.3 -42.124 211s Investment_corpProf -42.1 1.367 211s Investment_corpProfLag 35.4 -1.174 211s Investment_capitalLag -12.3 0.191 211s PrivateWages_(Intercept) 0.0 0.000 211s PrivateWages_gnp 0.0 0.000 211s PrivateWages_gnpLag 0.0 0.000 211s PrivateWages_trend 0.0 0.000 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_(Intercept) 0.000 0.0000 211s Consumption_corpProf 0.000 0.0000 211s Consumption_corpProfLag 0.000 0.0000 211s Consumption_wages 0.000 0.0000 211s Investment_(Intercept) 35.417 -12.2536 211s Investment_corpProf -1.174 0.1908 211s Investment_corpProfLag 1.207 -0.1763 211s Investment_capitalLag -0.176 0.0594 211s PrivateWages_(Intercept) 0.000 0.0000 211s PrivateWages_gnp 0.000 0.0000 211s PrivateWages_gnpLag 0.000 0.0000 211s PrivateWages_trend 0.000 0.0000 211s PrivateWages_(Intercept) PrivateWages_gnp 211s Consumption_(Intercept) 0.000 0.0000 211s Consumption_corpProf 0.000 0.0000 211s Consumption_corpProfLag 0.000 0.0000 211s Consumption_wages 0.000 0.0000 211s Investment_(Intercept) 0.000 0.0000 211s Investment_corpProf 0.000 0.0000 211s Investment_corpProfLag 0.000 0.0000 211s Investment_capitalLag 0.000 0.0000 211s PrivateWages_(Intercept) 174.205 -0.8839 211s PrivateWages_gnp -0.884 0.1679 211s PrivateWages_gnpLag -2.037 -0.1586 211s PrivateWages_trend 2.064 -0.0409 211s PrivateWages_gnpLag PrivateWages_trend 211s Consumption_(Intercept) 0.00000 0.00000 211s Consumption_corpProf 0.00000 0.00000 211s Consumption_corpProfLag 0.00000 0.00000 211s Consumption_wages 0.00000 0.00000 211s Investment_(Intercept) 0.00000 0.00000 211s Investment_corpProf 0.00000 0.00000 211s Investment_corpProfLag 0.00000 0.00000 211s Investment_capitalLag 0.00000 0.00000 211s PrivateWages_(Intercept) -2.03709 2.06394 211s PrivateWages_gnp -0.15864 -0.04088 211s PrivateWages_gnpLag 0.19944 0.00675 211s PrivateWages_trend 0.00675 0.11229 211s > 211s > # SUR 211s > summary 211s 211s systemfit results 211s method: SUR 211s 211s N DF SSR detRCov OLS-R2 McElroy-R2 211s system 63 51 46.5 0.158 0.977 0.993 211s 211s N DF SSR MSE RMSE R2 Adj R2 211s Consumption 21 17 18.1 1.065 1.032 0.981 0.977 211s Investment 21 17 17.6 1.036 1.018 0.930 0.918 211s PrivateWages 21 17 10.8 0.633 0.796 0.986 0.984 211s 211s The covariance matrix of the residuals used for estimation 211s Consumption Investment PrivateWages 211s Consumption 0.8514 0.0495 -0.381 211s Investment 0.0495 0.8249 0.121 211s PrivateWages -0.3808 0.1212 0.476 211s 211s The covariance matrix of the residuals 211s Consumption Investment PrivateWages 211s Consumption 0.8618 0.0766 -0.437 211s Investment 0.0766 0.8384 0.203 211s PrivateWages -0.4368 0.2027 0.513 211s 211s The correlations of the residuals 211s Consumption Investment PrivateWages 211s Consumption 1.0000 0.0901 -0.657 211s Investment 0.0901 1.0000 0.309 211s PrivateWages -0.6572 0.3092 1.000 211s 211s 211s SUR estimates for 'Consumption' (equation 1) 211s Model Formula: consump ~ corpProf + corpProfLag + wages 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 15.9805 1.1687 13.67 1.3e-10 *** 211s corpProf 0.2302 0.0767 3.00 0.008 ** 211s corpProfLag 0.0673 0.0769 0.87 0.394 211s wages 0.7962 0.0353 22.58 4.1e-14 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.032 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 18.098 MSE: 1.065 Root MSE: 1.032 211s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 211s 211s 211s SUR estimates for 'Investment' (equation 2) 211s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 12.9293 4.8014 2.69 0.01540 * 211s corpProf 0.4429 0.0861 5.15 8.1e-05 *** 211s corpProfLag 0.3655 0.0894 4.09 0.00077 *** 211s capitalLag -0.1253 0.0235 -5.34 5.4e-05 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.018 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 17.606 MSE: 1.036 Root MSE: 1.018 211s Multiple R-Squared: 0.93 Adjusted R-Squared: 0.918 211s 211s 211s SUR estimates for 'PrivateWages' (equation 3) 211s Model Formula: privWage ~ gnp + gnpLag + trend 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 1.6347 1.1173 1.46 0.16 211s gnp 0.4098 0.0273 15.04 3.0e-11 *** 211s gnpLag 0.1744 0.0312 5.59 3.2e-05 *** 211s trend 0.1558 0.0276 5.65 2.9e-05 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 0.796 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 10.763 MSE: 0.633 Root MSE: 0.796 211s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 211s 211s > residuals 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 -0.24064 -0.3522 -1.0960 211s 3 -1.34080 -0.1605 0.5818 211s 4 -1.61038 1.0687 1.5313 211s 5 -0.54147 -1.4707 -0.0220 211s 6 -0.04372 0.3299 -0.2587 211s 7 0.85234 1.4346 -0.3243 211s 8 1.30302 0.8306 -0.6674 211s 9 0.97574 -0.4918 0.3660 211s 10 -0.66060 1.2434 1.2682 211s 11 0.45069 0.2647 -0.3467 211s 12 -0.04295 0.0795 0.3057 211s 13 -0.06686 0.3369 -0.2602 211s 14 0.32177 0.4080 0.3434 211s 15 -0.00441 -0.1533 0.2628 211s 16 -0.01931 0.0158 -0.0216 211s 17 1.53656 1.0372 -0.7988 211s 18 -0.42317 0.0176 0.8550 211s 19 0.29041 -2.6364 -0.8217 211s 20 0.88685 -0.5822 -0.3869 211s 21 0.68839 -0.7015 -1.1838 211s 22 -2.31147 -0.5183 0.6742 211s > fitted 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 42.1 0.152 26.6 211s 3 46.3 2.060 28.7 211s 4 50.8 4.131 32.6 211s 5 51.1 4.471 33.9 211s 6 52.6 4.770 35.7 211s 7 54.2 4.165 37.7 211s 8 54.9 3.369 38.6 211s 9 56.3 3.492 38.8 211s 10 58.5 3.857 40.0 211s 11 54.5 0.735 38.2 211s 12 50.9 -3.479 34.2 211s 13 45.7 -6.537 29.3 211s 14 46.2 -5.508 28.2 211s 15 48.7 -2.847 30.3 211s 16 51.3 -1.316 33.2 211s 17 56.2 1.063 37.6 211s 18 59.1 1.982 40.1 211s 19 57.2 0.736 39.0 211s 20 60.7 1.882 42.0 211s 21 64.3 4.002 46.2 211s 22 72.0 5.418 52.6 211s > predict 211s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 211s 1 NA NA NA NA 211s 2 42.1 0.415 41.3 43.0 211s 3 46.3 0.449 45.4 47.2 211s 4 50.8 0.300 50.2 51.4 211s 5 51.1 0.348 50.4 51.8 211s 6 52.6 0.350 51.9 53.3 211s 7 54.2 0.317 53.6 54.9 211s 8 54.9 0.289 54.3 55.5 211s 9 56.3 0.309 55.7 56.9 211s 10 58.5 0.328 57.8 59.1 211s 11 54.5 0.516 53.5 55.6 211s 12 50.9 0.414 50.1 51.8 211s 13 45.7 0.544 44.6 46.8 211s 14 46.2 0.527 45.1 47.2 211s 15 48.7 0.332 48.0 49.4 211s 16 51.3 0.295 50.7 51.9 211s 17 56.2 0.319 55.5 56.8 211s 18 59.1 0.286 58.5 59.7 211s 19 57.2 0.323 56.6 57.9 211s 20 60.7 0.381 59.9 61.5 211s 21 64.3 0.381 63.5 65.1 211s 22 72.0 0.597 70.8 73.2 211s Investment.pred Investment.se.fit Investment.lwr Investment.upr 211s 1 NA NA NA NA 211s 2 0.152 0.536 -0.924 1.229 211s 3 2.060 0.446 1.166 2.955 211s 4 4.131 0.397 3.334 4.929 211s 5 4.471 0.329 3.809 5.132 211s 6 4.770 0.311 4.145 5.395 211s 7 4.165 0.294 3.575 4.756 211s 8 3.369 0.263 2.842 3.897 211s 9 3.492 0.347 2.796 4.188 211s 10 3.857 0.398 3.058 4.656 211s 11 0.735 0.539 -0.346 1.816 211s 12 -3.479 0.454 -4.390 -2.569 211s 13 -6.537 0.552 -7.646 -5.428 211s 14 -5.508 0.617 -6.747 -4.269 211s 15 -2.847 0.335 -3.519 -2.175 211s 16 -1.316 0.287 -1.892 -0.739 211s 17 1.063 0.311 0.439 1.686 211s 18 1.982 0.218 1.545 2.420 211s 19 0.736 0.279 0.176 1.296 211s 20 1.882 0.327 1.227 2.538 211s 21 4.002 0.297 3.405 4.598 211s 22 5.418 0.412 4.591 6.245 211s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 211s 1 NA NA NA NA 211s 2 26.6 0.313 26.0 27.2 211s 3 28.7 0.310 28.1 29.3 211s 4 32.6 0.305 32.0 33.2 211s 5 33.9 0.236 33.4 34.4 211s 6 35.7 0.233 35.2 36.1 211s 7 37.7 0.234 37.3 38.2 211s 8 38.6 0.239 38.1 39.0 211s 9 38.8 0.229 38.4 39.3 211s 10 40.0 0.219 39.6 40.5 211s 11 38.2 0.301 37.6 38.9 211s 12 34.2 0.308 33.6 34.8 211s 13 29.3 0.370 28.5 30.0 211s 14 28.2 0.332 27.5 28.8 211s 15 30.3 0.324 29.7 31.0 211s 16 33.2 0.271 32.7 33.8 211s 17 37.6 0.263 37.1 38.1 211s 18 40.1 0.211 39.7 40.6 211s 19 39.0 0.306 38.4 39.6 211s 20 42.0 0.280 41.4 42.5 211s 21 46.2 0.298 45.6 46.8 211s 22 52.6 0.445 51.7 53.5 211s > model.frame 211s [1] TRUE 211s > model.matrix 211s [1] TRUE 211s > nobs 211s [1] 63 211s > linearHypothesis 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 1.44 0.24 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 1.69 0.2 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 52 211s 2 51 1 1.69 0.19 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.77 0.47 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.91 0.41 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 53 211s 2 51 2 1.83 0.4 211s > logLik 211s 'log Lik.' -70 (df=18) 211s 'log Lik.' -79 (df=18) 211s Estimating function 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_2 -0.46275 -5.7381 211s Consumption_3 -2.57830 -43.5733 211s Consumption_4 -3.09670 -56.9792 211s Consumption_5 -1.04122 -20.1997 211s Consumption_6 -0.08406 -1.6897 211s Consumption_7 1.63901 32.1246 211s Consumption_8 2.50567 49.6122 211s Consumption_9 1.87631 39.5902 211s Consumption_10 -1.27032 -27.5659 211s Consumption_11 0.86667 13.5200 211s Consumption_12 -0.08259 -0.9415 211s Consumption_13 -0.12857 -0.9000 211s Consumption_14 0.61874 6.9299 211s Consumption_15 -0.00847 -0.1042 211s Consumption_16 -0.03714 -0.5200 211s Consumption_17 2.95475 52.0036 211s Consumption_18 -0.81375 -14.0778 211s Consumption_19 0.55845 8.5443 211s Consumption_20 1.70539 32.4023 211s Consumption_21 1.32376 27.9312 211s Consumption_22 -4.44487 -104.4543 211s Investment_2 0.12481 1.5477 211s Investment_3 0.05687 0.9611 211s Investment_4 -0.37877 -6.9693 211s Investment_5 0.52122 10.1116 211s Investment_6 -0.11690 -2.3498 211s Investment_7 -0.50845 -9.9656 211s Investment_8 -0.29439 -5.8289 211s Investment_9 0.17430 3.6777 211s Investment_10 -0.44066 -9.5623 211s Investment_11 -0.09381 -1.4634 211s Investment_12 -0.02816 -0.3210 211s Investment_13 -0.11941 -0.8359 211s Investment_14 -0.14460 -1.6195 211s Investment_15 0.05435 0.6685 211s Investment_16 -0.00559 -0.0783 211s Investment_17 -0.36761 -6.4700 211s Investment_18 -0.00622 -0.1077 211s Investment_19 0.93438 14.2960 211s Investment_20 0.20633 3.9202 211s Investment_21 0.24863 5.2460 211s Investment_22 0.18369 4.3168 211s PrivateWages_2 -1.78352 -22.1156 211s PrivateWages_3 0.94670 15.9992 211s PrivateWages_4 2.49170 45.8473 211s PrivateWages_5 -0.03583 -0.6950 211s PrivateWages_6 -0.42104 -8.4630 211s PrivateWages_7 -0.52776 -10.3441 211s PrivateWages_8 -1.08598 -21.5024 211s PrivateWages_9 0.59560 12.5672 211s PrivateWages_10 2.06359 44.7800 211s PrivateWages_11 -0.56422 -8.8019 211s PrivateWages_12 0.49749 5.6714 211s PrivateWages_13 -0.42337 -2.9636 211s PrivateWages_14 0.55874 6.2579 211s PrivateWages_15 0.42760 5.2595 211s PrivateWages_16 -0.03516 -0.4922 211s PrivateWages_17 -1.29986 -22.8775 211s PrivateWages_18 1.39131 24.0696 211s PrivateWages_19 -1.33711 -20.4578 211s PrivateWages_20 -0.62964 -11.9631 211s PrivateWages_21 -1.92625 -40.6439 211s PrivateWages_22 1.09700 25.7794 211s Consumption_corpProfLag Consumption_wages 211s Consumption_2 -5.8769 -13.049 211s Consumption_3 -31.9709 -83.021 211s Consumption_4 -52.3342 -114.578 211s Consumption_5 -19.1585 -38.525 211s Consumption_6 -1.6308 -3.245 211s Consumption_7 32.9441 66.708 211s Consumption_8 49.1110 103.985 211s Consumption_9 37.1510 80.494 211s Consumption_10 -26.8037 -57.545 211s Consumption_11 18.8066 36.487 211s Consumption_12 -1.2884 -3.246 211s Consumption_13 -1.4658 -4.410 211s Consumption_14 4.3312 21.099 211s Consumption_15 -0.0949 -0.310 211s Consumption_16 -0.4568 -1.460 211s Consumption_17 41.3665 130.600 211s Consumption_18 -14.3220 -38.816 211s Consumption_19 9.6612 25.633 211s Consumption_20 26.0924 84.246 211s Consumption_21 25.1514 70.159 211s Consumption_22 -93.7867 -274.693 211s Investment_2 1.5851 3.520 211s Investment_3 0.7052 1.831 211s Investment_4 -6.4012 -14.014 211s Investment_5 9.5904 19.285 211s Investment_6 -2.2679 -4.513 211s Investment_7 -10.2199 -20.694 211s Investment_8 -5.7700 -12.217 211s Investment_9 3.4511 7.477 211s Investment_10 -9.2979 -19.962 211s Investment_11 -2.0356 -3.949 211s Investment_12 -0.4393 -1.107 211s Investment_13 -1.3613 -4.096 211s Investment_14 -1.0122 -4.931 211s Investment_15 0.6087 1.989 211s Investment_16 -0.0688 -0.220 211s Investment_17 -5.1466 -16.248 211s Investment_18 -0.1095 -0.297 211s Investment_19 16.1648 42.888 211s Investment_20 3.1568 10.193 211s Investment_21 4.7239 13.177 211s Investment_22 3.8759 11.352 211s PrivateWages_2 -22.6507 -50.295 211s PrivateWages_3 11.7391 30.484 211s PrivateWages_4 42.1098 92.193 211s PrivateWages_5 -0.6592 -1.326 211s PrivateWages_6 -8.1683 -16.252 211s PrivateWages_7 -10.6080 -21.480 211s PrivateWages_8 -21.2852 -45.068 211s PrivateWages_9 11.7929 25.551 211s PrivateWages_10 43.5418 93.481 211s PrivateWages_11 -12.2437 -23.754 211s PrivateWages_12 7.7609 19.551 211s PrivateWages_13 -4.8264 -14.521 211s PrivateWages_14 3.9112 19.053 211s PrivateWages_15 4.7891 15.650 211s PrivateWages_16 -0.4325 -1.382 211s PrivateWages_17 -18.1980 -57.454 211s PrivateWages_18 24.4870 66.365 211s PrivateWages_19 -23.1320 -61.373 211s PrivateWages_20 -9.6335 -31.104 211s PrivateWages_21 -36.5988 -102.091 211s PrivateWages_22 23.1466 67.794 211s Investment_(Intercept) Investment_corpProf 211s Consumption_2 0.08529 1.0576 211s Consumption_3 0.47520 8.0308 211s Consumption_4 0.57074 10.5016 211s Consumption_5 0.19190 3.7229 211s Consumption_6 0.01549 0.3114 211s Consumption_7 -0.30208 -5.9207 211s Consumption_8 -0.46181 -9.1438 211s Consumption_9 -0.34582 -7.2967 211s Consumption_10 0.23413 5.0806 211s Consumption_11 -0.15973 -2.4918 211s Consumption_12 0.01522 0.1735 211s Consumption_13 0.02370 0.1659 211s Consumption_14 -0.11404 -1.2772 211s Consumption_15 0.00156 0.0192 211s Consumption_16 0.00685 0.0958 211s Consumption_17 -0.54458 -9.5846 211s Consumption_18 0.14998 2.5946 211s Consumption_19 -0.10293 -1.5748 211s Consumption_20 -0.31431 -5.9719 211s Consumption_21 -0.24398 -5.1479 211s Consumption_22 0.81921 19.2515 211s Investment_2 -0.46650 -5.7846 211s Investment_3 -0.21255 -3.5922 211s Investment_4 1.41568 26.0484 211s Investment_5 -1.94810 -37.7932 211s Investment_6 0.43694 8.7825 211s Investment_7 1.90038 37.2474 211s Investment_8 1.10030 21.7860 211s Investment_9 -0.65146 -13.7457 211s Investment_10 1.64701 35.7401 211s Investment_11 0.35062 5.4696 211s Investment_12 0.10525 1.1998 211s Investment_13 0.44632 3.1242 211s Investment_14 0.54045 6.0530 211s Investment_15 -0.20313 -2.4985 211s Investment_16 0.02090 0.2926 211s Investment_17 1.37398 24.1820 211s Investment_18 0.02326 0.4024 211s Investment_19 -3.49233 -53.4327 211s Investment_20 -0.77116 -14.6521 211s Investment_21 -0.92927 -19.6075 211s Investment_22 -0.68657 -16.1344 211s PrivateWages_2 0.67977 8.4291 211s PrivateWages_3 -0.36082 -6.0979 211s PrivateWages_4 -0.94969 -17.4742 211s PrivateWages_5 0.01365 0.2649 211s PrivateWages_6 0.16048 3.2256 211s PrivateWages_7 0.20115 3.9426 211s PrivateWages_8 0.41391 8.1954 211s PrivateWages_9 -0.22701 -4.7899 211s PrivateWages_10 -0.78652 -17.0674 211s PrivateWages_11 0.21505 3.3548 211s PrivateWages_12 -0.18961 -2.1616 211s PrivateWages_13 0.16136 1.1295 211s PrivateWages_14 -0.21296 -2.3851 211s PrivateWages_15 -0.16298 -2.0046 211s PrivateWages_16 0.01340 0.1876 211s PrivateWages_17 0.49543 8.7195 211s PrivateWages_18 -0.53028 -9.1739 211s PrivateWages_19 0.50963 7.7973 211s PrivateWages_20 0.23998 4.5596 211s PrivateWages_21 0.73417 15.4910 211s PrivateWages_22 -0.41811 -9.8256 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_2 1.0831 15.590 211s Consumption_3 5.8924 86.771 211s Consumption_4 9.6455 105.301 211s Consumption_5 3.5310 36.404 211s Consumption_6 0.3006 2.986 211s Consumption_7 -6.0718 -59.751 211s Consumption_8 -9.0514 -93.932 211s Consumption_9 -6.8471 -71.791 211s Consumption_10 4.9401 49.307 211s Consumption_11 -3.4662 -34.454 211s Consumption_12 0.2375 3.299 211s Consumption_13 0.2701 5.055 211s Consumption_14 -0.7983 -23.617 211s Consumption_15 0.0175 0.315 211s Consumption_16 0.0842 1.362 211s Consumption_17 -7.6241 -107.663 211s Consumption_18 2.6396 29.966 211s Consumption_19 -1.7806 -20.770 211s Consumption_20 -4.8090 -62.831 211s Consumption_21 -4.6355 -49.088 211s Consumption_22 17.2854 167.529 211s Investment_2 -5.9246 -85.277 211s Investment_3 -2.6357 -38.812 211s Investment_4 23.9249 261.192 211s Investment_5 -35.8451 -369.555 211s Investment_6 8.4767 84.199 211s Investment_7 38.1976 375.895 211s Investment_8 21.5660 223.802 211s Investment_9 -12.8988 -135.242 211s Investment_10 34.7519 346.860 211s Investment_11 7.6084 75.628 211s Investment_12 1.6419 22.807 211s Investment_13 5.0880 95.199 211s Investment_14 3.7831 111.927 211s Investment_15 -2.2751 -41.032 211s Investment_16 0.2571 4.159 211s Investment_17 19.2357 271.636 211s Investment_18 0.4094 4.648 211s Investment_19 -60.4174 -704.753 211s Investment_20 -11.7988 -154.156 211s Investment_21 -17.6560 -186.968 211s Investment_22 -14.4866 -140.403 211s PrivateWages_2 8.6331 124.262 211s PrivateWages_3 -4.4742 -65.887 211s PrivateWages_4 -16.0497 -175.217 211s PrivateWages_5 0.2512 2.590 211s PrivateWages_6 3.1132 30.924 211s PrivateWages_7 4.0431 39.788 211s PrivateWages_8 8.1126 84.189 211s PrivateWages_9 -4.4947 -47.127 211s PrivateWages_10 -16.5955 -165.640 211s PrivateWages_11 4.6666 46.386 211s PrivateWages_12 -2.9580 -41.089 211s PrivateWages_13 1.8395 34.418 211s PrivateWages_14 -1.4907 -44.104 211s PrivateWages_15 -1.8253 -32.921 211s PrivateWages_16 0.1648 2.667 211s PrivateWages_17 6.9360 97.946 211s PrivateWages_18 -9.3330 -105.950 211s PrivateWages_19 8.8165 102.843 211s PrivateWages_20 3.6717 47.972 211s PrivateWages_21 13.9492 147.715 211s PrivateWages_22 -8.8221 -85.503 211s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 211s Consumption_2 -0.39158 -17.856 -17.582 211s Consumption_3 -2.18178 -109.307 -99.489 211s Consumption_4 -2.62045 -149.890 -131.285 211s Consumption_5 -0.88109 -50.310 -50.398 211s Consumption_6 -0.07113 -4.339 -4.062 211s Consumption_7 1.38694 88.764 84.604 211s Consumption_8 2.12032 136.548 135.700 211s Consumption_9 1.58775 102.410 102.251 211s Consumption_10 -1.07495 -72.022 -69.335 211s Consumption_11 0.73338 44.883 49.136 211s Consumption_12 -0.06989 -3.732 -4.277 211s Consumption_13 -0.10880 -4.820 -5.810 211s Consumption_14 0.52359 23.614 23.195 211s Consumption_15 -0.00717 -0.356 -0.323 211s Consumption_16 -0.03143 -1.710 -1.562 211s Consumption_17 2.50033 156.771 136.018 211s Consumption_18 -0.68860 -44.759 -43.175 211s Consumption_19 0.47257 28.779 30.717 211s Consumption_20 1.44311 100.296 87.885 211s Consumption_21 1.12017 84.797 77.852 211s Consumption_22 -3.76128 -332.497 -284.729 211s Investment_2 0.21842 9.960 9.807 211s Investment_3 0.09952 4.986 4.538 211s Investment_4 -0.66282 -37.913 -33.207 211s Investment_5 0.91210 52.081 52.172 211s Investment_6 -0.20458 -12.479 -11.681 211s Investment_7 -0.88976 -56.944 -54.275 211s Investment_8 -0.51516 -33.176 -32.970 211s Investment_9 0.30501 19.673 19.643 211s Investment_10 -0.77113 -51.666 -49.738 211s Investment_11 -0.16416 -10.047 -10.999 211s Investment_12 -0.04928 -2.631 -3.016 211s Investment_13 -0.20897 -9.257 -11.159 211s Investment_14 -0.25304 -11.412 -11.210 211s Investment_15 0.09511 4.727 4.289 211s Investment_16 -0.00978 -0.532 -0.486 211s Investment_17 -0.64330 -40.335 -34.995 211s Investment_18 -0.01089 -0.708 -0.683 211s Investment_19 1.63511 99.578 106.282 211s Investment_20 0.36106 25.094 21.989 211s Investment_21 0.43508 32.936 30.238 211s Investment_22 0.32145 28.416 24.334 211s PrivateWages_2 -3.89912 -177.800 -175.070 211s PrivateWages_3 2.06967 103.690 94.377 211s PrivateWages_4 5.44735 311.588 272.912 211s PrivateWages_5 -0.07832 -4.472 -4.480 211s PrivateWages_6 -0.92048 -56.150 -52.560 211s PrivateWages_7 -1.15379 -73.843 -70.381 211s PrivateWages_8 -2.37416 -152.896 -151.946 211s PrivateWages_9 1.30210 83.986 83.855 211s PrivateWages_10 4.51142 302.265 290.986 211s PrivateWages_11 -1.23351 -75.491 -82.645 211s PrivateWages_12 1.08762 58.079 66.562 211s PrivateWages_13 -0.92556 -41.002 -49.425 211s PrivateWages_14 1.22152 55.091 54.114 211s PrivateWages_15 0.93482 46.461 42.160 211s PrivateWages_16 -0.07687 -4.182 -3.820 211s PrivateWages_17 -2.84174 -178.177 -154.591 211s PrivateWages_18 3.04167 197.708 190.713 211s PrivateWages_19 -2.92319 -178.022 -190.007 211s PrivateWages_20 -1.37651 -95.667 -83.829 211s PrivateWages_21 -4.21116 -318.785 -292.676 211s PrivateWages_22 2.39825 212.005 181.548 211s PrivateWages_trend 211s Consumption_2 3.9158 211s Consumption_3 19.6360 211s Consumption_4 20.9636 211s Consumption_5 6.1676 211s Consumption_6 0.4268 211s Consumption_7 -6.9347 211s Consumption_8 -8.4813 211s Consumption_9 -4.7633 211s Consumption_10 2.1499 211s Consumption_11 -0.7334 211s Consumption_12 0.0000 211s Consumption_13 -0.1088 211s Consumption_14 1.0472 211s Consumption_15 -0.0215 211s Consumption_16 -0.1257 211s Consumption_17 12.5017 211s Consumption_18 -4.1316 211s Consumption_19 3.3080 211s Consumption_20 11.5449 211s Consumption_21 10.0816 211s Consumption_22 -37.6128 211s Investment_2 -2.1842 211s Investment_3 -0.8957 211s Investment_4 5.3026 211s Investment_5 -6.3847 211s Investment_6 1.2275 211s Investment_7 4.4488 211s Investment_8 2.0606 211s Investment_9 -0.9150 211s Investment_10 1.5423 211s Investment_11 0.1642 211s Investment_12 0.0000 211s Investment_13 -0.2090 211s Investment_14 -0.5061 211s Investment_15 0.2853 211s Investment_16 -0.0391 211s Investment_17 -3.2165 211s Investment_18 -0.0653 211s Investment_19 11.4458 211s Investment_20 2.8885 211s Investment_21 3.9157 211s Investment_22 3.2145 211s PrivateWages_2 38.9912 211s PrivateWages_3 -18.6270 211s PrivateWages_4 -43.5788 211s PrivateWages_5 0.5483 211s PrivateWages_6 5.5229 211s PrivateWages_7 5.7689 211s PrivateWages_8 9.4967 211s PrivateWages_9 -3.9063 211s PrivateWages_10 -9.0228 211s PrivateWages_11 1.2335 211s PrivateWages_12 0.0000 211s PrivateWages_13 -0.9256 211s PrivateWages_14 2.4431 211s PrivateWages_15 2.8045 211s PrivateWages_16 -0.3075 211s PrivateWages_17 -14.2087 211s PrivateWages_18 18.2500 211s PrivateWages_19 -20.4623 211s PrivateWages_20 -11.0121 211s PrivateWages_21 -37.9005 211s PrivateWages_22 23.9825 211s [1] TRUE 211s > Bread 211s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 211s [1,] 86.0484 -0.02454 -0.83573 211s [2,] -0.0245 0.37055 -0.22831 211s [3,] -0.8357 -0.22831 0.37290 211s [4,] -1.6729 -0.06016 -0.03411 211s [5,] 10.1786 -0.46129 0.72764 211s [6,] -0.1293 0.03988 -0.03792 211s [7,] -0.0505 -0.03436 0.04602 211s [8,] -0.0350 0.00175 -0.00419 211s [9,] -37.4223 0.06800 1.80971 211s [10,] 0.4074 -0.06333 0.04058 211s [11,] 0.2037 0.06442 -0.07324 211s [12,] 0.2057 0.03217 0.03109 211s Consumption_wages Investment_(Intercept) Investment_corpProf 211s [1,] -1.67e+00 10.179 -0.12933 211s [2,] -6.02e-02 -0.461 0.03988 211s [3,] -3.41e-02 0.728 -0.03792 211s [4,] 7.83e-02 -0.341 0.00185 211s [5,] -3.41e-01 1452.346 -13.96098 211s [6,] 1.85e-03 -13.961 0.46676 211s [7,] -2.96e-03 11.230 -0.39879 211s [8,] 1.79e-03 -6.973 0.06288 211s [9,] 1.32e-01 19.427 -0.13338 211s [10,] -5.46e-05 0.416 0.01516 211s [11,] -2.23e-03 -0.760 -0.01340 211s [12,] -3.03e-02 -0.736 0.00571 211s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 211s [1,] -0.05046 -0.03501 -37.4223 211s [2,] -0.03436 0.00175 0.0680 211s [3,] 0.04602 -0.00419 1.8097 211s [4,] -0.00296 0.00179 0.1325 211s [5,] 11.22954 -6.97254 19.4266 211s [6,] -0.39879 0.06288 -0.1334 211s [7,] 0.50387 -0.06357 -0.5157 211s [8,] -0.06357 0.03467 -0.0417 211s [9,] -0.51574 -0.04172 78.6495 211s [10,] -0.00784 -0.00271 -0.3339 211s [11,] 0.01702 0.00353 -0.9859 211s [12,] -0.01390 0.00432 0.8712 211s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 211s [1,] 4.07e-01 0.20374 0.20573 211s [2,] -6.33e-02 0.06442 0.03217 211s [3,] 4.06e-02 -0.07324 0.03109 211s [4,] -5.46e-05 -0.00223 -0.03033 211s [5,] 4.16e-01 -0.75990 -0.73581 211s [6,] 1.52e-02 -0.01340 0.00571 211s [7,] -7.84e-03 0.01702 -0.01390 211s [8,] -2.71e-03 0.00353 0.00432 211s [9,] -3.34e-01 -0.98593 0.87119 211s [10,] 4.68e-02 -0.04271 -0.01162 211s [11,] -4.27e-02 0.06124 -0.00299 211s [12,] -1.16e-02 -0.00299 0.04791 211s > 211s > # 3SLS 211s > summary 211s 211s systemfit results 211s method: 3SLS 211s 211s N DF SSR detRCov OLS-R2 McElroy-R2 211s system 63 51 73.6 0.283 0.963 0.995 211s 211s N DF SSR MSE RMSE R2 Adj R2 211s Consumption 21 17 18.7 1.102 1.050 0.980 0.977 211s Investment 21 17 44.0 2.586 1.608 0.826 0.795 211s PrivateWages 21 17 10.9 0.642 0.801 0.986 0.984 211s 211s The covariance matrix of the residuals used for estimation 211s Consumption Investment PrivateWages 211s Consumption 1.044 0.438 -0.385 211s Investment 0.438 1.383 0.193 211s PrivateWages -0.385 0.193 0.476 211s 211s The covariance matrix of the residuals 211s Consumption Investment PrivateWages 211s Consumption 0.892 0.411 -0.394 211s Investment 0.411 2.093 0.403 211s PrivateWages -0.394 0.403 0.520 211s 211s The correlations of the residuals 211s Consumption Investment PrivateWages 211s Consumption 1.000 0.301 -0.578 211s Investment 0.301 1.000 0.386 211s PrivateWages -0.578 0.386 1.000 211s 211s 211s 3SLS estimates for 'Consumption' (equation 1) 211s Model Formula: consump ~ corpProf + corpProfLag + wages 211s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 211s gnpLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 16.4408 1.3045 12.60 4.7e-10 *** 211s corpProf 0.1249 0.1081 1.16 0.26 211s corpProfLag 0.1631 0.1004 1.62 0.12 211s wages 0.7901 0.0379 20.83 1.5e-13 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.05 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 18.727 MSE: 1.102 Root MSE: 1.05 211s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 211s 211s 211s 3SLS estimates for 'Investment' (equation 2) 211s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 211s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 211s gnpLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 28.1778 6.7938 4.15 0.00067 *** 211s corpProf -0.0131 0.1619 -0.08 0.93655 211s corpProfLag 0.7557 0.1529 4.94 0.00012 *** 211s capitalLag -0.1948 0.0325 -5.99 1.5e-05 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 1.608 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 43.954 MSE: 2.586 Root MSE: 1.608 211s Multiple R-Squared: 0.826 Adjusted R-Squared: 0.795 211s 211s 211s 3SLS estimates for 'PrivateWages' (equation 3) 211s Model Formula: privWage ~ gnp + gnpLag + trend 211s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 211s gnpLag 211s 211s Estimate Std. Error t value Pr(>|t|) 211s (Intercept) 1.7972 1.1159 1.61 0.13 211s gnp 0.4005 0.0318 12.59 4.8e-10 *** 211s gnpLag 0.1813 0.0342 5.31 5.8e-05 *** 211s trend 0.1497 0.0279 5.36 5.2e-05 *** 211s --- 211s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 211s 211s Residual standard error: 0.801 on 17 degrees of freedom 211s Number of observations: 21 Degrees of Freedom: 17 211s SSR: 10.921 MSE: 0.642 Root MSE: 0.801 211s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 211s 211s > residuals 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 -0.4416 -2.1951 -1.20287 211s 3 -1.0150 0.1515 0.51834 211s 4 -1.5289 0.4406 1.50936 211s 5 -0.4985 -1.8667 -0.08743 211s 6 -0.0132 0.0713 -0.28089 211s 7 0.7759 1.0294 -0.33908 211s 8 1.3004 1.1011 -0.69282 211s 9 1.0993 0.5853 0.34494 211s 10 -0.5839 2.2952 1.27590 211s 11 -0.1917 -1.3443 -0.40414 211s 12 -0.5598 -0.9944 0.22151 211s 13 -0.6746 -1.3404 -0.36962 211s 14 0.5767 1.9316 0.31006 211s 15 -0.0211 -0.1217 0.27309 211s 16 0.0539 0.1847 0.00716 211s 17 1.8555 2.0937 -0.71866 211s 18 -0.4596 -0.3216 0.90582 211s 19 0.0613 -3.6314 -0.81881 211s 20 1.2602 0.7582 -0.26942 211s 21 0.9500 0.2428 -1.06125 211s 22 -1.9451 0.9302 0.87883 211s > fitted 211s Consumption Investment PrivateWages 211s 1 NA NA NA 211s 2 42.3 1.99510 26.7 211s 3 46.0 1.74850 28.8 211s 4 50.7 4.75942 32.6 211s 5 51.1 4.86672 34.0 211s 6 52.6 5.02874 35.7 211s 7 54.3 4.57056 37.7 211s 8 54.9 3.09893 38.6 211s 9 56.2 2.41471 38.9 211s 10 58.4 2.80476 40.0 211s 11 55.2 2.34425 38.3 211s 12 51.5 -2.40558 34.3 211s 13 46.3 -4.85959 29.4 211s 14 45.9 -7.03164 28.2 211s 15 48.7 -2.87827 30.3 211s 16 51.2 -1.48466 33.2 211s 17 55.8 0.00629 37.5 211s 18 59.2 2.32164 40.1 211s 19 57.4 1.73138 39.0 211s 20 60.3 0.54175 41.9 211s 21 64.1 3.05716 46.1 211s 22 71.6 3.96979 52.4 211s > predict 211s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 211s 1 NA NA NA NA 211s 2 42.3 0.464 39.9 44.8 211s 3 46.0 0.541 43.5 48.5 211s 4 50.7 0.337 48.4 53.1 211s 5 51.1 0.385 48.7 53.5 211s 6 52.6 0.386 50.3 55.0 211s 7 54.3 0.349 52.0 56.7 211s 8 54.9 0.320 52.6 57.2 211s 9 56.2 0.355 53.9 58.5 211s 10 58.4 0.370 56.0 60.7 211s 11 55.2 0.682 52.6 57.8 211s 12 51.5 0.563 48.9 54.0 211s 13 46.3 0.719 43.6 49.0 211s 14 45.9 0.597 43.4 48.5 211s 15 48.7 0.370 46.4 51.1 211s 16 51.2 0.327 48.9 53.6 211s 17 55.8 0.391 53.5 58.2 211s 18 59.2 0.316 56.8 61.5 211s 19 57.4 0.389 55.1 59.8 211s 20 60.3 0.459 57.9 62.8 211s 21 64.1 0.438 61.7 66.4 211s 22 71.6 0.674 69.0 74.3 211s Investment.pred Investment.se.fit Investment.lwr Investment.upr 211s 1 NA NA NA NA 211s 2 1.99510 0.792 -1.787 5.777 211s 3 1.74850 0.585 -1.861 5.358 211s 4 4.75942 0.510 1.200 8.319 211s 5 4.86672 0.423 1.359 8.375 211s 6 5.02874 0.400 1.533 8.525 211s 7 4.57056 0.391 1.079 8.062 211s 8 3.09893 0.345 -0.371 6.568 211s 9 2.41471 0.511 -1.145 5.974 211s 10 2.80476 0.560 -0.788 6.397 211s 11 2.34425 0.839 -1.482 6.170 211s 12 -2.40558 0.673 -6.083 1.272 211s 13 -4.85959 0.862 -8.708 -1.011 211s 14 -7.03164 0.874 -10.893 -3.171 211s 15 -2.87827 0.433 -6.392 0.635 211s 16 -1.48466 0.375 -4.968 1.999 211s 17 0.00629 0.491 -3.541 3.554 211s 18 2.32164 0.294 -1.127 5.771 211s 19 1.73138 0.446 -1.789 5.252 211s 20 0.54175 0.547 -3.042 4.125 211s 21 3.05716 0.454 -0.468 6.582 211s 22 3.96979 0.642 0.317 7.623 211s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 211s 1 NA NA NA NA 211s 2 26.7 0.314 24.9 28.5 211s 3 28.8 0.318 27.0 30.6 211s 4 32.6 0.325 30.8 34.4 211s 5 34.0 0.235 32.2 35.7 211s 6 35.7 0.241 33.9 37.4 211s 7 37.7 0.238 36.0 39.5 211s 8 38.6 0.237 36.8 40.4 211s 9 38.9 0.227 37.1 40.6 211s 10 40.0 0.219 38.3 41.8 211s 11 38.3 0.317 36.5 40.1 211s 12 34.3 0.344 32.4 36.1 211s 13 29.4 0.419 27.5 31.3 211s 14 28.2 0.334 26.4 30.0 211s 15 30.3 0.320 28.5 32.1 211s 16 33.2 0.268 31.4 35.0 211s 17 37.5 0.269 35.7 39.3 211s 18 40.1 0.212 38.3 41.8 211s 19 39.0 0.331 37.2 40.8 211s 20 41.9 0.287 40.1 43.7 211s 21 46.1 0.301 44.3 47.9 211s 22 52.4 0.471 50.5 54.4 211s > model.frame 211s [1] TRUE 211s > model.matrix 211s [1] TRUE 211s > nobs 211s [1] 63 211s > linearHypothesis 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 0.29 0.59 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 52 211s 2 51 1 0.39 0.54 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 52 211s 2 51 1 0.39 0.53 211s Linear hypothesis test (Theil's F test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.3 0.74 211s Linear hypothesis test (F statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df F Pr(>F) 211s 1 53 211s 2 51 2 0.4 0.67 211s Linear hypothesis test (Chi^2 statistic of a Wald test) 211s 211s Hypothesis: 211s Consumption_corpProf + Investment_capitalLag = 0 211s Consumption_corpProfLag - PrivateWages_trend = 0 211s 211s Model 1: restricted model 211s Model 2: kleinModel 211s 211s Res.Df Df Chisq Pr(>Chisq) 211s 1 53 211s 2 51 2 0.8 0.67 211s > logLik 211s 'log Lik.' -76.1 (df=18) 211s 'log Lik.' -89.1 (df=18) 211s Estimating function 211s Consumption_(Intercept) Consumption_corpProf 211s Consumption_2 -3.2451 -43.02 211s Consumption_3 -1.3384 -22.19 211s Consumption_4 -1.4130 -27.25 211s Consumption_5 -5.0390 -105.62 211s Consumption_6 -0.8531 -16.86 211s Consumption_7 4.3438 79.23 211s Consumption_8 5.6608 99.48 211s Consumption_9 3.7666 73.61 211s Consumption_10 1.2798 26.08 211s Consumption_11 -3.5695 -61.32 211s Consumption_12 -1.8656 -23.70 211s Consumption_13 -3.4193 -30.77 211s Consumption_14 4.0738 36.88 211s Consumption_15 -1.6814 -21.31 211s Consumption_16 -1.4312 -20.64 211s Consumption_17 9.0552 133.22 211s Consumption_18 -1.9716 -39.03 211s Consumption_19 -6.7338 -129.33 211s Consumption_20 4.8735 84.89 211s Consumption_21 1.6324 33.15 211s Consumption_22 -2.1249 -48.14 211s Investment_2 2.1466 28.45 211s Investment_3 -0.1448 -2.40 211s Investment_4 -0.4444 -8.57 211s Investment_5 1.8148 38.04 211s Investment_6 -0.0658 -1.30 211s Investment_7 -0.9944 -18.14 211s Investment_8 -1.0536 -18.52 211s Investment_9 -0.5553 -10.85 211s Investment_10 -2.2390 -45.62 211s Investment_11 1.3010 22.35 211s Investment_12 0.9607 12.21 211s Investment_13 1.2918 11.63 211s Investment_14 -1.8711 -16.94 211s Investment_15 0.1149 1.46 211s Investment_16 -0.1869 -2.70 211s Investment_17 -2.0208 -29.73 211s Investment_18 0.2841 5.62 211s Investment_19 3.5191 67.59 211s Investment_20 -0.7250 -12.63 211s Investment_21 -0.2285 -4.64 211s Investment_22 -0.9035 -20.47 211s PrivateWages_2 -4.3513 -57.68 211s PrivateWages_3 1.7756 29.44 211s PrivateWages_4 3.5512 68.47 211s PrivateWages_5 -3.3088 -69.35 211s PrivateWages_6 -0.7761 -15.34 211s PrivateWages_7 1.5988 29.16 211s PrivateWages_8 1.5583 27.38 211s PrivateWages_9 2.5665 50.15 211s PrivateWages_10 4.9740 101.35 211s PrivateWages_11 -3.5972 -61.80 211s PrivateWages_12 -0.7986 -10.15 211s PrivateWages_13 -3.2258 -29.03 211s PrivateWages_14 3.6395 32.95 211s PrivateWages_15 -0.5056 -6.41 211s PrivateWages_16 -1.0680 -15.40 211s PrivateWages_17 3.0850 45.39 211s PrivateWages_18 -0.3546 -7.02 211s PrivateWages_19 -8.0362 -154.35 211s PrivateWages_20 1.6465 28.68 211s PrivateWages_21 -1.9137 -38.86 211s PrivateWages_22 3.5407 80.22 211s Consumption_corpProfLag Consumption_wages 211s Consumption_2 -41.21 -95.43 211s Consumption_3 -16.60 -42.49 211s Consumption_4 -23.88 -50.52 211s Consumption_5 -92.72 -196.89 211s Consumption_6 -16.55 -33.39 211s Consumption_7 87.31 170.95 211s Consumption_8 110.95 227.47 211s Consumption_9 74.58 159.45 211s Consumption_10 27.00 56.34 211s Consumption_11 -77.46 -155.98 211s Consumption_12 -29.10 -73.65 211s Consumption_13 -38.98 -120.13 211s Consumption_14 28.52 133.55 211s Consumption_15 -18.83 -63.05 211s Consumption_16 -17.60 -57.45 211s Consumption_17 126.77 377.63 211s Consumption_18 -34.70 -94.39 211s Consumption_19 -116.49 -332.00 211s Consumption_20 74.56 235.83 211s Consumption_21 31.02 87.12 211s Consumption_22 -44.84 -129.02 211s Investment_2 27.26 63.12 211s Investment_3 -1.80 -4.60 211s Investment_4 -7.51 -15.89 211s Investment_5 33.39 70.91 211s Investment_6 -1.28 -2.57 211s Investment_7 -19.99 -39.13 211s Investment_8 -20.65 -42.34 211s Investment_9 -10.99 -23.51 211s Investment_10 -47.24 -98.56 211s Investment_11 28.23 56.85 211s Investment_12 14.99 37.92 211s Investment_13 14.73 45.38 211s Investment_14 -13.10 -61.34 211s Investment_15 1.29 4.31 211s Investment_16 -2.30 -7.50 211s Investment_17 -28.29 -84.27 211s Investment_18 5.00 13.60 211s Investment_19 60.88 173.50 211s Investment_20 -11.09 -35.08 211s Investment_21 -4.34 -12.19 211s Investment_22 -19.06 -54.86 211s PrivateWages_2 -55.26 -127.96 211s PrivateWages_3 22.02 56.38 211s PrivateWages_4 60.01 126.96 211s PrivateWages_5 -60.88 -129.29 211s PrivateWages_6 -15.06 -30.37 211s PrivateWages_7 32.14 62.92 211s PrivateWages_8 30.54 62.62 211s PrivateWages_9 50.82 108.65 211s PrivateWages_10 104.95 218.96 211s PrivateWages_11 -78.06 -157.19 211s PrivateWages_12 -12.46 -31.53 211s PrivateWages_13 -36.77 -113.33 211s PrivateWages_14 25.48 119.32 211s PrivateWages_15 -5.66 -18.96 211s PrivateWages_16 -13.14 -42.87 211s PrivateWages_17 43.19 128.65 211s PrivateWages_18 -6.24 -16.98 211s PrivateWages_19 -139.03 -396.21 211s PrivateWages_20 25.19 79.68 211s PrivateWages_21 -36.36 -102.14 211s PrivateWages_22 74.71 214.98 211s Investment_(Intercept) Investment_corpProf 211s Consumption_2 1.4757 19.56 211s Consumption_3 0.6086 10.09 211s Consumption_4 0.6425 12.39 211s Consumption_5 2.2915 48.03 211s Consumption_6 0.3879 7.67 211s Consumption_7 -1.9753 -36.03 211s Consumption_8 -2.5742 -45.24 211s Consumption_9 -1.7128 -33.47 211s Consumption_10 -0.5820 -11.86 211s Consumption_11 1.6232 27.89 211s Consumption_12 0.8484 10.78 211s Consumption_13 1.5549 13.99 211s Consumption_14 -1.8525 -16.77 211s Consumption_15 0.7646 9.69 211s Consumption_16 0.6508 9.39 211s Consumption_17 -4.1178 -60.58 211s Consumption_18 0.8965 17.75 211s Consumption_19 3.0621 58.81 211s Consumption_20 -2.2162 -38.60 211s Consumption_21 -0.7423 -15.07 211s Consumption_22 0.9663 21.89 211s Investment_2 -2.6492 -35.12 211s Investment_3 0.1787 2.96 211s Investment_4 0.5485 10.58 211s Investment_5 -2.2397 -46.94 211s Investment_6 0.0811 1.60 211s Investment_7 1.2272 22.38 211s Investment_8 1.3003 22.85 211s Investment_9 0.6853 13.39 211s Investment_10 2.7633 56.30 211s Investment_11 -1.6056 -27.58 211s Investment_12 -1.1856 -15.06 211s Investment_13 -1.5943 -14.35 211s Investment_14 2.3092 20.91 211s Investment_15 -0.1418 -1.80 211s Investment_16 0.2307 3.33 211s Investment_17 2.4940 36.69 211s Investment_18 -0.3506 -6.94 211s Investment_19 -4.3431 -83.42 211s Investment_20 0.8947 15.59 211s Investment_21 0.2820 5.73 211s Investment_22 1.1150 25.26 211s PrivateWages_2 2.6070 34.56 211s PrivateWages_3 -1.0638 -17.64 211s PrivateWages_4 -2.1276 -41.02 211s PrivateWages_5 1.9824 41.55 211s PrivateWages_6 0.4650 9.19 211s PrivateWages_7 -0.9579 -17.47 211s PrivateWages_8 -0.9336 -16.41 211s PrivateWages_9 -1.5377 -30.05 211s PrivateWages_10 -2.9800 -60.72 211s PrivateWages_11 2.1552 37.03 211s PrivateWages_12 0.4785 6.08 211s PrivateWages_13 1.9327 17.39 211s PrivateWages_14 -2.1805 -19.74 211s PrivateWages_15 0.3029 3.84 211s PrivateWages_16 0.6398 9.23 211s PrivateWages_17 -1.8483 -27.19 211s PrivateWages_18 0.2125 4.21 211s PrivateWages_19 4.8147 92.47 211s PrivateWages_20 -0.9865 -17.18 211s PrivateWages_21 1.1466 23.28 211s PrivateWages_22 -2.1213 -48.06 211s Investment_corpProfLag Investment_capitalLag 211s Consumption_2 18.74 269.8 211s Consumption_3 7.55 111.1 211s Consumption_4 10.86 118.5 211s Consumption_5 42.16 434.7 211s Consumption_6 7.53 74.8 211s Consumption_7 -39.70 -390.7 211s Consumption_8 -50.45 -523.6 211s Consumption_9 -33.91 -355.6 211s Consumption_10 -12.28 -122.6 211s Consumption_11 35.22 350.1 211s Consumption_12 13.23 183.8 211s Consumption_13 17.73 331.7 211s Consumption_14 -12.97 -383.7 211s Consumption_15 8.56 154.5 211s Consumption_16 8.01 129.5 211s Consumption_17 -57.65 -814.1 211s Consumption_18 15.78 179.1 211s Consumption_19 52.98 617.9 211s Consumption_20 -33.91 -443.0 211s Consumption_21 -14.10 -149.4 211s Consumption_22 20.39 197.6 211s Investment_2 -33.65 -484.3 211s Investment_3 2.22 32.6 211s Investment_4 9.27 101.2 211s Investment_5 -41.21 -424.9 211s Investment_6 1.57 15.6 211s Investment_7 24.67 242.7 211s Investment_8 25.49 264.5 211s Investment_9 13.57 142.3 211s Investment_10 58.30 581.9 211s Investment_11 -34.84 -346.3 211s Investment_12 -18.50 -256.9 211s Investment_13 -18.17 -340.1 211s Investment_14 16.16 478.2 211s Investment_15 -1.59 -28.6 211s Investment_16 2.84 45.9 211s Investment_17 34.92 493.1 211s Investment_18 -6.17 -70.0 211s Investment_19 -75.14 -876.4 211s Investment_20 13.69 178.9 211s Investment_21 5.36 56.7 211s Investment_22 23.53 228.0 211s PrivateWages_2 33.11 476.6 211s PrivateWages_3 -13.19 -194.3 211s PrivateWages_4 -35.96 -392.5 211s PrivateWages_5 36.48 376.1 211s PrivateWages_6 9.02 89.6 211s PrivateWages_7 -19.25 -189.5 211s PrivateWages_8 -18.30 -189.9 211s PrivateWages_9 -30.45 -319.2 211s PrivateWages_10 -62.88 -627.6 211s PrivateWages_11 46.77 464.9 211s PrivateWages_12 7.46 103.7 211s PrivateWages_13 22.03 412.2 211s PrivateWages_14 -15.26 -451.6 211s PrivateWages_15 3.39 61.2 211s PrivateWages_16 7.87 127.3 211s PrivateWages_17 -25.88 -365.4 211s PrivateWages_18 3.74 42.5 211s PrivateWages_19 83.29 971.6 211s PrivateWages_20 -15.09 -197.2 211s PrivateWages_21 21.78 230.7 211s PrivateWages_22 -44.76 -433.8 211s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 211s Consumption_2 -3.220 -153.49 -144.60 211s Consumption_3 -1.328 -65.52 -60.57 211s Consumption_4 -1.402 -79.70 -70.25 211s Consumption_5 -5.001 -303.71 -286.05 211s Consumption_6 -0.847 -51.81 -48.34 211s Consumption_7 4.311 264.22 262.96 211s Consumption_8 5.618 341.88 359.54 211s Consumption_9 3.738 233.16 240.73 211s Consumption_10 1.270 81.79 81.92 211s Consumption_11 -3.542 -228.05 -237.34 211s Consumption_12 -1.851 -101.61 -113.31 211s Consumption_13 -3.393 -159.94 -181.21 211s Consumption_14 4.043 168.34 179.10 211s Consumption_15 -1.669 -85.05 -75.26 211s Consumption_16 -1.420 -79.06 -70.59 211s Consumption_17 8.987 515.06 488.87 211s Consumption_18 -1.957 -132.41 -122.68 211s Consumption_19 -6.683 -455.83 -434.38 211s Consumption_20 4.837 323.61 294.54 211s Consumption_21 1.620 121.95 112.59 211s Consumption_22 -2.109 -182.35 -159.64 211s Investment_2 2.807 133.77 126.02 211s Investment_3 -0.189 -9.34 -8.63 211s Investment_4 -0.581 -33.02 -29.11 211s Investment_5 2.373 144.11 135.73 211s Investment_6 -0.086 -5.26 -4.91 211s Investment_7 -1.300 -79.69 -79.31 211s Investment_8 -1.378 -83.84 -88.17 211s Investment_9 -0.726 -45.28 -46.75 211s Investment_10 -2.928 -188.52 -188.82 211s Investment_11 1.701 109.51 113.97 211s Investment_12 1.256 68.94 76.87 211s Investment_13 1.689 79.61 90.20 211s Investment_14 -2.446 -101.86 -108.38 211s Investment_15 0.150 7.66 6.77 211s Investment_16 -0.244 -13.60 -12.15 211s Investment_17 -2.642 -151.44 -143.74 211s Investment_18 0.371 25.13 23.29 211s Investment_19 4.601 313.85 299.09 211s Investment_20 -0.948 -63.43 -57.73 211s Investment_21 -0.299 -22.49 -20.76 211s Investment_22 -1.181 -102.15 -89.43 211s PrivateWages_2 -8.830 -420.86 -396.47 211s PrivateWages_3 3.603 177.74 164.31 211s PrivateWages_4 7.206 409.57 361.04 211s PrivateWages_5 -6.715 -407.80 -384.07 211s PrivateWages_6 -1.575 -96.39 -89.93 211s PrivateWages_7 3.244 198.86 197.91 211s PrivateWages_8 3.162 192.44 202.38 211s PrivateWages_9 5.208 324.85 335.40 211s PrivateWages_10 10.094 649.99 651.03 211s PrivateWages_11 -7.300 -469.94 -489.08 211s PrivateWages_12 -1.621 -88.94 -99.18 211s PrivateWages_13 -6.546 -308.53 -349.56 211s PrivateWages_14 7.386 307.52 327.18 211s PrivateWages_15 -1.026 -52.30 -46.27 211s PrivateWages_16 -2.167 -120.63 -107.71 211s PrivateWages_17 6.260 358.81 340.56 211s PrivateWages_18 -0.720 -48.70 -45.12 211s PrivateWages_19 -16.308 -1112.35 -1060.00 211s PrivateWages_20 3.341 223.57 203.48 211s PrivateWages_21 -3.883 -292.34 -269.90 211s PrivateWages_22 7.185 621.32 543.91 211s PrivateWages_trend 211s Consumption_2 32.205 211s Consumption_3 11.954 211s Consumption_4 11.218 211s Consumption_5 35.006 211s Consumption_6 5.080 211s Consumption_7 -21.554 211s Consumption_8 -22.471 211s Consumption_9 -11.214 211s Consumption_10 -2.540 211s Consumption_11 3.542 211s Consumption_12 0.000 211s Consumption_13 -3.393 211s Consumption_14 8.086 211s Consumption_15 -5.006 211s Consumption_16 -5.681 211s Consumption_17 44.933 211s Consumption_18 -11.740 211s Consumption_19 -46.779 211s Consumption_20 38.692 211s Consumption_21 14.580 211s Consumption_22 -21.088 211s Investment_2 -28.067 211s Investment_3 1.704 211s Investment_4 4.648 211s Investment_5 -16.610 211s Investment_6 0.516 211s Investment_7 6.501 211s Investment_8 5.511 211s Investment_9 2.178 211s Investment_10 5.855 211s Investment_11 -1.701 211s Investment_12 0.000 211s Investment_13 1.689 211s Investment_14 -4.893 211s Investment_15 0.451 211s Investment_16 -0.978 211s Investment_17 -13.211 211s Investment_18 2.228 211s Investment_19 32.209 211s Investment_20 -7.583 211s Investment_21 -2.689 211s Investment_22 -11.813 211s PrivateWages_2 88.301 211s PrivateWages_3 -32.429 211s PrivateWages_4 -57.650 211s PrivateWages_5 47.002 211s PrivateWages_6 9.450 211s PrivateWages_7 -16.222 211s PrivateWages_8 -12.649 211s PrivateWages_9 -15.624 211s PrivateWages_10 -20.187 211s PrivateWages_11 7.300 211s PrivateWages_12 0.000 211s PrivateWages_13 -6.546 211s PrivateWages_14 14.771 211s PrivateWages_15 -3.078 211s PrivateWages_16 -8.669 211s PrivateWages_17 31.301 211s PrivateWages_18 -4.318 211s PrivateWages_19 -114.154 211s PrivateWages_20 26.730 211s PrivateWages_21 -34.951 211s PrivateWages_22 71.851 211s [1] TRUE 211s > Bread 211s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 211s [1,] 1.07e+02 -1.06982 -0.3515 211s [2,] -1.07e+00 0.73659 -0.5079 211s [3,] -3.51e-01 -0.50793 0.6355 211s [4,] -1.93e+00 -0.07361 -0.0356 211s [5,] 1.24e+02 -0.98618 3.4455 211s [6,] -2.71e+00 0.38390 -0.3719 211s [7,] 9.65e-01 -0.31139 0.3992 211s [8,] -4.61e-01 -0.00199 -0.0185 211s [9,] -3.88e+01 0.05351 1.8003 211s [10,] 6.27e-01 -0.08533 0.0556 211s [11,] -5.96e-04 0.08746 -0.0887 211s [12,] 2.14e-01 0.04029 0.0279 211s Consumption_wages Investment_(Intercept) Investment_corpProf 211s [1,] -1.934840 123.765 -2.71e+00 211s [2,] -0.073613 -0.986 3.84e-01 211s [3,] -0.035606 3.445 -3.72e-01 211s [4,] 0.090675 -3.911 5.58e-02 211s [5,] -3.910682 2907.785 -4.61e+01 211s [6,] 0.055805 -46.132 1.65e+00 211s [7,] -0.054072 38.083 -1.41e+00 211s [8,] 0.019220 -13.707 2.06e-01 211s [9,] 0.174112 17.422 -1.06e-01 211s [10,] -0.002325 2.389 2.04e-03 211s [11,] -0.000594 -2.765 -2.91e-04 211s [12,] -0.032572 -2.080 3.10e-02 211s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 211s [1,] 0.96474 -0.46130 -38.76422 211s [2,] -0.31139 -0.00199 0.05351 211s [3,] 0.39923 -0.01847 1.80032 211s [4,] -0.05407 0.01922 0.17411 211s [5,] 38.08346 -13.70662 17.42245 211s [6,] -1.40785 0.20597 -0.10564 211s [7,] 1.47348 -0.19170 -0.93153 211s [8,] -0.19170 0.06667 0.00097 211s [9,] -0.93153 0.00097 78.44334 211s [10,] 0.01112 -0.01300 -0.49810 211s [11,] 0.00455 0.01344 -0.81226 211s [12,] -0.04174 0.01117 0.88592 211s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 211s [1,] 0.62679 -0.000596 0.21374 211s [2,] -0.08533 0.087455 0.04029 211s [3,] 0.05563 -0.088660 0.02790 211s [4,] -0.00233 -0.000594 -0.03257 211s [5,] 2.38888 -2.764716 -2.07974 211s [6,] 0.00204 -0.000291 0.03105 211s [7,] 0.01112 0.004547 -0.04174 211s [8,] -0.01300 0.013443 0.01117 211s [9,] -0.49810 -0.812260 0.88592 211s [10,] 0.06376 -0.057450 -0.01781 211s [11,] -0.05745 0.073510 0.00317 211s [12,] -0.01781 0.003170 0.04916 211s > 211s > # I3SLS 212s > summary 212s 212s systemfit results 212s method: iterated 3SLS 212s 212s convergence achieved after 20 iterations 212s 212s N DF SSR detRCov OLS-R2 McElroy-R2 212s system 63 51 128 0.509 0.936 0.996 212s 212s N DF SSR MSE RMSE R2 Adj R2 212s Consumption 21 17 19.2 1.130 1.063 0.980 0.976 212s Investment 21 17 95.7 5.627 2.372 0.621 0.554 212s PrivateWages 21 17 12.7 0.748 0.865 0.984 0.981 212s 212s The covariance matrix of the residuals used for estimation 212s Consumption Investment PrivateWages 212s Consumption 0.915 0.642 -0.435 212s Investment 0.642 4.555 0.734 212s PrivateWages -0.435 0.734 0.606 212s 212s The covariance matrix of the residuals 212s Consumption Investment PrivateWages 212s Consumption 0.915 0.642 -0.435 212s Investment 0.642 4.555 0.734 212s PrivateWages -0.435 0.734 0.606 212s 212s The correlations of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.000 0.314 -0.584 212s Investment 0.314 1.000 0.442 212s PrivateWages -0.584 0.442 1.000 212s 212s 212s 3SLS estimates for 'Consumption' (equation 1) 212s Model Formula: consump ~ corpProf + corpProfLag + wages 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 16.5590 1.2244 13.52 1.6e-10 *** 212s corpProf 0.1645 0.0962 1.71 0.105 212s corpProfLag 0.1766 0.0901 1.96 0.067 . 212s wages 0.7658 0.0348 22.03 6.1e-14 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.063 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 19.213 MSE: 1.13 Root MSE: 1.063 212s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 212s 212s 212s 3SLS estimates for 'Investment' (equation 2) 212s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 42.8959 10.5937 4.05 0.00083 *** 212s corpProf -0.3565 0.2602 -1.37 0.18838 212s corpProfLag 1.0113 0.2488 4.07 0.00081 *** 212s capitalLag -0.2602 0.0509 -5.12 8.6e-05 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 2.372 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 95.661 MSE: 5.627 Root MSE: 2.372 212s Multiple R-Squared: 0.621 Adjusted R-Squared: 0.554 212s 212s 212s 3SLS estimates for 'PrivateWages' (equation 3) 212s Model Formula: privWage ~ gnp + gnpLag + trend 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 2.6247 1.1956 2.20 0.042 * 212s gnp 0.3748 0.0311 12.05 9.4e-10 *** 212s gnpLag 0.1937 0.0324 5.98 1.5e-05 *** 212s trend 0.1679 0.0289 5.80 2.1e-05 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 0.865 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 12.719 MSE: 0.748 Root MSE: 0.865 212s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.981 212s 212s > residuals 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 -0.537 -3.95419 -1.2303 212s 3 -1.187 0.00151 0.5797 212s 4 -1.705 -0.22015 1.6794 212s 5 -0.734 -2.22753 -0.0260 212s 6 -0.251 -0.10866 -0.1362 212s 7 0.600 0.83218 -0.1837 212s 8 1.142 1.46624 -0.5825 212s 9 0.921 1.62030 0.4347 212s 10 -0.745 3.40013 1.4104 212s 11 -0.197 -2.15443 -0.4679 212s 12 -0.385 -1.62274 0.0106 212s 13 -0.390 -2.62869 -0.7363 212s 14 0.749 2.80517 0.0581 212s 15 0.112 -0.27710 0.1113 212s 16 0.170 0.13598 -0.1089 212s 17 1.925 2.76200 -0.6976 212s 18 -0.341 -0.53919 0.8651 212s 19 0.219 -4.32845 -1.0116 212s 20 1.383 1.71889 -0.2087 212s 21 1.028 1.06406 -0.9656 212s 22 -1.777 2.25466 1.2061 212s > fitted 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 42.4 3.754 26.7 212s 3 46.2 1.898 28.7 212s 4 50.9 5.420 32.4 212s 5 51.3 5.228 33.9 212s 6 52.9 5.209 35.5 212s 7 54.5 4.768 37.6 212s 8 55.1 2.734 38.5 212s 9 56.4 1.380 38.8 212s 10 58.5 1.700 39.9 212s 11 55.2 3.154 38.4 212s 12 51.3 -1.777 34.5 212s 13 46.0 -3.571 29.7 212s 14 45.8 -7.905 28.4 212s 15 48.6 -2.723 30.5 212s 16 51.1 -1.436 33.3 212s 17 55.8 -0.662 37.5 212s 18 59.0 2.539 40.1 212s 19 57.3 2.428 39.2 212s 20 60.2 -0.419 41.8 212s 21 64.0 2.236 46.0 212s 22 71.5 2.645 52.1 212s > predict 212s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 212s 1 NA NA NA NA 212s 2 42.4 0.434 41.6 43.3 212s 3 46.2 0.491 45.2 47.2 212s 4 50.9 0.309 50.3 51.5 212s 5 51.3 0.351 50.6 52.0 212s 6 52.9 0.352 52.1 53.6 212s 7 54.5 0.320 53.9 55.1 212s 8 55.1 0.293 54.5 55.6 212s 9 56.4 0.324 55.7 57.0 212s 10 58.5 0.340 57.9 59.2 212s 11 55.2 0.613 54.0 56.4 212s 12 51.3 0.506 50.3 52.3 212s 13 46.0 0.649 44.7 47.3 212s 14 45.8 0.546 44.7 46.8 212s 15 48.6 0.341 47.9 49.3 212s 16 51.1 0.301 50.5 51.7 212s 17 55.8 0.357 55.1 56.5 212s 18 59.0 0.293 58.5 59.6 212s 19 57.3 0.353 56.6 58.0 212s 20 60.2 0.421 59.4 61.1 212s 21 64.0 0.409 63.2 64.8 212s 22 71.5 0.630 70.2 72.7 212s Investment.pred Investment.se.fit Investment.lwr Investment.upr 212s 1 NA NA NA NA 212s 2 3.754 1.263 1.218 6.2906 212s 3 1.898 1.022 -0.153 3.9503 212s 4 5.420 0.853 3.709 7.1317 212s 5 5.228 0.727 3.767 6.6877 212s 6 5.209 0.703 3.797 6.6200 212s 7 4.768 0.688 3.387 6.1487 212s 8 2.734 0.615 1.499 3.9683 212s 9 1.380 0.852 -0.330 3.0893 212s 10 1.700 0.938 -0.184 3.5836 212s 11 3.154 1.437 0.269 6.0398 212s 12 -1.777 1.173 -4.133 0.5780 212s 13 -3.571 1.494 -6.570 -0.5725 212s 14 -7.905 1.479 -10.875 -4.9350 212s 15 -2.723 0.778 -4.285 -1.1613 212s 16 -1.436 0.672 -2.784 -0.0875 212s 17 -0.662 0.832 -2.333 1.0088 212s 18 2.539 0.522 1.491 3.5875 212s 19 2.428 0.753 0.918 3.9392 212s 20 -0.419 0.907 -2.240 1.4019 212s 21 2.236 0.775 0.679 3.7928 212s 22 2.645 1.076 0.486 4.8047 212s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 212s 1 NA NA NA NA 212s 2 26.7 0.340 26.0 27.4 212s 3 28.7 0.339 28.0 29.4 212s 4 32.4 0.340 31.7 33.1 212s 5 33.9 0.250 33.4 34.4 212s 6 35.5 0.258 35.0 36.1 212s 7 37.6 0.256 37.1 38.1 212s 8 38.5 0.252 38.0 39.0 212s 9 38.8 0.241 38.3 39.2 212s 10 39.9 0.239 39.4 40.4 212s 11 38.4 0.314 37.7 39.0 212s 12 34.5 0.342 33.8 35.2 212s 13 29.7 0.430 28.9 30.6 212s 14 28.4 0.361 27.7 29.2 212s 15 30.5 0.336 29.8 31.2 212s 16 33.3 0.281 32.7 33.9 212s 17 37.5 0.270 37.0 38.0 212s 18 40.1 0.231 39.7 40.6 212s 19 39.2 0.343 38.5 39.9 212s 20 41.8 0.294 41.2 42.4 212s 21 46.0 0.326 45.3 46.6 212s 22 52.1 0.501 51.1 53.1 212s > model.frame 212s [1] TRUE 212s > model.matrix 212s [1] TRUE 212s > nobs 212s [1] 63 212s > linearHypothesis 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 52 212s 2 51 1 0.59 0.45 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 52 212s 2 51 1 0.73 0.4 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 52 212s 2 51 1 0.73 0.39 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 53 212s 2 51 2 0.72 0.49 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 53 212s 2 51 2 0.88 0.42 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 53 212s 2 51 2 1.77 0.41 212s > logLik 212s 'log Lik.' -82.3 (df=18) 212s 'log Lik.' -99.1 (df=18) 212s Estimating function 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 -6.979 -92.51 212s Consumption_3 -3.442 -57.06 212s Consumption_4 -3.899 -75.19 212s Consumption_5 -11.237 -235.54 212s Consumption_6 -2.642 -52.22 212s Consumption_7 8.084 147.44 212s Consumption_8 10.972 192.80 212s Consumption_9 7.028 137.33 212s Consumption_10 1.972 40.17 212s Consumption_11 -7.325 -125.85 212s Consumption_12 -3.206 -40.73 212s Consumption_13 -5.913 -53.22 212s Consumption_14 9.196 83.26 212s Consumption_15 -2.781 -35.23 212s Consumption_16 -2.363 -34.08 212s Consumption_17 18.799 276.57 212s Consumption_18 -3.872 -76.65 212s Consumption_19 -13.205 -253.63 212s Consumption_20 10.531 183.44 212s Consumption_21 3.807 77.30 212s Consumption_22 -3.522 -79.79 212s Investment_2 5.075 67.27 212s Investment_3 0.158 2.62 212s Investment_4 -0.131 -2.53 212s Investment_5 2.324 48.72 212s Investment_6 0.316 6.26 212s Investment_7 -0.482 -8.80 212s Investment_8 -0.935 -16.43 212s Investment_9 -1.481 -28.94 212s Investment_10 -4.072 -82.96 212s Investment_11 2.213 38.01 212s Investment_12 1.610 20.45 212s Investment_13 2.664 23.98 212s Investment_14 -2.837 -25.69 212s Investment_15 0.201 2.55 212s Investment_16 -0.398 -5.74 212s Investment_17 -2.409 -35.45 212s Investment_18 -0.488 -9.66 212s Investment_19 4.083 78.42 212s Investment_20 -1.607 -27.99 212s Investment_21 -1.086 -22.05 212s Investment_22 -2.718 -61.58 212s PrivateWages_2 -9.649 -127.90 212s PrivateWages_3 4.187 69.41 212s PrivateWages_4 8.749 168.69 212s PrivateWages_5 -6.685 -140.11 212s PrivateWages_6 -1.021 -20.18 212s PrivateWages_7 4.003 73.02 212s PrivateWages_8 3.592 63.12 212s PrivateWages_9 5.932 115.93 212s PrivateWages_10 11.495 234.22 212s PrivateWages_11 -7.992 -137.30 212s PrivateWages_12 -2.626 -33.36 212s PrivateWages_13 -8.660 -77.94 212s PrivateWages_14 6.531 59.13 212s PrivateWages_15 -1.757 -22.27 212s PrivateWages_16 -2.801 -40.40 212s PrivateWages_17 6.362 93.60 212s PrivateWages_18 -0.661 -13.09 212s PrivateWages_19 -18.070 -347.06 212s PrivateWages_20 3.670 63.92 212s PrivateWages_21 -3.889 -78.97 212s PrivateWages_22 9.289 210.47 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 -88.63 -205.23 212s Consumption_3 -42.68 -109.29 212s Consumption_4 -65.90 -139.41 212s Consumption_5 -206.77 -439.08 212s Consumption_6 -51.26 -103.40 212s Consumption_7 162.48 318.13 212s Consumption_8 215.04 440.87 212s Consumption_9 139.15 297.49 212s Consumption_10 41.60 86.79 212s Consumption_11 -158.95 -320.08 212s Consumption_12 -50.01 -126.56 212s Consumption_13 -67.41 -207.75 212s Consumption_14 64.37 301.49 212s Consumption_15 -31.14 -104.27 212s Consumption_16 -29.07 -94.86 212s Consumption_17 263.19 783.97 212s Consumption_18 -68.15 -185.39 212s Consumption_19 -228.45 -651.06 212s Consumption_20 161.12 509.58 212s Consumption_21 72.33 203.19 212s Consumption_22 -74.31 -213.82 212s Investment_2 64.45 149.24 212s Investment_3 1.96 5.01 212s Investment_4 -2.22 -4.70 212s Investment_5 42.77 90.82 212s Investment_6 6.14 12.39 212s Investment_7 -9.70 -18.98 212s Investment_8 -18.33 -37.57 212s Investment_9 -29.32 -62.69 212s Investment_10 -85.92 -179.25 212s Investment_11 48.02 96.69 212s Investment_12 25.11 63.55 212s Investment_13 30.37 93.60 212s Investment_14 -19.86 -93.02 212s Investment_15 2.25 7.55 212s Investment_16 -4.90 -15.98 212s Investment_17 -33.73 -100.47 212s Investment_18 -8.59 -23.36 212s Investment_19 70.63 201.29 212s Investment_20 -24.59 -77.76 212s Investment_21 -20.63 -57.96 212s Investment_22 -57.35 -165.02 212s PrivateWages_2 -122.54 -283.73 212s PrivateWages_3 51.92 132.94 212s PrivateWages_4 147.85 312.78 212s PrivateWages_5 -123.00 -261.19 212s PrivateWages_6 -19.80 -39.95 212s PrivateWages_7 80.47 157.55 212s PrivateWages_8 70.40 144.33 212s PrivateWages_9 117.46 251.13 212s PrivateWages_10 242.55 506.03 212s PrivateWages_11 -173.42 -349.22 212s PrivateWages_12 -40.96 -103.66 212s PrivateWages_13 -98.72 -304.24 212s PrivateWages_14 45.71 214.10 212s PrivateWages_15 -19.68 -65.90 212s PrivateWages_16 -34.45 -112.44 212s PrivateWages_17 89.07 265.31 212s PrivateWages_18 -11.64 -31.65 212s PrivateWages_19 -312.61 -890.90 212s PrivateWages_20 56.14 177.57 212s PrivateWages_21 -73.89 -207.57 212s PrivateWages_22 196.00 564.00 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 2.2268 29.52 212s Consumption_3 1.0983 18.21 212s Consumption_4 1.2442 23.99 212s Consumption_5 3.5856 75.15 212s Consumption_6 0.8430 16.66 212s Consumption_7 -2.5793 -47.04 212s Consumption_8 -3.5007 -61.52 212s Consumption_9 -2.2423 -43.82 212s Consumption_10 -0.6291 -12.82 212s Consumption_11 2.3372 40.15 212s Consumption_12 1.0229 13.00 212s Consumption_13 1.8868 16.98 212s Consumption_14 -2.9343 -26.57 212s Consumption_15 0.8872 11.24 212s Consumption_16 0.7541 10.87 212s Consumption_17 -5.9983 -88.25 212s Consumption_18 1.2355 24.46 212s Consumption_19 4.2135 80.93 212s Consumption_20 -3.3600 -58.53 212s Consumption_21 -1.2147 -24.67 212s Consumption_22 1.1237 25.46 212s Investment_2 -2.6152 -34.67 212s Investment_3 -0.0813 -1.35 212s Investment_4 0.0677 1.30 212s Investment_5 -1.1977 -25.10 212s Investment_6 -0.1631 -3.22 212s Investment_7 0.2486 4.53 212s Investment_8 0.4818 8.47 212s Investment_9 0.7630 14.91 212s Investment_10 2.0982 42.75 212s Investment_11 -1.1402 -19.59 212s Investment_12 -0.8295 -10.54 212s Investment_13 -1.3729 -12.36 212s Investment_14 1.4620 13.24 212s Investment_15 -0.1037 -1.31 212s Investment_16 0.2051 2.96 212s Investment_17 1.2415 18.26 212s Investment_18 0.2514 4.98 212s Investment_19 -2.1038 -40.41 212s Investment_20 0.8280 14.42 212s Investment_21 0.5596 11.36 212s Investment_22 1.4005 31.73 212s PrivateWages_2 3.7415 49.60 212s PrivateWages_3 -1.6237 -26.92 212s PrivateWages_4 -3.3924 -65.41 212s PrivateWages_5 2.5921 54.33 212s PrivateWages_6 0.3959 7.82 212s PrivateWages_7 -1.5524 -28.31 212s PrivateWages_8 -1.3929 -24.48 212s PrivateWages_9 -2.3004 -44.95 212s PrivateWages_10 -4.4576 -90.82 212s PrivateWages_11 3.0990 53.24 212s PrivateWages_12 1.0182 12.94 212s PrivateWages_13 3.3581 30.22 212s PrivateWages_14 -2.5324 -22.93 212s PrivateWages_15 0.6815 8.64 212s PrivateWages_16 1.0862 15.66 212s PrivateWages_17 -2.4670 -36.29 212s PrivateWages_18 0.2564 5.07 212s PrivateWages_19 7.0070 134.58 212s PrivateWages_20 -1.4230 -24.79 212s PrivateWages_21 1.5081 30.62 212s PrivateWages_22 -3.6021 -81.61 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 28.28 407.1 212s Consumption_3 13.62 200.5 212s Consumption_4 21.03 229.5 212s Consumption_5 65.97 680.2 212s Consumption_6 16.35 162.4 212s Consumption_7 -51.84 -510.2 212s Consumption_8 -68.61 -712.1 212s Consumption_9 -44.40 -465.5 212s Consumption_10 -13.27 -132.5 212s Consumption_11 50.72 504.1 212s Consumption_12 15.96 221.7 212s Consumption_13 21.51 402.5 212s Consumption_14 -20.54 -607.7 212s Consumption_15 9.94 179.2 212s Consumption_16 9.27 150.1 212s Consumption_17 -83.98 -1185.9 212s Consumption_18 21.74 246.9 212s Consumption_19 72.89 850.3 212s Consumption_20 -51.41 -671.7 212s Consumption_21 -23.08 -244.4 212s Consumption_22 23.71 229.8 212s Investment_2 -33.21 -478.1 212s Investment_3 -1.01 -14.9 212s Investment_4 1.14 12.5 212s Investment_5 -22.04 -227.2 212s Investment_6 -3.16 -31.4 212s Investment_7 5.00 49.2 212s Investment_8 9.44 98.0 212s Investment_9 15.11 158.4 212s Investment_10 44.27 441.9 212s Investment_11 -24.74 -245.9 212s Investment_12 -12.94 -179.8 212s Investment_13 -15.65 -292.8 212s Investment_14 10.23 302.8 212s Investment_15 -1.16 -21.0 212s Investment_16 2.52 40.8 212s Investment_17 17.38 245.4 212s Investment_18 4.43 50.2 212s Investment_19 -36.40 -424.5 212s Investment_20 12.67 165.5 212s Investment_21 10.63 112.6 212s Investment_22 29.55 286.4 212s PrivateWages_2 47.52 683.9 212s PrivateWages_3 -20.13 -296.5 212s PrivateWages_4 -57.33 -625.9 212s PrivateWages_5 47.69 491.7 212s PrivateWages_6 7.68 76.3 212s PrivateWages_7 -31.20 -307.1 212s PrivateWages_8 -27.30 -283.3 212s PrivateWages_9 -45.55 -477.6 212s PrivateWages_10 -94.05 -938.8 212s PrivateWages_11 67.25 668.4 212s PrivateWages_12 15.88 220.6 212s PrivateWages_13 38.28 716.3 212s PrivateWages_14 -17.73 -524.5 212s PrivateWages_15 7.63 137.7 212s PrivateWages_16 13.36 216.2 212s PrivateWages_17 -34.54 -487.7 212s PrivateWages_18 4.51 51.2 212s PrivateWages_19 121.22 1414.0 212s PrivateWages_20 -21.77 -284.4 212s PrivateWages_21 28.65 303.4 212s PrivateWages_22 -76.00 -736.6 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 -7.713 -367.6 -346.32 212s Consumption_3 -3.804 -187.6 -173.47 212s Consumption_4 -4.309 -244.9 -215.90 212s Consumption_5 -12.419 -754.3 -710.38 212s Consumption_6 -2.920 -178.7 -166.72 212s Consumption_7 8.934 547.6 544.97 212s Consumption_8 12.125 737.9 776.02 212s Consumption_9 7.767 484.4 500.17 212s Consumption_10 2.179 140.3 140.54 212s Consumption_11 -8.095 -521.2 -542.38 212s Consumption_12 -3.543 -194.5 -216.84 212s Consumption_13 -6.535 -308.0 -348.98 212s Consumption_14 10.163 423.2 450.24 212s Consumption_15 -3.073 -156.6 -138.60 212s Consumption_16 -2.612 -145.4 -129.81 212s Consumption_17 20.776 1190.8 1130.21 212s Consumption_18 -4.279 -289.6 -268.32 212s Consumption_19 -14.594 -995.5 -948.61 212s Consumption_20 11.638 778.7 708.75 212s Consumption_21 4.207 316.7 292.41 212s Consumption_22 -3.892 -336.6 -294.62 212s Investment_2 6.817 324.9 306.06 212s Investment_3 0.212 10.5 9.67 212s Investment_4 -0.176 -10.0 -8.84 212s Investment_5 3.122 189.6 178.58 212s Investment_6 0.425 26.0 24.27 212s Investment_7 -0.648 -39.7 -39.52 212s Investment_8 -1.256 -76.4 -80.37 212s Investment_9 -1.989 -124.1 -128.08 212s Investment_10 -5.469 -352.2 -352.75 212s Investment_11 2.972 191.3 199.12 212s Investment_12 2.162 118.7 132.32 212s Investment_13 3.579 168.7 191.09 212s Investment_14 -3.811 -158.7 -168.82 212s Investment_15 0.270 13.8 12.19 212s Investment_16 -0.535 -29.8 -26.57 212s Investment_17 -3.236 -185.5 -176.04 212s Investment_18 -0.655 -44.4 -41.09 212s Investment_19 5.484 374.0 356.44 212s Investment_20 -2.158 -144.4 -131.44 212s Investment_21 -1.459 -109.8 -101.37 212s Investment_22 -3.650 -315.7 -276.34 212s PrivateWages_2 -14.774 -704.2 -663.37 212s PrivateWages_3 6.412 316.3 292.37 212s PrivateWages_4 13.396 761.4 671.14 212s PrivateWages_5 -10.236 -621.6 -585.48 212s PrivateWages_6 -1.563 -95.7 -89.26 212s PrivateWages_7 6.130 375.7 373.95 212s PrivateWages_8 5.500 334.7 352.01 212s PrivateWages_9 9.084 566.6 585.00 212s PrivateWages_10 17.602 1133.5 1135.33 212s PrivateWages_11 -12.237 -787.8 -819.89 212s PrivateWages_12 -4.021 -220.7 -246.06 212s PrivateWages_13 -13.260 -625.0 -708.11 212s PrivateWages_14 10.000 416.4 443.00 212s PrivateWages_15 -2.691 -137.2 -121.37 212s PrivateWages_16 -4.289 -238.7 -213.18 212s PrivateWages_17 9.742 558.3 529.95 212s PrivateWages_18 -1.012 -68.5 -63.47 212s PrivateWages_19 -27.669 -1887.3 -1798.51 212s PrivateWages_20 5.619 376.0 342.19 212s PrivateWages_21 -5.955 -448.3 -413.89 212s PrivateWages_22 14.224 1230.0 1076.76 212s PrivateWages_trend 212s Consumption_2 77.130 212s Consumption_3 34.237 212s Consumption_4 34.475 212s Consumption_5 86.935 212s Consumption_6 17.519 212s Consumption_7 -44.670 212s Consumption_8 -48.501 212s Consumption_9 -23.300 212s Consumption_10 -4.358 212s Consumption_11 8.095 212s Consumption_12 0.000 212s Consumption_13 -6.535 212s Consumption_14 20.327 212s Consumption_15 -9.219 212s Consumption_16 -10.447 212s Consumption_17 103.880 212s Consumption_18 -25.676 212s Consumption_19 -102.158 212s Consumption_20 93.104 212s Consumption_21 37.866 212s Consumption_22 -38.920 212s Investment_2 -68.165 212s Investment_3 -1.908 212s Investment_4 1.411 212s Investment_5 -21.854 212s Investment_6 -2.550 212s Investment_7 3.240 212s Investment_8 5.023 212s Investment_9 5.967 212s Investment_10 10.938 212s Investment_11 -2.972 212s Investment_12 0.000 212s Investment_13 3.579 212s Investment_14 -7.622 212s Investment_15 0.811 212s Investment_16 -2.138 212s Investment_17 -16.180 212s Investment_18 -3.932 212s Investment_19 38.386 212s Investment_20 -17.267 212s Investment_21 -13.128 212s Investment_22 -36.504 212s PrivateWages_2 147.744 212s PrivateWages_3 -57.704 212s PrivateWages_4 -107.168 212s PrivateWages_5 71.650 212s PrivateWages_6 9.379 212s PrivateWages_7 -30.651 212s PrivateWages_8 -22.000 212s PrivateWages_9 -27.251 212s PrivateWages_10 -35.204 212s PrivateWages_11 12.237 212s PrivateWages_12 0.000 212s PrivateWages_13 -13.260 212s PrivateWages_14 20.000 212s PrivateWages_15 -8.073 212s PrivateWages_16 -17.157 212s PrivateWages_17 48.709 212s PrivateWages_18 -6.074 212s PrivateWages_19 -193.685 212s PrivateWages_20 44.952 212s PrivateWages_21 -53.597 212s PrivateWages_22 142.240 212s [1] TRUE 212s > Bread 212s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 212s [1,] 94.44678 -0.9198 -0.3009 212s [2,] -0.91977 0.5830 -0.4036 212s [3,] -0.30085 -0.4036 0.5114 212s [4,] -1.71741 -0.0559 -0.0303 212s [5,] 169.11432 -7.0463 6.8731 212s [6,] -3.78719 0.8222 -0.7139 212s [7,] 1.24504 -0.6799 0.7545 212s [8,] -0.61653 0.0214 -0.0358 212s [9,] -43.93927 0.0941 1.6110 212s [10,] 0.70520 -0.0665 0.0417 212s [11,] 0.00487 0.0673 -0.0710 212s [12,] 0.27782 0.0450 0.0254 212s Consumption_wages Investment_(Intercept) Investment_corpProf 212s [1,] -1.71741 169.11 -3.79e+00 212s [2,] -0.05588 -7.05 8.22e-01 212s [3,] -0.03031 6.87 -7.14e-01 212s [4,] 0.07612 -3.87 3.83e-02 212s [5,] -3.87475 7070.32 -1.04e+02 212s [6,] 0.03834 -104.41 4.26e+00 212s [7,] -0.05106 83.93 -3.59e+00 212s [8,] 0.02027 -33.26 4.55e-01 212s [9,] 0.35346 48.43 -5.08e-01 212s [10,] -0.00637 6.61 4.29e-03 212s [11,] 0.00050 -7.65 4.31e-03 212s [12,] -0.03505 -5.67 7.94e-02 212s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 212s [1,] 1.24504 -0.6165 -43.9393 212s [2,] -0.67986 0.0214 0.0941 212s [3,] 0.75452 -0.0358 1.6110 212s [4,] -0.05106 0.0203 0.3535 212s [5,] 83.92612 -33.2552 48.4291 212s [6,] -3.59218 0.4550 -0.5077 212s [7,] 3.89889 -0.4344 -3.1131 212s [8,] -0.43443 0.1630 0.0665 212s [9,] -3.11309 0.0665 90.0495 212s [10,] 0.04234 -0.0368 -0.7131 212s [11,] 0.00984 0.0370 -0.7830 212s [12,] -0.11558 0.0310 0.9385 212s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 212s [1,] 0.70520 0.00487 0.27782 212s [2,] -0.06653 0.06728 0.04499 212s [3,] 0.04169 -0.07096 0.02543 212s [4,] -0.00637 0.00050 -0.03505 212s [5,] 6.61461 -7.64810 -5.66883 212s [6,] 0.00429 0.00431 0.07939 212s [7,] 0.04234 0.00984 -0.11558 212s [8,] -0.03681 0.03698 0.03103 212s [9,] -0.71315 -0.78300 0.93852 212s [10,] 0.06094 -0.05082 -0.02122 212s [11,] -0.05082 0.06614 0.00579 212s [12,] -0.02122 0.00579 0.05272 212s > 212s > # OLS 212s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 212s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 212s > summary 212s 212s systemfit results 212s method: OLS 212s 212s N DF SSR detRCov OLS-R2 McElroy-R2 212s system 62 50 44.9 0.372 0.977 0.991 212s 212s N DF SSR MSE RMSE R2 Adj R2 212s Consumption 21 17 17.88 1.052 1.03 0.981 0.978 212s Investment 21 17 17.32 1.019 1.01 0.931 0.919 212s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 212s 212s The covariance matrix of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.0703 -0.0161 -0.463 212s Investment -0.0161 0.9435 0.199 212s PrivateWages -0.4633 0.1993 0.609 212s 212s The correlations of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.0000 -0.0201 -0.575 212s Investment -0.0201 1.0000 0.264 212s PrivateWages -0.5747 0.2639 1.000 212s 212s 212s OLS estimates for 'Consumption' (equation 1) 212s Model Formula: consump ~ corpProf + corpProfLag + wages 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 16.2366 1.3141 12.36 6.4e-10 *** 212s corpProf 0.1929 0.0920 2.10 0.051 . 212s corpProfLag 0.0899 0.0914 0.98 0.339 212s wages 0.7962 0.0403 19.76 3.6e-13 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.026 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 212s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 212s 212s 212s OLS estimates for 'Investment' (equation 2) 212s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 10.1258 5.2592 1.93 0.07108 . 212s corpProf 0.4796 0.0934 5.13 8.3e-05 *** 212s corpProfLag 0.3330 0.0971 3.43 0.00318 ** 212s capitalLag -0.1118 0.0257 -4.35 0.00044 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.009 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 212s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 212s 212s 212s OLS estimates for 'PrivateWages' (equation 3) 212s Model Formula: privWage ~ gnp + gnpLag + trend 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 1.3550 1.3093 1.03 0.3161 212s gnp 0.4417 0.0331 13.33 4.4e-10 *** 212s gnpLag 0.1466 0.0381 3.85 0.0014 ** 212s trend 0.1244 0.0336 3.70 0.0020 ** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 0.78 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 212s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 212s 212s compare coef with single-equation OLS 212s [1] TRUE 212s > residuals 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 -0.32389 -0.0668 -1.3389 212s 3 -1.25001 -0.0476 0.2462 212s 4 -1.56574 1.2467 1.1255 212s 5 -0.49350 -1.3512 -0.1959 212s 6 0.00761 0.4154 -0.5284 212s 7 0.86910 1.4923 NA 212s 8 1.33848 0.7889 -0.7909 212s 9 1.05498 -0.6317 0.2819 212s 10 -0.58856 1.0830 1.1384 212s 11 0.28231 0.2791 -0.1904 212s 12 -0.22965 0.0369 0.5813 212s 13 -0.32213 0.3659 0.1206 212s 14 0.32228 0.2237 0.4773 212s 15 -0.05801 -0.1728 0.3035 212s 16 -0.03466 0.0101 0.0284 212s 17 1.61650 0.9719 -0.8517 212s 18 -0.43597 0.0516 0.9908 212s 19 0.21005 -2.5656 -0.4597 212s 20 0.98920 -0.6866 -0.3819 212s 21 0.78508 -0.7807 -1.1062 212s 22 -2.17345 -0.6623 0.5501 212s > fitted 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 42.2 -0.133 26.8 212s 3 46.3 1.948 29.1 212s 4 50.8 3.953 33.0 212s 5 51.1 4.351 34.1 212s 6 52.6 4.685 35.9 212s 7 54.2 4.108 NA 212s 8 54.9 3.411 38.7 212s 9 56.2 3.632 38.9 212s 10 58.4 4.017 40.2 212s 11 54.7 0.721 38.1 212s 12 51.1 -3.437 33.9 212s 13 45.9 -6.566 28.9 212s 14 46.2 -5.324 28.0 212s 15 48.8 -2.827 30.3 212s 16 51.3 -1.310 33.2 212s 17 56.1 1.128 37.7 212s 18 59.1 1.948 40.0 212s 19 57.3 0.666 38.7 212s 20 60.6 1.987 42.0 212s 21 64.2 4.081 46.1 212s 22 71.9 5.562 52.7 212s > predict 212s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 212s 1 NA NA NA NA 212s 2 42.2 0.466 40.0 44.5 212s 3 46.3 0.523 43.9 48.6 212s 4 50.8 0.344 48.6 52.9 212s 5 51.1 0.399 48.9 53.3 212s 6 52.6 0.401 50.4 54.8 212s 7 54.2 0.363 52.0 56.4 212s 8 54.9 0.330 52.7 57.0 212s 9 56.2 0.354 54.1 58.4 212s 10 58.4 0.373 56.2 60.6 212s 11 54.7 0.612 52.3 57.1 212s 12 51.1 0.489 48.8 53.4 212s 13 45.9 0.634 43.5 48.3 212s 14 46.2 0.608 43.8 48.6 212s 15 48.8 0.378 46.6 51.0 212s 16 51.3 0.336 49.2 53.5 212s 17 56.1 0.369 53.9 58.3 212s 18 59.1 0.324 57.0 61.3 212s 19 57.3 0.375 55.1 59.5 212s 20 60.6 0.437 58.4 62.9 212s 21 64.2 0.429 62.0 66.4 212s 22 71.9 0.672 69.4 74.3 212s Investment.pred Investment.se.fit Investment.lwr Investment.upr 212s 1 NA NA NA NA 212s 2 -0.133 0.584 -2.476 2.209 212s 3 1.948 0.480 -0.297 4.193 212s 4 3.953 0.432 1.748 6.159 212s 5 4.351 0.357 2.201 6.502 212s 6 4.685 0.336 2.548 6.821 212s 7 4.108 0.316 1.983 6.232 212s 8 3.411 0.281 1.306 5.516 212s 9 3.632 0.374 1.469 5.794 212s 10 4.017 0.430 1.813 6.221 212s 11 0.721 0.579 -1.616 3.058 212s 12 -3.437 0.488 -5.688 -1.185 212s 13 -6.566 0.592 -8.917 -4.215 212s 14 -5.324 0.667 -7.754 -2.893 212s 15 -2.827 0.359 -4.979 -0.675 212s 16 -1.310 0.308 -3.430 0.810 212s 17 1.128 0.334 -1.008 3.264 212s 18 1.948 0.234 -0.133 4.030 212s 19 0.666 0.300 -1.450 2.781 212s 20 1.987 0.353 -0.161 4.134 212s 21 4.081 0.319 1.954 6.207 212s 22 5.562 0.444 3.348 7.777 212s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 212s 1 NA NA NA NA 212s 2 26.8 0.366 25.1 28.6 212s 3 29.1 0.369 27.3 30.8 212s 4 33.0 0.372 31.2 34.7 212s 5 34.1 0.288 32.4 35.8 212s 6 35.9 0.287 34.3 37.6 212s 7 NA NA NA NA 212s 8 38.7 0.293 37.0 40.4 212s 9 38.9 0.279 37.3 40.6 212s 10 40.2 0.266 38.5 41.8 212s 11 38.1 0.365 36.4 39.8 212s 12 33.9 0.369 32.2 35.7 212s 13 28.9 0.438 27.1 30.7 212s 14 28.0 0.385 26.3 29.8 212s 15 30.3 0.379 28.6 32.0 212s 16 33.2 0.316 31.5 34.9 212s 17 37.7 0.310 36.0 39.3 212s 18 40.0 0.243 38.4 41.7 212s 19 38.7 0.363 36.9 40.4 212s 20 42.0 0.326 40.3 43.7 212s 21 46.1 0.341 44.4 47.8 212s 22 52.7 0.514 50.9 54.6 212s > model.frame 212s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 212s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 212s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 212s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 212s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 212s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 212s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 212s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 212s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 212s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 212s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 212s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 212s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 212s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 212s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 212s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 212s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 212s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 212s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 212s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 212s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 212s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 212s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 212s trend 212s 1 -11 212s 2 -10 212s 3 -9 212s 4 -8 212s 5 -7 212s 6 -6 212s 7 -5 212s 8 -4 212s 9 -3 212s 10 -2 212s 11 -1 212s 12 0 212s 13 1 212s 14 2 212s 15 3 212s 16 4 212s 17 5 212s 18 6 212s 19 7 212s 20 8 212s 21 9 212s 22 10 212s > model.matrix 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 1 12.4 212s Consumption_3 1 16.9 212s Consumption_4 1 18.4 212s Consumption_5 1 19.4 212s Consumption_6 1 20.1 212s Consumption_7 1 19.6 212s Consumption_8 1 19.8 212s Consumption_9 1 21.1 212s Consumption_10 1 21.7 212s Consumption_11 1 15.6 212s Consumption_12 1 11.4 212s Consumption_13 1 7.0 212s Consumption_14 1 11.2 212s Consumption_15 1 12.3 212s Consumption_16 1 14.0 212s Consumption_17 1 17.6 212s Consumption_18 1 17.3 212s Consumption_19 1 15.3 212s Consumption_20 1 19.0 212s Consumption_21 1 21.1 212s Consumption_22 1 23.5 212s Investment_2 0 0.0 212s Investment_3 0 0.0 212s Investment_4 0 0.0 212s Investment_5 0 0.0 212s Investment_6 0 0.0 212s Investment_7 0 0.0 212s Investment_8 0 0.0 212s Investment_9 0 0.0 212s Investment_10 0 0.0 212s Investment_11 0 0.0 212s Investment_12 0 0.0 212s Investment_13 0 0.0 212s Investment_14 0 0.0 212s Investment_15 0 0.0 212s Investment_16 0 0.0 212s Investment_17 0 0.0 212s Investment_18 0 0.0 212s Investment_19 0 0.0 212s Investment_20 0 0.0 212s Investment_21 0 0.0 212s Investment_22 0 0.0 212s PrivateWages_2 0 0.0 212s PrivateWages_3 0 0.0 212s PrivateWages_4 0 0.0 212s PrivateWages_5 0 0.0 212s PrivateWages_6 0 0.0 212s PrivateWages_8 0 0.0 212s PrivateWages_9 0 0.0 212s PrivateWages_10 0 0.0 212s PrivateWages_11 0 0.0 212s PrivateWages_12 0 0.0 212s PrivateWages_13 0 0.0 212s PrivateWages_14 0 0.0 212s PrivateWages_15 0 0.0 212s PrivateWages_16 0 0.0 212s PrivateWages_17 0 0.0 212s PrivateWages_18 0 0.0 212s PrivateWages_19 0 0.0 212s PrivateWages_20 0 0.0 212s PrivateWages_21 0 0.0 212s PrivateWages_22 0 0.0 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 12.7 28.2 212s Consumption_3 12.4 32.2 212s Consumption_4 16.9 37.0 212s Consumption_5 18.4 37.0 212s Consumption_6 19.4 38.6 212s Consumption_7 20.1 40.7 212s Consumption_8 19.6 41.5 212s Consumption_9 19.8 42.9 212s Consumption_10 21.1 45.3 212s Consumption_11 21.7 42.1 212s Consumption_12 15.6 39.3 212s Consumption_13 11.4 34.3 212s Consumption_14 7.0 34.1 212s Consumption_15 11.2 36.6 212s Consumption_16 12.3 39.3 212s Consumption_17 14.0 44.2 212s Consumption_18 17.6 47.7 212s Consumption_19 17.3 45.9 212s Consumption_20 15.3 49.4 212s Consumption_21 19.0 53.0 212s Consumption_22 21.1 61.8 212s Investment_2 0.0 0.0 212s Investment_3 0.0 0.0 212s Investment_4 0.0 0.0 212s Investment_5 0.0 0.0 212s Investment_6 0.0 0.0 212s Investment_7 0.0 0.0 212s Investment_8 0.0 0.0 212s Investment_9 0.0 0.0 212s Investment_10 0.0 0.0 212s Investment_11 0.0 0.0 212s Investment_12 0.0 0.0 212s Investment_13 0.0 0.0 212s Investment_14 0.0 0.0 212s Investment_15 0.0 0.0 212s Investment_16 0.0 0.0 212s Investment_17 0.0 0.0 212s Investment_18 0.0 0.0 212s Investment_19 0.0 0.0 212s Investment_20 0.0 0.0 212s Investment_21 0.0 0.0 212s Investment_22 0.0 0.0 212s PrivateWages_2 0.0 0.0 212s PrivateWages_3 0.0 0.0 212s PrivateWages_4 0.0 0.0 212s PrivateWages_5 0.0 0.0 212s PrivateWages_6 0.0 0.0 212s PrivateWages_8 0.0 0.0 212s PrivateWages_9 0.0 0.0 212s PrivateWages_10 0.0 0.0 212s PrivateWages_11 0.0 0.0 212s PrivateWages_12 0.0 0.0 212s PrivateWages_13 0.0 0.0 212s PrivateWages_14 0.0 0.0 212s PrivateWages_15 0.0 0.0 212s PrivateWages_16 0.0 0.0 212s PrivateWages_17 0.0 0.0 212s PrivateWages_18 0.0 0.0 212s PrivateWages_19 0.0 0.0 212s PrivateWages_20 0.0 0.0 212s PrivateWages_21 0.0 0.0 212s PrivateWages_22 0.0 0.0 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 0 0.0 212s Consumption_3 0 0.0 212s Consumption_4 0 0.0 212s Consumption_5 0 0.0 212s Consumption_6 0 0.0 212s Consumption_7 0 0.0 212s Consumption_8 0 0.0 212s Consumption_9 0 0.0 212s Consumption_10 0 0.0 212s Consumption_11 0 0.0 212s Consumption_12 0 0.0 212s Consumption_13 0 0.0 212s Consumption_14 0 0.0 212s Consumption_15 0 0.0 212s Consumption_16 0 0.0 212s Consumption_17 0 0.0 212s Consumption_18 0 0.0 212s Consumption_19 0 0.0 212s Consumption_20 0 0.0 212s Consumption_21 0 0.0 212s Consumption_22 0 0.0 212s Investment_2 1 12.4 212s Investment_3 1 16.9 212s Investment_4 1 18.4 212s Investment_5 1 19.4 212s Investment_6 1 20.1 212s Investment_7 1 19.6 212s Investment_8 1 19.8 212s Investment_9 1 21.1 212s Investment_10 1 21.7 212s Investment_11 1 15.6 212s Investment_12 1 11.4 212s Investment_13 1 7.0 212s Investment_14 1 11.2 212s Investment_15 1 12.3 212s Investment_16 1 14.0 212s Investment_17 1 17.6 212s Investment_18 1 17.3 212s Investment_19 1 15.3 212s Investment_20 1 19.0 212s Investment_21 1 21.1 212s Investment_22 1 23.5 212s PrivateWages_2 0 0.0 212s PrivateWages_3 0 0.0 212s PrivateWages_4 0 0.0 212s PrivateWages_5 0 0.0 212s PrivateWages_6 0 0.0 212s PrivateWages_8 0 0.0 212s PrivateWages_9 0 0.0 212s PrivateWages_10 0 0.0 212s PrivateWages_11 0 0.0 212s PrivateWages_12 0 0.0 212s PrivateWages_13 0 0.0 212s PrivateWages_14 0 0.0 212s PrivateWages_15 0 0.0 212s PrivateWages_16 0 0.0 212s PrivateWages_17 0 0.0 212s PrivateWages_18 0 0.0 212s PrivateWages_19 0 0.0 212s PrivateWages_20 0 0.0 212s PrivateWages_21 0 0.0 212s PrivateWages_22 0 0.0 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 0.0 0 212s Consumption_3 0.0 0 212s Consumption_4 0.0 0 212s Consumption_5 0.0 0 212s Consumption_6 0.0 0 212s Consumption_7 0.0 0 212s Consumption_8 0.0 0 212s Consumption_9 0.0 0 212s Consumption_10 0.0 0 212s Consumption_11 0.0 0 212s Consumption_12 0.0 0 212s Consumption_13 0.0 0 212s Consumption_14 0.0 0 212s Consumption_15 0.0 0 212s Consumption_16 0.0 0 212s Consumption_17 0.0 0 212s Consumption_18 0.0 0 212s Consumption_19 0.0 0 212s Consumption_20 0.0 0 212s Consumption_21 0.0 0 212s Consumption_22 0.0 0 212s Investment_2 12.7 183 212s Investment_3 12.4 183 212s Investment_4 16.9 184 212s Investment_5 18.4 190 212s Investment_6 19.4 193 212s Investment_7 20.1 198 212s Investment_8 19.6 203 212s Investment_9 19.8 208 212s Investment_10 21.1 211 212s Investment_11 21.7 216 212s Investment_12 15.6 217 212s Investment_13 11.4 213 212s Investment_14 7.0 207 212s Investment_15 11.2 202 212s Investment_16 12.3 199 212s Investment_17 14.0 198 212s Investment_18 17.6 200 212s Investment_19 17.3 202 212s Investment_20 15.3 200 212s Investment_21 19.0 201 212s Investment_22 21.1 204 212s PrivateWages_2 0.0 0 212s PrivateWages_3 0.0 0 212s PrivateWages_4 0.0 0 212s PrivateWages_5 0.0 0 212s PrivateWages_6 0.0 0 212s PrivateWages_8 0.0 0 212s PrivateWages_9 0.0 0 212s PrivateWages_10 0.0 0 212s PrivateWages_11 0.0 0 212s PrivateWages_12 0.0 0 212s PrivateWages_13 0.0 0 212s PrivateWages_14 0.0 0 212s PrivateWages_15 0.0 0 212s PrivateWages_16 0.0 0 212s PrivateWages_17 0.0 0 212s PrivateWages_18 0.0 0 212s PrivateWages_19 0.0 0 212s PrivateWages_20 0.0 0 212s PrivateWages_21 0.0 0 212s PrivateWages_22 0.0 0 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 0 0.0 0.0 212s Consumption_3 0 0.0 0.0 212s Consumption_4 0 0.0 0.0 212s Consumption_5 0 0.0 0.0 212s Consumption_6 0 0.0 0.0 212s Consumption_7 0 0.0 0.0 212s Consumption_8 0 0.0 0.0 212s Consumption_9 0 0.0 0.0 212s Consumption_10 0 0.0 0.0 212s Consumption_11 0 0.0 0.0 212s Consumption_12 0 0.0 0.0 212s Consumption_13 0 0.0 0.0 212s Consumption_14 0 0.0 0.0 212s Consumption_15 0 0.0 0.0 212s Consumption_16 0 0.0 0.0 212s Consumption_17 0 0.0 0.0 212s Consumption_18 0 0.0 0.0 212s Consumption_19 0 0.0 0.0 212s Consumption_20 0 0.0 0.0 212s Consumption_21 0 0.0 0.0 212s Consumption_22 0 0.0 0.0 212s Investment_2 0 0.0 0.0 212s Investment_3 0 0.0 0.0 212s Investment_4 0 0.0 0.0 212s Investment_5 0 0.0 0.0 212s Investment_6 0 0.0 0.0 212s Investment_7 0 0.0 0.0 212s Investment_8 0 0.0 0.0 212s Investment_9 0 0.0 0.0 212s Investment_10 0 0.0 0.0 212s Investment_11 0 0.0 0.0 212s Investment_12 0 0.0 0.0 212s Investment_13 0 0.0 0.0 212s Investment_14 0 0.0 0.0 212s Investment_15 0 0.0 0.0 212s Investment_16 0 0.0 0.0 212s Investment_17 0 0.0 0.0 212s Investment_18 0 0.0 0.0 212s Investment_19 0 0.0 0.0 212s Investment_20 0 0.0 0.0 212s Investment_21 0 0.0 0.0 212s Investment_22 0 0.0 0.0 212s PrivateWages_2 1 45.6 44.9 212s PrivateWages_3 1 50.1 45.6 212s PrivateWages_4 1 57.2 50.1 212s PrivateWages_5 1 57.1 57.2 212s PrivateWages_6 1 61.0 57.1 212s PrivateWages_8 1 64.4 64.0 212s PrivateWages_9 1 64.5 64.4 212s PrivateWages_10 1 67.0 64.5 212s PrivateWages_11 1 61.2 67.0 212s PrivateWages_12 1 53.4 61.2 212s PrivateWages_13 1 44.3 53.4 212s PrivateWages_14 1 45.1 44.3 212s PrivateWages_15 1 49.7 45.1 212s PrivateWages_16 1 54.4 49.7 212s PrivateWages_17 1 62.7 54.4 212s PrivateWages_18 1 65.0 62.7 212s PrivateWages_19 1 60.9 65.0 212s PrivateWages_20 1 69.5 60.9 212s PrivateWages_21 1 75.7 69.5 212s PrivateWages_22 1 88.4 75.7 212s PrivateWages_trend 212s Consumption_2 0 212s Consumption_3 0 212s Consumption_4 0 212s Consumption_5 0 212s Consumption_6 0 212s Consumption_7 0 212s Consumption_8 0 212s Consumption_9 0 212s Consumption_10 0 212s Consumption_11 0 212s Consumption_12 0 212s Consumption_13 0 212s Consumption_14 0 212s Consumption_15 0 212s Consumption_16 0 212s Consumption_17 0 212s Consumption_18 0 212s Consumption_19 0 212s Consumption_20 0 212s Consumption_21 0 212s Consumption_22 0 212s Investment_2 0 212s Investment_3 0 212s Investment_4 0 212s Investment_5 0 212s Investment_6 0 212s Investment_7 0 212s Investment_8 0 212s Investment_9 0 212s Investment_10 0 212s Investment_11 0 212s Investment_12 0 212s Investment_13 0 212s Investment_14 0 212s Investment_15 0 212s Investment_16 0 212s Investment_17 0 212s Investment_18 0 212s Investment_19 0 212s Investment_20 0 212s Investment_21 0 212s Investment_22 0 212s PrivateWages_2 -10 212s PrivateWages_3 -9 212s PrivateWages_4 -8 212s PrivateWages_5 -7 212s PrivateWages_6 -6 212s PrivateWages_8 -4 212s PrivateWages_9 -3 212s PrivateWages_10 -2 212s PrivateWages_11 -1 212s PrivateWages_12 0 212s PrivateWages_13 1 212s PrivateWages_14 2 212s PrivateWages_15 3 212s PrivateWages_16 4 212s PrivateWages_17 5 212s PrivateWages_18 6 212s PrivateWages_19 7 212s PrivateWages_20 8 212s PrivateWages_21 9 212s PrivateWages_22 10 212s > nobs 212s [1] 62 212s > linearHypothesis 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 51 212s 2 50 1 0.8 0.37 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 51 212s 2 50 1 0.72 0.4 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 51 212s 2 50 1 0.72 0.4 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 52 212s 2 50 2 0.42 0.66 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 52 212s 2 50 2 0.37 0.69 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 52 212s 2 50 2 0.75 0.69 212s > logLik 212s 'log Lik.' -71.9 (df=13) 212s 'log Lik.' -77.1 (df=13) 212s compare log likelihood value with single-equation OLS 212s [1] "Mean relative difference: 0.000555" 212s Estimating function 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 -0.32389 -4.016 212s Consumption_3 -1.25001 -21.125 212s Consumption_4 -1.56574 -28.810 212s Consumption_5 -0.49350 -9.574 212s Consumption_6 0.00761 0.153 212s Consumption_7 0.86910 17.034 212s Consumption_8 1.33848 26.502 212s Consumption_9 1.05498 22.260 212s Consumption_10 -0.58856 -12.772 212s Consumption_11 0.28231 4.404 212s Consumption_12 -0.22965 -2.618 212s Consumption_13 -0.32213 -2.255 212s Consumption_14 0.32228 3.610 212s Consumption_15 -0.05801 -0.714 212s Consumption_16 -0.03466 -0.485 212s Consumption_17 1.61650 28.450 212s Consumption_18 -0.43597 -7.542 212s Consumption_19 0.21005 3.214 212s Consumption_20 0.98920 18.795 212s Consumption_21 0.78508 16.565 212s Consumption_22 -2.17345 -51.076 212s Investment_2 0.00000 0.000 212s Investment_3 0.00000 0.000 212s Investment_4 0.00000 0.000 212s Investment_5 0.00000 0.000 212s Investment_6 0.00000 0.000 212s Investment_7 0.00000 0.000 212s Investment_8 0.00000 0.000 212s Investment_9 0.00000 0.000 212s Investment_10 0.00000 0.000 212s Investment_11 0.00000 0.000 212s Investment_12 0.00000 0.000 212s Investment_13 0.00000 0.000 212s Investment_14 0.00000 0.000 212s Investment_15 0.00000 0.000 212s Investment_16 0.00000 0.000 212s Investment_17 0.00000 0.000 212s Investment_18 0.00000 0.000 212s Investment_19 0.00000 0.000 212s Investment_20 0.00000 0.000 212s Investment_21 0.00000 0.000 212s Investment_22 0.00000 0.000 212s PrivateWages_2 0.00000 0.000 212s PrivateWages_3 0.00000 0.000 212s PrivateWages_4 0.00000 0.000 212s PrivateWages_5 0.00000 0.000 212s PrivateWages_6 0.00000 0.000 212s PrivateWages_8 0.00000 0.000 212s PrivateWages_9 0.00000 0.000 212s PrivateWages_10 0.00000 0.000 212s PrivateWages_11 0.00000 0.000 212s PrivateWages_12 0.00000 0.000 212s PrivateWages_13 0.00000 0.000 212s PrivateWages_14 0.00000 0.000 212s PrivateWages_15 0.00000 0.000 212s PrivateWages_16 0.00000 0.000 212s PrivateWages_17 0.00000 0.000 212s PrivateWages_18 0.00000 0.000 212s PrivateWages_19 0.00000 0.000 212s PrivateWages_20 0.00000 0.000 212s PrivateWages_21 0.00000 0.000 212s PrivateWages_22 0.00000 0.000 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 -4.113 -9.134 212s Consumption_3 -15.500 -40.250 212s Consumption_4 -26.461 -57.932 212s Consumption_5 -9.080 -18.260 212s Consumption_6 0.148 0.294 212s Consumption_7 17.469 35.372 212s Consumption_8 26.234 55.547 212s Consumption_9 20.889 45.259 212s Consumption_10 -12.419 -26.662 212s Consumption_11 6.126 11.885 212s Consumption_12 -3.583 -9.025 212s Consumption_13 -3.672 -11.049 212s Consumption_14 2.256 10.990 212s Consumption_15 -0.650 -2.123 212s Consumption_16 -0.426 -1.362 212s Consumption_17 22.631 71.449 212s Consumption_18 -7.673 -20.796 212s Consumption_19 3.634 9.641 212s Consumption_20 15.135 48.867 212s Consumption_21 14.916 41.609 212s Consumption_22 -45.860 -134.319 212s Investment_2 0.000 0.000 212s Investment_3 0.000 0.000 212s Investment_4 0.000 0.000 212s Investment_5 0.000 0.000 212s Investment_6 0.000 0.000 212s Investment_7 0.000 0.000 212s Investment_8 0.000 0.000 212s Investment_9 0.000 0.000 212s Investment_10 0.000 0.000 212s Investment_11 0.000 0.000 212s Investment_12 0.000 0.000 212s Investment_13 0.000 0.000 212s Investment_14 0.000 0.000 212s Investment_15 0.000 0.000 212s Investment_16 0.000 0.000 212s Investment_17 0.000 0.000 212s Investment_18 0.000 0.000 212s Investment_19 0.000 0.000 212s Investment_20 0.000 0.000 212s Investment_21 0.000 0.000 212s Investment_22 0.000 0.000 212s PrivateWages_2 0.000 0.000 212s PrivateWages_3 0.000 0.000 212s PrivateWages_4 0.000 0.000 212s PrivateWages_5 0.000 0.000 212s PrivateWages_6 0.000 0.000 212s PrivateWages_8 0.000 0.000 212s PrivateWages_9 0.000 0.000 212s PrivateWages_10 0.000 0.000 212s PrivateWages_11 0.000 0.000 212s PrivateWages_12 0.000 0.000 212s PrivateWages_13 0.000 0.000 212s PrivateWages_14 0.000 0.000 212s PrivateWages_15 0.000 0.000 212s PrivateWages_16 0.000 0.000 212s PrivateWages_17 0.000 0.000 212s PrivateWages_18 0.000 0.000 212s PrivateWages_19 0.000 0.000 212s PrivateWages_20 0.000 0.000 212s PrivateWages_21 0.000 0.000 212s PrivateWages_22 0.000 0.000 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 0.0000 0.000 212s Consumption_3 0.0000 0.000 212s Consumption_4 0.0000 0.000 212s Consumption_5 0.0000 0.000 212s Consumption_6 0.0000 0.000 212s Consumption_7 0.0000 0.000 212s Consumption_8 0.0000 0.000 212s Consumption_9 0.0000 0.000 212s Consumption_10 0.0000 0.000 212s Consumption_11 0.0000 0.000 212s Consumption_12 0.0000 0.000 212s Consumption_13 0.0000 0.000 212s Consumption_14 0.0000 0.000 212s Consumption_15 0.0000 0.000 212s Consumption_16 0.0000 0.000 212s Consumption_17 0.0000 0.000 212s Consumption_18 0.0000 0.000 212s Consumption_19 0.0000 0.000 212s Consumption_20 0.0000 0.000 212s Consumption_21 0.0000 0.000 212s Consumption_22 0.0000 0.000 212s Investment_2 -0.0668 -0.828 212s Investment_3 -0.0476 -0.804 212s Investment_4 1.2467 22.939 212s Investment_5 -1.3512 -26.213 212s Investment_6 0.4154 8.350 212s Investment_7 1.4923 29.248 212s Investment_8 0.7889 15.620 212s Investment_9 -0.6317 -13.329 212s Investment_10 1.0830 23.500 212s Investment_11 0.2791 4.353 212s Investment_12 0.0369 0.420 212s Investment_13 0.3659 2.561 212s Investment_14 0.2237 2.505 212s Investment_15 -0.1728 -2.126 212s Investment_16 0.0101 0.141 212s Investment_17 0.9719 17.105 212s Investment_18 0.0516 0.893 212s Investment_19 -2.5656 -39.254 212s Investment_20 -0.6866 -13.045 212s Investment_21 -0.7807 -16.474 212s Investment_22 -0.6623 -15.565 212s PrivateWages_2 0.0000 0.000 212s PrivateWages_3 0.0000 0.000 212s PrivateWages_4 0.0000 0.000 212s PrivateWages_5 0.0000 0.000 212s PrivateWages_6 0.0000 0.000 212s PrivateWages_8 0.0000 0.000 212s PrivateWages_9 0.0000 0.000 212s PrivateWages_10 0.0000 0.000 212s PrivateWages_11 0.0000 0.000 212s PrivateWages_12 0.0000 0.000 212s PrivateWages_13 0.0000 0.000 212s PrivateWages_14 0.0000 0.000 212s PrivateWages_15 0.0000 0.000 212s PrivateWages_16 0.0000 0.000 212s PrivateWages_17 0.0000 0.000 212s PrivateWages_18 0.0000 0.000 212s PrivateWages_19 0.0000 0.000 212s PrivateWages_20 0.0000 0.000 212s PrivateWages_21 0.0000 0.000 212s PrivateWages_22 0.0000 0.000 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 0.000 0.00 212s Consumption_3 0.000 0.00 212s Consumption_4 0.000 0.00 212s Consumption_5 0.000 0.00 212s Consumption_6 0.000 0.00 212s Consumption_7 0.000 0.00 212s Consumption_8 0.000 0.00 212s Consumption_9 0.000 0.00 212s Consumption_10 0.000 0.00 212s Consumption_11 0.000 0.00 212s Consumption_12 0.000 0.00 212s Consumption_13 0.000 0.00 212s Consumption_14 0.000 0.00 212s Consumption_15 0.000 0.00 212s Consumption_16 0.000 0.00 212s Consumption_17 0.000 0.00 212s Consumption_18 0.000 0.00 212s Consumption_19 0.000 0.00 212s Consumption_20 0.000 0.00 212s Consumption_21 0.000 0.00 212s Consumption_22 0.000 0.00 212s Investment_2 -0.848 -12.21 212s Investment_3 -0.590 -8.69 212s Investment_4 21.069 230.01 212s Investment_5 -24.862 -256.32 212s Investment_6 8.059 80.05 212s Investment_7 29.994 295.17 212s Investment_8 15.463 160.46 212s Investment_9 -12.507 -131.14 212s Investment_10 22.850 228.07 212s Investment_11 6.056 60.20 212s Investment_12 0.575 7.99 212s Investment_13 4.172 78.05 212s Investment_14 1.566 46.33 212s Investment_15 -1.936 -34.91 212s Investment_16 0.124 2.01 212s Investment_17 13.606 192.14 212s Investment_18 0.908 10.31 212s Investment_19 -44.385 -517.74 212s Investment_20 -10.505 -137.25 212s Investment_21 -14.834 -157.09 212s Investment_22 -13.975 -135.45 212s PrivateWages_2 0.000 0.00 212s PrivateWages_3 0.000 0.00 212s PrivateWages_4 0.000 0.00 212s PrivateWages_5 0.000 0.00 212s PrivateWages_6 0.000 0.00 212s PrivateWages_8 0.000 0.00 212s PrivateWages_9 0.000 0.00 212s PrivateWages_10 0.000 0.00 212s PrivateWages_11 0.000 0.00 212s PrivateWages_12 0.000 0.00 212s PrivateWages_13 0.000 0.00 212s PrivateWages_14 0.000 0.00 212s PrivateWages_15 0.000 0.00 212s PrivateWages_16 0.000 0.00 212s PrivateWages_17 0.000 0.00 212s PrivateWages_18 0.000 0.00 212s PrivateWages_19 0.000 0.00 212s PrivateWages_20 0.000 0.00 212s PrivateWages_21 0.000 0.00 212s PrivateWages_22 0.000 0.00 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 0.0000 0.00 0.00 212s Consumption_3 0.0000 0.00 0.00 212s Consumption_4 0.0000 0.00 0.00 212s Consumption_5 0.0000 0.00 0.00 212s Consumption_6 0.0000 0.00 0.00 212s Consumption_7 0.0000 0.00 0.00 212s Consumption_8 0.0000 0.00 0.00 212s Consumption_9 0.0000 0.00 0.00 212s Consumption_10 0.0000 0.00 0.00 212s Consumption_11 0.0000 0.00 0.00 212s Consumption_12 0.0000 0.00 0.00 212s Consumption_13 0.0000 0.00 0.00 212s Consumption_14 0.0000 0.00 0.00 212s Consumption_15 0.0000 0.00 0.00 212s Consumption_16 0.0000 0.00 0.00 212s Consumption_17 0.0000 0.00 0.00 212s Consumption_18 0.0000 0.00 0.00 212s Consumption_19 0.0000 0.00 0.00 212s Consumption_20 0.0000 0.00 0.00 212s Consumption_21 0.0000 0.00 0.00 212s Consumption_22 0.0000 0.00 0.00 212s Investment_2 0.0000 0.00 0.00 212s Investment_3 0.0000 0.00 0.00 212s Investment_4 0.0000 0.00 0.00 212s Investment_5 0.0000 0.00 0.00 212s Investment_6 0.0000 0.00 0.00 212s Investment_7 0.0000 0.00 0.00 212s Investment_8 0.0000 0.00 0.00 212s Investment_9 0.0000 0.00 0.00 212s Investment_10 0.0000 0.00 0.00 212s Investment_11 0.0000 0.00 0.00 212s Investment_12 0.0000 0.00 0.00 212s Investment_13 0.0000 0.00 0.00 212s Investment_14 0.0000 0.00 0.00 212s Investment_15 0.0000 0.00 0.00 212s Investment_16 0.0000 0.00 0.00 212s Investment_17 0.0000 0.00 0.00 212s Investment_18 0.0000 0.00 0.00 212s Investment_19 0.0000 0.00 0.00 212s Investment_20 0.0000 0.00 0.00 212s Investment_21 0.0000 0.00 0.00 212s Investment_22 0.0000 0.00 0.00 212s PrivateWages_2 -1.3389 -61.06 -60.12 212s PrivateWages_3 0.2462 12.33 11.23 212s PrivateWages_4 1.1255 64.38 56.39 212s PrivateWages_5 -0.1959 -11.18 -11.20 212s PrivateWages_6 -0.5284 -32.23 -30.17 212s PrivateWages_8 -0.7909 -50.94 -50.62 212s PrivateWages_9 0.2819 18.18 18.15 212s PrivateWages_10 1.1384 76.28 73.43 212s PrivateWages_11 -0.1904 -11.65 -12.76 212s PrivateWages_12 0.5813 31.04 35.58 212s PrivateWages_13 0.1206 5.34 6.44 212s PrivateWages_14 0.4773 21.53 21.14 212s PrivateWages_15 0.3035 15.09 13.69 212s PrivateWages_16 0.0284 1.55 1.41 212s PrivateWages_17 -0.8517 -53.40 -46.33 212s PrivateWages_18 0.9908 64.40 62.12 212s PrivateWages_19 -0.4597 -28.00 -29.88 212s PrivateWages_20 -0.3819 -26.54 -23.26 212s PrivateWages_21 -1.1062 -83.74 -76.88 212s PrivateWages_22 0.5501 48.63 41.64 212s PrivateWages_trend 212s Consumption_2 0.000 212s Consumption_3 0.000 212s Consumption_4 0.000 212s Consumption_5 0.000 212s Consumption_6 0.000 212s Consumption_7 0.000 212s Consumption_8 0.000 212s Consumption_9 0.000 212s Consumption_10 0.000 212s Consumption_11 0.000 212s Consumption_12 0.000 212s Consumption_13 0.000 212s Consumption_14 0.000 212s Consumption_15 0.000 212s Consumption_16 0.000 212s Consumption_17 0.000 212s Consumption_18 0.000 212s Consumption_19 0.000 212s Consumption_20 0.000 212s Consumption_21 0.000 212s Consumption_22 0.000 212s Investment_2 0.000 212s Investment_3 0.000 212s Investment_4 0.000 212s Investment_5 0.000 212s Investment_6 0.000 212s Investment_7 0.000 212s Investment_8 0.000 212s Investment_9 0.000 212s Investment_10 0.000 212s Investment_11 0.000 212s Investment_12 0.000 212s Investment_13 0.000 212s Investment_14 0.000 212s Investment_15 0.000 212s Investment_16 0.000 212s Investment_17 0.000 212s Investment_18 0.000 212s Investment_19 0.000 212s Investment_20 0.000 212s Investment_21 0.000 212s Investment_22 0.000 212s PrivateWages_2 13.389 212s PrivateWages_3 -2.216 212s PrivateWages_4 -9.004 212s PrivateWages_5 1.371 212s PrivateWages_6 3.170 212s PrivateWages_8 3.164 212s PrivateWages_9 -0.846 212s PrivateWages_10 -2.277 212s PrivateWages_11 0.190 212s PrivateWages_12 0.000 212s PrivateWages_13 0.121 212s PrivateWages_14 0.955 212s PrivateWages_15 0.911 212s PrivateWages_16 0.114 212s PrivateWages_17 -4.258 212s PrivateWages_18 5.945 212s PrivateWages_19 -3.218 212s PrivateWages_20 -3.055 212s PrivateWages_21 -9.956 212s PrivateWages_22 5.501 212s [1] TRUE 212s > Bread 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_(Intercept) 100.0401 0.0296 212s Consumption_corpProf 0.0296 0.4904 212s Consumption_corpProfLag -1.0438 -0.3107 212s Consumption_wages -1.9405 -0.0777 212s Investment_(Intercept) 0.0000 0.0000 212s Investment_corpProf 0.0000 0.0000 212s Investment_corpProfLag 0.0000 0.0000 212s Investment_capitalLag 0.0000 0.0000 212s PrivateWages_(Intercept) 0.0000 0.0000 212s PrivateWages_gnp 0.0000 0.0000 212s PrivateWages_gnpLag 0.0000 0.0000 212s PrivateWages_trend 0.0000 0.0000 212s Consumption_corpProfLag Consumption_wages 212s Consumption_(Intercept) -1.0438 -1.9405 212s Consumption_corpProf -0.3107 -0.0777 212s Consumption_corpProfLag 0.4844 -0.0396 212s Consumption_wages -0.0396 0.0941 212s Investment_(Intercept) 0.0000 0.0000 212s Investment_corpProf 0.0000 0.0000 212s Investment_corpProfLag 0.0000 0.0000 212s Investment_capitalLag 0.0000 0.0000 212s PrivateWages_(Intercept) 0.0000 0.0000 212s PrivateWages_gnp 0.0000 0.0000 212s PrivateWages_gnpLag 0.0000 0.0000 212s PrivateWages_trend 0.0000 0.0000 212s Investment_(Intercept) Investment_corpProf 212s Consumption_(Intercept) 0.00 0.0000 212s Consumption_corpProf 0.00 0.0000 212s Consumption_corpProfLag 0.00 0.0000 212s Consumption_wages 0.00 0.0000 212s Investment_(Intercept) 1817.57 -17.6857 212s Investment_corpProf -17.69 0.5738 212s Investment_corpProfLag 14.44 -0.4928 212s Investment_capitalLag -8.74 0.0801 212s PrivateWages_(Intercept) 0.00 0.0000 212s PrivateWages_gnp 0.00 0.0000 212s PrivateWages_gnpLag 0.00 0.0000 212s PrivateWages_trend 0.00 0.0000 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_(Intercept) 0.0000 0.0000 212s Consumption_corpProf 0.0000 0.0000 212s Consumption_corpProfLag 0.0000 0.0000 212s Consumption_wages 0.0000 0.0000 212s Investment_(Intercept) 14.4412 -8.7403 212s Investment_corpProf -0.4928 0.0801 212s Investment_corpProfLag 0.6190 -0.0811 212s Investment_capitalLag -0.0811 0.0435 212s PrivateWages_(Intercept) 0.0000 0.0000 212s PrivateWages_gnp 0.0000 0.0000 212s PrivateWages_gnpLag 0.0000 0.0000 212s PrivateWages_trend 0.0000 0.0000 212s PrivateWages_(Intercept) PrivateWages_gnp 212s Consumption_(Intercept) 0.000 0.000 212s Consumption_corpProf 0.000 0.000 212s Consumption_corpProfLag 0.000 0.000 212s Consumption_wages 0.000 0.000 212s Investment_(Intercept) 0.000 0.000 212s Investment_corpProf 0.000 0.000 212s Investment_corpProfLag 0.000 0.000 212s Investment_capitalLag 0.000 0.000 212s PrivateWages_(Intercept) 174.627 -0.658 212s PrivateWages_gnp -0.658 0.112 212s PrivateWages_gnpLag -2.295 -0.104 212s PrivateWages_trend 2.155 -0.030 212s PrivateWages_gnpLag PrivateWages_trend 212s Consumption_(Intercept) 0.00000 0.00000 212s Consumption_corpProf 0.00000 0.00000 212s Consumption_corpProfLag 0.00000 0.00000 212s Consumption_wages 0.00000 0.00000 212s Investment_(Intercept) 0.00000 0.00000 212s Investment_corpProf 0.00000 0.00000 212s Investment_corpProfLag 0.00000 0.00000 212s Investment_capitalLag 0.00000 0.00000 212s PrivateWages_(Intercept) -2.29451 2.15506 212s PrivateWages_gnp -0.10426 -0.03004 212s PrivateWages_gnpLag 0.14761 -0.00667 212s PrivateWages_trend -0.00667 0.11527 212s > 212s > # 2SLS 212s > summary 212s 212s systemfit results 212s method: 2SLS 212s 212s N DF SSR detRCov OLS-R2 McElroy-R2 212s system 60 48 53.4 0.274 0.973 0.992 212s 212s N DF SSR MSE RMSE R2 Adj R2 212s Consumption 20 16 20.67 1.292 1.14 0.978 0.974 212s Investment 20 16 23.02 1.438 1.20 0.901 0.883 212s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 212s 212s The covariance matrix of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.034 0.309 -0.383 212s Investment 0.309 1.151 0.202 212s PrivateWages -0.383 0.202 0.487 212s 212s The correlations of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.000 0.284 -0.540 212s Investment 0.284 1.000 0.269 212s PrivateWages -0.540 0.269 1.000 212s 212s 212s 2SLS estimates for 'Consumption' (equation 1) 212s Model Formula: consump ~ corpProf + corpProfLag + wages 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 16.5093 1.3121 12.58 1.0e-09 *** 212s corpProf 0.0219 0.1159 0.19 0.85 212s corpProfLag 0.1931 0.1071 1.80 0.09 . 212s wages 0.8174 0.0408 20.05 9.2e-13 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.137 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 20.671 MSE: 1.292 Root MSE: 1.137 212s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.974 212s 212s 212s 2SLS estimates for 'Investment' (equation 2) 212s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 17.843 6.850 2.60 0.01915 * 212s corpProf 0.217 0.155 1.40 0.18106 212s corpProfLag 0.542 0.148 3.65 0.00216 ** 212s capitalLag -0.145 0.033 -4.41 0.00044 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.199 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 212s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 212s 212s 212s 2SLS estimates for 'PrivateWages' (equation 3) 212s Model Formula: privWage ~ gnp + gnpLag + trend 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 1.3431 1.1772 1.14 0.27070 212s gnp 0.4438 0.0358 12.39 1.3e-09 *** 212s gnpLag 0.1447 0.0389 3.72 0.00185 ** 212s trend 0.1238 0.0306 4.05 0.00093 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 0.78 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 212s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 212s 212s > residuals 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 -0.383 -1.0104 -1.3401 212s 3 -0.593 0.2478 0.2378 212s 4 -1.219 1.0621 1.1117 212s 5 -0.130 -1.4104 -0.1954 212s 6 0.354 0.4328 -0.5355 212s 7 NA NA NA 212s 8 1.551 1.0463 -0.7908 212s 9 1.440 0.0674 0.2831 212s 10 -0.286 1.7698 1.1353 212s 11 -0.453 -0.5912 -0.1765 212s 12 -0.994 -0.6318 0.6007 212s 13 -1.300 -0.6983 0.1443 212s 14 0.521 0.9724 0.4826 212s 15 -0.157 -0.1827 0.3016 212s 16 -0.014 0.1167 0.0261 212s 17 1.974 1.6266 -0.8614 212s 18 -0.576 -0.0525 0.9927 212s 19 -0.203 -3.0656 -0.4446 212s 20 1.342 0.1393 -0.3914 212s 21 1.039 -0.1305 -1.1115 212s 22 -1.912 0.2922 0.5312 212s > fitted 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 42.3 0.810 26.8 212s 3 45.6 1.652 29.1 212s 4 50.4 4.138 33.0 212s 5 50.7 4.410 34.1 212s 6 52.2 4.667 35.9 212s 7 NA NA NA 212s 8 54.6 3.154 38.7 212s 9 55.9 2.933 38.9 212s 10 58.1 3.330 40.2 212s 11 55.5 1.591 38.1 212s 12 51.9 -2.768 33.9 212s 13 46.9 -5.502 28.9 212s 14 46.0 -6.072 28.0 212s 15 48.9 -2.817 30.3 212s 16 51.3 -1.417 33.2 212s 17 55.7 0.473 37.7 212s 18 59.3 2.053 40.0 212s 19 57.7 1.166 38.6 212s 20 60.3 1.161 42.0 212s 21 64.0 3.431 46.1 212s 22 71.6 4.608 52.8 212s > predict 212s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 212s 1 NA NA NA NA 212s 2 42.3 0.473 41.3 43.3 212s 3 45.6 0.573 44.4 46.8 212s 4 50.4 0.366 49.6 51.2 212s 5 50.7 0.423 49.8 51.6 212s 6 52.2 0.426 51.3 53.1 212s 7 NA NA NA NA 212s 8 54.6 0.347 53.9 55.4 212s 9 55.9 0.384 55.0 56.7 212s 10 58.1 0.395 57.2 58.9 212s 11 55.5 0.729 53.9 57.0 212s 12 51.9 0.594 50.6 53.2 212s 13 46.9 0.752 45.3 48.5 212s 14 46.0 0.616 44.7 47.3 212s 15 48.9 0.373 48.1 49.6 212s 16 51.3 0.331 50.6 52.0 212s 17 55.7 0.403 54.9 56.6 212s 18 59.3 0.326 58.6 60.0 212s 19 57.7 0.411 56.8 58.6 212s 20 60.3 0.472 59.3 61.3 212s 21 64.0 0.443 63.0 64.9 212s 22 71.6 0.683 70.2 73.1 212s Investment.pred Investment.se.fit Investment.lwr Investment.upr 212s 1 NA NA NA NA 212s 2 0.810 0.786 -0.8569 2.48 212s 3 1.652 0.541 0.5056 2.80 212s 4 4.138 0.511 3.0552 5.22 212s 5 4.410 0.421 3.5172 5.30 212s 6 4.667 0.395 3.8294 5.51 212s 7 NA NA NA NA 212s 8 3.154 0.327 2.4602 3.85 212s 9 2.933 0.489 1.8967 3.97 212s 10 3.330 0.537 2.1915 4.47 212s 11 1.591 0.786 -0.0748 3.26 212s 12 -2.768 0.615 -4.0716 -1.46 212s 13 -5.502 0.787 -7.1696 -3.83 212s 14 -6.072 0.842 -7.8568 -4.29 212s 15 -2.817 0.397 -3.6591 -1.98 212s 16 -1.417 0.343 -2.1436 -0.69 212s 17 0.473 0.457 -0.4954 1.44 212s 18 2.053 0.286 1.4471 2.66 212s 19 1.166 0.430 0.2549 2.08 212s 20 1.161 0.515 0.0698 2.25 212s 21 3.431 0.426 2.5282 4.33 212s 22 4.608 0.606 3.3223 5.89 212s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 212s 1 NA NA NA NA 212s 2 26.8 0.328 26.1 27.5 212s 3 29.1 0.340 28.3 29.8 212s 4 33.0 0.360 32.2 33.8 212s 5 34.1 0.258 33.5 34.6 212s 6 35.9 0.266 35.4 36.5 212s 7 NA NA NA NA 212s 8 38.7 0.262 38.1 39.2 212s 9 38.9 0.250 38.4 39.4 212s 10 40.2 0.240 39.7 40.7 212s 11 38.1 0.355 37.3 38.8 212s 12 33.9 0.382 33.1 34.7 212s 13 28.9 0.456 27.9 29.8 212s 14 28.0 0.348 27.3 28.8 212s 15 30.3 0.339 29.6 31.0 212s 16 33.2 0.284 32.6 33.8 212s 17 37.7 0.293 37.0 38.3 212s 18 40.0 0.218 39.5 40.5 212s 19 38.6 0.358 37.9 39.4 212s 20 42.0 0.307 41.3 42.6 212s 21 46.1 0.310 45.5 46.8 212s 22 52.8 0.496 51.7 53.8 212s > model.frame 212s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 212s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 212s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 212s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 212s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 212s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 212s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 212s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 212s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 212s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 212s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 212s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 212s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 212s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 212s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 212s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 212s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 212s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 212s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 212s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 212s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 212s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 212s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 212s trend 212s 1 -11 212s 2 -10 212s 3 -9 212s 4 -8 212s 5 -7 212s 6 -6 212s 7 -5 212s 8 -4 212s 9 -3 212s 10 -2 212s 11 -1 212s 12 0 212s 13 1 212s 14 2 212s 15 3 212s 16 4 212s 17 5 212s 18 6 212s 19 7 212s 20 8 212s 21 9 212s 22 10 212s > Frames of instrumental variables 212s govExp taxes govWage trend capitalLag corpProfLag gnpLag 212s 1 2.4 3.4 2.2 -11 180 NA NA 212s 2 3.9 7.7 2.7 -10 183 12.7 44.9 212s 3 3.2 3.9 2.9 -9 183 12.4 45.6 212s 4 2.8 4.7 2.9 -8 184 16.9 50.1 212s 5 3.5 3.8 3.1 -7 190 18.4 57.2 212s 6 3.3 5.5 3.2 -6 193 19.4 57.1 212s 7 3.3 7.0 3.3 -5 198 20.1 NA 212s 8 4.0 6.7 3.6 -4 203 19.6 64.0 212s 9 4.2 4.2 3.7 -3 208 19.8 64.4 212s 10 4.1 4.0 4.0 -2 211 21.1 64.5 212s 11 5.2 7.7 4.2 -1 216 21.7 67.0 212s 12 5.9 7.5 4.8 0 217 15.6 61.2 212s 13 4.9 8.3 5.3 1 213 11.4 53.4 212s 14 3.7 5.4 5.6 2 207 7.0 44.3 212s 15 4.0 6.8 6.0 3 202 11.2 45.1 212s 16 4.4 7.2 6.1 4 199 12.3 49.7 212s 17 2.9 8.3 7.4 5 198 14.0 54.4 212s 18 4.3 6.7 6.7 6 200 17.6 62.7 212s 19 5.3 7.4 7.7 7 202 17.3 65.0 212s 20 6.6 8.9 7.8 8 200 15.3 60.9 212s 21 7.4 9.6 8.0 9 201 19.0 69.5 212s 22 13.8 11.6 8.5 10 204 21.1 75.7 212s govExp taxes govWage trend capitalLag corpProfLag gnpLag 212s 1 2.4 3.4 2.2 -11 180 NA NA 212s 2 3.9 7.7 2.7 -10 183 12.7 44.9 212s 3 3.2 3.9 2.9 -9 183 12.4 45.6 212s 4 2.8 4.7 2.9 -8 184 16.9 50.1 212s 5 3.5 3.8 3.1 -7 190 18.4 57.2 212s 6 3.3 5.5 3.2 -6 193 19.4 57.1 212s 7 3.3 7.0 3.3 -5 198 20.1 NA 212s 8 4.0 6.7 3.6 -4 203 19.6 64.0 212s 9 4.2 4.2 3.7 -3 208 19.8 64.4 212s 10 4.1 4.0 4.0 -2 211 21.1 64.5 212s 11 5.2 7.7 4.2 -1 216 21.7 67.0 212s 12 5.9 7.5 4.8 0 217 15.6 61.2 212s 13 4.9 8.3 5.3 1 213 11.4 53.4 212s 14 3.7 5.4 5.6 2 207 7.0 44.3 212s 15 4.0 6.8 6.0 3 202 11.2 45.1 212s 16 4.4 7.2 6.1 4 199 12.3 49.7 212s 17 2.9 8.3 7.4 5 198 14.0 54.4 212s 18 4.3 6.7 6.7 6 200 17.6 62.7 212s 19 5.3 7.4 7.7 7 202 17.3 65.0 212s 20 6.6 8.9 7.8 8 200 15.3 60.9 212s 21 7.4 9.6 8.0 9 201 19.0 69.5 212s 22 13.8 11.6 8.5 10 204 21.1 75.7 212s govExp taxes govWage trend capitalLag corpProfLag gnpLag 212s 1 2.4 3.4 2.2 -11 180 NA NA 212s 2 3.9 7.7 2.7 -10 183 12.7 44.9 212s 3 3.2 3.9 2.9 -9 183 12.4 45.6 212s 4 2.8 4.7 2.9 -8 184 16.9 50.1 212s 5 3.5 3.8 3.1 -7 190 18.4 57.2 212s 6 3.3 5.5 3.2 -6 193 19.4 57.1 212s 7 3.3 7.0 3.3 -5 198 20.1 NA 212s 8 4.0 6.7 3.6 -4 203 19.6 64.0 212s 9 4.2 4.2 3.7 -3 208 19.8 64.4 212s 10 4.1 4.0 4.0 -2 211 21.1 64.5 212s 11 5.2 7.7 4.2 -1 216 21.7 67.0 212s 12 5.9 7.5 4.8 0 217 15.6 61.2 212s 13 4.9 8.3 5.3 1 213 11.4 53.4 212s 14 3.7 5.4 5.6 2 207 7.0 44.3 212s 15 4.0 6.8 6.0 3 202 11.2 45.1 212s 16 4.4 7.2 6.1 4 199 12.3 49.7 212s 17 2.9 8.3 7.4 5 198 14.0 54.4 212s 18 4.3 6.7 6.7 6 200 17.6 62.7 212s 19 5.3 7.4 7.7 7 202 17.3 65.0 212s 20 6.6 8.9 7.8 8 200 15.3 60.9 212s 21 7.4 9.6 8.0 9 201 19.0 69.5 212s 22 13.8 11.6 8.5 10 204 21.1 75.7 212s > model.matrix 212s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 212s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 212s [3] "Numeric: lengths (744, 720) differ" 212s > matrix of instrumental variables 212s Consumption_(Intercept) Consumption_govExp Consumption_taxes 212s Consumption_2 1 3.9 7.7 212s Consumption_3 1 3.2 3.9 212s Consumption_4 1 2.8 4.7 212s Consumption_5 1 3.5 3.8 212s Consumption_6 1 3.3 5.5 212s Consumption_8 1 4.0 6.7 212s Consumption_9 1 4.2 4.2 212s Consumption_10 1 4.1 4.0 212s Consumption_11 1 5.2 7.7 212s Consumption_12 1 5.9 7.5 212s Consumption_13 1 4.9 8.3 212s Consumption_14 1 3.7 5.4 212s Consumption_15 1 4.0 6.8 212s Consumption_16 1 4.4 7.2 212s Consumption_17 1 2.9 8.3 212s Consumption_18 1 4.3 6.7 212s Consumption_19 1 5.3 7.4 212s Consumption_20 1 6.6 8.9 212s Consumption_21 1 7.4 9.6 212s Consumption_22 1 13.8 11.6 212s Investment_2 0 0.0 0.0 212s Investment_3 0 0.0 0.0 212s Investment_4 0 0.0 0.0 212s Investment_5 0 0.0 0.0 212s Investment_6 0 0.0 0.0 212s Investment_8 0 0.0 0.0 212s Investment_9 0 0.0 0.0 212s Investment_10 0 0.0 0.0 212s Investment_11 0 0.0 0.0 212s Investment_12 0 0.0 0.0 212s Investment_13 0 0.0 0.0 212s Investment_14 0 0.0 0.0 212s Investment_15 0 0.0 0.0 212s Investment_16 0 0.0 0.0 212s Investment_17 0 0.0 0.0 212s Investment_18 0 0.0 0.0 212s Investment_19 0 0.0 0.0 212s Investment_20 0 0.0 0.0 212s Investment_21 0 0.0 0.0 212s Investment_22 0 0.0 0.0 212s PrivateWages_2 0 0.0 0.0 212s PrivateWages_3 0 0.0 0.0 212s PrivateWages_4 0 0.0 0.0 212s PrivateWages_5 0 0.0 0.0 212s PrivateWages_6 0 0.0 0.0 212s PrivateWages_8 0 0.0 0.0 212s PrivateWages_9 0 0.0 0.0 212s PrivateWages_10 0 0.0 0.0 212s PrivateWages_11 0 0.0 0.0 212s PrivateWages_12 0 0.0 0.0 212s PrivateWages_13 0 0.0 0.0 212s PrivateWages_14 0 0.0 0.0 212s PrivateWages_15 0 0.0 0.0 212s PrivateWages_16 0 0.0 0.0 212s PrivateWages_17 0 0.0 0.0 212s PrivateWages_18 0 0.0 0.0 212s PrivateWages_19 0 0.0 0.0 212s PrivateWages_20 0 0.0 0.0 212s PrivateWages_21 0 0.0 0.0 212s PrivateWages_22 0 0.0 0.0 212s Consumption_govWage Consumption_trend Consumption_capitalLag 212s Consumption_2 2.7 -10 183 212s Consumption_3 2.9 -9 183 212s Consumption_4 2.9 -8 184 212s Consumption_5 3.1 -7 190 212s Consumption_6 3.2 -6 193 212s Consumption_8 3.6 -4 203 212s Consumption_9 3.7 -3 208 212s Consumption_10 4.0 -2 211 212s Consumption_11 4.2 -1 216 212s Consumption_12 4.8 0 217 212s Consumption_13 5.3 1 213 212s Consumption_14 5.6 2 207 212s Consumption_15 6.0 3 202 212s Consumption_16 6.1 4 199 212s Consumption_17 7.4 5 198 212s Consumption_18 6.7 6 200 212s Consumption_19 7.7 7 202 212s Consumption_20 7.8 8 200 212s Consumption_21 8.0 9 201 212s Consumption_22 8.5 10 204 212s Investment_2 0.0 0 0 212s Investment_3 0.0 0 0 212s Investment_4 0.0 0 0 212s Investment_5 0.0 0 0 212s Investment_6 0.0 0 0 212s Investment_8 0.0 0 0 212s Investment_9 0.0 0 0 212s Investment_10 0.0 0 0 212s Investment_11 0.0 0 0 212s Investment_12 0.0 0 0 212s Investment_13 0.0 0 0 212s Investment_14 0.0 0 0 212s Investment_15 0.0 0 0 212s Investment_16 0.0 0 0 212s Investment_17 0.0 0 0 212s Investment_18 0.0 0 0 212s Investment_19 0.0 0 0 212s Investment_20 0.0 0 0 212s Investment_21 0.0 0 0 212s Investment_22 0.0 0 0 212s PrivateWages_2 0.0 0 0 212s PrivateWages_3 0.0 0 0 212s PrivateWages_4 0.0 0 0 212s PrivateWages_5 0.0 0 0 212s PrivateWages_6 0.0 0 0 212s PrivateWages_8 0.0 0 0 212s PrivateWages_9 0.0 0 0 212s PrivateWages_10 0.0 0 0 212s PrivateWages_11 0.0 0 0 212s PrivateWages_12 0.0 0 0 212s PrivateWages_13 0.0 0 0 212s PrivateWages_14 0.0 0 0 212s PrivateWages_15 0.0 0 0 212s PrivateWages_16 0.0 0 0 212s PrivateWages_17 0.0 0 0 212s PrivateWages_18 0.0 0 0 212s PrivateWages_19 0.0 0 0 212s PrivateWages_20 0.0 0 0 212s PrivateWages_21 0.0 0 0 212s PrivateWages_22 0.0 0 0 212s Consumption_corpProfLag Consumption_gnpLag 212s Consumption_2 12.7 44.9 212s Consumption_3 12.4 45.6 212s Consumption_4 16.9 50.1 212s Consumption_5 18.4 57.2 212s Consumption_6 19.4 57.1 212s Consumption_8 19.6 64.0 212s Consumption_9 19.8 64.4 212s Consumption_10 21.1 64.5 212s Consumption_11 21.7 67.0 212s Consumption_12 15.6 61.2 212s Consumption_13 11.4 53.4 212s Consumption_14 7.0 44.3 212s Consumption_15 11.2 45.1 212s Consumption_16 12.3 49.7 212s Consumption_17 14.0 54.4 212s Consumption_18 17.6 62.7 212s Consumption_19 17.3 65.0 212s Consumption_20 15.3 60.9 212s Consumption_21 19.0 69.5 212s Consumption_22 21.1 75.7 212s Investment_2 0.0 0.0 212s Investment_3 0.0 0.0 212s Investment_4 0.0 0.0 212s Investment_5 0.0 0.0 212s Investment_6 0.0 0.0 212s Investment_8 0.0 0.0 212s Investment_9 0.0 0.0 212s Investment_10 0.0 0.0 212s Investment_11 0.0 0.0 212s Investment_12 0.0 0.0 212s Investment_13 0.0 0.0 212s Investment_14 0.0 0.0 212s Investment_15 0.0 0.0 212s Investment_16 0.0 0.0 212s Investment_17 0.0 0.0 212s Investment_18 0.0 0.0 212s Investment_19 0.0 0.0 212s Investment_20 0.0 0.0 212s Investment_21 0.0 0.0 212s Investment_22 0.0 0.0 212s PrivateWages_2 0.0 0.0 212s PrivateWages_3 0.0 0.0 212s PrivateWages_4 0.0 0.0 212s PrivateWages_5 0.0 0.0 212s PrivateWages_6 0.0 0.0 212s PrivateWages_8 0.0 0.0 212s PrivateWages_9 0.0 0.0 212s PrivateWages_10 0.0 0.0 212s PrivateWages_11 0.0 0.0 212s PrivateWages_12 0.0 0.0 212s PrivateWages_13 0.0 0.0 212s PrivateWages_14 0.0 0.0 212s PrivateWages_15 0.0 0.0 212s PrivateWages_16 0.0 0.0 212s PrivateWages_17 0.0 0.0 212s PrivateWages_18 0.0 0.0 212s PrivateWages_19 0.0 0.0 212s PrivateWages_20 0.0 0.0 212s PrivateWages_21 0.0 0.0 212s PrivateWages_22 0.0 0.0 212s Investment_(Intercept) Investment_govExp Investment_taxes 212s Consumption_2 0 0.0 0.0 212s Consumption_3 0 0.0 0.0 212s Consumption_4 0 0.0 0.0 212s Consumption_5 0 0.0 0.0 212s Consumption_6 0 0.0 0.0 212s Consumption_8 0 0.0 0.0 212s Consumption_9 0 0.0 0.0 212s Consumption_10 0 0.0 0.0 212s Consumption_11 0 0.0 0.0 212s Consumption_12 0 0.0 0.0 212s Consumption_13 0 0.0 0.0 212s Consumption_14 0 0.0 0.0 212s Consumption_15 0 0.0 0.0 212s Consumption_16 0 0.0 0.0 212s Consumption_17 0 0.0 0.0 212s Consumption_18 0 0.0 0.0 212s Consumption_19 0 0.0 0.0 212s Consumption_20 0 0.0 0.0 212s Consumption_21 0 0.0 0.0 212s Consumption_22 0 0.0 0.0 212s Investment_2 1 3.9 7.7 212s Investment_3 1 3.2 3.9 212s Investment_4 1 2.8 4.7 212s Investment_5 1 3.5 3.8 212s Investment_6 1 3.3 5.5 212s Investment_8 1 4.0 6.7 212s Investment_9 1 4.2 4.2 212s Investment_10 1 4.1 4.0 212s Investment_11 1 5.2 7.7 212s Investment_12 1 5.9 7.5 212s Investment_13 1 4.9 8.3 212s Investment_14 1 3.7 5.4 212s Investment_15 1 4.0 6.8 212s Investment_16 1 4.4 7.2 212s Investment_17 1 2.9 8.3 212s Investment_18 1 4.3 6.7 212s Investment_19 1 5.3 7.4 212s Investment_20 1 6.6 8.9 212s Investment_21 1 7.4 9.6 212s Investment_22 1 13.8 11.6 212s PrivateWages_2 0 0.0 0.0 212s PrivateWages_3 0 0.0 0.0 212s PrivateWages_4 0 0.0 0.0 212s PrivateWages_5 0 0.0 0.0 212s PrivateWages_6 0 0.0 0.0 212s PrivateWages_8 0 0.0 0.0 212s PrivateWages_9 0 0.0 0.0 212s PrivateWages_10 0 0.0 0.0 212s PrivateWages_11 0 0.0 0.0 212s PrivateWages_12 0 0.0 0.0 212s PrivateWages_13 0 0.0 0.0 212s PrivateWages_14 0 0.0 0.0 212s PrivateWages_15 0 0.0 0.0 212s PrivateWages_16 0 0.0 0.0 212s PrivateWages_17 0 0.0 0.0 212s PrivateWages_18 0 0.0 0.0 212s PrivateWages_19 0 0.0 0.0 212s PrivateWages_20 0 0.0 0.0 212s PrivateWages_21 0 0.0 0.0 212s PrivateWages_22 0 0.0 0.0 212s Investment_govWage Investment_trend Investment_capitalLag 212s Consumption_2 0.0 0 0 212s Consumption_3 0.0 0 0 212s Consumption_4 0.0 0 0 212s Consumption_5 0.0 0 0 212s Consumption_6 0.0 0 0 212s Consumption_8 0.0 0 0 212s Consumption_9 0.0 0 0 212s Consumption_10 0.0 0 0 212s Consumption_11 0.0 0 0 212s Consumption_12 0.0 0 0 212s Consumption_13 0.0 0 0 212s Consumption_14 0.0 0 0 212s Consumption_15 0.0 0 0 212s Consumption_16 0.0 0 0 212s Consumption_17 0.0 0 0 212s Consumption_18 0.0 0 0 212s Consumption_19 0.0 0 0 212s Consumption_20 0.0 0 0 212s Consumption_21 0.0 0 0 212s Consumption_22 0.0 0 0 212s Investment_2 2.7 -10 183 212s Investment_3 2.9 -9 183 212s Investment_4 2.9 -8 184 212s Investment_5 3.1 -7 190 212s Investment_6 3.2 -6 193 212s Investment_8 3.6 -4 203 212s Investment_9 3.7 -3 208 212s Investment_10 4.0 -2 211 212s Investment_11 4.2 -1 216 212s Investment_12 4.8 0 217 212s Investment_13 5.3 1 213 212s Investment_14 5.6 2 207 212s Investment_15 6.0 3 202 212s Investment_16 6.1 4 199 212s Investment_17 7.4 5 198 212s Investment_18 6.7 6 200 212s Investment_19 7.7 7 202 212s Investment_20 7.8 8 200 212s Investment_21 8.0 9 201 212s Investment_22 8.5 10 204 212s PrivateWages_2 0.0 0 0 212s PrivateWages_3 0.0 0 0 212s PrivateWages_4 0.0 0 0 212s PrivateWages_5 0.0 0 0 212s PrivateWages_6 0.0 0 0 212s PrivateWages_8 0.0 0 0 212s PrivateWages_9 0.0 0 0 212s PrivateWages_10 0.0 0 0 212s PrivateWages_11 0.0 0 0 212s PrivateWages_12 0.0 0 0 212s PrivateWages_13 0.0 0 0 212s PrivateWages_14 0.0 0 0 212s PrivateWages_15 0.0 0 0 212s PrivateWages_16 0.0 0 0 212s PrivateWages_17 0.0 0 0 212s PrivateWages_18 0.0 0 0 212s PrivateWages_19 0.0 0 0 212s PrivateWages_20 0.0 0 0 212s PrivateWages_21 0.0 0 0 212s PrivateWages_22 0.0 0 0 212s Investment_corpProfLag Investment_gnpLag 212s Consumption_2 0.0 0.0 212s Consumption_3 0.0 0.0 212s Consumption_4 0.0 0.0 212s Consumption_5 0.0 0.0 212s Consumption_6 0.0 0.0 212s Consumption_8 0.0 0.0 212s Consumption_9 0.0 0.0 212s Consumption_10 0.0 0.0 212s Consumption_11 0.0 0.0 212s Consumption_12 0.0 0.0 212s Consumption_13 0.0 0.0 212s Consumption_14 0.0 0.0 212s Consumption_15 0.0 0.0 212s Consumption_16 0.0 0.0 212s Consumption_17 0.0 0.0 212s Consumption_18 0.0 0.0 212s Consumption_19 0.0 0.0 212s Consumption_20 0.0 0.0 212s Consumption_21 0.0 0.0 212s Consumption_22 0.0 0.0 212s Investment_2 12.7 44.9 212s Investment_3 12.4 45.6 212s Investment_4 16.9 50.1 212s Investment_5 18.4 57.2 212s Investment_6 19.4 57.1 212s Investment_8 19.6 64.0 212s Investment_9 19.8 64.4 212s Investment_10 21.1 64.5 212s Investment_11 21.7 67.0 212s Investment_12 15.6 61.2 212s Investment_13 11.4 53.4 212s Investment_14 7.0 44.3 212s Investment_15 11.2 45.1 212s Investment_16 12.3 49.7 212s Investment_17 14.0 54.4 212s Investment_18 17.6 62.7 212s Investment_19 17.3 65.0 212s Investment_20 15.3 60.9 212s Investment_21 19.0 69.5 212s Investment_22 21.1 75.7 212s PrivateWages_2 0.0 0.0 212s PrivateWages_3 0.0 0.0 212s PrivateWages_4 0.0 0.0 212s PrivateWages_5 0.0 0.0 212s PrivateWages_6 0.0 0.0 212s PrivateWages_8 0.0 0.0 212s PrivateWages_9 0.0 0.0 212s PrivateWages_10 0.0 0.0 212s PrivateWages_11 0.0 0.0 212s PrivateWages_12 0.0 0.0 212s PrivateWages_13 0.0 0.0 212s PrivateWages_14 0.0 0.0 212s PrivateWages_15 0.0 0.0 212s PrivateWages_16 0.0 0.0 212s PrivateWages_17 0.0 0.0 212s PrivateWages_18 0.0 0.0 212s PrivateWages_19 0.0 0.0 212s PrivateWages_20 0.0 0.0 212s PrivateWages_21 0.0 0.0 212s PrivateWages_22 0.0 0.0 212s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 212s Consumption_2 0 0.0 0.0 212s Consumption_3 0 0.0 0.0 212s Consumption_4 0 0.0 0.0 212s Consumption_5 0 0.0 0.0 212s Consumption_6 0 0.0 0.0 212s Consumption_8 0 0.0 0.0 212s Consumption_9 0 0.0 0.0 212s Consumption_10 0 0.0 0.0 212s Consumption_11 0 0.0 0.0 212s Consumption_12 0 0.0 0.0 212s Consumption_13 0 0.0 0.0 212s Consumption_14 0 0.0 0.0 212s Consumption_15 0 0.0 0.0 212s Consumption_16 0 0.0 0.0 212s Consumption_17 0 0.0 0.0 212s Consumption_18 0 0.0 0.0 212s Consumption_19 0 0.0 0.0 212s Consumption_20 0 0.0 0.0 212s Consumption_21 0 0.0 0.0 212s Consumption_22 0 0.0 0.0 212s Investment_2 0 0.0 0.0 212s Investment_3 0 0.0 0.0 212s Investment_4 0 0.0 0.0 212s Investment_5 0 0.0 0.0 212s Investment_6 0 0.0 0.0 212s Investment_8 0 0.0 0.0 212s Investment_9 0 0.0 0.0 212s Investment_10 0 0.0 0.0 212s Investment_11 0 0.0 0.0 212s Investment_12 0 0.0 0.0 212s Investment_13 0 0.0 0.0 212s Investment_14 0 0.0 0.0 212s Investment_15 0 0.0 0.0 212s Investment_16 0 0.0 0.0 212s Investment_17 0 0.0 0.0 212s Investment_18 0 0.0 0.0 212s Investment_19 0 0.0 0.0 212s Investment_20 0 0.0 0.0 212s Investment_21 0 0.0 0.0 212s Investment_22 0 0.0 0.0 212s PrivateWages_2 1 3.9 7.7 212s PrivateWages_3 1 3.2 3.9 212s PrivateWages_4 1 2.8 4.7 212s PrivateWages_5 1 3.5 3.8 212s PrivateWages_6 1 3.3 5.5 212s PrivateWages_8 1 4.0 6.7 212s PrivateWages_9 1 4.2 4.2 212s PrivateWages_10 1 4.1 4.0 212s PrivateWages_11 1 5.2 7.7 212s PrivateWages_12 1 5.9 7.5 212s PrivateWages_13 1 4.9 8.3 212s PrivateWages_14 1 3.7 5.4 212s PrivateWages_15 1 4.0 6.8 212s PrivateWages_16 1 4.4 7.2 212s PrivateWages_17 1 2.9 8.3 212s PrivateWages_18 1 4.3 6.7 212s PrivateWages_19 1 5.3 7.4 212s PrivateWages_20 1 6.6 8.9 212s PrivateWages_21 1 7.4 9.6 212s PrivateWages_22 1 13.8 11.6 212s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 212s Consumption_2 0.0 0 0 212s Consumption_3 0.0 0 0 212s Consumption_4 0.0 0 0 212s Consumption_5 0.0 0 0 212s Consumption_6 0.0 0 0 212s Consumption_8 0.0 0 0 212s Consumption_9 0.0 0 0 212s Consumption_10 0.0 0 0 212s Consumption_11 0.0 0 0 212s Consumption_12 0.0 0 0 212s Consumption_13 0.0 0 0 212s Consumption_14 0.0 0 0 212s Consumption_15 0.0 0 0 212s Consumption_16 0.0 0 0 212s Consumption_17 0.0 0 0 212s Consumption_18 0.0 0 0 212s Consumption_19 0.0 0 0 212s Consumption_20 0.0 0 0 212s Consumption_21 0.0 0 0 212s Consumption_22 0.0 0 0 212s Investment_2 0.0 0 0 212s Investment_3 0.0 0 0 212s Investment_4 0.0 0 0 212s Investment_5 0.0 0 0 212s Investment_6 0.0 0 0 212s Investment_8 0.0 0 0 212s Investment_9 0.0 0 0 212s Investment_10 0.0 0 0 212s Investment_11 0.0 0 0 212s Investment_12 0.0 0 0 212s Investment_13 0.0 0 0 212s Investment_14 0.0 0 0 212s Investment_15 0.0 0 0 212s Investment_16 0.0 0 0 212s Investment_17 0.0 0 0 212s Investment_18 0.0 0 0 212s Investment_19 0.0 0 0 212s Investment_20 0.0 0 0 212s Investment_21 0.0 0 0 212s Investment_22 0.0 0 0 212s PrivateWages_2 2.7 -10 183 212s PrivateWages_3 2.9 -9 183 212s PrivateWages_4 2.9 -8 184 212s PrivateWages_5 3.1 -7 190 212s PrivateWages_6 3.2 -6 193 212s PrivateWages_8 3.6 -4 203 212s PrivateWages_9 3.7 -3 208 212s PrivateWages_10 4.0 -2 211 212s PrivateWages_11 4.2 -1 216 212s PrivateWages_12 4.8 0 217 212s PrivateWages_13 5.3 1 213 212s PrivateWages_14 5.6 2 207 212s PrivateWages_15 6.0 3 202 212s PrivateWages_16 6.1 4 199 212s PrivateWages_17 7.4 5 198 212s PrivateWages_18 6.7 6 200 212s PrivateWages_19 7.7 7 202 212s PrivateWages_20 7.8 8 200 212s PrivateWages_21 8.0 9 201 212s PrivateWages_22 8.5 10 204 212s PrivateWages_corpProfLag PrivateWages_gnpLag 212s Consumption_2 0.0 0.0 212s Consumption_3 0.0 0.0 212s Consumption_4 0.0 0.0 212s Consumption_5 0.0 0.0 212s Consumption_6 0.0 0.0 212s Consumption_8 0.0 0.0 212s Consumption_9 0.0 0.0 212s Consumption_10 0.0 0.0 212s Consumption_11 0.0 0.0 212s Consumption_12 0.0 0.0 212s Consumption_13 0.0 0.0 212s Consumption_14 0.0 0.0 212s Consumption_15 0.0 0.0 212s Consumption_16 0.0 0.0 212s Consumption_17 0.0 0.0 212s Consumption_18 0.0 0.0 212s Consumption_19 0.0 0.0 212s Consumption_20 0.0 0.0 212s Consumption_21 0.0 0.0 212s Consumption_22 0.0 0.0 212s Investment_2 0.0 0.0 212s Investment_3 0.0 0.0 212s Investment_4 0.0 0.0 212s Investment_5 0.0 0.0 212s Investment_6 0.0 0.0 212s Investment_8 0.0 0.0 212s Investment_9 0.0 0.0 212s Investment_10 0.0 0.0 212s Investment_11 0.0 0.0 212s Investment_12 0.0 0.0 212s Investment_13 0.0 0.0 212s Investment_14 0.0 0.0 212s Investment_15 0.0 0.0 212s Investment_16 0.0 0.0 212s Investment_17 0.0 0.0 212s Investment_18 0.0 0.0 212s Investment_19 0.0 0.0 212s Investment_20 0.0 0.0 212s Investment_21 0.0 0.0 212s Investment_22 0.0 0.0 212s PrivateWages_2 12.7 44.9 212s PrivateWages_3 12.4 45.6 212s PrivateWages_4 16.9 50.1 212s PrivateWages_5 18.4 57.2 212s PrivateWages_6 19.4 57.1 212s PrivateWages_8 19.6 64.0 212s PrivateWages_9 19.8 64.4 212s PrivateWages_10 21.1 64.5 212s PrivateWages_11 21.7 67.0 212s PrivateWages_12 15.6 61.2 212s PrivateWages_13 11.4 53.4 212s PrivateWages_14 7.0 44.3 212s PrivateWages_15 11.2 45.1 212s PrivateWages_16 12.3 49.7 212s PrivateWages_17 14.0 54.4 212s PrivateWages_18 17.6 62.7 212s PrivateWages_19 17.3 65.0 212s PrivateWages_20 15.3 60.9 212s PrivateWages_21 19.0 69.5 212s PrivateWages_22 21.1 75.7 212s > matrix of fitted regressors 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 1 12.96 212s Consumption_3 1 16.70 212s Consumption_4 1 19.14 212s Consumption_5 1 20.94 212s Consumption_6 1 19.47 212s Consumption_8 1 17.14 212s Consumption_9 1 19.49 212s Consumption_10 1 20.46 212s Consumption_11 1 16.85 212s Consumption_12 1 12.68 212s Consumption_13 1 8.92 212s Consumption_14 1 9.30 212s Consumption_15 1 12.79 212s Consumption_16 1 14.26 212s Consumption_17 1 14.75 212s Consumption_18 1 19.54 212s Consumption_19 1 19.36 212s Consumption_20 1 17.39 212s Consumption_21 1 20.10 212s Consumption_22 1 22.86 212s Investment_2 0 0.00 212s Investment_3 0 0.00 212s Investment_4 0 0.00 212s Investment_5 0 0.00 212s Investment_6 0 0.00 212s Investment_8 0 0.00 212s Investment_9 0 0.00 212s Investment_10 0 0.00 212s Investment_11 0 0.00 212s Investment_12 0 0.00 212s Investment_13 0 0.00 212s Investment_14 0 0.00 212s Investment_15 0 0.00 212s Investment_16 0 0.00 212s Investment_17 0 0.00 212s Investment_18 0 0.00 212s Investment_19 0 0.00 212s Investment_20 0 0.00 212s Investment_21 0 0.00 212s Investment_22 0 0.00 212s PrivateWages_2 0 0.00 212s PrivateWages_3 0 0.00 212s PrivateWages_4 0 0.00 212s PrivateWages_5 0 0.00 212s PrivateWages_6 0 0.00 212s PrivateWages_8 0 0.00 212s PrivateWages_9 0 0.00 212s PrivateWages_10 0 0.00 212s PrivateWages_11 0 0.00 212s PrivateWages_12 0 0.00 212s PrivateWages_13 0 0.00 212s PrivateWages_14 0 0.00 212s PrivateWages_15 0 0.00 212s PrivateWages_16 0 0.00 212s PrivateWages_17 0 0.00 212s PrivateWages_18 0 0.00 212s PrivateWages_19 0 0.00 212s PrivateWages_20 0 0.00 212s PrivateWages_21 0 0.00 212s PrivateWages_22 0 0.00 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 12.7 29.1 212s Consumption_3 12.4 31.9 212s Consumption_4 16.9 35.6 212s Consumption_5 18.4 39.0 212s Consumption_6 19.4 38.8 212s Consumption_8 19.6 39.8 212s Consumption_9 19.8 42.3 212s Consumption_10 21.1 44.1 212s Consumption_11 21.7 43.4 212s Consumption_12 15.6 39.5 212s Consumption_13 11.4 35.1 212s Consumption_14 7.0 33.0 212s Consumption_15 11.2 37.6 212s Consumption_16 12.3 40.0 212s Consumption_17 14.0 41.7 212s Consumption_18 17.6 47.6 212s Consumption_19 17.3 49.5 212s Consumption_20 15.3 48.4 212s Consumption_21 19.0 53.2 212s Consumption_22 21.1 60.9 212s Investment_2 0.0 0.0 212s Investment_3 0.0 0.0 212s Investment_4 0.0 0.0 212s Investment_5 0.0 0.0 212s Investment_6 0.0 0.0 212s Investment_8 0.0 0.0 212s Investment_9 0.0 0.0 212s Investment_10 0.0 0.0 212s Investment_11 0.0 0.0 212s Investment_12 0.0 0.0 212s Investment_13 0.0 0.0 212s Investment_14 0.0 0.0 212s Investment_15 0.0 0.0 212s Investment_16 0.0 0.0 212s Investment_17 0.0 0.0 212s Investment_18 0.0 0.0 212s Investment_19 0.0 0.0 212s Investment_20 0.0 0.0 212s Investment_21 0.0 0.0 212s Investment_22 0.0 0.0 212s PrivateWages_2 0.0 0.0 212s PrivateWages_3 0.0 0.0 212s PrivateWages_4 0.0 0.0 212s PrivateWages_5 0.0 0.0 212s PrivateWages_6 0.0 0.0 212s PrivateWages_8 0.0 0.0 212s PrivateWages_9 0.0 0.0 212s PrivateWages_10 0.0 0.0 212s PrivateWages_11 0.0 0.0 212s PrivateWages_12 0.0 0.0 212s PrivateWages_13 0.0 0.0 212s PrivateWages_14 0.0 0.0 212s PrivateWages_15 0.0 0.0 212s PrivateWages_16 0.0 0.0 212s PrivateWages_17 0.0 0.0 212s PrivateWages_18 0.0 0.0 212s PrivateWages_19 0.0 0.0 212s PrivateWages_20 0.0 0.0 212s PrivateWages_21 0.0 0.0 212s PrivateWages_22 0.0 0.0 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 0 0.00 212s Consumption_3 0 0.00 212s Consumption_4 0 0.00 212s Consumption_5 0 0.00 212s Consumption_6 0 0.00 212s Consumption_8 0 0.00 212s Consumption_9 0 0.00 212s Consumption_10 0 0.00 212s Consumption_11 0 0.00 212s Consumption_12 0 0.00 212s Consumption_13 0 0.00 212s Consumption_14 0 0.00 212s Consumption_15 0 0.00 212s Consumption_16 0 0.00 212s Consumption_17 0 0.00 212s Consumption_18 0 0.00 212s Consumption_19 0 0.00 212s Consumption_20 0 0.00 212s Consumption_21 0 0.00 212s Consumption_22 0 0.00 212s Investment_2 1 12.96 212s Investment_3 1 16.70 212s Investment_4 1 19.14 212s Investment_5 1 20.94 212s Investment_6 1 19.47 212s Investment_8 1 17.14 212s Investment_9 1 19.49 212s Investment_10 1 20.46 212s Investment_11 1 16.85 212s Investment_12 1 12.68 212s Investment_13 1 8.92 212s Investment_14 1 9.30 212s Investment_15 1 12.79 212s Investment_16 1 14.26 212s Investment_17 1 14.75 212s Investment_18 1 19.54 212s Investment_19 1 19.36 212s Investment_20 1 17.39 212s Investment_21 1 20.10 212s Investment_22 1 22.86 212s PrivateWages_2 0 0.00 212s PrivateWages_3 0 0.00 212s PrivateWages_4 0 0.00 212s PrivateWages_5 0 0.00 212s PrivateWages_6 0 0.00 212s PrivateWages_8 0 0.00 212s PrivateWages_9 0 0.00 212s PrivateWages_10 0 0.00 212s PrivateWages_11 0 0.00 212s PrivateWages_12 0 0.00 212s PrivateWages_13 0 0.00 212s PrivateWages_14 0 0.00 212s PrivateWages_15 0 0.00 212s PrivateWages_16 0 0.00 212s PrivateWages_17 0 0.00 212s PrivateWages_18 0 0.00 212s PrivateWages_19 0 0.00 212s PrivateWages_20 0 0.00 212s PrivateWages_21 0 0.00 212s PrivateWages_22 0 0.00 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 0.0 0 212s Consumption_3 0.0 0 212s Consumption_4 0.0 0 212s Consumption_5 0.0 0 212s Consumption_6 0.0 0 212s Consumption_8 0.0 0 212s Consumption_9 0.0 0 212s Consumption_10 0.0 0 212s Consumption_11 0.0 0 212s Consumption_12 0.0 0 212s Consumption_13 0.0 0 212s Consumption_14 0.0 0 212s Consumption_15 0.0 0 212s Consumption_16 0.0 0 212s Consumption_17 0.0 0 212s Consumption_18 0.0 0 212s Consumption_19 0.0 0 212s Consumption_20 0.0 0 212s Consumption_21 0.0 0 212s Consumption_22 0.0 0 212s Investment_2 12.7 183 212s Investment_3 12.4 183 212s Investment_4 16.9 184 212s Investment_5 18.4 190 212s Investment_6 19.4 193 212s Investment_8 19.6 203 212s Investment_9 19.8 208 212s Investment_10 21.1 211 212s Investment_11 21.7 216 212s Investment_12 15.6 217 212s Investment_13 11.4 213 212s Investment_14 7.0 207 212s Investment_15 11.2 202 212s Investment_16 12.3 199 212s Investment_17 14.0 198 212s Investment_18 17.6 200 212s Investment_19 17.3 202 212s Investment_20 15.3 200 212s Investment_21 19.0 201 212s Investment_22 21.1 204 212s PrivateWages_2 0.0 0 212s PrivateWages_3 0.0 0 212s PrivateWages_4 0.0 0 212s PrivateWages_5 0.0 0 212s PrivateWages_6 0.0 0 212s PrivateWages_8 0.0 0 212s PrivateWages_9 0.0 0 212s PrivateWages_10 0.0 0 212s PrivateWages_11 0.0 0 212s PrivateWages_12 0.0 0 212s PrivateWages_13 0.0 0 212s PrivateWages_14 0.0 0 212s PrivateWages_15 0.0 0 212s PrivateWages_16 0.0 0 212s PrivateWages_17 0.0 0 212s PrivateWages_18 0.0 0 212s PrivateWages_19 0.0 0 212s PrivateWages_20 0.0 0 212s PrivateWages_21 0.0 0 212s PrivateWages_22 0.0 0 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 0 0.0 0.0 212s Consumption_3 0 0.0 0.0 212s Consumption_4 0 0.0 0.0 212s Consumption_5 0 0.0 0.0 212s Consumption_6 0 0.0 0.0 212s Consumption_8 0 0.0 0.0 212s Consumption_9 0 0.0 0.0 212s Consumption_10 0 0.0 0.0 212s Consumption_11 0 0.0 0.0 212s Consumption_12 0 0.0 0.0 212s Consumption_13 0 0.0 0.0 212s Consumption_14 0 0.0 0.0 212s Consumption_15 0 0.0 0.0 212s Consumption_16 0 0.0 0.0 212s Consumption_17 0 0.0 0.0 212s Consumption_18 0 0.0 0.0 212s Consumption_19 0 0.0 0.0 212s Consumption_20 0 0.0 0.0 212s Consumption_21 0 0.0 0.0 212s Consumption_22 0 0.0 0.0 212s Investment_2 0 0.0 0.0 212s Investment_3 0 0.0 0.0 212s Investment_4 0 0.0 0.0 212s Investment_5 0 0.0 0.0 212s Investment_6 0 0.0 0.0 212s Investment_8 0 0.0 0.0 212s Investment_9 0 0.0 0.0 212s Investment_10 0 0.0 0.0 212s Investment_11 0 0.0 0.0 212s Investment_12 0 0.0 0.0 212s Investment_13 0 0.0 0.0 212s Investment_14 0 0.0 0.0 212s Investment_15 0 0.0 0.0 212s Investment_16 0 0.0 0.0 212s Investment_17 0 0.0 0.0 212s Investment_18 0 0.0 0.0 212s Investment_19 0 0.0 0.0 212s Investment_20 0 0.0 0.0 212s Investment_21 0 0.0 0.0 212s Investment_22 0 0.0 0.0 212s PrivateWages_2 1 47.1 44.9 212s PrivateWages_3 1 49.6 45.6 212s PrivateWages_4 1 56.5 50.1 212s PrivateWages_5 1 60.7 57.2 212s PrivateWages_6 1 60.6 57.1 212s PrivateWages_8 1 60.0 64.0 212s PrivateWages_9 1 62.3 64.4 212s PrivateWages_10 1 64.6 64.5 212s PrivateWages_11 1 63.7 67.0 212s PrivateWages_12 1 54.8 61.2 212s PrivateWages_13 1 47.0 53.4 212s PrivateWages_14 1 42.1 44.3 212s PrivateWages_15 1 51.2 45.1 212s PrivateWages_16 1 55.3 49.7 212s PrivateWages_17 1 57.4 54.4 212s PrivateWages_18 1 67.2 62.7 212s PrivateWages_19 1 68.5 65.0 212s PrivateWages_20 1 66.8 60.9 212s PrivateWages_21 1 74.9 69.5 212s PrivateWages_22 1 86.9 75.7 212s PrivateWages_trend 212s Consumption_2 0 212s Consumption_3 0 212s Consumption_4 0 212s Consumption_5 0 212s Consumption_6 0 212s Consumption_8 0 212s Consumption_9 0 212s Consumption_10 0 212s Consumption_11 0 212s Consumption_12 0 212s Consumption_13 0 212s Consumption_14 0 212s Consumption_15 0 212s Consumption_16 0 212s Consumption_17 0 212s Consumption_18 0 212s Consumption_19 0 212s Consumption_20 0 212s Consumption_21 0 212s Consumption_22 0 212s Investment_2 0 212s Investment_3 0 212s Investment_4 0 212s Investment_5 0 212s Investment_6 0 212s Investment_8 0 212s Investment_9 0 212s Investment_10 0 212s Investment_11 0 212s Investment_12 0 212s Investment_13 0 212s Investment_14 0 212s Investment_15 0 212s Investment_16 0 212s Investment_17 0 212s Investment_18 0 212s Investment_19 0 212s Investment_20 0 212s Investment_21 0 212s Investment_22 0 212s PrivateWages_2 -10 212s PrivateWages_3 -9 212s PrivateWages_4 -8 212s PrivateWages_5 -7 212s PrivateWages_6 -6 212s PrivateWages_8 -4 212s PrivateWages_9 -3 212s PrivateWages_10 -2 212s PrivateWages_11 -1 212s PrivateWages_12 0 212s PrivateWages_13 1 212s PrivateWages_14 2 212s PrivateWages_15 3 212s PrivateWages_16 4 212s PrivateWages_17 5 212s PrivateWages_18 6 212s PrivateWages_19 7 212s PrivateWages_20 8 212s PrivateWages_21 9 212s PrivateWages_22 10 212s > nobs 212s [1] 60 212s > linearHypothesis 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 49 212s 2 48 1 0.95 0.34 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 49 212s 2 48 1 1.05 0.31 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 49 212s 2 48 1 1.05 0.3 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 48 2 0.48 0.62 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 48 2 0.53 0.59 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 50 212s 2 48 2 1.06 0.59 212s > logLik 212s 'log Lik.' -72.2 (df=13) 212s 'log Lik.' -79.7 (df=13) 212s Estimating function 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 -1.1407 -14.78 212s Consumption_3 -0.3242 -5.42 212s Consumption_4 -0.0963 -1.84 212s Consumption_5 -1.8392 -38.51 212s Consumption_6 0.1702 3.31 212s Consumption_8 3.0349 52.02 212s Consumption_9 1.9822 38.63 212s Consumption_10 0.7162 14.65 212s Consumption_11 -1.5151 -25.52 212s Consumption_12 -1.1471 -14.54 212s Consumption_13 -1.9595 -17.48 212s Consumption_14 1.4394 13.39 212s Consumption_15 -1.0033 -12.84 212s Consumption_16 -0.5750 -8.20 212s Consumption_17 4.0452 59.67 212s Consumption_18 -0.5669 -11.08 212s Consumption_19 -3.1962 -61.88 212s Consumption_20 2.2286 38.75 212s Consumption_21 0.9237 18.57 212s Consumption_22 -1.1770 -26.91 212s Investment_2 0.0000 0.00 212s Investment_3 0.0000 0.00 212s Investment_4 0.0000 0.00 212s Investment_5 0.0000 0.00 212s Investment_6 0.0000 0.00 212s Investment_8 0.0000 0.00 212s Investment_9 0.0000 0.00 212s Investment_10 0.0000 0.00 212s Investment_11 0.0000 0.00 212s Investment_12 0.0000 0.00 212s Investment_13 0.0000 0.00 212s Investment_14 0.0000 0.00 212s Investment_15 0.0000 0.00 212s Investment_16 0.0000 0.00 212s Investment_17 0.0000 0.00 212s Investment_18 0.0000 0.00 212s Investment_19 0.0000 0.00 212s Investment_20 0.0000 0.00 212s Investment_21 0.0000 0.00 212s Investment_22 0.0000 0.00 212s PrivateWages_2 0.0000 0.00 212s PrivateWages_3 0.0000 0.00 212s PrivateWages_4 0.0000 0.00 212s PrivateWages_5 0.0000 0.00 212s PrivateWages_6 0.0000 0.00 212s PrivateWages_8 0.0000 0.00 212s PrivateWages_9 0.0000 0.00 212s PrivateWages_10 0.0000 0.00 212s PrivateWages_11 0.0000 0.00 212s PrivateWages_12 0.0000 0.00 212s PrivateWages_13 0.0000 0.00 212s PrivateWages_14 0.0000 0.00 212s PrivateWages_15 0.0000 0.00 212s PrivateWages_16 0.0000 0.00 212s PrivateWages_17 0.0000 0.00 212s PrivateWages_18 0.0000 0.00 212s PrivateWages_19 0.0000 0.00 212s PrivateWages_20 0.0000 0.00 212s PrivateWages_21 0.0000 0.00 212s PrivateWages_22 0.0000 0.00 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 -14.49 -33.21 212s Consumption_3 -4.02 -10.33 212s Consumption_4 -1.63 -3.43 212s Consumption_5 -33.84 -71.82 212s Consumption_6 3.30 6.61 212s Consumption_8 59.48 120.65 212s Consumption_9 39.25 83.81 212s Consumption_10 15.11 31.59 212s Consumption_11 -32.88 -65.70 212s Consumption_12 -17.89 -45.25 212s Consumption_13 -22.34 -68.69 212s Consumption_14 10.08 47.54 212s Consumption_15 -11.24 -37.74 212s Consumption_16 -7.07 -22.99 212s Consumption_17 56.63 168.85 212s Consumption_18 -9.98 -27.00 212s Consumption_19 -55.29 -158.06 212s Consumption_20 34.10 107.77 212s Consumption_21 17.55 49.11 212s Consumption_22 -24.84 -71.70 212s Investment_2 0.00 0.00 212s Investment_3 0.00 0.00 212s Investment_4 0.00 0.00 212s Investment_5 0.00 0.00 212s Investment_6 0.00 0.00 212s Investment_8 0.00 0.00 212s Investment_9 0.00 0.00 212s Investment_10 0.00 0.00 212s Investment_11 0.00 0.00 212s Investment_12 0.00 0.00 212s Investment_13 0.00 0.00 212s Investment_14 0.00 0.00 212s Investment_15 0.00 0.00 212s Investment_16 0.00 0.00 212s Investment_17 0.00 0.00 212s Investment_18 0.00 0.00 212s Investment_19 0.00 0.00 212s Investment_20 0.00 0.00 212s Investment_21 0.00 0.00 212s Investment_22 0.00 0.00 212s PrivateWages_2 0.00 0.00 212s PrivateWages_3 0.00 0.00 212s PrivateWages_4 0.00 0.00 212s PrivateWages_5 0.00 0.00 212s PrivateWages_6 0.00 0.00 212s PrivateWages_8 0.00 0.00 212s PrivateWages_9 0.00 0.00 212s PrivateWages_10 0.00 0.00 212s PrivateWages_11 0.00 0.00 212s PrivateWages_12 0.00 0.00 212s PrivateWages_13 0.00 0.00 212s PrivateWages_14 0.00 0.00 212s PrivateWages_15 0.00 0.00 212s PrivateWages_16 0.00 0.00 212s PrivateWages_17 0.00 0.00 212s PrivateWages_18 0.00 0.00 212s PrivateWages_19 0.00 0.00 212s PrivateWages_20 0.00 0.00 212s PrivateWages_21 0.00 0.00 212s PrivateWages_22 0.00 0.00 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 0.0000 0.000 212s Consumption_3 0.0000 0.000 212s Consumption_4 0.0000 0.000 212s Consumption_5 0.0000 0.000 212s Consumption_6 0.0000 0.000 212s Consumption_8 0.0000 0.000 212s Consumption_9 0.0000 0.000 212s Consumption_10 0.0000 0.000 212s Consumption_11 0.0000 0.000 212s Consumption_12 0.0000 0.000 212s Consumption_13 0.0000 0.000 212s Consumption_14 0.0000 0.000 212s Consumption_15 0.0000 0.000 212s Consumption_16 0.0000 0.000 212s Consumption_17 0.0000 0.000 212s Consumption_18 0.0000 0.000 212s Consumption_19 0.0000 0.000 212s Consumption_20 0.0000 0.000 212s Consumption_21 0.0000 0.000 212s Consumption_22 0.0000 0.000 212s Investment_2 -1.1313 -14.660 212s Investment_3 0.2902 4.847 212s Investment_4 0.9027 17.274 212s Investment_5 -1.7434 -36.502 212s Investment_6 0.5695 11.088 212s Investment_8 1.6225 27.812 212s Investment_9 0.4166 8.119 212s Investment_10 2.0381 41.703 212s Investment_11 -0.8611 -14.505 212s Investment_12 -0.9091 -11.527 212s Investment_13 -1.1148 -9.946 212s Investment_14 1.3841 12.873 212s Investment_15 -0.2900 -3.710 212s Investment_16 0.0605 0.862 212s Investment_17 2.2439 33.101 212s Investment_18 -0.5390 -10.534 212s Investment_19 -3.9452 -76.375 212s Investment_20 0.4890 8.502 212s Investment_21 0.0864 1.737 212s Investment_22 0.4306 9.843 212s PrivateWages_2 0.0000 0.000 212s PrivateWages_3 0.0000 0.000 212s PrivateWages_4 0.0000 0.000 212s PrivateWages_5 0.0000 0.000 212s PrivateWages_6 0.0000 0.000 212s PrivateWages_8 0.0000 0.000 212s PrivateWages_9 0.0000 0.000 212s PrivateWages_10 0.0000 0.000 212s PrivateWages_11 0.0000 0.000 212s PrivateWages_12 0.0000 0.000 212s PrivateWages_13 0.0000 0.000 212s PrivateWages_14 0.0000 0.000 212s PrivateWages_15 0.0000 0.000 212s PrivateWages_16 0.0000 0.000 212s PrivateWages_17 0.0000 0.000 212s PrivateWages_18 0.0000 0.000 212s PrivateWages_19 0.0000 0.000 212s PrivateWages_20 0.0000 0.000 212s PrivateWages_21 0.0000 0.000 212s PrivateWages_22 0.0000 0.000 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 0.000 0.0 212s Consumption_3 0.000 0.0 212s Consumption_4 0.000 0.0 212s Consumption_5 0.000 0.0 212s Consumption_6 0.000 0.0 212s Consumption_8 0.000 0.0 212s Consumption_9 0.000 0.0 212s Consumption_10 0.000 0.0 212s Consumption_11 0.000 0.0 212s Consumption_12 0.000 0.0 212s Consumption_13 0.000 0.0 212s Consumption_14 0.000 0.0 212s Consumption_15 0.000 0.0 212s Consumption_16 0.000 0.0 212s Consumption_17 0.000 0.0 212s Consumption_18 0.000 0.0 212s Consumption_19 0.000 0.0 212s Consumption_20 0.000 0.0 212s Consumption_21 0.000 0.0 212s Consumption_22 0.000 0.0 212s Investment_2 -14.368 -206.8 212s Investment_3 3.598 53.0 212s Investment_4 15.256 166.5 212s Investment_5 -32.079 -330.7 212s Investment_6 11.048 109.7 212s Investment_8 31.801 330.0 212s Investment_9 8.248 86.5 212s Investment_10 43.003 429.2 212s Investment_11 -18.685 -185.7 212s Investment_12 -14.182 -197.0 212s Investment_13 -12.709 -237.8 212s Investment_14 9.689 286.6 212s Investment_15 -3.247 -58.6 212s Investment_16 0.744 12.0 212s Investment_17 31.414 443.6 212s Investment_18 -9.486 -107.7 212s Investment_19 -68.252 -796.1 212s Investment_20 7.482 97.7 212s Investment_21 1.642 17.4 212s Investment_22 9.085 88.0 212s PrivateWages_2 0.000 0.0 212s PrivateWages_3 0.000 0.0 212s PrivateWages_4 0.000 0.0 212s PrivateWages_5 0.000 0.0 212s PrivateWages_6 0.000 0.0 212s PrivateWages_8 0.000 0.0 212s PrivateWages_9 0.000 0.0 212s PrivateWages_10 0.000 0.0 212s PrivateWages_11 0.000 0.0 212s PrivateWages_12 0.000 0.0 212s PrivateWages_13 0.000 0.0 212s PrivateWages_14 0.000 0.0 212s PrivateWages_15 0.000 0.0 212s PrivateWages_16 0.000 0.0 212s PrivateWages_17 0.000 0.0 212s PrivateWages_18 0.000 0.0 212s PrivateWages_19 0.000 0.0 212s PrivateWages_20 0.000 0.0 212s PrivateWages_21 0.000 0.0 212s PrivateWages_22 0.000 0.0 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 0.0000 0.00 0.00 212s Consumption_3 0.0000 0.00 0.00 212s Consumption_4 0.0000 0.00 0.00 212s Consumption_5 0.0000 0.00 0.00 212s Consumption_6 0.0000 0.00 0.00 212s Consumption_8 0.0000 0.00 0.00 212s Consumption_9 0.0000 0.00 0.00 212s Consumption_10 0.0000 0.00 0.00 212s Consumption_11 0.0000 0.00 0.00 212s Consumption_12 0.0000 0.00 0.00 212s Consumption_13 0.0000 0.00 0.00 212s Consumption_14 0.0000 0.00 0.00 212s Consumption_15 0.0000 0.00 0.00 212s Consumption_16 0.0000 0.00 0.00 212s Consumption_17 0.0000 0.00 0.00 212s Consumption_18 0.0000 0.00 0.00 212s Consumption_19 0.0000 0.00 0.00 212s Consumption_20 0.0000 0.00 0.00 212s Consumption_21 0.0000 0.00 0.00 212s Consumption_22 0.0000 0.00 0.00 212s Investment_2 0.0000 0.00 0.00 212s Investment_3 0.0000 0.00 0.00 212s Investment_4 0.0000 0.00 0.00 212s Investment_5 0.0000 0.00 0.00 212s Investment_6 0.0000 0.00 0.00 212s Investment_8 0.0000 0.00 0.00 212s Investment_9 0.0000 0.00 0.00 212s Investment_10 0.0000 0.00 0.00 212s Investment_11 0.0000 0.00 0.00 212s Investment_12 0.0000 0.00 0.00 212s Investment_13 0.0000 0.00 0.00 212s Investment_14 0.0000 0.00 0.00 212s Investment_15 0.0000 0.00 0.00 212s Investment_16 0.0000 0.00 0.00 212s Investment_17 0.0000 0.00 0.00 212s Investment_18 0.0000 0.00 0.00 212s Investment_19 0.0000 0.00 0.00 212s Investment_20 0.0000 0.00 0.00 212s Investment_21 0.0000 0.00 0.00 212s Investment_22 0.0000 0.00 0.00 212s PrivateWages_2 -1.9924 -93.78 -89.46 212s PrivateWages_3 0.4683 23.22 21.35 212s PrivateWages_4 1.4034 79.35 70.31 212s PrivateWages_5 -1.7870 -108.45 -102.22 212s PrivateWages_6 -0.3627 -21.98 -20.71 212s PrivateWages_8 1.1629 69.77 74.43 212s PrivateWages_9 1.2735 79.30 82.01 212s PrivateWages_10 2.2141 142.96 142.81 212s PrivateWages_11 -1.2912 -82.26 -86.51 212s PrivateWages_12 -0.0350 -1.92 -2.14 212s PrivateWages_13 -1.0438 -49.04 -55.74 212s PrivateWages_14 1.8016 75.90 79.81 212s PrivateWages_15 -0.3714 -19.02 -16.75 212s PrivateWages_16 -0.3904 -21.61 -19.40 212s PrivateWages_17 1.4934 85.71 81.24 212s PrivateWages_18 0.0279 1.88 1.75 212s PrivateWages_19 -3.8229 -261.91 -248.49 212s PrivateWages_20 0.7870 52.61 47.93 212s PrivateWages_21 -0.7415 -55.52 -51.54 212s PrivateWages_22 1.2062 104.79 91.31 212s PrivateWages_trend 212s Consumption_2 0.000 212s Consumption_3 0.000 212s Consumption_4 0.000 212s Consumption_5 0.000 212s Consumption_6 0.000 212s Consumption_8 0.000 212s Consumption_9 0.000 212s Consumption_10 0.000 212s Consumption_11 0.000 212s Consumption_12 0.000 212s Consumption_13 0.000 212s Consumption_14 0.000 212s Consumption_15 0.000 212s Consumption_16 0.000 212s Consumption_17 0.000 212s Consumption_18 0.000 212s Consumption_19 0.000 212s Consumption_20 0.000 212s Consumption_21 0.000 212s Consumption_22 0.000 212s Investment_2 0.000 212s Investment_3 0.000 212s Investment_4 0.000 212s Investment_5 0.000 212s Investment_6 0.000 212s Investment_8 0.000 212s Investment_9 0.000 212s Investment_10 0.000 212s Investment_11 0.000 212s Investment_12 0.000 212s Investment_13 0.000 212s Investment_14 0.000 212s Investment_15 0.000 212s Investment_16 0.000 212s Investment_17 0.000 212s Investment_18 0.000 212s Investment_19 0.000 212s Investment_20 0.000 212s Investment_21 0.000 212s Investment_22 0.000 212s PrivateWages_2 19.924 212s PrivateWages_3 -4.214 212s PrivateWages_4 -11.227 212s PrivateWages_5 12.509 212s PrivateWages_6 2.176 212s PrivateWages_8 -4.652 212s PrivateWages_9 -3.820 212s PrivateWages_10 -4.428 212s PrivateWages_11 1.291 212s PrivateWages_12 0.000 212s PrivateWages_13 -1.044 212s PrivateWages_14 3.603 212s PrivateWages_15 -1.114 212s PrivateWages_16 -1.562 212s PrivateWages_17 7.467 212s PrivateWages_18 0.168 212s PrivateWages_19 -26.760 212s PrivateWages_20 6.296 212s PrivateWages_21 -6.674 212s PrivateWages_22 12.062 212s [1] TRUE 212s > Bread 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_(Intercept) 99.945 -0.7943 212s Consumption_corpProf -0.794 0.7797 212s Consumption_corpProfLag -0.325 -0.5285 212s Consumption_wages -1.888 -0.0894 212s Investment_(Intercept) 0.000 0.0000 212s Investment_corpProf 0.000 0.0000 212s Investment_corpProfLag 0.000 0.0000 212s Investment_capitalLag 0.000 0.0000 212s PrivateWages_(Intercept) 0.000 0.0000 212s PrivateWages_gnp 0.000 0.0000 212s PrivateWages_gnpLag 0.000 0.0000 212s PrivateWages_trend 0.000 0.0000 212s Consumption_corpProfLag Consumption_wages 212s Consumption_(Intercept) -0.3246 -1.8878 212s Consumption_corpProf -0.5285 -0.0894 212s Consumption_corpProfLag 0.6654 -0.0384 212s Consumption_wages -0.0384 0.0965 212s Investment_(Intercept) 0.0000 0.0000 212s Investment_corpProf 0.0000 0.0000 212s Investment_corpProfLag 0.0000 0.0000 212s Investment_capitalLag 0.0000 0.0000 212s PrivateWages_(Intercept) 0.0000 0.0000 212s PrivateWages_gnp 0.0000 0.0000 212s PrivateWages_gnpLag 0.0000 0.0000 212s PrivateWages_trend 0.0000 0.0000 212s Investment_(Intercept) Investment_corpProf 212s Consumption_(Intercept) 0.0 0.000 212s Consumption_corpProf 0.0 0.000 212s Consumption_corpProfLag 0.0 0.000 212s Consumption_wages 0.0 0.000 212s Investment_(Intercept) 2446.2 -38.918 212s Investment_corpProf -38.9 1.252 212s Investment_corpProfLag 33.4 -1.090 212s Investment_capitalLag -11.6 0.177 212s PrivateWages_(Intercept) 0.0 0.000 212s PrivateWages_gnp 0.0 0.000 212s PrivateWages_gnpLag 0.0 0.000 212s PrivateWages_trend 0.0 0.000 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_(Intercept) 0.000 0.0000 212s Consumption_corpProf 0.000 0.0000 212s Consumption_corpProfLag 0.000 0.0000 212s Consumption_wages 0.000 0.0000 212s Investment_(Intercept) 33.384 -11.6216 212s Investment_corpProf -1.090 0.1774 212s Investment_corpProfLag 1.148 -0.1680 212s Investment_capitalLag -0.168 0.0567 212s PrivateWages_(Intercept) 0.000 0.0000 212s PrivateWages_gnp 0.000 0.0000 212s PrivateWages_gnpLag 0.000 0.0000 212s PrivateWages_trend 0.000 0.0000 212s PrivateWages_(Intercept) PrivateWages_gnp 212s Consumption_(Intercept) 0.000 0.0000 212s Consumption_corpProf 0.000 0.0000 212s Consumption_corpProfLag 0.000 0.0000 212s Consumption_wages 0.000 0.0000 212s Investment_(Intercept) 0.000 0.0000 212s Investment_corpProf 0.000 0.0000 212s Investment_corpProfLag 0.000 0.0000 212s Investment_capitalLag 0.000 0.0000 212s PrivateWages_(Intercept) 170.714 -0.9289 212s PrivateWages_gnp -0.929 0.1580 212s PrivateWages_gnpLag -1.948 -0.1473 212s PrivateWages_trend 2.164 -0.0424 212s PrivateWages_gnpLag PrivateWages_trend 212s Consumption_(Intercept) 0.000 0.0000 212s Consumption_corpProf 0.000 0.0000 212s Consumption_corpProfLag 0.000 0.0000 212s Consumption_wages 0.000 0.0000 212s Investment_(Intercept) 0.000 0.0000 212s Investment_corpProf 0.000 0.0000 212s Investment_corpProfLag 0.000 0.0000 212s Investment_capitalLag 0.000 0.0000 212s PrivateWages_(Intercept) -1.948 2.1641 212s PrivateWages_gnp -0.147 -0.0424 212s PrivateWages_gnpLag 0.186 0.0060 212s PrivateWages_trend 0.006 0.1151 212s > 212s > # SUR 212s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 212s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 212s > summary 212s 212s systemfit results 212s method: SUR 212s 212s N DF SSR detRCov OLS-R2 McElroy-R2 212s system 62 50 46.2 0.154 0.977 0.993 212s 212s N DF SSR MSE RMSE R2 Adj R2 212s Consumption 21 17 18.1 1.062 1.031 0.981 0.977 212s Investment 21 17 17.5 1.030 1.015 0.931 0.918 212s PrivateWages 20 16 10.6 0.663 0.814 0.987 0.984 212s 212s The covariance matrix of the residuals used for estimation 212s Consumption Investment PrivateWages 212s Consumption 0.8562 -0.0129 -0.371 212s Investment -0.0129 0.7548 0.159 212s PrivateWages -0.3706 0.1594 0.487 212s 212s The covariance matrix of the residuals 212s Consumption Investment PrivateWages 212s Consumption 0.8684 0.0078 -0.442 212s Investment 0.0078 0.7702 0.237 212s PrivateWages -0.4416 0.2366 0.531 212s 212s The correlations of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.00000 0.00562 -0.651 212s Investment 0.00562 1.00000 0.372 212s PrivateWages -0.65109 0.37198 1.000 212s 212s 212s SUR estimates for 'Consumption' (equation 1) 212s Model Formula: consump ~ corpProf + corpProfLag + wages 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 16.0647 1.1729 13.70 1.3e-10 *** 212s corpProf 0.2283 0.0775 2.94 0.0091 ** 212s corpProfLag 0.0723 0.0771 0.94 0.3615 212s wages 0.7930 0.0352 22.51 4.3e-14 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.031 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 18.06 MSE: 1.062 Root MSE: 1.031 212s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 212s 212s 212s SUR estimates for 'Investment' (equation 2) 212s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 12.3516 4.5762 2.70 0.01520 * 212s corpProf 0.4461 0.0818 5.45 4.3e-05 *** 212s corpProfLag 0.3609 0.0849 4.25 0.00054 *** 212s capitalLag -0.1224 0.0223 -5.47 4.1e-05 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.015 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 17.514 MSE: 1.03 Root MSE: 1.015 212s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 212s 212s 212s SUR estimates for 'PrivateWages' (equation 3) 212s Model Formula: privWage ~ gnp + gnpLag + trend 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 1.5433 1.1371 1.36 0.19 212s gnp 0.4117 0.0279 14.77 9.6e-11 *** 212s gnpLag 0.1743 0.0317 5.50 4.8e-05 *** 212s trend 0.1550 0.0283 5.49 5.0e-05 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 0.814 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 10.611 MSE: 0.663 Root MSE: 0.814 212s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 212s 212s > residuals 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 -0.27628 -0.3003 -1.0910 212s 3 -1.35400 -0.1239 0.5795 212s 4 -1.62816 1.1154 1.5172 212s 5 -0.56494 -1.4358 -0.0341 212s 6 -0.06584 0.3581 -0.2772 212s 7 0.83245 1.4526 NA 212s 8 1.28855 0.8290 -0.6896 212s 9 0.96709 -0.5092 0.3445 212s 10 -0.66705 1.2210 1.2429 212s 11 0.41992 0.2497 -0.3602 212s 12 -0.05971 0.0470 0.3068 212s 13 -0.08649 0.3096 -0.2426 212s 14 0.33124 0.3652 0.3591 212s 15 -0.00604 -0.1652 0.2710 212s 16 -0.01478 0.0124 -0.0207 212s 17 1.55472 1.0339 -0.8117 212s 18 -0.41250 0.0255 0.8398 212s 19 0.29322 -2.6293 -0.8283 212s 20 0.91756 -0.5906 -0.4091 212s 21 0.71583 -0.7036 -1.2154 212s 22 -2.26223 -0.5283 0.6207 212s > fitted 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 42.2 0.100 26.6 212s 3 46.4 2.024 28.7 212s 4 50.8 4.085 32.6 212s 5 51.2 4.436 33.9 212s 6 52.7 4.742 35.7 212s 7 54.3 4.147 NA 212s 8 54.9 3.371 38.6 212s 9 56.3 3.509 38.9 212s 10 58.5 3.879 40.1 212s 11 54.6 0.750 38.3 212s 12 51.0 -3.447 34.2 212s 13 45.7 -6.510 29.2 212s 14 46.2 -5.465 28.1 212s 15 48.7 -2.835 30.3 212s 16 51.3 -1.312 33.2 212s 17 56.1 1.066 37.6 212s 18 59.1 1.974 40.2 212s 19 57.2 0.729 39.0 212s 20 60.7 1.891 42.0 212s 21 64.3 4.004 46.2 212s 22 72.0 5.428 52.7 212s > predict 212s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 212s 1 NA NA NA NA 212s 2 42.2 0.414 41.3 43.0 212s 3 46.4 0.451 45.4 47.3 212s 4 50.8 0.296 50.2 51.4 212s 5 51.2 0.342 50.5 51.9 212s 6 52.7 0.342 52.0 53.4 212s 7 54.3 0.309 53.6 54.9 212s 8 54.9 0.282 54.3 55.5 212s 9 56.3 0.303 55.7 56.9 212s 10 58.5 0.321 57.8 59.1 212s 11 54.6 0.515 53.5 55.6 212s 12 51.0 0.418 50.1 51.8 212s 13 45.7 0.548 44.6 46.8 212s 14 46.2 0.528 45.1 47.2 212s 15 48.7 0.333 48.0 49.4 212s 16 51.3 0.296 50.7 51.9 212s 17 56.1 0.321 55.5 56.8 212s 18 59.1 0.287 58.5 59.7 212s 19 57.2 0.325 56.6 57.9 212s 20 60.7 0.383 59.9 61.5 212s 21 64.3 0.382 63.5 65.1 212s 22 72.0 0.599 70.8 73.2 212s Investment.pred Investment.se.fit Investment.lwr Investment.upr 212s 1 NA NA NA NA 212s 2 0.100 0.511 -0.926 1.127 212s 3 2.024 0.425 1.170 2.878 212s 4 4.085 0.378 3.325 4.845 212s 5 4.436 0.313 3.806 5.065 212s 6 4.742 0.296 4.147 5.336 212s 7 4.147 0.279 3.586 4.709 212s 8 3.371 0.250 2.868 3.874 212s 9 3.509 0.331 2.845 4.174 212s 10 3.879 0.380 3.116 4.642 212s 11 0.750 0.512 -0.279 1.779 212s 12 -3.447 0.433 -4.316 -2.578 212s 13 -6.510 0.527 -7.568 -5.451 212s 14 -5.465 0.587 -6.645 -4.285 212s 15 -2.835 0.320 -3.477 -2.193 212s 16 -1.312 0.274 -1.863 -0.761 212s 17 1.066 0.296 0.472 1.661 212s 18 1.974 0.208 1.558 2.391 212s 19 0.729 0.265 0.197 1.262 212s 20 1.891 0.311 1.266 2.515 212s 21 4.004 0.283 3.435 4.572 212s 22 5.428 0.393 4.640 6.217 212s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 212s 1 NA NA NA NA 212s 2 26.6 0.318 26.0 27.2 212s 3 28.7 0.317 28.1 29.4 212s 4 32.6 0.315 32.0 33.2 212s 5 33.9 0.243 33.4 34.4 212s 6 35.7 0.242 35.2 36.2 212s 7 NA NA NA NA 212s 8 38.6 0.247 38.1 39.1 212s 9 38.9 0.236 38.4 39.3 212s 10 40.1 0.227 39.6 40.5 212s 11 38.3 0.306 37.6 38.9 212s 12 34.2 0.312 33.6 34.8 212s 13 29.2 0.376 28.5 30.0 212s 14 28.1 0.337 27.5 28.8 212s 15 30.3 0.328 29.7 31.0 212s 16 33.2 0.274 32.7 33.8 212s 17 37.6 0.266 37.1 38.1 212s 18 40.2 0.213 39.7 40.6 212s 19 39.0 0.310 38.4 39.7 212s 20 42.0 0.282 41.4 42.6 212s 21 46.2 0.300 45.6 46.8 212s 22 52.7 0.451 51.8 53.6 212s > model.frame 212s [1] TRUE 212s > model.matrix 212s [1] TRUE 212s > nobs 212s [1] 62 212s > linearHypothesis 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 51 212s 2 50 1 1.39 0.24 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 51 212s 2 50 1 1.7 0.2 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 51 212s 2 50 1 1.7 0.19 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 52 212s 2 50 2 0.72 0.49 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 52 212s 2 50 2 0.87 0.42 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 52 212s 2 50 2 1.75 0.42 212s > logLik 212s 'log Lik.' -69.4 (df=18) 212s 'log Lik.' -78.2 (df=18) 212s Estimating function 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 -0.49572 -6.1470 212s Consumption_3 -2.42943 -41.0573 212s Consumption_4 -2.92134 -53.7526 212s Consumption_5 -1.01365 -19.6648 212s Consumption_6 -0.11814 -2.3746 212s Consumption_7 1.49363 29.2752 212s Consumption_8 2.31199 45.7775 212s Consumption_9 1.73521 36.6129 212s Consumption_10 -1.19687 -25.9720 212s Consumption_11 0.75344 11.7537 212s Consumption_12 -0.10714 -1.2214 212s Consumption_13 -0.15519 -1.0863 212s Consumption_14 0.59434 6.6566 212s Consumption_15 -0.01083 -0.1332 212s Consumption_16 -0.02651 -0.3712 212s Consumption_17 2.78956 49.0963 212s Consumption_18 -0.74013 -12.8043 212s Consumption_19 0.52610 8.0494 212s Consumption_20 1.64635 31.2806 212s Consumption_21 1.28438 27.1004 212s Consumption_22 -4.05902 -95.3870 212s Investment_2 0.08318 1.0314 212s Investment_3 0.03433 0.5802 212s Investment_4 -0.30897 -5.6851 212s Investment_5 0.39771 7.7155 212s Investment_6 -0.09921 -1.9941 212s Investment_7 -0.40237 -7.8864 212s Investment_8 -0.22963 -4.5466 212s Investment_9 0.14106 2.9764 212s Investment_10 -0.33822 -7.3394 212s Investment_11 -0.06917 -1.0790 212s Investment_12 -0.01303 -0.1485 212s Investment_13 -0.08575 -0.6003 212s Investment_14 -0.10117 -1.1331 212s Investment_15 0.04575 0.5628 212s Investment_16 -0.00344 -0.0482 212s Investment_17 -0.28639 -5.0405 212s Investment_18 -0.00707 -0.1223 212s Investment_19 0.72832 11.1433 212s Investment_20 0.16360 3.1083 212s Investment_21 0.19490 4.1123 212s Investment_22 0.14635 3.4391 212s PrivateWages_2 -1.58896 -19.7031 212s PrivateWages_3 0.84394 14.2626 212s PrivateWages_4 2.20977 40.6598 212s PrivateWages_5 -0.04965 -0.9631 212s PrivateWages_6 -0.40373 -8.1150 212s PrivateWages_8 -1.00430 -19.8851 212s PrivateWages_9 0.50179 10.5878 212s PrivateWages_10 1.81021 39.2815 212s PrivateWages_11 -0.52455 -8.1830 212s PrivateWages_12 0.44676 5.0931 212s PrivateWages_13 -0.35330 -2.4731 212s PrivateWages_14 0.52303 5.8579 212s PrivateWages_15 0.39464 4.8541 212s PrivateWages_16 -0.03009 -0.4213 212s PrivateWages_17 -1.18225 -20.8075 212s PrivateWages_18 1.22307 21.1590 212s PrivateWages_19 -1.20633 -18.4569 212s PrivateWages_20 -0.59580 -11.3203 212s PrivateWages_21 -1.77014 -37.3499 212s PrivateWages_22 0.90407 21.2457 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 -6.2957 -13.979 212s Consumption_3 -30.1249 -78.228 212s Consumption_4 -49.3706 -108.090 212s Consumption_5 -18.6512 -37.505 212s Consumption_6 -2.2919 -4.560 212s Consumption_7 30.0220 60.791 212s Consumption_8 45.3151 95.948 212s Consumption_9 34.3571 74.440 212s Consumption_10 -25.2539 -54.218 212s Consumption_11 16.3496 31.720 212s Consumption_12 -1.6714 -4.211 212s Consumption_13 -1.7691 -5.323 212s Consumption_14 4.1604 20.267 212s Consumption_15 -0.1213 -0.396 212s Consumption_16 -0.3261 -1.042 212s Consumption_17 39.0539 123.299 212s Consumption_18 -13.0263 -35.304 212s Consumption_19 9.1016 24.148 212s Consumption_20 25.1891 81.330 212s Consumption_21 24.4032 68.072 212s Consumption_22 -85.6453 -250.847 212s Investment_2 1.0563 2.346 212s Investment_3 0.4257 1.105 212s Investment_4 -5.2216 -11.432 212s Investment_5 7.3178 14.715 212s Investment_6 -1.9246 -3.829 212s Investment_7 -8.0876 -16.376 212s Investment_8 -4.5007 -9.530 212s Investment_9 2.7930 6.052 212s Investment_10 -7.1364 -15.321 212s Investment_11 -1.5009 -2.912 212s Investment_12 -0.2033 -0.512 212s Investment_13 -0.9776 -2.941 212s Investment_14 -0.7082 -3.450 212s Investment_15 0.5124 1.675 212s Investment_16 -0.0423 -0.135 212s Investment_17 -4.0095 -12.659 212s Investment_18 -0.1244 -0.337 212s Investment_19 12.5999 33.430 212s Investment_20 2.5030 8.082 212s Investment_21 3.7031 10.330 212s Investment_22 3.0879 9.044 212s PrivateWages_2 -20.1798 -44.809 212s PrivateWages_3 10.4649 27.175 212s PrivateWages_4 37.3452 81.762 212s PrivateWages_5 -0.9135 -1.837 212s PrivateWages_6 -7.8324 -15.584 212s PrivateWages_8 -19.6842 -41.678 212s PrivateWages_9 9.9355 21.527 212s PrivateWages_10 38.1953 82.002 212s PrivateWages_11 -11.3827 -22.084 212s PrivateWages_12 6.9695 17.558 212s PrivateWages_13 -4.0277 -12.118 212s PrivateWages_14 3.6612 17.835 212s PrivateWages_15 4.4200 14.444 212s PrivateWages_16 -0.3701 -1.183 212s PrivateWages_17 -16.5515 -52.255 212s PrivateWages_18 21.5260 58.340 212s PrivateWages_19 -20.8696 -55.371 212s PrivateWages_20 -9.1158 -29.433 212s PrivateWages_21 -33.6326 -93.817 212s PrivateWages_22 19.0759 55.872 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 0.07653 0.9490 212s Consumption_3 0.37506 6.3385 212s Consumption_4 0.45100 8.2984 212s Consumption_5 0.15649 3.0359 212s Consumption_6 0.01824 0.3666 212s Consumption_7 -0.23059 -4.5195 212s Consumption_8 -0.35693 -7.0672 212s Consumption_9 -0.26788 -5.6523 212s Consumption_10 0.18477 4.0096 212s Consumption_11 -0.11632 -1.8145 212s Consumption_12 0.01654 0.1886 212s Consumption_13 0.02396 0.1677 212s Consumption_14 -0.09175 -1.0277 212s Consumption_15 0.00167 0.0206 212s Consumption_16 0.00409 0.0573 212s Consumption_17 -0.43066 -7.5796 212s Consumption_18 0.11426 1.9767 212s Consumption_19 -0.08122 -1.2427 212s Consumption_20 -0.25417 -4.8291 212s Consumption_21 -0.19828 -4.1838 212s Consumption_22 0.62664 14.7260 212s Investment_2 -0.44022 -5.4587 212s Investment_3 -0.18170 -3.0707 212s Investment_4 1.63526 30.0888 212s Investment_5 -2.10489 -40.8348 212s Investment_6 0.52506 10.5537 212s Investment_7 2.12955 41.7392 212s Investment_8 1.21532 24.0633 212s Investment_9 -0.74658 -15.7528 212s Investment_10 1.79005 38.8441 212s Investment_11 0.36607 5.7107 212s Investment_12 0.06896 0.7861 212s Investment_13 0.45385 3.1769 212s Investment_14 0.53544 5.9969 212s Investment_15 -0.24215 -2.9785 212s Investment_16 0.01822 0.2551 212s Investment_17 1.51576 26.6774 212s Investment_18 0.03741 0.6472 212s Investment_19 -3.85468 -58.9766 212s Investment_20 -0.86584 -16.4509 212s Investment_21 -1.03151 -21.7649 212s Investment_22 -0.77455 -18.2019 212s PrivateWages_2 0.75366 9.3454 212s PrivateWages_3 -0.40029 -6.7649 212s PrivateWages_4 -1.04812 -19.2855 212s PrivateWages_5 0.02355 0.4568 212s PrivateWages_6 0.19149 3.8490 212s PrivateWages_8 0.47635 9.4317 212s PrivateWages_9 -0.23801 -5.0219 212s PrivateWages_10 -0.85860 -18.6317 212s PrivateWages_11 0.24880 3.8813 212s PrivateWages_12 -0.21191 -2.4157 212s PrivateWages_13 0.16758 1.1730 212s PrivateWages_14 -0.24808 -2.7785 212s PrivateWages_15 -0.18718 -2.3024 212s PrivateWages_16 0.01427 0.1998 212s PrivateWages_17 0.56075 9.8693 212s PrivateWages_18 -0.58012 -10.0360 212s PrivateWages_19 0.57218 8.7543 212s PrivateWages_20 0.28260 5.3694 212s PrivateWages_21 0.83960 17.7155 212s PrivateWages_22 -0.42881 -10.0771 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 0.9719 13.990 212s Consumption_3 4.6507 68.486 212s Consumption_4 7.6219 83.210 212s Consumption_5 2.8794 29.686 212s Consumption_6 0.3538 3.515 212s Consumption_7 -4.6348 -45.611 212s Consumption_8 -6.9958 -72.599 212s Consumption_9 -5.3041 -55.613 212s Consumption_10 3.8987 38.913 212s Consumption_11 -2.5241 -25.090 212s Consumption_12 0.2580 3.584 212s Consumption_13 0.2731 5.110 212s Consumption_14 -0.6423 -19.002 212s Consumption_15 0.0187 0.338 212s Consumption_16 0.0503 0.815 212s Consumption_17 -6.0292 -85.141 212s Consumption_18 2.0110 22.830 212s Consumption_19 -1.4051 -16.390 212s Consumption_20 -3.8887 -50.808 212s Consumption_21 -3.7674 -39.895 212s Consumption_22 13.2221 128.147 212s Investment_2 -5.5908 -80.472 212s Investment_3 -2.2531 -33.179 212s Investment_4 27.6359 301.706 212s Investment_5 -38.7299 -399.297 212s Investment_6 10.1862 101.179 212s Investment_7 42.8040 421.225 212s Investment_8 23.8203 247.196 212s Investment_9 -14.7822 -154.989 212s Investment_10 37.7701 376.985 212s Investment_11 7.9437 78.961 212s Investment_12 1.0757 14.943 212s Investment_13 5.1739 96.806 212s Investment_14 3.7481 110.889 212s Investment_15 -2.7121 -48.915 212s Investment_16 0.2241 3.626 212s Investment_17 21.2206 299.666 212s Investment_18 0.6585 7.475 212s Investment_19 -66.6860 -777.874 212s Investment_20 -13.2473 -173.081 212s Investment_21 -19.5987 -207.540 212s Investment_22 -16.3429 -158.395 212s PrivateWages_2 9.5715 137.769 212s PrivateWages_3 -4.9636 -73.093 212s PrivateWages_4 -17.7133 -193.379 212s PrivateWages_5 0.4333 4.467 212s PrivateWages_6 3.7150 36.901 212s PrivateWages_8 9.3365 96.890 212s PrivateWages_9 -4.7125 -49.410 212s PrivateWages_10 -18.1165 -180.822 212s PrivateWages_11 5.3990 53.666 212s PrivateWages_12 -3.3057 -45.920 212s PrivateWages_13 1.9104 35.744 212s PrivateWages_14 -1.7366 -51.377 212s PrivateWages_15 -2.0965 -37.811 212s PrivateWages_16 0.1756 2.840 212s PrivateWages_17 7.8506 110.861 212s PrivateWages_18 -10.2100 -115.907 212s PrivateWages_19 9.8987 115.466 212s PrivateWages_20 4.3237 56.491 212s PrivateWages_21 15.9524 168.927 212s PrivateWages_22 -9.0479 -87.692 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 -0.40239 -18.349 -18.067 212s Consumption_3 -1.97202 -98.798 -89.924 212s Consumption_4 -2.37131 -135.639 -118.803 212s Consumption_5 -0.82280 -46.982 -47.064 212s Consumption_6 -0.09590 -5.850 -5.476 212s Consumption_7 0.00000 0.000 0.000 212s Consumption_8 1.87670 120.859 120.108 212s Consumption_9 1.40851 90.849 90.708 212s Consumption_10 -0.97152 -65.092 -62.663 212s Consumption_11 0.61158 37.429 40.976 212s Consumption_12 -0.08697 -4.644 -5.322 212s Consumption_13 -0.12597 -5.580 -6.727 212s Consumption_14 0.48244 21.758 21.372 212s Consumption_15 -0.00879 -0.437 -0.396 212s Consumption_16 -0.02152 -1.171 -1.070 212s Consumption_17 2.26435 141.975 123.181 212s Consumption_18 -0.60078 -39.051 -37.669 212s Consumption_19 0.42705 26.007 27.758 212s Consumption_20 1.33638 92.878 81.385 212s Consumption_21 1.04256 78.922 72.458 212s Consumption_22 -3.29479 -291.260 -249.416 212s Investment_2 0.20743 9.459 9.314 212s Investment_3 0.08562 4.289 3.904 212s Investment_4 -0.77054 -44.075 -38.604 212s Investment_5 0.99183 56.634 56.733 212s Investment_6 -0.24741 -15.092 -14.127 212s Investment_7 0.00000 0.000 0.000 212s Investment_8 -0.57266 -36.880 -36.650 212s Investment_9 0.35179 22.690 22.655 212s Investment_10 -0.84348 -56.513 -54.405 212s Investment_11 -0.17249 -10.557 -11.557 212s Investment_12 -0.03249 -1.735 -1.989 212s Investment_13 -0.21385 -9.474 -11.420 212s Investment_14 -0.25230 -11.379 -11.177 212s Investment_15 0.11410 5.671 5.146 212s Investment_16 -0.00859 -0.467 -0.427 212s Investment_17 -0.71423 -44.782 -38.854 212s Investment_18 -0.01763 -1.146 -1.105 212s Investment_19 1.81634 110.615 118.062 212s Investment_20 0.40799 28.355 24.846 212s Investment_21 0.48605 36.794 33.781 212s Investment_22 0.36497 32.263 27.628 212s PrivateWages_2 -3.69675 -168.572 -165.984 212s PrivateWages_3 1.96345 98.369 89.533 212s PrivateWages_4 5.14109 294.070 257.568 212s PrivateWages_5 -0.11550 -6.595 -6.607 212s PrivateWages_6 -0.93929 -57.297 -53.633 212s PrivateWages_8 -2.33652 -150.472 -149.537 212s PrivateWages_9 1.16743 75.299 75.183 212s PrivateWages_10 4.21148 282.169 271.641 212s PrivateWages_11 -1.22037 -74.687 -81.765 212s PrivateWages_12 1.03941 55.504 63.612 212s PrivateWages_13 -0.82197 -36.413 -43.893 212s PrivateWages_14 1.21684 54.880 53.906 212s PrivateWages_15 0.91815 45.632 41.409 212s PrivateWages_16 -0.07001 -3.809 -3.480 212s PrivateWages_17 -2.75052 -172.458 -149.628 212s PrivateWages_18 2.84549 184.957 178.412 212s PrivateWages_19 -2.80656 -170.920 -182.427 212s PrivateWages_20 -1.38615 -96.338 -84.417 212s PrivateWages_21 -4.11826 -311.753 -286.219 212s PrivateWages_22 2.10334 185.935 159.223 212s PrivateWages_trend 212s Consumption_2 4.0239 212s Consumption_3 17.7482 212s Consumption_4 18.9705 212s Consumption_5 5.7596 212s Consumption_6 0.5754 212s Consumption_7 0.0000 212s Consumption_8 -7.5068 212s Consumption_9 -4.2255 212s Consumption_10 1.9430 212s Consumption_11 -0.6116 212s Consumption_12 0.0000 212s Consumption_13 -0.1260 212s Consumption_14 0.9649 212s Consumption_15 -0.0264 212s Consumption_16 -0.0861 212s Consumption_17 11.3217 212s Consumption_18 -3.6047 212s Consumption_19 2.9894 212s Consumption_20 10.6910 212s Consumption_21 9.3830 212s Consumption_22 -32.9479 212s Investment_2 -2.0743 212s Investment_3 -0.7706 212s Investment_4 6.1643 212s Investment_5 -6.9428 212s Investment_6 1.4845 212s Investment_7 0.0000 212s Investment_8 2.2907 212s Investment_9 -1.0554 212s Investment_10 1.6870 212s Investment_11 0.1725 212s Investment_12 0.0000 212s Investment_13 -0.2139 212s Investment_14 -0.5046 212s Investment_15 0.3423 212s Investment_16 -0.0343 212s Investment_17 -3.5712 212s Investment_18 -0.1058 212s Investment_19 12.7144 212s Investment_20 3.2639 212s Investment_21 4.3745 212s Investment_22 3.6497 212s PrivateWages_2 36.9675 212s PrivateWages_3 -17.6711 212s PrivateWages_4 -41.1287 212s PrivateWages_5 0.8085 212s PrivateWages_6 5.6357 212s PrivateWages_8 9.3461 212s PrivateWages_9 -3.5023 212s PrivateWages_10 -8.4230 212s PrivateWages_11 1.2204 212s PrivateWages_12 0.0000 212s PrivateWages_13 -0.8220 212s PrivateWages_14 2.4337 212s PrivateWages_15 2.7544 212s PrivateWages_16 -0.2801 212s PrivateWages_17 -13.7526 212s PrivateWages_18 17.0729 212s PrivateWages_19 -19.6459 212s PrivateWages_20 -11.0892 212s PrivateWages_21 -37.0644 212s PrivateWages_22 21.0334 212s [1] TRUE 212s > Bread 212s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 212s [1,] 85.2889 -0.01362 -0.83841 212s [2,] -0.0136 0.37283 -0.23220 212s [3,] -0.8384 -0.23220 0.36858 212s [4,] -1.6590 -0.05994 -0.03120 212s [5,] -3.1844 -0.68255 0.70355 212s [6,] 0.0595 0.01846 -0.01774 212s [7,] -0.0239 -0.01745 0.02009 212s [8,] 0.0127 0.00329 -0.00362 212s [9,] -36.0142 0.07978 1.66083 212s [10,] 0.3888 -0.06209 0.04032 212s [11,] 0.2001 0.06287 -0.07012 212s [12,] 0.1814 0.03185 0.02619 212s Consumption_wages Investment_(Intercept) Investment_corpProf 212s [1,] -1.66e+00 -3.184 0.05950 212s [2,] -5.99e-02 -0.683 0.01846 212s [3,] -3.12e-02 0.704 -0.01774 212s [4,] 7.69e-02 0.082 -0.00204 212s [5,] 8.20e-02 1298.386 -12.39923 212s [6,] -2.04e-03 -12.399 0.41486 212s [7,] -2.16e-05 9.908 -0.35328 212s [8,] -2.54e-04 -6.230 0.05576 212s [9,] 1.50e-01 24.451 -0.18195 212s [10,] 6.53e-06 0.391 0.02158 212s [11,] -2.68e-03 -0.821 -0.01913 212s [12,] -2.78e-02 -0.890 0.00590 212s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 212s [1,] -2.39e-02 0.012670 -36.0142 212s [2,] -1.75e-02 0.003286 0.0798 212s [3,] 2.01e-02 -0.003616 1.6608 212s [4,] -2.16e-05 -0.000254 0.1499 212s [5,] 9.91e+00 -6.230058 24.4513 212s [6,] -3.53e-01 0.055757 -0.1819 212s [7,] 4.47e-01 -0.056152 -0.6460 212s [8,] -5.62e-02 0.030966 -0.0512 212s [9,] -6.46e-01 -0.051180 80.1680 212s [10,] -1.22e-02 -0.002778 -0.3588 212s [11,] 2.36e-02 0.003775 -0.9890 212s [12,] -1.61e-02 0.005268 0.9201 212s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 212s [1,] 3.89e-01 0.20005 0.18143 212s [2,] -6.21e-02 0.06287 0.03185 212s [3,] 4.03e-02 -0.07012 0.02619 212s [4,] 6.53e-06 -0.00268 -0.02782 212s [5,] 3.91e-01 -0.82129 -0.89038 212s [6,] 2.16e-02 -0.01913 0.00590 212s [7,] -1.22e-02 0.02360 -0.01606 212s [8,] -2.78e-03 0.00377 0.00527 212s [9,] -3.59e-01 -0.98896 0.92007 212s [10,] 4.82e-02 -0.04360 -0.01308 212s [11,] -4.36e-02 0.06217 -0.00244 212s [12,] -1.31e-02 -0.00244 0.04948 212s > 212s > # 3SLS 212s > summary 212s 212s systemfit results 212s method: 3SLS 212s 212s N DF SSR detRCov OLS-R2 McElroy-R2 212s system 60 48 62.6 0.265 0.968 0.994 212s 212s N DF SSR MSE RMSE R2 Adj R2 212s Consumption 20 16 17.8 1.114 1.06 0.981 0.977 212s Investment 20 16 34.3 2.143 1.46 0.853 0.825 212s PrivateWages 20 16 10.5 0.656 0.81 0.987 0.984 212s 212s The covariance matrix of the residuals used for estimation 212s Consumption Investment PrivateWages 212s Consumption 1.034 0.309 -0.383 212s Investment 0.309 1.151 0.202 212s PrivateWages -0.383 0.202 0.487 212s 212s The covariance matrix of the residuals 212s Consumption Investment PrivateWages 212s Consumption 0.891 0.304 -0.391 212s Investment 0.304 1.715 0.388 212s PrivateWages -0.391 0.388 0.525 212s 212s The correlations of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.000 0.246 -0.571 212s Investment 0.246 1.000 0.409 212s PrivateWages -0.571 0.409 1.000 212s 212s 212s 3SLS estimates for 'Consumption' (equation 1) 212s Model Formula: consump ~ corpProf + corpProfLag + wages 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 16.3668 1.3024 12.57 1.1e-09 *** 212s corpProf 0.1186 0.1073 1.10 0.29 212s corpProfLag 0.1448 0.1008 1.44 0.17 212s wages 0.8006 0.0391 20.47 6.7e-13 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.056 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 17.825 MSE: 1.114 Root MSE: 1.056 212s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 212s 212s 212s 3SLS estimates for 'Investment' (equation 2) 212s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 24.8872 6.2956 3.95 0.00114 ** 212s corpProf 0.0702 0.1458 0.48 0.63648 212s corpProfLag 0.6688 0.1402 4.77 0.00021 *** 212s capitalLag -0.1786 0.0303 -5.90 2.3e-05 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.464 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 34.295 MSE: 2.143 Root MSE: 1.464 212s Multiple R-Squared: 0.853 Adjusted R-Squared: 0.825 212s 212s 212s 3SLS estimates for 'PrivateWages' (equation 3) 212s Model Formula: privWage ~ gnp + gnpLag + trend 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 1.6387 1.1457 1.43 0.17188 212s gnp 0.4062 0.0324 12.52 1.1e-09 *** 212s gnpLag 0.1784 0.0347 5.14 1.0e-04 *** 212s trend 0.1435 0.0292 4.91 0.00016 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 0.81 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 10.497 MSE: 0.656 Root MSE: 0.81 212s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 212s 212s > residuals 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 -0.3538 -1.795 -1.2388 212s 3 -0.9465 0.154 0.4649 212s 4 -1.4189 0.678 1.4344 212s 5 -0.3546 -1.666 -0.1354 212s 6 0.1366 0.251 -0.3452 212s 7 NA NA NA 212s 8 1.4213 1.150 -0.7445 212s 9 1.2173 0.476 0.3001 212s 10 -0.4636 2.200 1.2232 212s 11 -0.0650 -0.962 -0.4104 212s 12 -0.5422 -0.808 0.2495 212s 13 -0.7092 -1.098 -0.3057 212s 14 0.4898 1.542 0.3497 212s 15 -0.0502 -0.155 0.2949 212s 16 0.0272 0.154 0.0214 212s 17 1.8311 1.932 -0.7322 212s 18 -0.4567 -0.180 0.9090 212s 19 0.0650 -3.381 -0.7795 212s 20 1.2135 0.557 -0.2847 212s 21 0.9466 0.167 -1.0812 212s 22 -1.9877 0.784 0.8102 212s > fitted 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 42.3 1.595 26.7 212s 3 45.9 1.746 28.8 212s 4 50.6 4.522 32.7 212s 5 51.0 4.666 34.0 212s 6 52.5 4.849 35.7 212s 7 NA NA NA 212s 8 54.8 3.050 38.6 212s 9 56.1 2.524 38.9 212s 10 58.3 2.900 40.1 212s 11 55.1 1.962 38.3 212s 12 51.4 -2.592 34.3 212s 13 46.3 -5.102 29.3 212s 14 46.0 -6.642 28.2 212s 15 48.8 -2.845 30.3 212s 16 51.3 -1.454 33.2 212s 17 55.9 0.168 37.5 212s 18 59.2 2.180 40.1 212s 19 57.4 1.481 39.0 212s 20 60.4 0.743 41.9 212s 21 64.1 3.133 46.1 212s 22 71.7 4.116 52.5 212s > predict 212s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 212s 1 NA NA NA NA 212s 2 42.3 0.468 39.8 44.7 212s 3 45.9 0.543 43.4 48.5 212s 4 50.6 0.352 48.3 53.0 212s 5 51.0 0.407 48.6 53.4 212s 6 52.5 0.411 50.1 54.9 212s 7 NA NA NA NA 212s 8 54.8 0.340 52.4 57.1 212s 9 56.1 0.372 53.7 58.5 212s 10 58.3 0.387 55.9 60.6 212s 11 55.1 0.687 52.4 57.7 212s 12 51.4 0.558 48.9 54.0 212s 13 46.3 0.713 43.6 49.0 212s 14 46.0 0.599 43.4 48.6 212s 15 48.8 0.368 46.4 51.1 212s 16 51.3 0.326 48.9 53.6 212s 17 55.9 0.388 53.5 58.3 212s 18 59.2 0.319 56.8 61.5 212s 19 57.4 0.391 55.0 59.8 212s 20 60.4 0.457 57.9 62.8 212s 21 64.1 0.437 61.6 66.5 212s 22 71.7 0.674 69.0 74.3 212s Investment.pred Investment.se.fit Investment.lwr Investment.upr 212s 1 NA NA NA NA 212s 2 1.595 0.731 -1.8742 5.065 212s 3 1.746 0.533 -1.5566 5.050 212s 4 4.522 0.484 1.2530 7.791 212s 5 4.666 0.406 1.4458 7.887 212s 6 4.849 0.386 1.6390 8.058 212s 7 NA NA NA NA 212s 8 3.050 0.325 -0.1296 6.229 212s 9 2.524 0.467 -0.7334 5.782 212s 10 2.900 0.515 -0.3900 6.190 212s 11 1.962 0.769 -1.5438 5.467 212s 12 -2.592 0.608 -5.9519 0.769 212s 13 -5.102 0.774 -8.6129 -1.592 212s 14 -6.642 0.807 -10.1867 -3.098 212s 15 -2.845 0.395 -6.0599 0.370 212s 16 -1.454 0.341 -4.6409 1.733 212s 17 0.168 0.442 -3.0739 3.410 212s 18 2.180 0.281 -0.9807 5.340 212s 19 1.481 0.414 -1.7440 4.706 212s 20 0.743 0.492 -2.5310 4.017 212s 21 3.133 0.414 -0.0924 6.358 212s 22 4.116 0.583 0.7756 7.457 212s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 212s 1 NA NA NA NA 212s 2 26.7 0.322 24.9 28.6 212s 3 28.8 0.328 27.0 30.7 212s 4 32.7 0.340 30.8 34.5 212s 5 34.0 0.250 32.2 35.8 212s 6 35.7 0.257 33.9 37.5 212s 7 NA NA NA NA 212s 8 38.6 0.254 36.8 40.4 212s 9 38.9 0.241 37.1 40.7 212s 10 40.1 0.235 38.3 41.9 212s 11 38.3 0.325 36.5 40.2 212s 12 34.3 0.349 32.4 36.1 212s 13 29.3 0.425 27.4 31.2 212s 14 28.2 0.340 26.3 30.0 212s 15 30.3 0.326 28.5 32.2 212s 16 33.2 0.272 31.4 35.0 212s 17 37.5 0.273 35.7 39.3 212s 18 40.1 0.214 38.3 41.9 212s 19 39.0 0.336 37.1 40.8 212s 20 41.9 0.290 40.1 43.7 212s 21 46.1 0.305 44.2 47.9 212s 22 52.5 0.479 50.5 54.5 212s > model.frame 212s [1] TRUE 212s > model.matrix 212s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 212s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 212s [3] "Numeric: lengths (744, 720) differ" 212s > nobs 212s [1] 60 212s > linearHypothesis 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 49 212s 2 48 1 0.22 0.64 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 49 212s 2 48 1 0.29 0.59 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 49 212s 2 48 1 0.29 0.59 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 48 2 0.29 0.75 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 48 2 0.38 0.68 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 50 212s 2 48 2 0.77 0.68 212s > logLik 212s 'log Lik.' -71.9 (df=18) 212s 'log Lik.' -82.9 (df=18) 212s Estimating function 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 -2.1852 -28.316 212s Consumption_3 -1.2615 -21.074 212s Consumption_4 -0.7432 -14.221 212s Consumption_5 -4.1386 -86.649 212s Consumption_6 0.0344 0.669 212s Consumption_8 5.9528 102.039 212s Consumption_9 3.6199 70.548 212s Consumption_10 1.2130 24.820 212s Consumption_11 -2.3309 -39.266 212s Consumption_12 -1.5509 -19.665 212s Consumption_13 -2.9298 -26.139 212s Consumption_14 2.9907 27.815 212s Consumption_15 -1.7611 -22.533 212s Consumption_16 -1.0403 -14.834 212s Consumption_17 7.8605 115.957 212s Consumption_18 -1.2660 -24.744 212s Consumption_19 -6.1974 -119.976 212s Consumption_20 4.2546 73.971 212s Consumption_21 1.7695 35.564 212s Consumption_22 -2.2905 -52.365 212s Investment_2 1.5294 19.818 212s Investment_3 -0.1395 -2.330 212s Investment_4 -0.5222 -9.992 212s Investment_5 1.4794 30.973 212s Investment_6 -0.2466 -4.801 212s Investment_8 -1.1148 -19.108 212s Investment_9 -0.4909 -9.566 212s Investment_10 -1.9066 -39.013 212s Investment_11 0.8748 14.736 212s Investment_12 0.7489 9.496 212s Investment_13 1.0277 9.169 212s Investment_14 -1.3972 -12.995 212s Investment_15 0.1582 2.024 212s Investment_16 -0.1132 -1.614 212s Investment_17 -1.7775 -26.221 212s Investment_18 0.2812 5.496 212s Investment_19 3.0567 59.173 212s Investment_20 -0.5590 -9.719 212s Investment_21 -0.1981 -3.981 212s Investment_22 -0.6908 -15.792 212s PrivateWages_2 -3.3803 -43.802 212s PrivateWages_3 1.2445 20.789 212s PrivateWages_4 3.1328 59.947 212s PrivateWages_5 -2.9316 -61.378 212s PrivateWages_6 -0.3443 -6.703 212s PrivateWages_8 1.9219 32.944 212s PrivateWages_9 2.2216 43.296 212s PrivateWages_10 4.0703 83.288 212s PrivateWages_11 -2.6344 -44.377 212s PrivateWages_12 -0.6120 -7.760 212s PrivateWages_13 -2.5653 -22.887 212s PrivateWages_14 2.8669 26.663 212s PrivateWages_15 -0.5912 -7.565 212s PrivateWages_16 -0.6625 -9.447 212s PrivateWages_17 2.6204 38.656 212s PrivateWages_18 0.0477 0.933 212s PrivateWages_19 -7.1288 -138.006 212s PrivateWages_20 1.4620 25.419 212s PrivateWages_21 -1.3672 -27.479 212s PrivateWages_22 2.6294 60.113 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 -27.752 -63.61 212s Consumption_3 -15.643 -40.21 212s Consumption_4 -12.560 -26.46 212s Consumption_5 -76.150 -161.61 212s Consumption_6 0.667 1.34 212s Consumption_8 116.675 236.66 212s Consumption_9 71.675 153.05 212s Consumption_10 25.593 53.50 212s Consumption_11 -50.581 -101.08 212s Consumption_12 -24.194 -61.19 212s Consumption_13 -33.399 -102.70 212s Consumption_14 20.935 98.78 212s Consumption_15 -19.724 -66.25 212s Consumption_16 -12.795 -41.59 212s Consumption_17 110.047 328.11 212s Consumption_18 -22.282 -60.30 212s Consumption_19 -107.216 -306.49 212s Consumption_20 65.095 205.74 212s Consumption_21 33.620 94.08 212s Consumption_22 -48.330 -139.53 212s Investment_2 19.424 44.52 212s Investment_3 -1.729 -4.45 212s Investment_4 -8.825 -18.59 212s Investment_5 27.221 57.77 212s Investment_6 -4.784 -9.58 212s Investment_8 -21.849 -44.32 212s Investment_9 -9.719 -20.75 212s Investment_10 -40.229 -84.09 212s Investment_11 18.983 37.94 212s Investment_12 11.683 29.55 212s Investment_13 11.716 36.03 212s Investment_14 -9.780 -46.15 212s Investment_15 1.772 5.95 212s Investment_16 -1.392 -4.53 212s Investment_17 -24.885 -74.20 212s Investment_18 4.949 13.39 212s Investment_19 52.880 151.16 212s Investment_20 -8.553 -27.03 212s Investment_21 -3.764 -10.53 212s Investment_22 -14.576 -42.08 212s PrivateWages_2 -42.929 -98.41 212s PrivateWages_3 15.432 39.67 212s PrivateWages_4 52.944 111.55 212s PrivateWages_5 -53.942 -114.48 212s PrivateWages_6 -6.679 -13.37 212s PrivateWages_8 37.670 76.41 212s PrivateWages_9 43.987 93.93 212s PrivateWages_10 85.884 179.53 212s PrivateWages_11 -57.165 -114.24 212s PrivateWages_12 -9.547 -24.14 212s PrivateWages_13 -29.244 -89.93 212s PrivateWages_14 20.068 94.68 212s PrivateWages_15 -6.622 -22.24 212s PrivateWages_16 -8.149 -26.49 212s PrivateWages_17 36.686 109.38 212s PrivateWages_18 0.840 2.27 212s PrivateWages_19 -123.329 -352.55 212s PrivateWages_20 22.369 70.70 212s PrivateWages_21 -25.977 -72.69 212s PrivateWages_22 55.481 160.18 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 0.9588 12.424 212s Consumption_3 0.5535 9.246 212s Consumption_4 0.3261 6.240 212s Consumption_5 1.8159 38.018 212s Consumption_6 -0.0151 -0.294 212s Consumption_8 -2.6118 -44.771 212s Consumption_9 -1.5883 -30.954 212s Consumption_10 -0.5322 -10.890 212s Consumption_11 1.0227 17.228 212s Consumption_12 0.6805 8.628 212s Consumption_13 1.2855 11.469 212s Consumption_14 -1.3122 -12.204 212s Consumption_15 0.7727 9.887 212s Consumption_16 0.4564 6.508 212s Consumption_17 -3.4489 -50.877 212s Consumption_18 0.5555 10.857 212s Consumption_19 2.7192 52.640 212s Consumption_20 -1.8667 -32.456 212s Consumption_21 -0.7764 -15.604 212s Consumption_22 1.0050 22.976 212s Investment_2 -2.3899 -30.969 212s Investment_3 0.2179 3.641 212s Investment_4 0.8160 15.614 212s Investment_5 -2.3118 -48.401 212s Investment_6 0.3854 7.502 212s Investment_8 1.7420 29.860 212s Investment_9 0.7670 14.948 212s Investment_10 2.9794 60.964 212s Investment_11 -1.3670 -23.027 212s Investment_12 -1.1702 -14.838 212s Investment_13 -1.6060 -14.328 212s Investment_14 2.1833 20.306 212s Investment_15 -0.2472 -3.163 212s Investment_16 0.1769 2.522 212s Investment_17 2.7776 40.974 212s Investment_18 -0.4394 -8.588 212s Investment_19 -4.7765 -92.468 212s Investment_20 0.8735 15.187 212s Investment_21 0.3095 6.221 212s Investment_22 1.0795 24.678 212s PrivateWages_2 2.1957 28.452 212s PrivateWages_3 -0.8084 -13.504 212s PrivateWages_4 -2.0349 -38.939 212s PrivateWages_5 1.9043 39.869 212s PrivateWages_6 0.2236 4.354 212s PrivateWages_8 -1.2484 -21.399 212s PrivateWages_9 -1.4431 -28.123 212s PrivateWages_10 -2.6439 -54.100 212s PrivateWages_11 1.7112 28.826 212s PrivateWages_12 0.3975 5.041 212s PrivateWages_13 1.6663 14.867 212s PrivateWages_14 -1.8622 -17.319 212s PrivateWages_15 0.3840 4.914 212s PrivateWages_16 0.4304 6.137 212s PrivateWages_17 -1.7021 -25.110 212s PrivateWages_18 -0.0310 -0.606 212s PrivateWages_19 4.6306 89.644 212s PrivateWages_20 -0.9497 -16.511 212s PrivateWages_21 0.8881 17.849 212s PrivateWages_22 -1.7080 -39.047 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 12.176 175.26 212s Consumption_3 6.864 101.07 212s Consumption_4 5.511 60.16 212s Consumption_5 33.412 344.47 212s Consumption_6 -0.293 -2.91 212s Consumption_8 -51.192 -531.25 212s Consumption_9 -31.448 -329.73 212s Consumption_10 -11.229 -112.08 212s Consumption_11 22.193 220.60 212s Consumption_12 10.615 147.46 212s Consumption_13 14.654 274.19 212s Consumption_14 -9.185 -271.76 212s Consumption_15 8.654 156.08 212s Consumption_16 5.614 90.83 212s Consumption_17 -48.284 -681.84 212s Consumption_18 9.776 110.98 212s Consumption_19 47.042 548.73 212s Consumption_20 -28.561 -373.16 212s Consumption_21 -14.751 -156.21 212s Consumption_22 21.205 205.52 212s Investment_2 -30.352 -436.88 212s Investment_3 2.702 39.79 212s Investment_4 13.790 150.55 212s Investment_5 -42.537 -438.54 212s Investment_6 7.476 74.26 212s Investment_8 34.143 354.32 212s Investment_9 15.187 159.24 212s Investment_10 62.865 627.45 212s Investment_11 -29.663 -294.86 212s Investment_12 -18.256 -253.59 212s Investment_13 -18.308 -342.55 212s Investment_14 15.283 452.17 212s Investment_15 -2.768 -49.93 212s Investment_16 2.176 35.20 212s Investment_17 38.886 549.13 212s Investment_18 -7.734 -87.79 212s Investment_19 -82.633 -963.90 212s Investment_20 13.365 174.61 212s Investment_21 5.881 62.28 212s Investment_22 22.777 220.75 212s PrivateWages_2 27.885 401.37 212s PrivateWages_3 -10.024 -147.61 212s PrivateWages_4 -34.390 -375.44 212s PrivateWages_5 35.039 361.24 212s PrivateWages_6 4.339 43.10 212s PrivateWages_8 -24.469 -253.93 212s PrivateWages_9 -28.572 -299.58 212s PrivateWages_10 -55.787 -556.81 212s PrivateWages_11 37.132 369.10 212s PrivateWages_12 6.201 86.14 212s PrivateWages_13 18.996 355.42 212s PrivateWages_14 -13.035 -385.66 212s PrivateWages_15 4.301 77.58 212s PrivateWages_16 5.293 85.64 212s PrivateWages_17 -23.830 -336.51 212s PrivateWages_18 -0.546 -6.19 212s PrivateWages_19 80.110 934.46 212s PrivateWages_20 -14.530 -189.84 212s PrivateWages_21 16.874 178.68 212s PrivateWages_22 -36.038 -349.28 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 -2.1174 -99.67 -95.07 212s Consumption_3 -1.2224 -60.61 -55.74 212s Consumption_4 -0.7201 -40.72 -36.08 212s Consumption_5 -4.0103 -243.37 -229.39 212s Consumption_6 0.0333 2.02 1.90 212s Consumption_8 5.7682 346.08 369.17 212s Consumption_9 3.5077 218.42 225.90 212s Consumption_10 1.1754 75.89 75.81 212s Consumption_11 -2.2587 -143.90 -151.33 212s Consumption_12 -1.5028 -82.40 -91.97 212s Consumption_13 -2.8389 -133.36 -151.60 212s Consumption_14 2.8980 122.09 128.38 212s Consumption_15 -1.7065 -87.40 -76.96 212s Consumption_16 -1.0080 -55.78 -50.10 212s Consumption_17 7.6168 437.16 414.35 212s Consumption_18 -1.2268 -82.41 -76.92 212s Consumption_19 -6.0053 -411.44 -390.34 212s Consumption_20 4.1227 275.58 251.07 212s Consumption_21 1.7146 128.37 119.16 212s Consumption_22 -2.2195 -192.83 -168.02 212s Investment_2 2.1940 103.27 98.51 212s Investment_3 -0.2001 -9.92 -9.12 212s Investment_4 -0.7491 -42.36 -37.53 212s Investment_5 2.1223 128.79 121.39 212s Investment_6 -0.3538 -21.44 -20.20 212s Investment_8 -1.5992 -95.95 -102.35 212s Investment_9 -0.7042 -43.85 -45.35 212s Investment_10 -2.7351 -176.60 -176.41 212s Investment_11 1.2549 79.95 84.08 212s Investment_12 1.0743 58.91 65.75 212s Investment_13 1.4743 69.26 78.73 212s Investment_14 -2.0044 -84.44 -88.79 212s Investment_15 0.2269 11.62 10.23 212s Investment_16 -0.1624 -8.99 -8.07 212s Investment_17 -2.5499 -146.35 -138.71 212s Investment_18 0.4034 27.10 25.29 212s Investment_19 4.3849 300.42 285.02 212s Investment_20 -0.8019 -53.60 -48.84 212s Investment_21 -0.2842 -21.27 -19.75 212s Investment_22 -0.9910 -86.09 -75.02 212s PrivateWages_2 -7.3399 -345.49 -329.56 212s PrivateWages_3 2.7024 133.99 123.23 212s PrivateWages_4 6.8025 384.63 340.81 212s PrivateWages_5 -6.3658 -386.31 -364.12 212s PrivateWages_6 -0.7476 -45.31 -42.69 212s PrivateWages_8 4.1733 250.39 267.09 212s PrivateWages_9 4.8240 300.38 310.66 212s PrivateWages_10 8.8383 570.68 570.07 212s PrivateWages_11 -5.7203 -364.45 -383.26 212s PrivateWages_12 -1.3289 -72.87 -81.33 212s PrivateWages_13 -5.5702 -261.67 -297.45 212s PrivateWages_14 6.2251 262.25 275.77 212s PrivateWages_15 -1.2838 -65.75 -57.90 212s PrivateWages_16 -1.4387 -79.61 -71.50 212s PrivateWages_17 5.6900 326.57 309.54 212s PrivateWages_18 0.1036 6.96 6.50 212s PrivateWages_19 -15.4796 -1060.55 -1006.17 212s PrivateWages_20 3.1746 212.21 193.34 212s PrivateWages_21 -2.9688 -222.26 -206.33 212s PrivateWages_22 5.7096 496.04 432.21 212s PrivateWages_trend 212s Consumption_2 21.174 212s Consumption_3 11.002 212s Consumption_4 5.761 212s Consumption_5 28.072 212s Consumption_6 -0.200 212s Consumption_8 -23.073 212s Consumption_9 -10.523 212s Consumption_10 -2.351 212s Consumption_11 2.259 212s Consumption_12 0.000 212s Consumption_13 -2.839 212s Consumption_14 5.796 212s Consumption_15 -5.119 212s Consumption_16 -4.032 212s Consumption_17 38.084 212s Consumption_18 -7.361 212s Consumption_19 -42.037 212s Consumption_20 32.981 212s Consumption_21 15.431 212s Consumption_22 -22.195 212s Investment_2 -21.940 212s Investment_3 1.801 212s Investment_4 5.993 212s Investment_5 -14.856 212s Investment_6 2.123 212s Investment_8 6.397 212s Investment_9 2.112 212s Investment_10 5.470 212s Investment_11 -1.255 212s Investment_12 0.000 212s Investment_13 1.474 212s Investment_14 -4.009 212s Investment_15 0.681 212s Investment_16 -0.650 212s Investment_17 -12.749 212s Investment_18 2.420 212s Investment_19 30.694 212s Investment_20 -6.415 212s Investment_21 -2.557 212s Investment_22 -9.910 212s PrivateWages_2 73.399 212s PrivateWages_3 -24.321 212s PrivateWages_4 -54.420 212s PrivateWages_5 44.560 212s PrivateWages_6 4.486 212s PrivateWages_8 -16.693 212s PrivateWages_9 -14.472 212s PrivateWages_10 -17.677 212s PrivateWages_11 5.720 212s PrivateWages_12 0.000 212s PrivateWages_13 -5.570 212s PrivateWages_14 12.450 212s PrivateWages_15 -3.851 212s PrivateWages_16 -5.755 212s PrivateWages_17 28.450 212s PrivateWages_18 0.622 212s PrivateWages_19 -108.357 212s PrivateWages_20 25.397 212s PrivateWages_21 -26.719 212s PrivateWages_22 57.096 212s [1] TRUE 212s > Bread 212s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 212s [1,] 101.7742 -0.858360 -0.3736 212s [2,] -0.8584 0.690973 -0.4670 212s [3,] -0.3736 -0.466994 0.6099 212s [4,] -1.8845 -0.076066 -0.0404 212s [5,] 84.1239 -0.877202 2.8173 212s [6,] -1.7843 0.267204 -0.2636 212s [7,] 0.6061 -0.218819 0.2875 212s [8,] -0.3146 -0.000285 -0.0152 212s [9,] -36.6570 0.120759 1.7724 212s [10,] 0.5673 -0.083944 0.0542 212s [11,] 0.0259 0.084615 -0.0868 212s [12,] 0.2015 0.041756 0.0283 212s Consumption_wages Investment_(Intercept) Investment_corpProf 212s [1,] -1.884465 84.124 -1.7843 212s [2,] -0.076066 -0.877 0.2672 212s [3,] -0.040367 2.817 -0.2636 212s [4,] 0.091823 -2.748 0.0379 212s [5,] -2.748307 2378.068 -36.8158 212s [6,] 0.037919 -36.816 1.2756 212s [7,] -0.038383 31.099 -1.1022 212s [8,] 0.013629 -11.271 0.1659 212s [9,] 0.115318 17.951 -0.1175 212s [10,] -0.000915 1.841 0.0121 212s [11,] -0.000905 -2.197 -0.0106 212s [12,] -0.032751 -1.985 0.0278 212s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 212s [1,] 0.60609 -3.15e-01 -3.67e+01 212s [2,] -0.21882 -2.85e-04 1.21e-01 212s [3,] 0.28746 -1.52e-02 1.77e+00 212s [4,] -0.03838 1.36e-02 1.15e-01 212s [5,] 31.09923 -1.13e+01 1.80e+01 212s [6,] -1.10217 1.66e-01 -1.17e-01 212s [7,] 1.17984 -1.58e-01 -9.59e-01 212s [8,] -0.15817 5.51e-02 7.31e-04 212s [9,] -0.95890 7.31e-04 7.88e+01 212s [10,] 0.00248 -1.04e-02 -5.11e-01 212s [11,] 0.01419 1.07e-02 -8.12e-01 212s [12,] -0.04010 1.08e-02 9.53e-01 212s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 212s [1,] 0.567318 0.025878 0.20145 212s [2,] -0.083944 0.084615 0.04176 212s [3,] 0.054179 -0.086845 0.02834 212s [4,] -0.000915 -0.000905 -0.03275 212s [5,] 1.840734 -2.196531 -1.98486 212s [6,] 0.012109 -0.010622 0.02782 212s [7,] 0.002479 0.014187 -0.04010 212s [8,] -0.010386 0.010690 0.01081 212s [9,] -0.511083 -0.811688 0.95314 212s [10,] 0.063161 -0.056453 -0.01901 212s [11,] -0.056453 0.072451 0.00297 212s [12,] -0.019011 0.002975 0.05128 212s > 212s > # I3SLS 212s > summary 212s 212s systemfit results 212s method: iterated 3SLS 212s 212s convergence achieved after 22 iterations 212s 212s N DF SSR detRCov OLS-R2 McElroy-R2 212s system 60 48 107 0.47 0.946 0.996 212s 212s N DF SSR MSE RMSE R2 Adj R2 212s Consumption 20 16 18.1 1.13 1.063 0.981 0.977 212s Investment 20 16 76.4 4.77 2.185 0.672 0.610 212s PrivateWages 20 16 12.3 0.77 0.877 0.984 0.982 212s 212s The covariance matrix of the residuals used for estimation 212s Consumption Investment PrivateWages 212s Consumption 0.905 0.509 -0.437 212s Investment 0.509 3.819 0.709 212s PrivateWages -0.437 0.709 0.616 212s 212s The covariance matrix of the residuals 212s Consumption Investment PrivateWages 212s Consumption 0.905 0.509 -0.437 212s Investment 0.509 3.819 0.709 212s PrivateWages -0.437 0.709 0.616 212s 212s The correlations of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.000 0.274 -0.585 212s Investment 0.274 1.000 0.462 212s PrivateWages -0.585 0.462 1.000 212s 212s 212s 3SLS estimates for 'Consumption' (equation 1) 212s Model Formula: consump ~ corpProf + corpProfLag + wages 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 16.4728 1.2187 13.52 3.6e-10 *** 212s corpProf 0.1642 0.0952 1.73 0.10 212s corpProfLag 0.1552 0.0903 1.72 0.11 212s wages 0.7756 0.0356 21.82 2.5e-13 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.063 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 18.095 MSE: 1.131 Root MSE: 1.063 212s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 212s 212s 212s 3SLS estimates for 'Investment' (equation 2) 212s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 38.7938 9.7249 3.99 0.00106 ** 212s corpProf -0.2501 0.2337 -1.07 0.30036 212s corpProfLag 0.9129 0.2271 4.02 0.00099 *** 212s capitalLag -0.2409 0.0469 -5.14 9.9e-05 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 2.185 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 76.371 MSE: 4.773 Root MSE: 2.185 212s Multiple R-Squared: 0.672 Adjusted R-Squared: 0.61 212s 212s 212s 3SLS estimates for 'PrivateWages' (equation 3) 212s Model Formula: privWage ~ gnp + gnpLag + trend 212s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 212s gnpLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 2.4620 1.2228 2.01 0.061 . 212s gnp 0.3776 0.0318 11.88 2.4e-09 *** 212s gnpLag 0.1937 0.0331 5.85 2.5e-05 *** 212s trend 0.1619 0.0300 5.40 5.9e-05 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 0.877 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 12.318 MSE: 0.77 Root MSE: 0.877 212s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.982 212s 212s > residuals 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 -0.4522 -3.4485 -1.2596 212s 3 -1.1470 0.0027 0.5437 212s 4 -1.6147 0.0274 1.6290 212s 5 -0.6117 -2.0392 -0.0707 212s 6 -0.1229 0.0457 -0.1859 212s 7 NA NA NA 212s 8 1.2461 1.4658 -0.6304 212s 9 1.0158 1.4202 0.3924 212s 10 -0.6460 3.2062 1.3671 212s 11 -0.0554 -1.7386 -0.4891 212s 12 -0.3472 -1.3793 0.0179 212s 13 -0.3947 -2.2646 -0.6968 212s 14 0.6536 2.4092 0.1021 212s 15 0.0821 -0.2787 0.1482 212s 16 0.1381 0.1196 -0.0796 212s 17 1.8826 2.5548 -0.6862 212s 18 -0.3415 -0.4009 0.8755 212s 19 0.2296 -4.0454 -0.9839 212s 20 1.3178 1.4481 -0.1989 212s 21 1.0065 0.9087 -0.9681 212s 22 -1.8388 1.9868 1.1734 212s > fitted 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 42.4 3.249 26.8 212s 3 46.1 1.897 28.8 212s 4 50.8 5.173 32.5 212s 5 51.2 5.039 34.0 212s 6 52.7 5.054 35.6 212s 7 NA NA NA 212s 8 55.0 2.734 38.5 212s 9 56.3 1.580 38.8 212s 10 58.4 1.894 39.9 212s 11 55.1 2.739 38.4 212s 12 51.2 -2.021 34.5 212s 13 46.0 -3.935 29.7 212s 14 45.8 -7.509 28.4 212s 15 48.6 -2.721 30.5 212s 16 51.2 -1.420 33.3 212s 17 55.8 -0.455 37.5 212s 18 59.0 2.401 40.1 212s 19 57.3 2.145 39.2 212s 20 60.3 -0.148 41.8 212s 21 64.0 2.391 46.0 212s 22 71.5 2.913 52.1 212s > predict 212s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 212s 1 NA NA NA NA 212s 2 42.4 0.437 41.5 43.2 212s 3 46.1 0.492 45.2 47.1 212s 4 50.8 0.321 50.2 51.5 212s 5 51.2 0.369 50.5 52.0 212s 6 52.7 0.372 52.0 53.5 212s 7 NA NA NA NA 212s 8 55.0 0.310 54.3 55.6 212s 9 56.3 0.338 55.6 57.0 212s 10 58.4 0.355 57.7 59.2 212s 11 55.1 0.618 53.8 56.3 212s 12 51.2 0.501 50.2 52.3 212s 13 46.0 0.642 44.7 47.3 212s 14 45.8 0.547 44.7 46.9 212s 15 48.6 0.340 47.9 49.3 212s 16 51.2 0.300 50.6 51.8 212s 17 55.8 0.354 55.1 56.5 212s 18 59.0 0.294 58.4 59.6 212s 19 57.3 0.354 56.6 58.0 212s 20 60.3 0.418 59.4 61.1 212s 21 64.0 0.407 63.2 64.8 212s 22 71.5 0.628 70.3 72.8 212s Investment.pred Investment.se.fit Investment.lwr Investment.upr 212s 1 NA NA NA NA 212s 2 3.249 1.160 0.91672 5.580 212s 3 1.897 0.934 0.02009 3.775 212s 4 5.173 0.803 3.55865 6.787 212s 5 5.039 0.693 3.64486 6.433 212s 6 5.054 0.674 3.69840 6.410 212s 7 NA NA NA NA 212s 8 2.734 0.584 1.56002 3.908 212s 9 1.580 0.783 0.00466 3.155 212s 10 1.894 0.868 0.14846 3.639 212s 11 2.739 1.321 0.08241 5.395 212s 12 -2.021 1.064 -4.16036 0.119 212s 13 -3.935 1.349 -6.64712 -1.224 212s 14 -7.509 1.360 -10.24349 -4.775 212s 15 -2.721 0.712 -4.15288 -1.290 212s 16 -1.420 0.614 -2.65412 -0.185 212s 17 -0.455 0.751 -1.96433 1.055 212s 18 2.401 0.498 1.39939 3.402 212s 19 2.145 0.698 0.74152 3.549 212s 20 -0.148 0.816 -1.78957 1.493 212s 21 2.391 0.713 0.95855 3.824 212s 22 2.913 0.984 0.93419 4.892 212s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 212s 1 NA NA NA NA 212s 2 26.8 0.347 26.1 27.5 212s 3 28.8 0.348 28.1 29.5 212s 4 32.5 0.354 31.8 33.2 212s 5 34.0 0.263 33.4 34.5 212s 6 35.6 0.274 35.0 36.1 212s 7 NA NA NA NA 212s 8 38.5 0.268 38.0 39.1 212s 9 38.8 0.256 38.3 39.3 212s 10 39.9 0.254 39.4 40.4 212s 11 38.4 0.323 37.7 39.0 212s 12 34.5 0.347 33.8 35.2 212s 13 29.7 0.435 28.8 30.6 212s 14 28.4 0.366 27.7 29.1 212s 15 30.5 0.341 29.8 31.1 212s 16 33.3 0.285 32.7 33.9 212s 17 37.5 0.275 36.9 38.0 212s 18 40.1 0.233 39.7 40.6 212s 19 39.2 0.346 38.5 39.9 212s 20 41.8 0.298 41.2 42.4 212s 21 46.0 0.329 45.3 46.6 212s 22 52.1 0.510 51.1 53.2 212s > model.frame 212s [1] TRUE 212s > model.matrix 212s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 212s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 212s [3] "Numeric: lengths (744, 720) differ" 212s > nobs 212s [1] 60 212s > linearHypothesis 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 49 212s 2 48 1 0.4 0.53 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 49 212s 2 48 1 0.5 0.49 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 49 212s 2 48 1 0.5 0.48 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 48 2 0.66 0.52 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 48 2 0.83 0.44 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 50 212s 2 48 2 1.66 0.44 212s > logLik 212s 'log Lik.' -77.6 (df=18) 212s 'log Lik.' -92.7 (df=18) 212s Estimating function 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 -4.9216 -63.77 212s Consumption_3 -3.3974 -56.75 212s Consumption_4 -2.5781 -49.33 212s Consumption_5 -9.6538 -202.12 212s Consumption_6 -0.8124 -15.82 212s Consumption_8 11.9408 204.68 212s Consumption_9 6.9299 135.05 212s Consumption_10 1.8984 38.85 212s Consumption_11 -4.8868 -82.32 212s Consumption_12 -2.6585 -33.71 212s Consumption_13 -5.0990 -45.49 212s Consumption_14 7.0717 65.77 212s Consumption_15 -3.1138 -39.84 212s Consumption_16 -1.6973 -24.20 212s Consumption_17 16.7458 247.03 212s Consumption_18 -2.5779 -50.39 212s Consumption_19 -12.5621 -243.19 212s Consumption_20 9.4057 163.53 212s Consumption_21 4.0953 82.31 212s Consumption_22 -4.1289 -94.39 212s Investment_2 4.3863 56.84 212s Investment_3 0.0612 1.02 212s Investment_4 -0.2801 -5.36 212s Investment_5 2.1936 45.93 212s Investment_6 0.1486 2.89 212s Investment_8 -1.0616 -18.20 212s Investment_9 -1.3484 -26.28 212s Investment_10 -3.8396 -78.57 212s Investment_11 1.8918 31.87 212s Investment_12 1.4041 17.80 212s Investment_13 2.3647 21.10 212s Investment_14 -2.5638 -23.84 212s Investment_15 0.2053 2.63 212s Investment_16 -0.2445 -3.49 212s Investment_17 -2.4423 -36.03 212s Investment_18 -0.2128 -4.16 212s Investment_19 4.0168 77.76 212s Investment_20 -1.3846 -24.07 212s Investment_21 -0.8726 -17.54 212s Investment_22 -2.4220 -55.37 212s PrivateWages_2 -7.8312 -101.48 212s PrivateWages_3 3.1927 53.33 212s PrivateWages_4 8.1013 155.02 212s PrivateWages_5 -6.1495 -128.75 212s PrivateWages_6 -0.1677 -3.26 212s PrivateWages_8 4.4536 76.34 212s PrivateWages_9 5.3302 103.88 212s PrivateWages_10 9.8611 201.78 212s PrivateWages_11 -6.2042 -104.51 212s PrivateWages_12 -2.2572 -28.62 212s PrivateWages_13 -7.3701 -65.76 212s PrivateWages_14 5.2841 49.14 212s PrivateWages_15 -1.8316 -23.44 212s PrivateWages_16 -1.8732 -26.71 212s PrivateWages_17 5.6855 83.87 212s PrivateWages_18 0.2354 4.60 212s PrivateWages_19 -16.6516 -322.36 212s PrivateWages_20 3.4690 60.31 212s PrivateWages_21 -2.8192 -56.66 212s PrivateWages_22 7.5425 172.43 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 -62.504 -143.28 212s Consumption_3 -42.128 -108.30 212s Consumption_4 -43.571 -91.80 212s Consumption_5 -177.629 -376.98 212s Consumption_6 -15.760 -31.55 212s Consumption_8 234.039 474.72 212s Consumption_9 137.212 292.99 212s Consumption_10 40.056 83.73 212s Consumption_11 -106.045 -211.93 212s Consumption_12 -41.472 -104.88 212s Consumption_13 -58.128 -178.75 212s Consumption_14 49.502 233.56 212s Consumption_15 -34.874 -117.14 212s Consumption_16 -20.877 -67.86 212s Consumption_17 234.441 699.00 212s Consumption_18 -45.372 -122.79 212s Consumption_19 -217.325 -621.24 212s Consumption_20 143.908 454.84 212s Consumption_21 77.811 217.74 212s Consumption_22 -87.120 -251.52 212s Investment_2 55.705 127.69 212s Investment_3 0.759 1.95 212s Investment_4 -4.734 -9.97 212s Investment_5 40.363 85.66 212s Investment_6 2.882 5.77 212s Investment_8 -20.807 -42.21 212s Investment_9 -26.697 -57.01 212s Investment_10 -81.017 -169.36 212s Investment_11 41.052 82.04 212s Investment_12 21.904 55.40 212s Investment_13 26.957 82.89 212s Investment_14 -17.946 -84.67 212s Investment_15 2.299 7.72 212s Investment_16 -3.007 -9.77 212s Investment_17 -34.192 -101.95 212s Investment_18 -3.746 -10.14 212s Investment_19 69.491 198.65 212s Investment_20 -21.185 -66.96 212s Investment_21 -16.580 -46.40 212s Investment_22 -51.104 -147.54 212s PrivateWages_2 -99.457 -227.98 212s PrivateWages_3 39.589 101.77 212s PrivateWages_4 136.911 288.46 212s PrivateWages_5 -113.151 -240.14 212s PrivateWages_6 -3.252 -6.51 212s PrivateWages_8 87.291 177.06 212s PrivateWages_9 105.538 225.36 212s PrivateWages_10 208.070 434.95 212s PrivateWages_11 -134.631 -269.05 212s PrivateWages_12 -35.213 -89.05 212s PrivateWages_13 -84.019 -258.36 212s PrivateWages_14 36.989 174.52 212s PrivateWages_15 -20.514 -68.91 212s PrivateWages_16 -23.040 -74.89 212s PrivateWages_17 79.598 237.33 212s PrivateWages_18 4.143 11.21 212s PrivateWages_19 -288.073 -823.48 212s PrivateWages_20 53.076 167.75 212s PrivateWages_21 -53.565 -149.89 212s PrivateWages_22 159.147 459.47 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 1.6584 21.489 212s Consumption_3 1.1448 19.123 212s Consumption_4 0.8687 16.623 212s Consumption_5 3.2529 68.104 212s Consumption_6 0.2737 5.329 212s Consumption_8 -4.0235 -68.968 212s Consumption_9 -2.3351 -45.507 212s Consumption_10 -0.6397 -13.089 212s Consumption_11 1.6466 27.739 212s Consumption_12 0.8958 11.358 212s Consumption_13 1.7181 15.329 212s Consumption_14 -2.3828 -22.161 212s Consumption_15 1.0492 13.424 212s Consumption_16 0.5719 8.155 212s Consumption_17 -5.6426 -83.238 212s Consumption_18 0.8686 16.978 212s Consumption_19 4.2329 81.944 212s Consumption_20 -3.1693 -55.102 212s Consumption_21 -1.3799 -27.735 212s Consumption_22 1.3913 31.806 212s Investment_2 -2.5801 -33.433 212s Investment_3 -0.0360 -0.601 212s Investment_4 0.1648 3.153 212s Investment_5 -1.2904 -27.016 212s Investment_6 -0.0874 -1.701 212s Investment_8 0.6245 10.704 212s Investment_9 0.7931 15.457 212s Investment_10 2.2586 46.215 212s Investment_11 -1.1128 -18.746 212s Investment_12 -0.8259 -10.473 212s Investment_13 -1.3910 -12.410 212s Investment_14 1.5081 14.026 212s Investment_15 -0.1208 -1.545 212s Investment_16 0.1438 2.050 212s Investment_17 1.4366 21.193 212s Investment_18 0.1252 2.447 212s Investment_19 -2.3628 -45.741 212s Investment_20 0.8145 14.161 212s Investment_21 0.5133 10.317 212s Investment_22 1.4247 32.570 212s PrivateWages_2 3.3346 43.210 212s PrivateWages_3 -1.3594 -22.709 212s PrivateWages_4 -3.4495 -66.008 212s PrivateWages_5 2.6185 54.822 212s PrivateWages_6 0.0714 1.390 212s PrivateWages_8 -1.8964 -32.506 212s PrivateWages_9 -2.2696 -44.232 212s PrivateWages_10 -4.1989 -85.919 212s PrivateWages_11 2.6418 44.502 212s PrivateWages_12 0.9611 12.187 212s PrivateWages_13 3.1382 27.999 212s PrivateWages_14 -2.2500 -20.926 212s PrivateWages_15 0.7799 9.979 212s PrivateWages_16 0.7976 11.373 212s PrivateWages_17 -2.4209 -35.713 212s PrivateWages_18 -0.1002 -1.959 212s PrivateWages_19 7.0903 137.261 212s PrivateWages_20 -1.4771 -25.682 212s PrivateWages_21 1.2004 24.127 212s PrivateWages_22 -3.2116 -73.422 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 21.061 303.15 212s Consumption_3 14.195 209.04 212s Consumption_4 14.681 160.28 212s Consumption_5 59.853 617.07 212s Consumption_6 5.310 52.75 212s Consumption_8 -78.860 -818.38 212s Consumption_9 -46.234 -484.76 212s Consumption_10 -13.497 -134.72 212s Consumption_11 35.732 355.18 212s Consumption_12 13.974 194.12 212s Consumption_13 19.587 366.47 212s Consumption_14 -16.680 -493.49 212s Consumption_15 11.751 211.94 212s Consumption_16 7.034 113.81 212s Consumption_17 -78.996 -1115.54 212s Consumption_18 15.288 173.56 212s Consumption_19 73.229 854.19 212s Consumption_20 -48.490 -633.54 212s Consumption_21 -26.219 -277.64 212s Consumption_22 29.355 284.51 212s Investment_2 -32.767 -471.64 212s Investment_3 -0.446 -6.57 212s Investment_4 2.785 30.40 212s Investment_5 -23.742 -244.78 212s Investment_6 -1.695 -16.84 212s Investment_8 12.239 127.02 212s Investment_9 15.704 164.66 212s Investment_10 47.656 475.66 212s Investment_11 -24.148 -240.03 212s Investment_12 -12.884 -178.98 212s Investment_13 -15.857 -296.69 212s Investment_14 10.556 312.32 212s Investment_15 -1.352 -24.39 212s Investment_16 1.769 28.62 212s Investment_17 20.113 284.02 212s Investment_18 2.203 25.01 212s Investment_19 -40.876 -476.81 212s Investment_20 12.461 162.81 212s Investment_21 9.753 103.28 212s Investment_22 30.061 291.35 212s PrivateWages_2 42.349 609.56 212s PrivateWages_3 -16.857 -248.23 212s PrivateWages_4 -58.297 -636.44 212s PrivateWages_5 48.180 496.72 212s PrivateWages_6 1.385 13.76 212s PrivateWages_8 -37.169 -385.72 212s PrivateWages_9 -44.939 -471.17 212s PrivateWages_10 -88.597 -884.29 212s PrivateWages_11 57.326 569.83 212s PrivateWages_12 14.994 208.28 212s PrivateWages_13 35.776 669.38 212s PrivateWages_14 -15.750 -465.97 212s PrivateWages_15 8.735 157.54 212s PrivateWages_16 9.810 158.72 212s PrivateWages_17 -33.893 -478.62 212s PrivateWages_18 -1.764 -20.03 212s PrivateWages_19 122.662 1430.82 212s PrivateWages_20 -22.600 -295.28 212s PrivateWages_21 22.808 241.53 212s PrivateWages_22 -67.765 -656.78 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 -5.3990 -254.13 -242.42 212s Consumption_3 -3.7270 -184.79 -169.95 212s Consumption_4 -2.8282 -159.92 -141.69 212s Consumption_5 -10.5903 -642.68 -605.76 212s Consumption_6 -0.8912 -54.02 -50.89 212s Consumption_8 13.0991 785.91 838.34 212s Consumption_9 7.6022 473.37 489.58 212s Consumption_10 2.0826 134.47 134.33 212s Consumption_11 -5.3609 -341.55 -359.18 212s Consumption_12 -2.9163 -159.91 -178.48 212s Consumption_13 -5.5936 -262.77 -298.70 212s Consumption_14 7.7577 326.81 343.67 212s Consumption_15 -3.4158 -174.95 -154.05 212s Consumption_16 -1.8619 -103.04 -92.54 212s Consumption_17 18.3702 1054.34 999.34 212s Consumption_18 -2.8280 -189.97 -177.32 212s Consumption_19 -13.7808 -944.16 -895.75 212s Consumption_20 10.3182 689.71 628.38 212s Consumption_21 4.4926 336.34 312.24 212s Consumption_22 -4.5294 -393.51 -342.88 212s Investment_2 6.0805 286.21 273.02 212s Investment_3 0.0848 4.21 3.87 212s Investment_4 -0.3883 -21.96 -19.45 212s Investment_5 3.0410 184.55 173.94 212s Investment_6 0.2060 12.48 11.76 212s Investment_8 -1.4717 -88.30 -94.19 212s Investment_9 -1.8692 -116.39 -120.38 212s Investment_10 -5.3228 -343.69 -343.32 212s Investment_11 2.6225 167.09 175.71 212s Investment_12 1.9465 106.73 119.12 212s Investment_13 3.2781 154.00 175.05 212s Investment_14 -3.5541 -149.72 -157.44 212s Investment_15 0.2846 14.58 12.84 212s Investment_16 -0.3389 -18.75 -16.84 212s Investment_17 -3.3857 -194.32 -184.18 212s Investment_18 -0.2951 -19.82 -18.50 212s Investment_19 5.5684 381.50 361.95 212s Investment_20 -1.9195 -128.31 -116.90 212s Investment_21 -1.2097 -90.57 -84.07 212s Investment_22 -3.3575 -291.70 -254.16 212s PrivateWages_2 -12.3381 -580.75 -553.98 212s PrivateWages_3 5.0300 249.39 229.37 212s PrivateWages_4 12.7635 721.68 639.45 212s PrivateWages_5 -9.6885 -587.96 -554.18 212s PrivateWages_6 -0.2641 -16.01 -15.08 212s PrivateWages_8 7.0167 420.99 449.07 212s PrivateWages_9 8.3978 522.92 540.82 212s PrivateWages_10 15.5362 1003.16 1002.09 212s PrivateWages_11 -9.7747 -622.76 -654.90 212s PrivateWages_12 -3.5562 -195.00 -217.64 212s PrivateWages_13 -11.6116 -545.48 -620.06 212s PrivateWages_14 8.3251 350.72 368.80 212s PrivateWages_15 -2.8858 -147.80 -130.15 212s PrivateWages_16 -2.9512 -163.31 -146.67 212s PrivateWages_17 8.9576 514.11 487.29 212s PrivateWages_18 0.3709 24.92 23.26 212s PrivateWages_19 -26.2346 -1797.40 -1705.25 212s PrivateWages_20 5.4654 365.33 332.84 212s PrivateWages_21 -4.4417 -332.53 -308.70 212s PrivateWages_22 11.8832 1032.40 899.56 212s PrivateWages_trend 212s Consumption_2 53.990 212s Consumption_3 33.543 212s Consumption_4 22.626 212s Consumption_5 74.132 212s Consumption_6 5.347 212s Consumption_8 -52.396 212s Consumption_9 -22.806 212s Consumption_10 -4.165 212s Consumption_11 5.361 212s Consumption_12 0.000 212s Consumption_13 -5.594 212s Consumption_14 15.515 212s Consumption_15 -10.247 212s Consumption_16 -7.448 212s Consumption_17 91.851 212s Consumption_18 -16.968 212s Consumption_19 -96.465 212s Consumption_20 82.545 212s Consumption_21 40.433 212s Consumption_22 -45.294 212s Investment_2 -60.805 212s Investment_3 -0.763 212s Investment_4 3.106 212s Investment_5 -21.287 212s Investment_6 -1.236 212s Investment_8 5.887 212s Investment_9 5.608 212s Investment_10 10.646 212s Investment_11 -2.623 212s Investment_12 0.000 212s Investment_13 3.278 212s Investment_14 -7.108 212s Investment_15 0.854 212s Investment_16 -1.356 212s Investment_17 -16.928 212s Investment_18 -1.770 212s Investment_19 38.979 212s Investment_20 -15.356 212s Investment_21 -10.887 212s Investment_22 -33.575 212s PrivateWages_2 123.381 212s PrivateWages_3 -45.270 212s PrivateWages_4 -102.108 212s PrivateWages_5 67.820 212s PrivateWages_6 1.585 212s PrivateWages_8 -28.067 212s PrivateWages_9 -25.193 212s PrivateWages_10 -31.072 212s PrivateWages_11 9.775 212s PrivateWages_12 0.000 212s PrivateWages_13 -11.612 212s PrivateWages_14 16.650 212s PrivateWages_15 -8.657 212s PrivateWages_16 -11.805 212s PrivateWages_17 44.788 212s PrivateWages_18 2.225 212s PrivateWages_19 -183.642 212s PrivateWages_20 43.723 212s PrivateWages_21 -39.975 212s PrivateWages_22 118.832 212s [1] TRUE 212s > Bread 212s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 212s [1,] 89.117 -0.7628 -0.3161 212s [2,] -0.763 0.5437 -0.3702 212s [3,] -0.316 -0.3702 0.4897 212s [4,] -1.650 -0.0567 -0.0339 212s [5,] 127.149 -5.8142 6.0484 212s [6,] -2.757 0.6390 -0.5640 212s [7,] 0.822 -0.5332 0.6080 212s [8,] -0.462 0.0186 -0.0321 212s [9,] -41.723 0.1554 1.5996 212s [10,] 0.652 -0.0670 0.0422 212s [11,] 0.023 0.0665 -0.0715 212s [12,] 0.266 0.0460 0.0263 212s Consumption_wages Investment_(Intercept) Investment_corpProf 212s [1,] -1.649949 127.15 -2.7567 212s [2,] -0.056675 -5.81 0.6390 212s [3,] -0.033922 6.05 -0.5640 212s [4,] 0.075837 -3.04 0.0284 212s [5,] -3.037786 5674.46 -81.6232 212s [6,] 0.028439 -81.62 3.2764 212s [7,] -0.041721 66.55 -2.7837 212s [8,] 0.016133 -26.78 0.3579 212s [9,] 0.286845 49.74 -0.5482 212s [10,] -0.005120 5.39 0.0206 212s [11,] 0.000492 -6.38 -0.0122 212s [12,] -0.035219 -5.00 0.0650 212s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 212s [1,] 0.8223 -0.4623 -41.7225 212s [2,] -0.5332 0.0186 0.1554 212s [3,] 0.6080 -0.0321 1.5996 212s [4,] -0.0417 0.0161 0.2868 212s [5,] 66.5535 -26.7802 49.7422 212s [6,] -2.7837 0.3579 -0.5482 212s [7,] 3.0944 -0.3490 -2.9105 212s [8,] -0.3490 0.1318 0.0433 212s [9,] -2.9105 0.0433 89.7087 212s [10,] 0.0256 -0.0306 -0.7102 212s [11,] 0.0243 0.0308 -0.7883 212s [12,] -0.1021 0.0277 0.9946 212s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 212s [1,] 0.65175 0.023034 0.26557 212s [2,] -0.06703 0.066494 0.04602 212s [3,] 0.04225 -0.071498 0.02630 212s [4,] -0.00512 0.000492 -0.03522 212s [5,] 5.38683 -6.377135 -4.99571 212s [6,] 0.02064 -0.012164 0.06501 212s [7,] 0.02556 0.024313 -0.10213 212s [8,] -0.03064 0.030839 0.02771 212s [9,] -0.71025 -0.788347 0.99462 212s [10,] 0.06062 -0.050369 -0.02195 212s [11,] -0.05037 0.065741 0.00529 212s [12,] -0.02195 0.005286 0.05391 212s > 212s > # OLS 212s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 212s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 212s > summary 212s 212s systemfit results 212s method: OLS 212s 212s N DF SSR detRCov OLS-R2 McElroy-R2 212s system 61 49 44.5 0.382 0.977 0.99 212s 212s N DF SSR MSE RMSE R2 Adj R2 212s Consumption 20 16 17.48 1.093 1.04 0.981 0.978 212s Investment 21 17 17.32 1.019 1.01 0.931 0.919 212s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 212s 212s The covariance matrix of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.124 0.034 -0.442 212s Investment 0.034 0.928 0.130 212s PrivateWages -0.442 0.130 0.563 212s 212s The correlations of the residuals 212s Consumption Investment PrivateWages 212s Consumption 1.0000 0.0266 -0.563 212s Investment 0.0266 1.0000 0.169 212s PrivateWages -0.5630 0.1689 1.000 212s 212s 212s OLS estimates for 'Consumption' (equation 1) 212s Model Formula: consump ~ corpProf + corpProfLag + wages 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 16.1357 1.3571 11.89 2.4e-09 *** 212s corpProf 0.1994 0.0949 2.10 0.052 . 212s corpProfLag 0.0969 0.0944 1.03 0.320 212s wages 0.7940 0.0415 19.16 1.9e-12 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.045 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 17.481 MSE: 1.093 Root MSE: 1.045 212s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 212s 212s 212s OLS estimates for 'Investment' (equation 2) 212s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 10.1258 5.2164 1.94 0.06901 . 212s corpProf 0.4796 0.0927 5.17 7.6e-05 *** 212s corpProfLag 0.3330 0.0963 3.46 0.00299 ** 212s capitalLag -0.1118 0.0255 -4.38 0.00041 *** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 1.009 on 17 degrees of freedom 212s Number of observations: 21 Degrees of Freedom: 17 212s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 212s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 212s 212s 212s OLS estimates for 'PrivateWages' (equation 3) 212s Model Formula: privWage ~ gnp + gnpLag + trend 212s 212s Estimate Std. Error t value Pr(>|t|) 212s (Intercept) 1.3550 1.2591 1.08 0.2978 212s gnp 0.4417 0.0319 13.86 2.5e-10 *** 212s gnpLag 0.1466 0.0366 4.01 0.0010 ** 212s trend 0.1244 0.0323 3.85 0.0014 ** 212s --- 212s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 212s 212s Residual standard error: 0.78 on 16 degrees of freedom 212s Number of observations: 20 Degrees of Freedom: 16 212s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 212s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 212s 212s compare coef with single-equation OLS 212s [1] TRUE 212s > residuals 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 -0.3304 -0.0668 -1.3389 212s 3 -1.2748 -0.0476 0.2462 212s 4 -1.6213 1.2467 1.1255 212s 5 -0.5661 -1.3512 -0.1959 212s 6 -0.0730 0.4154 -0.5284 212s 7 0.7915 1.4923 NA 212s 8 1.2648 0.7889 -0.7909 212s 9 0.9746 -0.6317 0.2819 212s 10 NA 1.0830 1.1384 212s 11 0.2225 0.2791 -0.1904 212s 12 -0.2256 0.0369 0.5813 212s 13 -0.2711 0.3659 0.1206 212s 14 0.3765 0.2237 0.4773 212s 15 -0.0349 -0.1728 0.3035 212s 16 -0.0243 0.0101 0.0284 212s 17 1.6023 0.9719 -0.8517 212s 18 -0.4658 0.0516 0.9908 212s 19 0.1914 -2.5656 -0.4597 212s 20 0.9683 -0.6866 -0.3819 212s 21 0.7325 -0.7807 -1.1062 212s 22 -2.2370 -0.6623 0.5501 212s > fitted 212s Consumption Investment PrivateWages 212s 1 NA NA NA 212s 2 42.2 -0.133 26.8 212s 3 46.3 1.948 29.1 212s 4 50.8 3.953 33.0 212s 5 51.2 4.351 34.1 212s 6 52.7 4.685 35.9 212s 7 54.3 4.108 NA 212s 8 54.9 3.411 38.7 212s 9 56.3 3.632 38.9 212s 10 NA 4.017 40.2 212s 11 54.8 0.721 38.1 212s 12 51.1 -3.437 33.9 212s 13 45.9 -6.566 28.9 212s 14 46.1 -5.324 28.0 212s 15 48.7 -2.827 30.3 212s 16 51.3 -1.310 33.2 212s 17 56.1 1.128 37.7 212s 18 59.2 1.948 40.0 212s 19 57.3 0.666 38.7 212s 20 60.6 1.987 42.0 212s 21 64.3 4.081 46.1 212s 22 71.9 5.562 52.7 212s > predict 212s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 212s 1 NA NA NA NA 212s 2 42.2 0.478 39.9 44.5 212s 3 46.3 0.537 43.9 48.6 212s 4 50.8 0.364 48.6 53.0 212s 5 51.2 0.427 48.9 53.4 212s 6 52.7 0.433 50.4 54.9 212s 7 54.3 0.394 52.1 56.6 212s 8 54.9 0.360 52.7 57.2 212s 9 56.3 0.387 54.1 58.6 212s 10 NA NA NA NA 212s 11 54.8 0.635 52.3 57.2 212s 12 51.1 0.501 48.8 53.5 212s 13 45.9 0.656 43.4 48.4 212s 14 46.1 0.629 43.7 48.6 212s 15 48.7 0.389 46.5 51.0 212s 16 51.3 0.345 49.1 53.5 212s 17 56.1 0.379 53.9 58.3 212s 18 59.2 0.336 57.0 61.4 212s 19 57.3 0.385 55.1 59.5 212s 20 60.6 0.450 58.3 62.9 212s 21 64.3 0.448 62.0 66.6 212s 22 71.9 0.697 69.4 74.5 212s Investment.pred Investment.se.fit Investment.lwr Investment.upr 212s 1 NA NA NA NA 212s 2 -0.133 0.579 -2.472 2.206 212s 3 1.948 0.476 -0.295 4.190 212s 4 3.953 0.428 1.750 6.157 212s 5 4.351 0.354 2.202 6.501 212s 6 4.685 0.333 2.548 6.821 212s 7 4.108 0.314 1.983 6.232 212s 8 3.411 0.279 1.306 5.516 212s 9 3.632 0.371 1.470 5.793 212s 10 4.017 0.426 1.815 6.219 212s 11 0.721 0.574 -1.613 3.054 212s 12 -3.437 0.484 -5.686 -1.188 212s 13 -6.566 0.588 -8.913 -4.219 212s 14 -5.324 0.662 -7.750 -2.898 212s 15 -2.827 0.356 -4.978 -0.676 212s 16 -1.310 0.305 -3.429 0.809 212s 17 1.128 0.332 -1.007 3.263 212s 18 1.948 0.232 -0.133 4.030 212s 19 0.666 0.298 -1.449 2.781 212s 20 1.987 0.350 -0.160 4.133 212s 21 4.081 0.317 1.955 6.207 212s 22 5.562 0.440 3.349 7.775 212s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 212s 1 NA NA NA NA 212s 2 26.8 0.352 25.1 28.6 212s 3 29.1 0.355 27.3 30.8 212s 4 33.0 0.358 31.2 34.7 212s 5 34.1 0.277 32.4 35.8 212s 6 35.9 0.276 34.3 37.6 212s 7 NA NA NA NA 212s 8 38.7 0.282 37.0 40.4 212s 9 38.9 0.268 37.3 40.6 212s 10 40.2 0.255 38.5 41.8 212s 11 38.1 0.351 36.4 39.8 212s 12 33.9 0.355 32.2 35.6 212s 13 28.9 0.421 27.1 30.7 212s 14 28.0 0.370 26.3 29.8 212s 15 30.3 0.364 28.6 32.0 212s 16 33.2 0.304 31.5 34.9 212s 17 37.7 0.298 36.0 39.3 212s 18 40.0 0.233 38.4 41.6 212s 19 38.7 0.349 36.9 40.4 212s 20 42.0 0.314 40.3 43.7 212s 21 46.1 0.328 44.4 47.8 212s 22 52.7 0.494 50.9 54.6 212s > model.frame 212s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 212s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 212s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 212s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 212s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 212s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 212s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 212s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 212s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 212s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 212s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 212s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 212s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 212s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 212s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 212s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 212s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 212s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 212s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 212s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 212s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 212s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 212s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 212s trend 212s 1 -11 212s 2 -10 212s 3 -9 212s 4 -8 212s 5 -7 212s 6 -6 212s 7 -5 212s 8 -4 212s 9 -3 212s 10 -2 212s 11 -1 212s 12 0 212s 13 1 212s 14 2 212s 15 3 212s 16 4 212s 17 5 212s 18 6 212s 19 7 212s 20 8 212s 21 9 212s 22 10 212s > model.matrix 212s Consumption_(Intercept) Consumption_corpProf 212s Consumption_2 1 12.4 212s Consumption_3 1 16.9 212s Consumption_4 1 18.4 212s Consumption_5 1 19.4 212s Consumption_6 1 20.1 212s Consumption_7 1 19.6 212s Consumption_8 1 19.8 212s Consumption_9 1 21.1 212s Consumption_11 1 15.6 212s Consumption_12 1 11.4 212s Consumption_13 1 7.0 212s Consumption_14 1 11.2 212s Consumption_15 1 12.3 212s Consumption_16 1 14.0 212s Consumption_17 1 17.6 212s Consumption_18 1 17.3 212s Consumption_19 1 15.3 212s Consumption_20 1 19.0 212s Consumption_21 1 21.1 212s Consumption_22 1 23.5 212s Investment_2 0 0.0 212s Investment_3 0 0.0 212s Investment_4 0 0.0 212s Investment_5 0 0.0 212s Investment_6 0 0.0 212s Investment_7 0 0.0 212s Investment_8 0 0.0 212s Investment_9 0 0.0 212s Investment_10 0 0.0 212s Investment_11 0 0.0 212s Investment_12 0 0.0 212s Investment_13 0 0.0 212s Investment_14 0 0.0 212s Investment_15 0 0.0 212s Investment_16 0 0.0 212s Investment_17 0 0.0 212s Investment_18 0 0.0 212s Investment_19 0 0.0 212s Investment_20 0 0.0 212s Investment_21 0 0.0 212s Investment_22 0 0.0 212s PrivateWages_2 0 0.0 212s PrivateWages_3 0 0.0 212s PrivateWages_4 0 0.0 212s PrivateWages_5 0 0.0 212s PrivateWages_6 0 0.0 212s PrivateWages_8 0 0.0 212s PrivateWages_9 0 0.0 212s PrivateWages_10 0 0.0 212s PrivateWages_11 0 0.0 212s PrivateWages_12 0 0.0 212s PrivateWages_13 0 0.0 212s PrivateWages_14 0 0.0 212s PrivateWages_15 0 0.0 212s PrivateWages_16 0 0.0 212s PrivateWages_17 0 0.0 212s PrivateWages_18 0 0.0 212s PrivateWages_19 0 0.0 212s PrivateWages_20 0 0.0 212s PrivateWages_21 0 0.0 212s PrivateWages_22 0 0.0 212s Consumption_corpProfLag Consumption_wages 212s Consumption_2 12.7 28.2 212s Consumption_3 12.4 32.2 212s Consumption_4 16.9 37.0 212s Consumption_5 18.4 37.0 212s Consumption_6 19.4 38.6 212s Consumption_7 20.1 40.7 212s Consumption_8 19.6 41.5 212s Consumption_9 19.8 42.9 212s Consumption_11 21.7 42.1 212s Consumption_12 15.6 39.3 212s Consumption_13 11.4 34.3 212s Consumption_14 7.0 34.1 212s Consumption_15 11.2 36.6 212s Consumption_16 12.3 39.3 212s Consumption_17 14.0 44.2 212s Consumption_18 17.6 47.7 212s Consumption_19 17.3 45.9 212s Consumption_20 15.3 49.4 212s Consumption_21 19.0 53.0 212s Consumption_22 21.1 61.8 212s Investment_2 0.0 0.0 212s Investment_3 0.0 0.0 212s Investment_4 0.0 0.0 212s Investment_5 0.0 0.0 212s Investment_6 0.0 0.0 212s Investment_7 0.0 0.0 212s Investment_8 0.0 0.0 212s Investment_9 0.0 0.0 212s Investment_10 0.0 0.0 212s Investment_11 0.0 0.0 212s Investment_12 0.0 0.0 212s Investment_13 0.0 0.0 212s Investment_14 0.0 0.0 212s Investment_15 0.0 0.0 212s Investment_16 0.0 0.0 212s Investment_17 0.0 0.0 212s Investment_18 0.0 0.0 212s Investment_19 0.0 0.0 212s Investment_20 0.0 0.0 212s Investment_21 0.0 0.0 212s Investment_22 0.0 0.0 212s PrivateWages_2 0.0 0.0 212s PrivateWages_3 0.0 0.0 212s PrivateWages_4 0.0 0.0 212s PrivateWages_5 0.0 0.0 212s PrivateWages_6 0.0 0.0 212s PrivateWages_8 0.0 0.0 212s PrivateWages_9 0.0 0.0 212s PrivateWages_10 0.0 0.0 212s PrivateWages_11 0.0 0.0 212s PrivateWages_12 0.0 0.0 212s PrivateWages_13 0.0 0.0 212s PrivateWages_14 0.0 0.0 212s PrivateWages_15 0.0 0.0 212s PrivateWages_16 0.0 0.0 212s PrivateWages_17 0.0 0.0 212s PrivateWages_18 0.0 0.0 212s PrivateWages_19 0.0 0.0 212s PrivateWages_20 0.0 0.0 212s PrivateWages_21 0.0 0.0 212s PrivateWages_22 0.0 0.0 212s Investment_(Intercept) Investment_corpProf 212s Consumption_2 0 0.0 212s Consumption_3 0 0.0 212s Consumption_4 0 0.0 212s Consumption_5 0 0.0 212s Consumption_6 0 0.0 212s Consumption_7 0 0.0 212s Consumption_8 0 0.0 212s Consumption_9 0 0.0 212s Consumption_11 0 0.0 212s Consumption_12 0 0.0 212s Consumption_13 0 0.0 212s Consumption_14 0 0.0 212s Consumption_15 0 0.0 212s Consumption_16 0 0.0 212s Consumption_17 0 0.0 212s Consumption_18 0 0.0 212s Consumption_19 0 0.0 212s Consumption_20 0 0.0 212s Consumption_21 0 0.0 212s Consumption_22 0 0.0 212s Investment_2 1 12.4 212s Investment_3 1 16.9 212s Investment_4 1 18.4 212s Investment_5 1 19.4 212s Investment_6 1 20.1 212s Investment_7 1 19.6 212s Investment_8 1 19.8 212s Investment_9 1 21.1 212s Investment_10 1 21.7 212s Investment_11 1 15.6 212s Investment_12 1 11.4 212s Investment_13 1 7.0 212s Investment_14 1 11.2 212s Investment_15 1 12.3 212s Investment_16 1 14.0 212s Investment_17 1 17.6 212s Investment_18 1 17.3 212s Investment_19 1 15.3 212s Investment_20 1 19.0 212s Investment_21 1 21.1 212s Investment_22 1 23.5 212s PrivateWages_2 0 0.0 212s PrivateWages_3 0 0.0 212s PrivateWages_4 0 0.0 212s PrivateWages_5 0 0.0 212s PrivateWages_6 0 0.0 212s PrivateWages_8 0 0.0 212s PrivateWages_9 0 0.0 212s PrivateWages_10 0 0.0 212s PrivateWages_11 0 0.0 212s PrivateWages_12 0 0.0 212s PrivateWages_13 0 0.0 212s PrivateWages_14 0 0.0 212s PrivateWages_15 0 0.0 212s PrivateWages_16 0 0.0 212s PrivateWages_17 0 0.0 212s PrivateWages_18 0 0.0 212s PrivateWages_19 0 0.0 212s PrivateWages_20 0 0.0 212s PrivateWages_21 0 0.0 212s PrivateWages_22 0 0.0 212s Investment_corpProfLag Investment_capitalLag 212s Consumption_2 0.0 0 212s Consumption_3 0.0 0 212s Consumption_4 0.0 0 212s Consumption_5 0.0 0 212s Consumption_6 0.0 0 212s Consumption_7 0.0 0 212s Consumption_8 0.0 0 212s Consumption_9 0.0 0 212s Consumption_11 0.0 0 212s Consumption_12 0.0 0 212s Consumption_13 0.0 0 212s Consumption_14 0.0 0 212s Consumption_15 0.0 0 212s Consumption_16 0.0 0 212s Consumption_17 0.0 0 212s Consumption_18 0.0 0 212s Consumption_19 0.0 0 212s Consumption_20 0.0 0 212s Consumption_21 0.0 0 212s Consumption_22 0.0 0 212s Investment_2 12.7 183 212s Investment_3 12.4 183 212s Investment_4 16.9 184 212s Investment_5 18.4 190 212s Investment_6 19.4 193 212s Investment_7 20.1 198 212s Investment_8 19.6 203 212s Investment_9 19.8 208 212s Investment_10 21.1 211 212s Investment_11 21.7 216 212s Investment_12 15.6 217 212s Investment_13 11.4 213 212s Investment_14 7.0 207 212s Investment_15 11.2 202 212s Investment_16 12.3 199 212s Investment_17 14.0 198 212s Investment_18 17.6 200 212s Investment_19 17.3 202 212s Investment_20 15.3 200 212s Investment_21 19.0 201 212s Investment_22 21.1 204 212s PrivateWages_2 0.0 0 212s PrivateWages_3 0.0 0 212s PrivateWages_4 0.0 0 212s PrivateWages_5 0.0 0 212s PrivateWages_6 0.0 0 212s PrivateWages_8 0.0 0 212s PrivateWages_9 0.0 0 212s PrivateWages_10 0.0 0 212s PrivateWages_11 0.0 0 212s PrivateWages_12 0.0 0 212s PrivateWages_13 0.0 0 212s PrivateWages_14 0.0 0 212s PrivateWages_15 0.0 0 212s PrivateWages_16 0.0 0 212s PrivateWages_17 0.0 0 212s PrivateWages_18 0.0 0 212s PrivateWages_19 0.0 0 212s PrivateWages_20 0.0 0 212s PrivateWages_21 0.0 0 212s PrivateWages_22 0.0 0 212s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 212s Consumption_2 0 0.0 0.0 212s Consumption_3 0 0.0 0.0 212s Consumption_4 0 0.0 0.0 212s Consumption_5 0 0.0 0.0 212s Consumption_6 0 0.0 0.0 212s Consumption_7 0 0.0 0.0 212s Consumption_8 0 0.0 0.0 212s Consumption_9 0 0.0 0.0 212s Consumption_11 0 0.0 0.0 212s Consumption_12 0 0.0 0.0 212s Consumption_13 0 0.0 0.0 212s Consumption_14 0 0.0 0.0 212s Consumption_15 0 0.0 0.0 212s Consumption_16 0 0.0 0.0 212s Consumption_17 0 0.0 0.0 212s Consumption_18 0 0.0 0.0 212s Consumption_19 0 0.0 0.0 212s Consumption_20 0 0.0 0.0 212s Consumption_21 0 0.0 0.0 212s Consumption_22 0 0.0 0.0 212s Investment_2 0 0.0 0.0 212s Investment_3 0 0.0 0.0 212s Investment_4 0 0.0 0.0 212s Investment_5 0 0.0 0.0 212s Investment_6 0 0.0 0.0 212s Investment_7 0 0.0 0.0 212s Investment_8 0 0.0 0.0 212s Investment_9 0 0.0 0.0 212s Investment_10 0 0.0 0.0 212s Investment_11 0 0.0 0.0 212s Investment_12 0 0.0 0.0 212s Investment_13 0 0.0 0.0 212s Investment_14 0 0.0 0.0 212s Investment_15 0 0.0 0.0 212s Investment_16 0 0.0 0.0 212s Investment_17 0 0.0 0.0 212s Investment_18 0 0.0 0.0 212s Investment_19 0 0.0 0.0 212s Investment_20 0 0.0 0.0 212s Investment_21 0 0.0 0.0 212s Investment_22 0 0.0 0.0 212s PrivateWages_2 1 45.6 44.9 212s PrivateWages_3 1 50.1 45.6 212s PrivateWages_4 1 57.2 50.1 212s PrivateWages_5 1 57.1 57.2 212s PrivateWages_6 1 61.0 57.1 212s PrivateWages_8 1 64.4 64.0 212s PrivateWages_9 1 64.5 64.4 212s PrivateWages_10 1 67.0 64.5 212s PrivateWages_11 1 61.2 67.0 212s PrivateWages_12 1 53.4 61.2 212s PrivateWages_13 1 44.3 53.4 212s PrivateWages_14 1 45.1 44.3 212s PrivateWages_15 1 49.7 45.1 212s PrivateWages_16 1 54.4 49.7 212s PrivateWages_17 1 62.7 54.4 212s PrivateWages_18 1 65.0 62.7 212s PrivateWages_19 1 60.9 65.0 212s PrivateWages_20 1 69.5 60.9 212s PrivateWages_21 1 75.7 69.5 212s PrivateWages_22 1 88.4 75.7 212s PrivateWages_trend 212s Consumption_2 0 212s Consumption_3 0 212s Consumption_4 0 212s Consumption_5 0 212s Consumption_6 0 212s Consumption_7 0 212s Consumption_8 0 212s Consumption_9 0 212s Consumption_11 0 212s Consumption_12 0 212s Consumption_13 0 212s Consumption_14 0 212s Consumption_15 0 212s Consumption_16 0 212s Consumption_17 0 212s Consumption_18 0 212s Consumption_19 0 212s Consumption_20 0 212s Consumption_21 0 212s Consumption_22 0 212s Investment_2 0 212s Investment_3 0 212s Investment_4 0 212s Investment_5 0 212s Investment_6 0 212s Investment_7 0 212s Investment_8 0 212s Investment_9 0 212s Investment_10 0 212s Investment_11 0 212s Investment_12 0 212s Investment_13 0 212s Investment_14 0 212s Investment_15 0 212s Investment_16 0 212s Investment_17 0 212s Investment_18 0 212s Investment_19 0 212s Investment_20 0 212s Investment_21 0 212s Investment_22 0 212s PrivateWages_2 -10 212s PrivateWages_3 -9 212s PrivateWages_4 -8 212s PrivateWages_5 -7 212s PrivateWages_6 -6 212s PrivateWages_8 -4 212s PrivateWages_9 -3 212s PrivateWages_10 -2 212s PrivateWages_11 -1 212s PrivateWages_12 0 212s PrivateWages_13 1 212s PrivateWages_14 2 212s PrivateWages_15 3 212s PrivateWages_16 4 212s PrivateWages_17 5 212s PrivateWages_18 6 212s PrivateWages_19 7 212s PrivateWages_20 8 212s PrivateWages_21 9 212s PrivateWages_22 10 212s > nobs 212s [1] 61 212s > linearHypothesis 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 49 1 0.87 0.35 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 50 212s 2 49 1 0.8 0.38 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 50 212s 2 49 1 0.8 0.37 212s Linear hypothesis test (Theil's F test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 51 212s 2 49 2 0.48 0.62 212s Linear hypothesis test (F statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df F Pr(>F) 212s 1 51 212s 2 49 2 0.43 0.65 212s Linear hypothesis test (Chi^2 statistic of a Wald test) 212s 212s Hypothesis: 212s Consumption_corpProf + Investment_capitalLag = 0 212s Consumption_corpProfLag - PrivateWages_trend = 0 212s 212s Model 1: restricted model 212s Model 2: kleinModel 212s 212s Res.Df Df Chisq Pr(>Chisq) 212s 1 51 212s 2 49 2 0.87 0.65 212s > logLik 213s 'log Lik.' -71.7 (df=13) 213s 'log Lik.' -76.1 (df=13) 213s compare log likelihood value with single-equation OLS 213s [1] "Mean relative difference: 0.00159" 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -0.3304 -4.097 213s Consumption_3 -1.2748 -21.544 213s Consumption_4 -1.6213 -29.832 213s Consumption_5 -0.5661 -10.982 213s Consumption_6 -0.0730 -1.467 213s Consumption_7 0.7915 15.513 213s Consumption_8 1.2648 25.043 213s Consumption_9 0.9746 20.563 213s Consumption_11 0.2225 3.470 213s Consumption_12 -0.2256 -2.572 213s Consumption_13 -0.2711 -1.898 213s Consumption_14 0.3765 4.217 213s Consumption_15 -0.0349 -0.429 213s Consumption_16 -0.0243 -0.341 213s Consumption_17 1.6023 28.201 213s Consumption_18 -0.4658 -8.058 213s Consumption_19 0.1914 2.928 213s Consumption_20 0.9683 18.397 213s Consumption_21 0.7325 15.456 213s Consumption_22 -2.2370 -52.569 213s Investment_2 0.0000 0.000 213s Investment_3 0.0000 0.000 213s Investment_4 0.0000 0.000 213s Investment_5 0.0000 0.000 213s Investment_6 0.0000 0.000 213s Investment_7 0.0000 0.000 213s Investment_8 0.0000 0.000 213s Investment_9 0.0000 0.000 213s Investment_10 0.0000 0.000 213s Investment_11 0.0000 0.000 213s Investment_12 0.0000 0.000 213s Investment_13 0.0000 0.000 213s Investment_14 0.0000 0.000 213s Investment_15 0.0000 0.000 213s Investment_16 0.0000 0.000 213s Investment_17 0.0000 0.000 213s Investment_18 0.0000 0.000 213s Investment_19 0.0000 0.000 213s Investment_20 0.0000 0.000 213s Investment_21 0.0000 0.000 213s Investment_22 0.0000 0.000 213s PrivateWages_2 0.0000 0.000 213s PrivateWages_3 0.0000 0.000 213s PrivateWages_4 0.0000 0.000 213s PrivateWages_5 0.0000 0.000 213s PrivateWages_6 0.0000 0.000 213s PrivateWages_8 0.0000 0.000 213s PrivateWages_9 0.0000 0.000 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 0.0000 0.000 213s PrivateWages_12 0.0000 0.000 213s PrivateWages_13 0.0000 0.000 213s PrivateWages_14 0.0000 0.000 213s PrivateWages_15 0.0000 0.000 213s PrivateWages_16 0.0000 0.000 213s PrivateWages_17 0.0000 0.000 213s PrivateWages_18 0.0000 0.000 213s PrivateWages_19 0.0000 0.000 213s PrivateWages_20 0.0000 0.000 213s PrivateWages_21 0.0000 0.000 213s PrivateWages_22 0.0000 0.000 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -4.196 -9.318 213s Consumption_3 -15.808 -41.049 213s Consumption_4 -27.400 -59.988 213s Consumption_5 -10.416 -20.944 213s Consumption_6 -1.416 -2.817 213s Consumption_7 15.908 32.212 213s Consumption_8 24.790 52.490 213s Consumption_9 19.296 41.809 213s Consumption_11 4.827 9.366 213s Consumption_12 -3.520 -8.867 213s Consumption_13 -3.091 -9.299 213s Consumption_14 2.636 12.839 213s Consumption_15 -0.391 -1.277 213s Consumption_16 -0.299 -0.957 213s Consumption_17 22.433 70.823 213s Consumption_18 -8.197 -22.217 213s Consumption_19 3.311 8.785 213s Consumption_20 14.815 47.833 213s Consumption_21 13.917 38.822 213s Consumption_22 -47.200 -138.245 213s Investment_2 0.000 0.000 213s Investment_3 0.000 0.000 213s Investment_4 0.000 0.000 213s Investment_5 0.000 0.000 213s Investment_6 0.000 0.000 213s Investment_7 0.000 0.000 213s Investment_8 0.000 0.000 213s Investment_9 0.000 0.000 213s Investment_10 0.000 0.000 213s Investment_11 0.000 0.000 213s Investment_12 0.000 0.000 213s Investment_13 0.000 0.000 213s Investment_14 0.000 0.000 213s Investment_15 0.000 0.000 213s Investment_16 0.000 0.000 213s Investment_17 0.000 0.000 213s Investment_18 0.000 0.000 213s Investment_19 0.000 0.000 213s Investment_20 0.000 0.000 213s Investment_21 0.000 0.000 213s Investment_22 0.000 0.000 213s PrivateWages_2 0.000 0.000 213s PrivateWages_3 0.000 0.000 213s PrivateWages_4 0.000 0.000 213s PrivateWages_5 0.000 0.000 213s PrivateWages_6 0.000 0.000 213s PrivateWages_8 0.000 0.000 213s PrivateWages_9 0.000 0.000 213s PrivateWages_10 0.000 0.000 213s PrivateWages_11 0.000 0.000 213s PrivateWages_12 0.000 0.000 213s PrivateWages_13 0.000 0.000 213s PrivateWages_14 0.000 0.000 213s PrivateWages_15 0.000 0.000 213s PrivateWages_16 0.000 0.000 213s PrivateWages_17 0.000 0.000 213s PrivateWages_18 0.000 0.000 213s PrivateWages_19 0.000 0.000 213s PrivateWages_20 0.000 0.000 213s PrivateWages_21 0.000 0.000 213s PrivateWages_22 0.000 0.000 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0.0000 0.000 213s Consumption_3 0.0000 0.000 213s Consumption_4 0.0000 0.000 213s Consumption_5 0.0000 0.000 213s Consumption_6 0.0000 0.000 213s Consumption_7 0.0000 0.000 213s Consumption_8 0.0000 0.000 213s Consumption_9 0.0000 0.000 213s Consumption_11 0.0000 0.000 213s Consumption_12 0.0000 0.000 213s Consumption_13 0.0000 0.000 213s Consumption_14 0.0000 0.000 213s Consumption_15 0.0000 0.000 213s Consumption_16 0.0000 0.000 213s Consumption_17 0.0000 0.000 213s Consumption_18 0.0000 0.000 213s Consumption_19 0.0000 0.000 213s Consumption_20 0.0000 0.000 213s Consumption_21 0.0000 0.000 213s Consumption_22 0.0000 0.000 213s Investment_2 -0.0668 -0.828 213s Investment_3 -0.0476 -0.804 213s Investment_4 1.2467 22.939 213s Investment_5 -1.3512 -26.213 213s Investment_6 0.4154 8.350 213s Investment_7 1.4923 29.248 213s Investment_8 0.7889 15.620 213s Investment_9 -0.6317 -13.329 213s Investment_10 1.0830 23.500 213s Investment_11 0.2791 4.353 213s Investment_12 0.0369 0.420 213s Investment_13 0.3659 2.561 213s Investment_14 0.2237 2.505 213s Investment_15 -0.1728 -2.126 213s Investment_16 0.0101 0.141 213s Investment_17 0.9719 17.105 213s Investment_18 0.0516 0.893 213s Investment_19 -2.5656 -39.254 213s Investment_20 -0.6866 -13.045 213s Investment_21 -0.7807 -16.474 213s Investment_22 -0.6623 -15.565 213s PrivateWages_2 0.0000 0.000 213s PrivateWages_3 0.0000 0.000 213s PrivateWages_4 0.0000 0.000 213s PrivateWages_5 0.0000 0.000 213s PrivateWages_6 0.0000 0.000 213s PrivateWages_8 0.0000 0.000 213s PrivateWages_9 0.0000 0.000 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 0.0000 0.000 213s PrivateWages_12 0.0000 0.000 213s PrivateWages_13 0.0000 0.000 213s PrivateWages_14 0.0000 0.000 213s PrivateWages_15 0.0000 0.000 213s PrivateWages_16 0.0000 0.000 213s PrivateWages_17 0.0000 0.000 213s PrivateWages_18 0.0000 0.000 213s PrivateWages_19 0.0000 0.000 213s PrivateWages_20 0.0000 0.000 213s PrivateWages_21 0.0000 0.000 213s PrivateWages_22 0.0000 0.000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.000 0.00 213s Consumption_3 0.000 0.00 213s Consumption_4 0.000 0.00 213s Consumption_5 0.000 0.00 213s Consumption_6 0.000 0.00 213s Consumption_7 0.000 0.00 213s Consumption_8 0.000 0.00 213s Consumption_9 0.000 0.00 213s Consumption_11 0.000 0.00 213s Consumption_12 0.000 0.00 213s Consumption_13 0.000 0.00 213s Consumption_14 0.000 0.00 213s Consumption_15 0.000 0.00 213s Consumption_16 0.000 0.00 213s Consumption_17 0.000 0.00 213s Consumption_18 0.000 0.00 213s Consumption_19 0.000 0.00 213s Consumption_20 0.000 0.00 213s Consumption_21 0.000 0.00 213s Consumption_22 0.000 0.00 213s Investment_2 -0.848 -12.21 213s Investment_3 -0.590 -8.69 213s Investment_4 21.069 230.01 213s Investment_5 -24.862 -256.32 213s Investment_6 8.059 80.05 213s Investment_7 29.994 295.17 213s Investment_8 15.463 160.46 213s Investment_9 -12.507 -131.14 213s Investment_10 22.850 228.07 213s Investment_11 6.056 60.20 213s Investment_12 0.575 7.99 213s Investment_13 4.172 78.05 213s Investment_14 1.566 46.33 213s Investment_15 -1.936 -34.91 213s Investment_16 0.124 2.01 213s Investment_17 13.606 192.14 213s Investment_18 0.908 10.31 213s Investment_19 -44.385 -517.74 213s Investment_20 -10.505 -137.25 213s Investment_21 -14.834 -157.09 213s Investment_22 -13.975 -135.45 213s PrivateWages_2 0.000 0.00 213s PrivateWages_3 0.000 0.00 213s PrivateWages_4 0.000 0.00 213s PrivateWages_5 0.000 0.00 213s PrivateWages_6 0.000 0.00 213s PrivateWages_8 0.000 0.00 213s PrivateWages_9 0.000 0.00 213s PrivateWages_10 0.000 0.00 213s PrivateWages_11 0.000 0.00 213s PrivateWages_12 0.000 0.00 213s PrivateWages_13 0.000 0.00 213s PrivateWages_14 0.000 0.00 213s PrivateWages_15 0.000 0.00 213s PrivateWages_16 0.000 0.00 213s PrivateWages_17 0.000 0.00 213s PrivateWages_18 0.000 0.00 213s PrivateWages_19 0.000 0.00 213s PrivateWages_20 0.000 0.00 213s PrivateWages_21 0.000 0.00 213s PrivateWages_22 0.000 0.00 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 0.0000 0.00 0.00 213s Consumption_3 0.0000 0.00 0.00 213s Consumption_4 0.0000 0.00 0.00 213s Consumption_5 0.0000 0.00 0.00 213s Consumption_6 0.0000 0.00 0.00 213s Consumption_7 0.0000 0.00 0.00 213s Consumption_8 0.0000 0.00 0.00 213s Consumption_9 0.0000 0.00 0.00 213s Consumption_11 0.0000 0.00 0.00 213s Consumption_12 0.0000 0.00 0.00 213s Consumption_13 0.0000 0.00 0.00 213s Consumption_14 0.0000 0.00 0.00 213s Consumption_15 0.0000 0.00 0.00 213s Consumption_16 0.0000 0.00 0.00 213s Consumption_17 0.0000 0.00 0.00 213s Consumption_18 0.0000 0.00 0.00 213s Consumption_19 0.0000 0.00 0.00 213s Consumption_20 0.0000 0.00 0.00 213s Consumption_21 0.0000 0.00 0.00 213s Consumption_22 0.0000 0.00 0.00 213s Investment_2 0.0000 0.00 0.00 213s Investment_3 0.0000 0.00 0.00 213s Investment_4 0.0000 0.00 0.00 213s Investment_5 0.0000 0.00 0.00 213s Investment_6 0.0000 0.00 0.00 213s Investment_7 0.0000 0.00 0.00 213s Investment_8 0.0000 0.00 0.00 213s Investment_9 0.0000 0.00 0.00 213s Investment_10 0.0000 0.00 0.00 213s Investment_11 0.0000 0.00 0.00 213s Investment_12 0.0000 0.00 0.00 213s Investment_13 0.0000 0.00 0.00 213s Investment_14 0.0000 0.00 0.00 213s Investment_15 0.0000 0.00 0.00 213s Investment_16 0.0000 0.00 0.00 213s Investment_17 0.0000 0.00 0.00 213s Investment_18 0.0000 0.00 0.00 213s Investment_19 0.0000 0.00 0.00 213s Investment_20 0.0000 0.00 0.00 213s Investment_21 0.0000 0.00 0.00 213s Investment_22 0.0000 0.00 0.00 213s PrivateWages_2 -1.3389 -61.06 -60.12 213s PrivateWages_3 0.2462 12.33 11.23 213s PrivateWages_4 1.1255 64.38 56.39 213s PrivateWages_5 -0.1959 -11.18 -11.20 213s PrivateWages_6 -0.5284 -32.23 -30.17 213s PrivateWages_8 -0.7909 -50.94 -50.62 213s PrivateWages_9 0.2819 18.18 18.15 213s PrivateWages_10 1.1384 76.28 73.43 213s PrivateWages_11 -0.1904 -11.65 -12.76 213s PrivateWages_12 0.5813 31.04 35.58 213s PrivateWages_13 0.1206 5.34 6.44 213s PrivateWages_14 0.4773 21.53 21.14 213s PrivateWages_15 0.3035 15.09 13.69 213s PrivateWages_16 0.0284 1.55 1.41 213s PrivateWages_17 -0.8517 -53.40 -46.33 213s PrivateWages_18 0.9908 64.40 62.12 213s PrivateWages_19 -0.4597 -28.00 -29.88 213s PrivateWages_20 -0.3819 -26.54 -23.26 213s PrivateWages_21 -1.1062 -83.74 -76.88 213s PrivateWages_22 0.5501 48.63 41.64 213s PrivateWages_trend 213s Consumption_2 0.000 213s Consumption_3 0.000 213s Consumption_4 0.000 213s Consumption_5 0.000 213s Consumption_6 0.000 213s Consumption_7 0.000 213s Consumption_8 0.000 213s Consumption_9 0.000 213s Consumption_11 0.000 213s Consumption_12 0.000 213s Consumption_13 0.000 213s Consumption_14 0.000 213s Consumption_15 0.000 213s Consumption_16 0.000 213s Consumption_17 0.000 213s Consumption_18 0.000 213s Consumption_19 0.000 213s Consumption_20 0.000 213s Consumption_21 0.000 213s Consumption_22 0.000 213s Investment_2 0.000 213s Investment_3 0.000 213s Investment_4 0.000 213s Investment_5 0.000 213s Investment_6 0.000 213s Investment_7 0.000 213s Investment_8 0.000 213s Investment_9 0.000 213s Investment_10 0.000 213s Investment_11 0.000 213s Investment_12 0.000 213s Investment_13 0.000 213s Investment_14 0.000 213s Investment_15 0.000 213s Investment_16 0.000 213s Investment_17 0.000 213s Investment_18 0.000 213s Investment_19 0.000 213s Investment_20 0.000 213s Investment_21 0.000 213s Investment_22 0.000 213s PrivateWages_2 13.389 213s PrivateWages_3 -2.216 213s PrivateWages_4 -9.004 213s PrivateWages_5 1.371 213s PrivateWages_6 3.170 213s PrivateWages_8 3.164 213s PrivateWages_9 -0.846 213s PrivateWages_10 -2.277 213s PrivateWages_11 0.190 213s PrivateWages_12 0.000 213s PrivateWages_13 0.121 213s PrivateWages_14 0.955 213s PrivateWages_15 0.911 213s PrivateWages_16 0.114 213s PrivateWages_17 -4.258 213s PrivateWages_18 5.945 213s PrivateWages_19 -3.218 213s PrivateWages_20 -3.055 213s PrivateWages_21 -9.956 213s PrivateWages_22 5.501 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_(Intercept) 99.9867 -0.0712 213s Consumption_corpProf -0.0712 0.4890 213s Consumption_corpProfLag -1.1355 -0.2987 213s Consumption_wages -1.8752 -0.0787 213s Investment_(Intercept) 0.0000 0.0000 213s Investment_corpProf 0.0000 0.0000 213s Investment_corpProfLag 0.0000 0.0000 213s Investment_capitalLag 0.0000 0.0000 213s PrivateWages_(Intercept) 0.0000 0.0000 213s PrivateWages_gnp 0.0000 0.0000 213s PrivateWages_gnpLag 0.0000 0.0000 213s PrivateWages_trend 0.0000 0.0000 213s Consumption_corpProfLag Consumption_wages 213s Consumption_(Intercept) -1.1355 -1.8752 213s Consumption_corpProf -0.2987 -0.0787 213s Consumption_corpProfLag 0.4841 -0.0413 213s Consumption_wages -0.0413 0.0933 213s Investment_(Intercept) 0.0000 0.0000 213s Investment_corpProf 0.0000 0.0000 213s Investment_corpProfLag 0.0000 0.0000 213s Investment_capitalLag 0.0000 0.0000 213s PrivateWages_(Intercept) 0.0000 0.0000 213s PrivateWages_gnp 0.0000 0.0000 213s PrivateWages_gnpLag 0.0000 0.0000 213s PrivateWages_trend 0.0000 0.0000 213s Investment_(Intercept) Investment_corpProf 213s Consumption_(Intercept) 0.0 0.0000 213s Consumption_corpProf 0.0 0.0000 213s Consumption_corpProfLag 0.0 0.0000 213s Consumption_wages 0.0 0.0000 213s Investment_(Intercept) 1788.3 -17.4004 213s Investment_corpProf -17.4 0.5646 213s Investment_corpProfLag 14.2 -0.4849 213s Investment_capitalLag -8.6 0.0788 213s PrivateWages_(Intercept) 0.0 0.0000 213s PrivateWages_gnp 0.0 0.0000 213s PrivateWages_gnpLag 0.0 0.0000 213s PrivateWages_trend 0.0 0.0000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_(Intercept) 0.0000 0.0000 213s Consumption_corpProf 0.0000 0.0000 213s Consumption_corpProfLag 0.0000 0.0000 213s Consumption_wages 0.0000 0.0000 213s Investment_(Intercept) 14.2083 -8.5994 213s Investment_corpProf -0.4849 0.0788 213s Investment_corpProfLag 0.6090 -0.0798 213s Investment_capitalLag -0.0798 0.0428 213s PrivateWages_(Intercept) 0.0000 0.0000 213s PrivateWages_gnp 0.0000 0.0000 213s PrivateWages_gnpLag 0.0000 0.0000 213s PrivateWages_trend 0.0000 0.0000 213s PrivateWages_(Intercept) PrivateWages_gnp 213s Consumption_(Intercept) 0.000 0.0000 213s Consumption_corpProf 0.000 0.0000 213s Consumption_corpProfLag 0.000 0.0000 213s Consumption_wages 0.000 0.0000 213s Investment_(Intercept) 0.000 0.0000 213s Investment_corpProf 0.000 0.0000 213s Investment_corpProfLag 0.000 0.0000 213s Investment_capitalLag 0.000 0.0000 213s PrivateWages_(Intercept) 171.811 -0.6470 213s PrivateWages_gnp -0.647 0.1100 213s PrivateWages_gnpLag -2.257 -0.1026 213s PrivateWages_trend 2.120 -0.0296 213s PrivateWages_gnpLag PrivateWages_trend 213s Consumption_(Intercept) 0.00000 0.00000 213s Consumption_corpProf 0.00000 0.00000 213s Consumption_corpProfLag 0.00000 0.00000 213s Consumption_wages 0.00000 0.00000 213s Investment_(Intercept) 0.00000 0.00000 213s Investment_corpProf 0.00000 0.00000 213s Investment_corpProfLag 0.00000 0.00000 213s Investment_capitalLag 0.00000 0.00000 213s PrivateWages_(Intercept) -2.25750 2.12030 213s PrivateWages_gnp -0.10258 -0.02955 213s PrivateWages_gnpLag 0.14523 -0.00656 213s PrivateWages_trend -0.00656 0.11341 213s > 213s > # 2SLS 213s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: 2SLS 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 59 47 53.2 0.251 0.973 0.991 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 19 15 20.49 1.366 1.17 0.978 0.973 213s Investment 20 16 23.02 1.438 1.20 0.901 0.883 213s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.079 0.354 -0.383 213s Investment 0.354 1.047 0.107 213s PrivateWages -0.383 0.107 0.445 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.000 0.335 -0.556 213s Investment 0.335 1.000 0.149 213s PrivateWages -0.556 0.149 1.000 213s 213s 213s 2SLS estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 16.4657 1.3505 12.19 3.5e-09 *** 213s corpProf 0.0243 0.1180 0.21 0.839 213s corpProfLag 0.1981 0.1087 1.82 0.088 . 213s wages 0.8159 0.0420 19.45 4.7e-12 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.169 on 15 degrees of freedom 213s Number of observations: 19 Degrees of Freedom: 15 213s SSR: 20.493 MSE: 1.366 Root MSE: 1.169 213s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.973 213s 213s 213s 2SLS estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 17.8425 6.5319 2.73 0.01478 * 213s corpProf 0.2167 0.1478 1.47 0.16189 213s corpProfLag 0.5416 0.1415 3.83 0.00149 ** 213s capitalLag -0.1455 0.0314 -4.63 0.00028 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.199 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 213s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 213s 213s 213s 2SLS estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 1.3431 1.1250 1.19 0.24995 213s gnp 0.4438 0.0342 12.97 6.6e-10 *** 213s gnpLag 0.1447 0.0371 3.90 0.00128 ** 213s trend 0.1238 0.0292 4.24 0.00063 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.78 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 213s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 213s 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.39161 -1.0104 -1.3401 213s 3 -0.60524 0.2478 0.2378 213s 4 -1.24952 1.0621 1.1117 213s 5 -0.17101 -1.4104 -0.1954 213s 6 0.30841 0.4328 -0.5355 213s 7 NA NA NA 213s 8 1.50999 1.0463 -0.7908 213s 9 1.39649 0.0674 0.2831 213s 10 NA 1.7698 1.1353 213s 11 -0.49339 -0.5912 -0.1765 213s 12 -0.99824 -0.6318 0.6007 213s 13 -1.27965 -0.6983 0.1443 213s 14 0.55302 0.9724 0.4826 213s 15 -0.14553 -0.1827 0.3016 213s 16 -0.00773 0.1167 0.0261 213s 17 1.97001 1.6266 -0.8614 213s 18 -0.59152 -0.0525 0.9927 213s 19 -0.21481 -3.0656 -0.4446 213s 20 1.33575 0.1393 -0.3914 213s 21 1.01443 -0.1305 -1.1115 213s 22 -1.93986 0.2922 0.5312 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.3 0.810 26.8 213s 3 45.6 1.652 29.1 213s 4 50.4 4.138 33.0 213s 5 50.8 4.410 34.1 213s 6 52.3 4.667 35.9 213s 7 NA NA NA 213s 8 54.7 3.154 38.7 213s 9 55.9 2.933 38.9 213s 10 NA 3.330 40.2 213s 11 55.5 1.591 38.1 213s 12 51.9 -2.768 33.9 213s 13 46.9 -5.502 28.9 213s 14 45.9 -6.072 28.0 213s 15 48.8 -2.817 30.3 213s 16 51.3 -1.417 33.2 213s 17 55.7 0.473 37.7 213s 18 59.3 2.053 40.0 213s 19 57.7 1.166 38.6 213s 20 60.3 1.161 42.0 213s 21 64.0 3.431 46.1 213s 22 71.6 4.608 52.8 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.3 0.483 41.3 43.3 213s 3 45.6 0.586 44.4 46.9 213s 4 50.4 0.390 49.6 51.3 213s 5 50.8 0.456 49.8 51.7 213s 6 52.3 0.463 51.3 53.3 213s 7 NA NA NA NA 213s 8 54.7 0.382 53.9 55.5 213s 9 55.9 0.422 55.0 56.8 213s 10 NA NA NA NA 213s 11 55.5 0.742 53.9 57.1 213s 12 51.9 0.600 50.6 53.2 213s 13 46.9 0.770 45.2 48.5 213s 14 45.9 0.635 44.6 47.3 213s 15 48.8 0.383 48.0 49.7 213s 16 51.3 0.339 50.6 52.0 213s 17 55.7 0.410 54.9 56.6 213s 18 59.3 0.336 58.6 60.0 213s 19 57.7 0.418 56.8 58.6 213s 20 60.3 0.481 59.2 61.3 213s 21 64.0 0.462 63.0 65.0 213s 22 71.6 0.706 70.1 73.1 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 0.810 0.750 -0.77956 2.400 213s 3 1.652 0.516 0.55883 2.746 213s 4 4.138 0.487 3.10541 5.170 213s 5 4.410 0.402 3.55860 5.262 213s 6 4.667 0.377 3.86830 5.466 213s 7 NA NA NA NA 213s 8 3.154 0.312 2.49238 3.815 213s 9 2.933 0.466 1.94478 3.920 213s 10 3.330 0.512 2.24435 4.416 213s 11 1.591 0.749 0.00249 3.180 213s 12 -2.768 0.586 -4.01111 -1.525 213s 13 -5.502 0.750 -7.09222 -3.911 213s 14 -6.072 0.803 -7.77404 -4.371 213s 15 -2.817 0.379 -3.62002 -2.015 213s 16 -1.417 0.327 -2.10985 -0.723 213s 17 0.473 0.436 -0.45046 1.397 213s 18 2.053 0.272 1.47523 2.630 213s 19 1.166 0.410 0.29710 2.034 213s 20 1.161 0.491 0.12044 2.201 213s 21 3.431 0.406 2.57004 4.291 213s 22 4.608 0.578 3.38197 5.834 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.8 0.313 26.2 27.5 213s 3 29.1 0.325 28.4 29.8 213s 4 33.0 0.344 32.3 33.7 213s 5 34.1 0.246 33.6 34.6 213s 6 35.9 0.254 35.4 36.5 213s 7 NA NA NA NA 213s 8 38.7 0.251 38.2 39.2 213s 9 38.9 0.239 38.4 39.4 213s 10 40.2 0.229 39.7 40.7 213s 11 38.1 0.339 37.4 38.8 213s 12 33.9 0.365 33.1 34.7 213s 13 28.9 0.436 27.9 29.8 213s 14 28.0 0.333 27.3 28.7 213s 15 30.3 0.324 29.6 31.0 213s 16 33.2 0.271 32.6 33.7 213s 17 37.7 0.280 37.1 38.3 213s 18 40.0 0.208 39.6 40.4 213s 19 38.6 0.342 37.9 39.4 213s 20 42.0 0.293 41.4 42.6 213s 21 46.1 0.296 45.5 46.7 213s 22 52.8 0.474 51.8 53.8 213s > model.frame 213s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 213s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 213s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 213s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 213s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 213s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 213s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 213s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 213s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 213s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 213s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 213s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 213s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 213s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 213s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 213s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 213s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 213s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 213s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 213s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 213s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 213s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 213s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 213s trend 213s 1 -11 213s 2 -10 213s 3 -9 213s 4 -8 213s 5 -7 213s 6 -6 213s 7 -5 213s 8 -4 213s 9 -3 213s 10 -2 213s 11 -1 213s 12 0 213s 13 1 213s 14 2 213s 15 3 213s 16 4 213s 17 5 213s 18 6 213s 19 7 213s 20 8 213s 21 9 213s 22 10 213s > Frames of instrumental variables 213s govExp taxes govWage trend capitalLag corpProfLag gnpLag 213s 1 2.4 3.4 2.2 -11 180 NA NA 213s 2 3.9 7.7 2.7 -10 183 12.7 44.9 213s 3 3.2 3.9 2.9 -9 183 12.4 45.6 213s 4 2.8 4.7 2.9 -8 184 16.9 50.1 213s 5 3.5 3.8 3.1 -7 190 18.4 57.2 213s 6 3.3 5.5 3.2 -6 193 19.4 57.1 213s 7 3.3 7.0 3.3 -5 198 20.1 NA 213s 8 4.0 6.7 3.6 -4 203 19.6 64.0 213s 9 4.2 4.2 3.7 -3 208 19.8 64.4 213s 10 4.1 4.0 4.0 -2 211 21.1 64.5 213s 11 5.2 7.7 4.2 -1 216 21.7 67.0 213s 12 5.9 7.5 4.8 0 217 15.6 61.2 213s 13 4.9 8.3 5.3 1 213 11.4 53.4 213s 14 3.7 5.4 5.6 2 207 7.0 44.3 213s 15 4.0 6.8 6.0 3 202 11.2 45.1 213s 16 4.4 7.2 6.1 4 199 12.3 49.7 213s 17 2.9 8.3 7.4 5 198 14.0 54.4 213s 18 4.3 6.7 6.7 6 200 17.6 62.7 213s 19 5.3 7.4 7.7 7 202 17.3 65.0 213s 20 6.6 8.9 7.8 8 200 15.3 60.9 213s 21 7.4 9.6 8.0 9 201 19.0 69.5 213s 22 13.8 11.6 8.5 10 204 21.1 75.7 213s govExp taxes govWage trend capitalLag corpProfLag gnpLag 213s 1 2.4 3.4 2.2 -11 180 NA NA 213s 2 3.9 7.7 2.7 -10 183 12.7 44.9 213s 3 3.2 3.9 2.9 -9 183 12.4 45.6 213s 4 2.8 4.7 2.9 -8 184 16.9 50.1 213s 5 3.5 3.8 3.1 -7 190 18.4 57.2 213s 6 3.3 5.5 3.2 -6 193 19.4 57.1 213s 7 3.3 7.0 3.3 -5 198 20.1 NA 213s 8 4.0 6.7 3.6 -4 203 19.6 64.0 213s 9 4.2 4.2 3.7 -3 208 19.8 64.4 213s 10 4.1 4.0 4.0 -2 211 21.1 64.5 213s 11 5.2 7.7 4.2 -1 216 21.7 67.0 213s 12 5.9 7.5 4.8 0 217 15.6 61.2 213s 13 4.9 8.3 5.3 1 213 11.4 53.4 213s 14 3.7 5.4 5.6 2 207 7.0 44.3 213s 15 4.0 6.8 6.0 3 202 11.2 45.1 213s 16 4.4 7.2 6.1 4 199 12.3 49.7 213s 17 2.9 8.3 7.4 5 198 14.0 54.4 213s 18 4.3 6.7 6.7 6 200 17.6 62.7 213s 19 5.3 7.4 7.7 7 202 17.3 65.0 213s 20 6.6 8.9 7.8 8 200 15.3 60.9 213s 21 7.4 9.6 8.0 9 201 19.0 69.5 213s 22 13.8 11.6 8.5 10 204 21.1 75.7 213s govExp taxes govWage trend capitalLag corpProfLag gnpLag 213s 1 2.4 3.4 2.2 -11 180 NA NA 213s 2 3.9 7.7 2.7 -10 183 12.7 44.9 213s 3 3.2 3.9 2.9 -9 183 12.4 45.6 213s 4 2.8 4.7 2.9 -8 184 16.9 50.1 213s 5 3.5 3.8 3.1 -7 190 18.4 57.2 213s 6 3.3 5.5 3.2 -6 193 19.4 57.1 213s 7 3.3 7.0 3.3 -5 198 20.1 NA 213s 8 4.0 6.7 3.6 -4 203 19.6 64.0 213s 9 4.2 4.2 3.7 -3 208 19.8 64.4 213s 10 4.1 4.0 4.0 -2 211 21.1 64.5 213s 11 5.2 7.7 4.2 -1 216 21.7 67.0 213s 12 5.9 7.5 4.8 0 217 15.6 61.2 213s 13 4.9 8.3 5.3 1 213 11.4 53.4 213s 14 3.7 5.4 5.6 2 207 7.0 44.3 213s 15 4.0 6.8 6.0 3 202 11.2 45.1 213s 16 4.4 7.2 6.1 4 199 12.3 49.7 213s 17 2.9 8.3 7.4 5 198 14.0 54.4 213s 18 4.3 6.7 6.7 6 200 17.6 62.7 213s 19 5.3 7.4 7.7 7 202 17.3 65.0 213s 20 6.6 8.9 7.8 8 200 15.3 60.9 213s 21 7.4 9.6 8.0 9 201 19.0 69.5 213s 22 13.8 11.6 8.5 10 204 21.1 75.7 213s > model.matrix 213s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 213s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 213s [3] "Numeric: lengths (732, 708) differ" 213s > matrix of instrumental variables 213s Consumption_(Intercept) Consumption_govExp Consumption_taxes 213s Consumption_2 1 3.9 7.7 213s Consumption_3 1 3.2 3.9 213s Consumption_4 1 2.8 4.7 213s Consumption_5 1 3.5 3.8 213s Consumption_6 1 3.3 5.5 213s Consumption_8 1 4.0 6.7 213s Consumption_9 1 4.2 4.2 213s Consumption_11 1 5.2 7.7 213s Consumption_12 1 5.9 7.5 213s Consumption_13 1 4.9 8.3 213s Consumption_14 1 3.7 5.4 213s Consumption_15 1 4.0 6.8 213s Consumption_16 1 4.4 7.2 213s Consumption_17 1 2.9 8.3 213s Consumption_18 1 4.3 6.7 213s Consumption_19 1 5.3 7.4 213s Consumption_20 1 6.6 8.9 213s Consumption_21 1 7.4 9.6 213s Consumption_22 1 13.8 11.6 213s Investment_2 0 0.0 0.0 213s Investment_3 0 0.0 0.0 213s Investment_4 0 0.0 0.0 213s Investment_5 0 0.0 0.0 213s Investment_6 0 0.0 0.0 213s Investment_8 0 0.0 0.0 213s Investment_9 0 0.0 0.0 213s Investment_10 0 0.0 0.0 213s Investment_11 0 0.0 0.0 213s Investment_12 0 0.0 0.0 213s Investment_13 0 0.0 0.0 213s Investment_14 0 0.0 0.0 213s Investment_15 0 0.0 0.0 213s Investment_16 0 0.0 0.0 213s Investment_17 0 0.0 0.0 213s Investment_18 0 0.0 0.0 213s Investment_19 0 0.0 0.0 213s Investment_20 0 0.0 0.0 213s Investment_21 0 0.0 0.0 213s Investment_22 0 0.0 0.0 213s PrivateWages_2 0 0.0 0.0 213s PrivateWages_3 0 0.0 0.0 213s PrivateWages_4 0 0.0 0.0 213s PrivateWages_5 0 0.0 0.0 213s PrivateWages_6 0 0.0 0.0 213s PrivateWages_8 0 0.0 0.0 213s PrivateWages_9 0 0.0 0.0 213s PrivateWages_10 0 0.0 0.0 213s PrivateWages_11 0 0.0 0.0 213s PrivateWages_12 0 0.0 0.0 213s PrivateWages_13 0 0.0 0.0 213s PrivateWages_14 0 0.0 0.0 213s PrivateWages_15 0 0.0 0.0 213s PrivateWages_16 0 0.0 0.0 213s PrivateWages_17 0 0.0 0.0 213s PrivateWages_18 0 0.0 0.0 213s PrivateWages_19 0 0.0 0.0 213s PrivateWages_20 0 0.0 0.0 213s PrivateWages_21 0 0.0 0.0 213s PrivateWages_22 0 0.0 0.0 213s Consumption_govWage Consumption_trend Consumption_capitalLag 213s Consumption_2 2.7 -10 183 213s Consumption_3 2.9 -9 183 213s Consumption_4 2.9 -8 184 213s Consumption_5 3.1 -7 190 213s Consumption_6 3.2 -6 193 213s Consumption_8 3.6 -4 203 213s Consumption_9 3.7 -3 208 213s Consumption_11 4.2 -1 216 213s Consumption_12 4.8 0 217 213s Consumption_13 5.3 1 213 213s Consumption_14 5.6 2 207 213s Consumption_15 6.0 3 202 213s Consumption_16 6.1 4 199 213s Consumption_17 7.4 5 198 213s Consumption_18 6.7 6 200 213s Consumption_19 7.7 7 202 213s Consumption_20 7.8 8 200 213s Consumption_21 8.0 9 201 213s Consumption_22 8.5 10 204 213s Investment_2 0.0 0 0 213s Investment_3 0.0 0 0 213s Investment_4 0.0 0 0 213s Investment_5 0.0 0 0 213s Investment_6 0.0 0 0 213s Investment_8 0.0 0 0 213s Investment_9 0.0 0 0 213s Investment_10 0.0 0 0 213s Investment_11 0.0 0 0 213s Investment_12 0.0 0 0 213s Investment_13 0.0 0 0 213s Investment_14 0.0 0 0 213s Investment_15 0.0 0 0 213s Investment_16 0.0 0 0 213s Investment_17 0.0 0 0 213s Investment_18 0.0 0 0 213s Investment_19 0.0 0 0 213s Investment_20 0.0 0 0 213s Investment_21 0.0 0 0 213s Investment_22 0.0 0 0 213s PrivateWages_2 0.0 0 0 213s PrivateWages_3 0.0 0 0 213s PrivateWages_4 0.0 0 0 213s PrivateWages_5 0.0 0 0 213s PrivateWages_6 0.0 0 0 213s PrivateWages_8 0.0 0 0 213s PrivateWages_9 0.0 0 0 213s PrivateWages_10 0.0 0 0 213s PrivateWages_11 0.0 0 0 213s PrivateWages_12 0.0 0 0 213s PrivateWages_13 0.0 0 0 213s PrivateWages_14 0.0 0 0 213s PrivateWages_15 0.0 0 0 213s PrivateWages_16 0.0 0 0 213s PrivateWages_17 0.0 0 0 213s PrivateWages_18 0.0 0 0 213s PrivateWages_19 0.0 0 0 213s PrivateWages_20 0.0 0 0 213s PrivateWages_21 0.0 0 0 213s PrivateWages_22 0.0 0 0 213s Consumption_corpProfLag Consumption_gnpLag 213s Consumption_2 12.7 44.9 213s Consumption_3 12.4 45.6 213s Consumption_4 16.9 50.1 213s Consumption_5 18.4 57.2 213s Consumption_6 19.4 57.1 213s Consumption_8 19.6 64.0 213s Consumption_9 19.8 64.4 213s Consumption_11 21.7 67.0 213s Consumption_12 15.6 61.2 213s Consumption_13 11.4 53.4 213s Consumption_14 7.0 44.3 213s Consumption_15 11.2 45.1 213s Consumption_16 12.3 49.7 213s Consumption_17 14.0 54.4 213s Consumption_18 17.6 62.7 213s Consumption_19 17.3 65.0 213s Consumption_20 15.3 60.9 213s Consumption_21 19.0 69.5 213s Consumption_22 21.1 75.7 213s Investment_2 0.0 0.0 213s Investment_3 0.0 0.0 213s Investment_4 0.0 0.0 213s Investment_5 0.0 0.0 213s Investment_6 0.0 0.0 213s Investment_8 0.0 0.0 213s Investment_9 0.0 0.0 213s Investment_10 0.0 0.0 213s Investment_11 0.0 0.0 213s Investment_12 0.0 0.0 213s Investment_13 0.0 0.0 213s Investment_14 0.0 0.0 213s Investment_15 0.0 0.0 213s Investment_16 0.0 0.0 213s Investment_17 0.0 0.0 213s Investment_18 0.0 0.0 213s Investment_19 0.0 0.0 213s Investment_20 0.0 0.0 213s Investment_21 0.0 0.0 213s Investment_22 0.0 0.0 213s PrivateWages_2 0.0 0.0 213s PrivateWages_3 0.0 0.0 213s PrivateWages_4 0.0 0.0 213s PrivateWages_5 0.0 0.0 213s PrivateWages_6 0.0 0.0 213s PrivateWages_8 0.0 0.0 213s PrivateWages_9 0.0 0.0 213s PrivateWages_10 0.0 0.0 213s PrivateWages_11 0.0 0.0 213s PrivateWages_12 0.0 0.0 213s PrivateWages_13 0.0 0.0 213s PrivateWages_14 0.0 0.0 213s PrivateWages_15 0.0 0.0 213s PrivateWages_16 0.0 0.0 213s PrivateWages_17 0.0 0.0 213s PrivateWages_18 0.0 0.0 213s PrivateWages_19 0.0 0.0 213s PrivateWages_20 0.0 0.0 213s PrivateWages_21 0.0 0.0 213s PrivateWages_22 0.0 0.0 213s Investment_(Intercept) Investment_govExp Investment_taxes 213s Consumption_2 0 0.0 0.0 213s Consumption_3 0 0.0 0.0 213s Consumption_4 0 0.0 0.0 213s Consumption_5 0 0.0 0.0 213s Consumption_6 0 0.0 0.0 213s Consumption_8 0 0.0 0.0 213s Consumption_9 0 0.0 0.0 213s Consumption_11 0 0.0 0.0 213s Consumption_12 0 0.0 0.0 213s Consumption_13 0 0.0 0.0 213s Consumption_14 0 0.0 0.0 213s Consumption_15 0 0.0 0.0 213s Consumption_16 0 0.0 0.0 213s Consumption_17 0 0.0 0.0 213s Consumption_18 0 0.0 0.0 213s Consumption_19 0 0.0 0.0 213s Consumption_20 0 0.0 0.0 213s Consumption_21 0 0.0 0.0 213s Consumption_22 0 0.0 0.0 213s Investment_2 1 3.9 7.7 213s Investment_3 1 3.2 3.9 213s Investment_4 1 2.8 4.7 213s Investment_5 1 3.5 3.8 213s Investment_6 1 3.3 5.5 213s Investment_8 1 4.0 6.7 213s Investment_9 1 4.2 4.2 213s Investment_10 1 4.1 4.0 213s Investment_11 1 5.2 7.7 213s Investment_12 1 5.9 7.5 213s Investment_13 1 4.9 8.3 213s Investment_14 1 3.7 5.4 213s Investment_15 1 4.0 6.8 213s Investment_16 1 4.4 7.2 213s Investment_17 1 2.9 8.3 213s Investment_18 1 4.3 6.7 213s Investment_19 1 5.3 7.4 213s Investment_20 1 6.6 8.9 213s Investment_21 1 7.4 9.6 213s Investment_22 1 13.8 11.6 213s PrivateWages_2 0 0.0 0.0 213s PrivateWages_3 0 0.0 0.0 213s PrivateWages_4 0 0.0 0.0 213s PrivateWages_5 0 0.0 0.0 213s PrivateWages_6 0 0.0 0.0 213s PrivateWages_8 0 0.0 0.0 213s PrivateWages_9 0 0.0 0.0 213s PrivateWages_10 0 0.0 0.0 213s PrivateWages_11 0 0.0 0.0 213s PrivateWages_12 0 0.0 0.0 213s PrivateWages_13 0 0.0 0.0 213s PrivateWages_14 0 0.0 0.0 213s PrivateWages_15 0 0.0 0.0 213s PrivateWages_16 0 0.0 0.0 213s PrivateWages_17 0 0.0 0.0 213s PrivateWages_18 0 0.0 0.0 213s PrivateWages_19 0 0.0 0.0 213s PrivateWages_20 0 0.0 0.0 213s PrivateWages_21 0 0.0 0.0 213s PrivateWages_22 0 0.0 0.0 213s Investment_govWage Investment_trend Investment_capitalLag 213s Consumption_2 0.0 0 0 213s Consumption_3 0.0 0 0 213s Consumption_4 0.0 0 0 213s Consumption_5 0.0 0 0 213s Consumption_6 0.0 0 0 213s Consumption_8 0.0 0 0 213s Consumption_9 0.0 0 0 213s Consumption_11 0.0 0 0 213s Consumption_12 0.0 0 0 213s Consumption_13 0.0 0 0 213s Consumption_14 0.0 0 0 213s Consumption_15 0.0 0 0 213s Consumption_16 0.0 0 0 213s Consumption_17 0.0 0 0 213s Consumption_18 0.0 0 0 213s Consumption_19 0.0 0 0 213s Consumption_20 0.0 0 0 213s Consumption_21 0.0 0 0 213s Consumption_22 0.0 0 0 213s Investment_2 2.7 -10 183 213s Investment_3 2.9 -9 183 213s Investment_4 2.9 -8 184 213s Investment_5 3.1 -7 190 213s Investment_6 3.2 -6 193 213s Investment_8 3.6 -4 203 213s Investment_9 3.7 -3 208 213s Investment_10 4.0 -2 211 213s Investment_11 4.2 -1 216 213s Investment_12 4.8 0 217 213s Investment_13 5.3 1 213 213s Investment_14 5.6 2 207 213s Investment_15 6.0 3 202 213s Investment_16 6.1 4 199 213s Investment_17 7.4 5 198 213s Investment_18 6.7 6 200 213s Investment_19 7.7 7 202 213s Investment_20 7.8 8 200 213s Investment_21 8.0 9 201 213s Investment_22 8.5 10 204 213s PrivateWages_2 0.0 0 0 213s PrivateWages_3 0.0 0 0 213s PrivateWages_4 0.0 0 0 213s PrivateWages_5 0.0 0 0 213s PrivateWages_6 0.0 0 0 213s PrivateWages_8 0.0 0 0 213s PrivateWages_9 0.0 0 0 213s PrivateWages_10 0.0 0 0 213s PrivateWages_11 0.0 0 0 213s PrivateWages_12 0.0 0 0 213s PrivateWages_13 0.0 0 0 213s PrivateWages_14 0.0 0 0 213s PrivateWages_15 0.0 0 0 213s PrivateWages_16 0.0 0 0 213s PrivateWages_17 0.0 0 0 213s PrivateWages_18 0.0 0 0 213s PrivateWages_19 0.0 0 0 213s PrivateWages_20 0.0 0 0 213s PrivateWages_21 0.0 0 0 213s PrivateWages_22 0.0 0 0 213s Investment_corpProfLag Investment_gnpLag 213s Consumption_2 0.0 0.0 213s Consumption_3 0.0 0.0 213s Consumption_4 0.0 0.0 213s Consumption_5 0.0 0.0 213s Consumption_6 0.0 0.0 213s Consumption_8 0.0 0.0 213s Consumption_9 0.0 0.0 213s Consumption_11 0.0 0.0 213s Consumption_12 0.0 0.0 213s Consumption_13 0.0 0.0 213s Consumption_14 0.0 0.0 213s Consumption_15 0.0 0.0 213s Consumption_16 0.0 0.0 213s Consumption_17 0.0 0.0 213s Consumption_18 0.0 0.0 213s Consumption_19 0.0 0.0 213s Consumption_20 0.0 0.0 213s Consumption_21 0.0 0.0 213s Consumption_22 0.0 0.0 213s Investment_2 12.7 44.9 213s Investment_3 12.4 45.6 213s Investment_4 16.9 50.1 213s Investment_5 18.4 57.2 213s Investment_6 19.4 57.1 213s Investment_8 19.6 64.0 213s Investment_9 19.8 64.4 213s Investment_10 21.1 64.5 213s Investment_11 21.7 67.0 213s Investment_12 15.6 61.2 213s Investment_13 11.4 53.4 213s Investment_14 7.0 44.3 213s Investment_15 11.2 45.1 213s Investment_16 12.3 49.7 213s Investment_17 14.0 54.4 213s Investment_18 17.6 62.7 213s Investment_19 17.3 65.0 213s Investment_20 15.3 60.9 213s Investment_21 19.0 69.5 213s Investment_22 21.1 75.7 213s PrivateWages_2 0.0 0.0 213s PrivateWages_3 0.0 0.0 213s PrivateWages_4 0.0 0.0 213s PrivateWages_5 0.0 0.0 213s PrivateWages_6 0.0 0.0 213s PrivateWages_8 0.0 0.0 213s PrivateWages_9 0.0 0.0 213s PrivateWages_10 0.0 0.0 213s PrivateWages_11 0.0 0.0 213s PrivateWages_12 0.0 0.0 213s PrivateWages_13 0.0 0.0 213s PrivateWages_14 0.0 0.0 213s PrivateWages_15 0.0 0.0 213s PrivateWages_16 0.0 0.0 213s PrivateWages_17 0.0 0.0 213s PrivateWages_18 0.0 0.0 213s PrivateWages_19 0.0 0.0 213s PrivateWages_20 0.0 0.0 213s PrivateWages_21 0.0 0.0 213s PrivateWages_22 0.0 0.0 213s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 213s Consumption_2 0 0.0 0.0 213s Consumption_3 0 0.0 0.0 213s Consumption_4 0 0.0 0.0 213s Consumption_5 0 0.0 0.0 213s Consumption_6 0 0.0 0.0 213s Consumption_8 0 0.0 0.0 213s Consumption_9 0 0.0 0.0 213s Consumption_11 0 0.0 0.0 213s Consumption_12 0 0.0 0.0 213s Consumption_13 0 0.0 0.0 213s Consumption_14 0 0.0 0.0 213s Consumption_15 0 0.0 0.0 213s Consumption_16 0 0.0 0.0 213s Consumption_17 0 0.0 0.0 213s Consumption_18 0 0.0 0.0 213s Consumption_19 0 0.0 0.0 213s Consumption_20 0 0.0 0.0 213s Consumption_21 0 0.0 0.0 213s Consumption_22 0 0.0 0.0 213s Investment_2 0 0.0 0.0 213s Investment_3 0 0.0 0.0 213s Investment_4 0 0.0 0.0 213s Investment_5 0 0.0 0.0 213s Investment_6 0 0.0 0.0 213s Investment_8 0 0.0 0.0 213s Investment_9 0 0.0 0.0 213s Investment_10 0 0.0 0.0 213s Investment_11 0 0.0 0.0 213s Investment_12 0 0.0 0.0 213s Investment_13 0 0.0 0.0 213s Investment_14 0 0.0 0.0 213s Investment_15 0 0.0 0.0 213s Investment_16 0 0.0 0.0 213s Investment_17 0 0.0 0.0 213s Investment_18 0 0.0 0.0 213s Investment_19 0 0.0 0.0 213s Investment_20 0 0.0 0.0 213s Investment_21 0 0.0 0.0 213s Investment_22 0 0.0 0.0 213s PrivateWages_2 1 3.9 7.7 213s PrivateWages_3 1 3.2 3.9 213s PrivateWages_4 1 2.8 4.7 213s PrivateWages_5 1 3.5 3.8 213s PrivateWages_6 1 3.3 5.5 213s PrivateWages_8 1 4.0 6.7 213s PrivateWages_9 1 4.2 4.2 213s PrivateWages_10 1 4.1 4.0 213s PrivateWages_11 1 5.2 7.7 213s PrivateWages_12 1 5.9 7.5 213s PrivateWages_13 1 4.9 8.3 213s PrivateWages_14 1 3.7 5.4 213s PrivateWages_15 1 4.0 6.8 213s PrivateWages_16 1 4.4 7.2 213s PrivateWages_17 1 2.9 8.3 213s PrivateWages_18 1 4.3 6.7 213s PrivateWages_19 1 5.3 7.4 213s PrivateWages_20 1 6.6 8.9 213s PrivateWages_21 1 7.4 9.6 213s PrivateWages_22 1 13.8 11.6 213s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 213s Consumption_2 0.0 0 0 213s Consumption_3 0.0 0 0 213s Consumption_4 0.0 0 0 213s Consumption_5 0.0 0 0 213s Consumption_6 0.0 0 0 213s Consumption_8 0.0 0 0 213s Consumption_9 0.0 0 0 213s Consumption_11 0.0 0 0 213s Consumption_12 0.0 0 0 213s Consumption_13 0.0 0 0 213s Consumption_14 0.0 0 0 213s Consumption_15 0.0 0 0 213s Consumption_16 0.0 0 0 213s Consumption_17 0.0 0 0 213s Consumption_18 0.0 0 0 213s Consumption_19 0.0 0 0 213s Consumption_20 0.0 0 0 213s Consumption_21 0.0 0 0 213s Consumption_22 0.0 0 0 213s Investment_2 0.0 0 0 213s Investment_3 0.0 0 0 213s Investment_4 0.0 0 0 213s Investment_5 0.0 0 0 213s Investment_6 0.0 0 0 213s Investment_8 0.0 0 0 213s Investment_9 0.0 0 0 213s Investment_10 0.0 0 0 213s Investment_11 0.0 0 0 213s Investment_12 0.0 0 0 213s Investment_13 0.0 0 0 213s Investment_14 0.0 0 0 213s Investment_15 0.0 0 0 213s Investment_16 0.0 0 0 213s Investment_17 0.0 0 0 213s Investment_18 0.0 0 0 213s Investment_19 0.0 0 0 213s Investment_20 0.0 0 0 213s Investment_21 0.0 0 0 213s Investment_22 0.0 0 0 213s PrivateWages_2 2.7 -10 183 213s PrivateWages_3 2.9 -9 183 213s PrivateWages_4 2.9 -8 184 213s PrivateWages_5 3.1 -7 190 213s PrivateWages_6 3.2 -6 193 213s PrivateWages_8 3.6 -4 203 213s PrivateWages_9 3.7 -3 208 213s PrivateWages_10 4.0 -2 211 213s PrivateWages_11 4.2 -1 216 213s PrivateWages_12 4.8 0 217 213s PrivateWages_13 5.3 1 213 213s PrivateWages_14 5.6 2 207 213s PrivateWages_15 6.0 3 202 213s PrivateWages_16 6.1 4 199 213s PrivateWages_17 7.4 5 198 213s PrivateWages_18 6.7 6 200 213s PrivateWages_19 7.7 7 202 213s PrivateWages_20 7.8 8 200 213s PrivateWages_21 8.0 9 201 213s PrivateWages_22 8.5 10 204 213s PrivateWages_corpProfLag PrivateWages_gnpLag 213s Consumption_2 0.0 0.0 213s Consumption_3 0.0 0.0 213s Consumption_4 0.0 0.0 213s Consumption_5 0.0 0.0 213s Consumption_6 0.0 0.0 213s Consumption_8 0.0 0.0 213s Consumption_9 0.0 0.0 213s Consumption_11 0.0 0.0 213s Consumption_12 0.0 0.0 213s Consumption_13 0.0 0.0 213s Consumption_14 0.0 0.0 213s Consumption_15 0.0 0.0 213s Consumption_16 0.0 0.0 213s Consumption_17 0.0 0.0 213s Consumption_18 0.0 0.0 213s Consumption_19 0.0 0.0 213s Consumption_20 0.0 0.0 213s Consumption_21 0.0 0.0 213s Consumption_22 0.0 0.0 213s Investment_2 0.0 0.0 213s Investment_3 0.0 0.0 213s Investment_4 0.0 0.0 213s Investment_5 0.0 0.0 213s Investment_6 0.0 0.0 213s Investment_8 0.0 0.0 213s Investment_9 0.0 0.0 213s Investment_10 0.0 0.0 213s Investment_11 0.0 0.0 213s Investment_12 0.0 0.0 213s Investment_13 0.0 0.0 213s Investment_14 0.0 0.0 213s Investment_15 0.0 0.0 213s Investment_16 0.0 0.0 213s Investment_17 0.0 0.0 213s Investment_18 0.0 0.0 213s Investment_19 0.0 0.0 213s Investment_20 0.0 0.0 213s Investment_21 0.0 0.0 213s Investment_22 0.0 0.0 213s PrivateWages_2 12.7 44.9 213s PrivateWages_3 12.4 45.6 213s PrivateWages_4 16.9 50.1 213s PrivateWages_5 18.4 57.2 213s PrivateWages_6 19.4 57.1 213s PrivateWages_8 19.6 64.0 213s PrivateWages_9 19.8 64.4 213s PrivateWages_10 21.1 64.5 213s PrivateWages_11 21.7 67.0 213s PrivateWages_12 15.6 61.2 213s PrivateWages_13 11.4 53.4 213s PrivateWages_14 7.0 44.3 213s PrivateWages_15 11.2 45.1 213s PrivateWages_16 12.3 49.7 213s PrivateWages_17 14.0 54.4 213s PrivateWages_18 17.6 62.7 213s PrivateWages_19 17.3 65.0 213s PrivateWages_20 15.3 60.9 213s PrivateWages_21 19.0 69.5 213s PrivateWages_22 21.1 75.7 213s > matrix of fitted regressors 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 1 13.44 213s Consumption_3 1 16.68 213s Consumption_4 1 18.95 213s Consumption_5 1 20.63 213s Consumption_6 1 19.28 213s Consumption_8 1 17.21 213s Consumption_9 1 18.99 213s Consumption_11 1 16.43 213s Consumption_12 1 12.49 213s Consumption_13 1 9.06 213s Consumption_14 1 9.28 213s Consumption_15 1 12.49 213s Consumption_16 1 14.39 213s Consumption_17 1 14.69 213s Consumption_18 1 19.60 213s Consumption_19 1 19.15 213s Consumption_20 1 17.54 213s Consumption_21 1 20.33 213s Consumption_22 1 22.78 213s Investment_2 0 0.00 213s Investment_3 0 0.00 213s Investment_4 0 0.00 213s Investment_5 0 0.00 213s Investment_6 0 0.00 213s Investment_8 0 0.00 213s Investment_9 0 0.00 213s Investment_10 0 0.00 213s Investment_11 0 0.00 213s Investment_12 0 0.00 213s Investment_13 0 0.00 213s Investment_14 0 0.00 213s Investment_15 0 0.00 213s Investment_16 0 0.00 213s Investment_17 0 0.00 213s Investment_18 0 0.00 213s Investment_19 0 0.00 213s Investment_20 0 0.00 213s Investment_21 0 0.00 213s Investment_22 0 0.00 213s PrivateWages_2 0 0.00 213s PrivateWages_3 0 0.00 213s PrivateWages_4 0 0.00 213s PrivateWages_5 0 0.00 213s PrivateWages_6 0 0.00 213s PrivateWages_8 0 0.00 213s PrivateWages_9 0 0.00 213s PrivateWages_10 0 0.00 213s PrivateWages_11 0 0.00 213s PrivateWages_12 0 0.00 213s PrivateWages_13 0 0.00 213s PrivateWages_14 0 0.00 213s PrivateWages_15 0 0.00 213s PrivateWages_16 0 0.00 213s PrivateWages_17 0 0.00 213s PrivateWages_18 0 0.00 213s PrivateWages_19 0 0.00 213s PrivateWages_20 0 0.00 213s PrivateWages_21 0 0.00 213s PrivateWages_22 0 0.00 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 12.7 29.6 213s Consumption_3 12.4 31.9 213s Consumption_4 16.9 35.4 213s Consumption_5 18.4 38.8 213s Consumption_6 19.4 38.7 213s Consumption_8 19.6 39.8 213s Consumption_9 19.8 41.8 213s Consumption_11 21.7 43.0 213s Consumption_12 15.6 39.3 213s Consumption_13 11.4 35.2 213s Consumption_14 7.0 33.0 213s Consumption_15 11.2 37.3 213s Consumption_16 12.3 40.1 213s Consumption_17 14.0 41.7 213s Consumption_18 17.6 47.7 213s Consumption_19 17.3 49.2 213s Consumption_20 15.3 48.5 213s Consumption_21 19.0 53.4 213s Consumption_22 21.1 60.8 213s Investment_2 0.0 0.0 213s Investment_3 0.0 0.0 213s Investment_4 0.0 0.0 213s Investment_5 0.0 0.0 213s Investment_6 0.0 0.0 213s Investment_8 0.0 0.0 213s Investment_9 0.0 0.0 213s Investment_10 0.0 0.0 213s Investment_11 0.0 0.0 213s Investment_12 0.0 0.0 213s Investment_13 0.0 0.0 213s Investment_14 0.0 0.0 213s Investment_15 0.0 0.0 213s Investment_16 0.0 0.0 213s Investment_17 0.0 0.0 213s Investment_18 0.0 0.0 213s Investment_19 0.0 0.0 213s Investment_20 0.0 0.0 213s Investment_21 0.0 0.0 213s Investment_22 0.0 0.0 213s PrivateWages_2 0.0 0.0 213s PrivateWages_3 0.0 0.0 213s PrivateWages_4 0.0 0.0 213s PrivateWages_5 0.0 0.0 213s PrivateWages_6 0.0 0.0 213s PrivateWages_8 0.0 0.0 213s PrivateWages_9 0.0 0.0 213s PrivateWages_10 0.0 0.0 213s PrivateWages_11 0.0 0.0 213s PrivateWages_12 0.0 0.0 213s PrivateWages_13 0.0 0.0 213s PrivateWages_14 0.0 0.0 213s PrivateWages_15 0.0 0.0 213s PrivateWages_16 0.0 0.0 213s PrivateWages_17 0.0 0.0 213s PrivateWages_18 0.0 0.0 213s PrivateWages_19 0.0 0.0 213s PrivateWages_20 0.0 0.0 213s PrivateWages_21 0.0 0.0 213s PrivateWages_22 0.0 0.0 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0 0.00 213s Consumption_3 0 0.00 213s Consumption_4 0 0.00 213s Consumption_5 0 0.00 213s Consumption_6 0 0.00 213s Consumption_8 0 0.00 213s Consumption_9 0 0.00 213s Consumption_11 0 0.00 213s Consumption_12 0 0.00 213s Consumption_13 0 0.00 213s Consumption_14 0 0.00 213s Consumption_15 0 0.00 213s Consumption_16 0 0.00 213s Consumption_17 0 0.00 213s Consumption_18 0 0.00 213s Consumption_19 0 0.00 213s Consumption_20 0 0.00 213s Consumption_21 0 0.00 213s Consumption_22 0 0.00 213s Investment_2 1 12.96 213s Investment_3 1 16.70 213s Investment_4 1 19.14 213s Investment_5 1 20.94 213s Investment_6 1 19.47 213s Investment_8 1 17.14 213s Investment_9 1 19.49 213s Investment_10 1 20.46 213s Investment_11 1 16.85 213s Investment_12 1 12.68 213s Investment_13 1 8.92 213s Investment_14 1 9.30 213s Investment_15 1 12.79 213s Investment_16 1 14.26 213s Investment_17 1 14.75 213s Investment_18 1 19.54 213s Investment_19 1 19.36 213s Investment_20 1 17.39 213s Investment_21 1 20.10 213s Investment_22 1 22.86 213s PrivateWages_2 0 0.00 213s PrivateWages_3 0 0.00 213s PrivateWages_4 0 0.00 213s PrivateWages_5 0 0.00 213s PrivateWages_6 0 0.00 213s PrivateWages_8 0 0.00 213s PrivateWages_9 0 0.00 213s PrivateWages_10 0 0.00 213s PrivateWages_11 0 0.00 213s PrivateWages_12 0 0.00 213s PrivateWages_13 0 0.00 213s PrivateWages_14 0 0.00 213s PrivateWages_15 0 0.00 213s PrivateWages_16 0 0.00 213s PrivateWages_17 0 0.00 213s PrivateWages_18 0 0.00 213s PrivateWages_19 0 0.00 213s PrivateWages_20 0 0.00 213s PrivateWages_21 0 0.00 213s PrivateWages_22 0 0.00 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.0 0 213s Consumption_3 0.0 0 213s Consumption_4 0.0 0 213s Consumption_5 0.0 0 213s Consumption_6 0.0 0 213s Consumption_8 0.0 0 213s Consumption_9 0.0 0 213s Consumption_11 0.0 0 213s Consumption_12 0.0 0 213s Consumption_13 0.0 0 213s Consumption_14 0.0 0 213s Consumption_15 0.0 0 213s Consumption_16 0.0 0 213s Consumption_17 0.0 0 213s Consumption_18 0.0 0 213s Consumption_19 0.0 0 213s Consumption_20 0.0 0 213s Consumption_21 0.0 0 213s Consumption_22 0.0 0 213s Investment_2 12.7 183 213s Investment_3 12.4 183 213s Investment_4 16.9 184 213s Investment_5 18.4 190 213s Investment_6 19.4 193 213s Investment_8 19.6 203 213s Investment_9 19.8 208 213s Investment_10 21.1 211 213s Investment_11 21.7 216 213s Investment_12 15.6 217 213s Investment_13 11.4 213 213s Investment_14 7.0 207 213s Investment_15 11.2 202 213s Investment_16 12.3 199 213s Investment_17 14.0 198 213s Investment_18 17.6 200 213s Investment_19 17.3 202 213s Investment_20 15.3 200 213s Investment_21 19.0 201 213s Investment_22 21.1 204 213s PrivateWages_2 0.0 0 213s PrivateWages_3 0.0 0 213s PrivateWages_4 0.0 0 213s PrivateWages_5 0.0 0 213s PrivateWages_6 0.0 0 213s PrivateWages_8 0.0 0 213s PrivateWages_9 0.0 0 213s PrivateWages_10 0.0 0 213s PrivateWages_11 0.0 0 213s PrivateWages_12 0.0 0 213s PrivateWages_13 0.0 0 213s PrivateWages_14 0.0 0 213s PrivateWages_15 0.0 0 213s PrivateWages_16 0.0 0 213s PrivateWages_17 0.0 0 213s PrivateWages_18 0.0 0 213s PrivateWages_19 0.0 0 213s PrivateWages_20 0.0 0 213s PrivateWages_21 0.0 0 213s PrivateWages_22 0.0 0 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 0 0.0 0.0 213s Consumption_3 0 0.0 0.0 213s Consumption_4 0 0.0 0.0 213s Consumption_5 0 0.0 0.0 213s Consumption_6 0 0.0 0.0 213s Consumption_8 0 0.0 0.0 213s Consumption_9 0 0.0 0.0 213s Consumption_11 0 0.0 0.0 213s Consumption_12 0 0.0 0.0 213s Consumption_13 0 0.0 0.0 213s Consumption_14 0 0.0 0.0 213s Consumption_15 0 0.0 0.0 213s Consumption_16 0 0.0 0.0 213s Consumption_17 0 0.0 0.0 213s Consumption_18 0 0.0 0.0 213s Consumption_19 0 0.0 0.0 213s Consumption_20 0 0.0 0.0 213s Consumption_21 0 0.0 0.0 213s Consumption_22 0 0.0 0.0 213s Investment_2 0 0.0 0.0 213s Investment_3 0 0.0 0.0 213s Investment_4 0 0.0 0.0 213s Investment_5 0 0.0 0.0 213s Investment_6 0 0.0 0.0 213s Investment_8 0 0.0 0.0 213s Investment_9 0 0.0 0.0 213s Investment_10 0 0.0 0.0 213s Investment_11 0 0.0 0.0 213s Investment_12 0 0.0 0.0 213s Investment_13 0 0.0 0.0 213s Investment_14 0 0.0 0.0 213s Investment_15 0 0.0 0.0 213s Investment_16 0 0.0 0.0 213s Investment_17 0 0.0 0.0 213s Investment_18 0 0.0 0.0 213s Investment_19 0 0.0 0.0 213s Investment_20 0 0.0 0.0 213s Investment_21 0 0.0 0.0 213s Investment_22 0 0.0 0.0 213s PrivateWages_2 1 47.1 44.9 213s PrivateWages_3 1 49.6 45.6 213s PrivateWages_4 1 56.5 50.1 213s PrivateWages_5 1 60.7 57.2 213s PrivateWages_6 1 60.6 57.1 213s PrivateWages_8 1 60.0 64.0 213s PrivateWages_9 1 62.3 64.4 213s PrivateWages_10 1 64.6 64.5 213s PrivateWages_11 1 63.7 67.0 213s PrivateWages_12 1 54.8 61.2 213s PrivateWages_13 1 47.0 53.4 213s PrivateWages_14 1 42.1 44.3 213s PrivateWages_15 1 51.2 45.1 213s PrivateWages_16 1 55.3 49.7 213s PrivateWages_17 1 57.4 54.4 213s PrivateWages_18 1 67.2 62.7 213s PrivateWages_19 1 68.5 65.0 213s PrivateWages_20 1 66.8 60.9 213s PrivateWages_21 1 74.9 69.5 213s PrivateWages_22 1 86.9 75.7 213s PrivateWages_trend 213s Consumption_2 0 213s Consumption_3 0 213s Consumption_4 0 213s Consumption_5 0 213s Consumption_6 0 213s Consumption_8 0 213s Consumption_9 0 213s Consumption_11 0 213s Consumption_12 0 213s Consumption_13 0 213s Consumption_14 0 213s Consumption_15 0 213s Consumption_16 0 213s Consumption_17 0 213s Consumption_18 0 213s Consumption_19 0 213s Consumption_20 0 213s Consumption_21 0 213s Consumption_22 0 213s Investment_2 0 213s Investment_3 0 213s Investment_4 0 213s Investment_5 0 213s Investment_6 0 213s Investment_8 0 213s Investment_9 0 213s Investment_10 0 213s Investment_11 0 213s Investment_12 0 213s Investment_13 0 213s Investment_14 0 213s Investment_15 0 213s Investment_16 0 213s Investment_17 0 213s Investment_18 0 213s Investment_19 0 213s Investment_20 0 213s Investment_21 0 213s Investment_22 0 213s PrivateWages_2 -10 213s PrivateWages_3 -9 213s PrivateWages_4 -8 213s PrivateWages_5 -7 213s PrivateWages_6 -6 213s PrivateWages_8 -4 213s PrivateWages_9 -3 213s PrivateWages_10 -2 213s PrivateWages_11 -1 213s PrivateWages_12 0 213s PrivateWages_13 1 213s PrivateWages_14 2 213s PrivateWages_15 3 213s PrivateWages_16 4 213s PrivateWages_17 5 213s PrivateWages_18 6 213s PrivateWages_19 7 213s PrivateWages_20 8 213s PrivateWages_21 9 213s PrivateWages_22 10 213s > nobs 213s [1] 59 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.87 0.36 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.98 0.33 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 48 213s 2 47 1 0.98 0.32 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.43 0.65 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.49 0.61 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 49 213s 2 47 2 0.98 0.61 213s > logLik 213s 'log Lik.' -71.5 (df=13) 213s 'log Lik.' -78.7 (df=13) 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -1.5371 -20.65 213s Consumption_3 -0.3191 -5.32 213s Consumption_4 0.0169 0.32 213s Consumption_5 -1.6346 -33.73 213s Consumption_6 0.2820 5.44 213s Consumption_8 2.9429 50.64 213s Consumption_9 2.3495 44.61 213s Consumption_11 -1.2221 -20.08 213s Consumption_12 -1.0034 -12.54 213s Consumption_13 -2.0551 -18.62 213s Consumption_14 1.4937 13.86 213s Consumption_15 -0.7418 -9.26 213s Consumption_16 -0.6703 -9.64 213s Consumption_17 4.0943 60.15 213s Consumption_18 -0.6347 -12.44 213s Consumption_19 -3.0409 -58.22 213s Consumption_20 2.1019 36.86 213s Consumption_21 0.7142 14.52 213s Consumption_22 -1.1363 -25.88 213s Investment_2 0.0000 0.00 213s Investment_3 0.0000 0.00 213s Investment_4 0.0000 0.00 213s Investment_5 0.0000 0.00 213s Investment_6 0.0000 0.00 213s Investment_8 0.0000 0.00 213s Investment_9 0.0000 0.00 213s Investment_10 0.0000 0.00 213s Investment_11 0.0000 0.00 213s Investment_12 0.0000 0.00 213s Investment_13 0.0000 0.00 213s Investment_14 0.0000 0.00 213s Investment_15 0.0000 0.00 213s Investment_16 0.0000 0.00 213s Investment_17 0.0000 0.00 213s Investment_18 0.0000 0.00 213s Investment_19 0.0000 0.00 213s Investment_20 0.0000 0.00 213s Investment_21 0.0000 0.00 213s Investment_22 0.0000 0.00 213s PrivateWages_2 0.0000 0.00 213s PrivateWages_3 0.0000 0.00 213s PrivateWages_4 0.0000 0.00 213s PrivateWages_5 0.0000 0.00 213s PrivateWages_6 0.0000 0.00 213s PrivateWages_8 0.0000 0.00 213s PrivateWages_9 0.0000 0.00 213s PrivateWages_10 0.0000 0.00 213s PrivateWages_11 0.0000 0.00 213s PrivateWages_12 0.0000 0.00 213s PrivateWages_13 0.0000 0.00 213s PrivateWages_14 0.0000 0.00 213s PrivateWages_15 0.0000 0.00 213s PrivateWages_16 0.0000 0.00 213s PrivateWages_17 0.0000 0.00 213s PrivateWages_18 0.0000 0.00 213s PrivateWages_19 0.0000 0.00 213s PrivateWages_20 0.0000 0.00 213s PrivateWages_21 0.0000 0.00 213s PrivateWages_22 0.0000 0.00 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -19.521 -45.456 213s Consumption_3 -3.957 -10.167 213s Consumption_4 0.286 0.599 213s Consumption_5 -30.078 -63.354 213s Consumption_6 5.471 10.901 213s Consumption_8 57.681 117.190 213s Consumption_9 46.520 98.197 213s Consumption_11 -26.520 -52.512 213s Consumption_12 -15.653 -39.407 213s Consumption_13 -23.428 -72.317 213s Consumption_14 10.456 49.297 213s Consumption_15 -8.308 -27.687 213s Consumption_16 -8.244 -26.878 213s Consumption_17 57.321 170.665 213s Consumption_18 -11.170 -30.264 213s Consumption_19 -52.608 -149.761 213s Consumption_20 32.159 101.952 213s Consumption_21 13.570 38.131 213s Consumption_22 -23.976 -69.128 213s Investment_2 0.000 0.000 213s Investment_3 0.000 0.000 213s Investment_4 0.000 0.000 213s Investment_5 0.000 0.000 213s Investment_6 0.000 0.000 213s Investment_8 0.000 0.000 213s Investment_9 0.000 0.000 213s Investment_10 0.000 0.000 213s Investment_11 0.000 0.000 213s Investment_12 0.000 0.000 213s Investment_13 0.000 0.000 213s Investment_14 0.000 0.000 213s Investment_15 0.000 0.000 213s Investment_16 0.000 0.000 213s Investment_17 0.000 0.000 213s Investment_18 0.000 0.000 213s Investment_19 0.000 0.000 213s Investment_20 0.000 0.000 213s Investment_21 0.000 0.000 213s Investment_22 0.000 0.000 213s PrivateWages_2 0.000 0.000 213s PrivateWages_3 0.000 0.000 213s PrivateWages_4 0.000 0.000 213s PrivateWages_5 0.000 0.000 213s PrivateWages_6 0.000 0.000 213s PrivateWages_8 0.000 0.000 213s PrivateWages_9 0.000 0.000 213s PrivateWages_10 0.000 0.000 213s PrivateWages_11 0.000 0.000 213s PrivateWages_12 0.000 0.000 213s PrivateWages_13 0.000 0.000 213s PrivateWages_14 0.000 0.000 213s PrivateWages_15 0.000 0.000 213s PrivateWages_16 0.000 0.000 213s PrivateWages_17 0.000 0.000 213s PrivateWages_18 0.000 0.000 213s PrivateWages_19 0.000 0.000 213s PrivateWages_20 0.000 0.000 213s PrivateWages_21 0.000 0.000 213s PrivateWages_22 0.000 0.000 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0.0000 0.000 213s Consumption_3 0.0000 0.000 213s Consumption_4 0.0000 0.000 213s Consumption_5 0.0000 0.000 213s Consumption_6 0.0000 0.000 213s Consumption_8 0.0000 0.000 213s Consumption_9 0.0000 0.000 213s Consumption_11 0.0000 0.000 213s Consumption_12 0.0000 0.000 213s Consumption_13 0.0000 0.000 213s Consumption_14 0.0000 0.000 213s Consumption_15 0.0000 0.000 213s Consumption_16 0.0000 0.000 213s Consumption_17 0.0000 0.000 213s Consumption_18 0.0000 0.000 213s Consumption_19 0.0000 0.000 213s Consumption_20 0.0000 0.000 213s Consumption_21 0.0000 0.000 213s Consumption_22 0.0000 0.000 213s Investment_2 -1.1313 -14.660 213s Investment_3 0.2902 4.847 213s Investment_4 0.9027 17.274 213s Investment_5 -1.7434 -36.502 213s Investment_6 0.5695 11.088 213s Investment_8 1.6225 27.812 213s Investment_9 0.4166 8.119 213s Investment_10 2.0381 41.703 213s Investment_11 -0.8611 -14.505 213s Investment_12 -0.9091 -11.527 213s Investment_13 -1.1148 -9.946 213s Investment_14 1.3841 12.873 213s Investment_15 -0.2900 -3.710 213s Investment_16 0.0605 0.862 213s Investment_17 2.2439 33.101 213s Investment_18 -0.5390 -10.534 213s Investment_19 -3.9452 -76.375 213s Investment_20 0.4890 8.502 213s Investment_21 0.0864 1.737 213s Investment_22 0.4306 9.843 213s PrivateWages_2 0.0000 0.000 213s PrivateWages_3 0.0000 0.000 213s PrivateWages_4 0.0000 0.000 213s PrivateWages_5 0.0000 0.000 213s PrivateWages_6 0.0000 0.000 213s PrivateWages_8 0.0000 0.000 213s PrivateWages_9 0.0000 0.000 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 0.0000 0.000 213s PrivateWages_12 0.0000 0.000 213s PrivateWages_13 0.0000 0.000 213s PrivateWages_14 0.0000 0.000 213s PrivateWages_15 0.0000 0.000 213s PrivateWages_16 0.0000 0.000 213s PrivateWages_17 0.0000 0.000 213s PrivateWages_18 0.0000 0.000 213s PrivateWages_19 0.0000 0.000 213s PrivateWages_20 0.0000 0.000 213s PrivateWages_21 0.0000 0.000 213s PrivateWages_22 0.0000 0.000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.000 0.0 213s Consumption_3 0.000 0.0 213s Consumption_4 0.000 0.0 213s Consumption_5 0.000 0.0 213s Consumption_6 0.000 0.0 213s Consumption_8 0.000 0.0 213s Consumption_9 0.000 0.0 213s Consumption_11 0.000 0.0 213s Consumption_12 0.000 0.0 213s Consumption_13 0.000 0.0 213s Consumption_14 0.000 0.0 213s Consumption_15 0.000 0.0 213s Consumption_16 0.000 0.0 213s Consumption_17 0.000 0.0 213s Consumption_18 0.000 0.0 213s Consumption_19 0.000 0.0 213s Consumption_20 0.000 0.0 213s Consumption_21 0.000 0.0 213s Consumption_22 0.000 0.0 213s Investment_2 -14.368 -206.8 213s Investment_3 3.598 53.0 213s Investment_4 15.256 166.5 213s Investment_5 -32.079 -330.7 213s Investment_6 11.048 109.7 213s Investment_8 31.801 330.0 213s Investment_9 8.248 86.5 213s Investment_10 43.003 429.2 213s Investment_11 -18.685 -185.7 213s Investment_12 -14.182 -197.0 213s Investment_13 -12.709 -237.8 213s Investment_14 9.689 286.6 213s Investment_15 -3.247 -58.6 213s Investment_16 0.744 12.0 213s Investment_17 31.414 443.6 213s Investment_18 -9.486 -107.7 213s Investment_19 -68.252 -796.1 213s Investment_20 7.482 97.7 213s Investment_21 1.642 17.4 213s Investment_22 9.085 88.0 213s PrivateWages_2 0.000 0.0 213s PrivateWages_3 0.000 0.0 213s PrivateWages_4 0.000 0.0 213s PrivateWages_5 0.000 0.0 213s PrivateWages_6 0.000 0.0 213s PrivateWages_8 0.000 0.0 213s PrivateWages_9 0.000 0.0 213s PrivateWages_10 0.000 0.0 213s PrivateWages_11 0.000 0.0 213s PrivateWages_12 0.000 0.0 213s PrivateWages_13 0.000 0.0 213s PrivateWages_14 0.000 0.0 213s PrivateWages_15 0.000 0.0 213s PrivateWages_16 0.000 0.0 213s PrivateWages_17 0.000 0.0 213s PrivateWages_18 0.000 0.0 213s PrivateWages_19 0.000 0.0 213s PrivateWages_20 0.000 0.0 213s PrivateWages_21 0.000 0.0 213s PrivateWages_22 0.000 0.0 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 0.0000 0.00 0.00 213s Consumption_3 0.0000 0.00 0.00 213s Consumption_4 0.0000 0.00 0.00 213s Consumption_5 0.0000 0.00 0.00 213s Consumption_6 0.0000 0.00 0.00 213s Consumption_8 0.0000 0.00 0.00 213s Consumption_9 0.0000 0.00 0.00 213s Consumption_11 0.0000 0.00 0.00 213s Consumption_12 0.0000 0.00 0.00 213s Consumption_13 0.0000 0.00 0.00 213s Consumption_14 0.0000 0.00 0.00 213s Consumption_15 0.0000 0.00 0.00 213s Consumption_16 0.0000 0.00 0.00 213s Consumption_17 0.0000 0.00 0.00 213s Consumption_18 0.0000 0.00 0.00 213s Consumption_19 0.0000 0.00 0.00 213s Consumption_20 0.0000 0.00 0.00 213s Consumption_21 0.0000 0.00 0.00 213s Consumption_22 0.0000 0.00 0.00 213s Investment_2 0.0000 0.00 0.00 213s Investment_3 0.0000 0.00 0.00 213s Investment_4 0.0000 0.00 0.00 213s Investment_5 0.0000 0.00 0.00 213s Investment_6 0.0000 0.00 0.00 213s Investment_8 0.0000 0.00 0.00 213s Investment_9 0.0000 0.00 0.00 213s Investment_10 0.0000 0.00 0.00 213s Investment_11 0.0000 0.00 0.00 213s Investment_12 0.0000 0.00 0.00 213s Investment_13 0.0000 0.00 0.00 213s Investment_14 0.0000 0.00 0.00 213s Investment_15 0.0000 0.00 0.00 213s Investment_16 0.0000 0.00 0.00 213s Investment_17 0.0000 0.00 0.00 213s Investment_18 0.0000 0.00 0.00 213s Investment_19 0.0000 0.00 0.00 213s Investment_20 0.0000 0.00 0.00 213s Investment_21 0.0000 0.00 0.00 213s Investment_22 0.0000 0.00 0.00 213s PrivateWages_2 -1.9924 -93.78 -89.46 213s PrivateWages_3 0.4683 23.22 21.35 213s PrivateWages_4 1.4034 79.35 70.31 213s PrivateWages_5 -1.7870 -108.45 -102.22 213s PrivateWages_6 -0.3627 -21.98 -20.71 213s PrivateWages_8 1.1629 69.77 74.43 213s PrivateWages_9 1.2735 79.30 82.01 213s PrivateWages_10 2.2141 142.96 142.81 213s PrivateWages_11 -1.2912 -82.26 -86.51 213s PrivateWages_12 -0.0350 -1.92 -2.14 213s PrivateWages_13 -1.0438 -49.04 -55.74 213s PrivateWages_14 1.8016 75.90 79.81 213s PrivateWages_15 -0.3714 -19.02 -16.75 213s PrivateWages_16 -0.3904 -21.61 -19.40 213s PrivateWages_17 1.4934 85.71 81.24 213s PrivateWages_18 0.0279 1.88 1.75 213s PrivateWages_19 -3.8229 -261.91 -248.49 213s PrivateWages_20 0.7870 52.61 47.93 213s PrivateWages_21 -0.7415 -55.52 -51.54 213s PrivateWages_22 1.2062 104.79 91.31 213s PrivateWages_trend 213s Consumption_2 0.000 213s Consumption_3 0.000 213s Consumption_4 0.000 213s Consumption_5 0.000 213s Consumption_6 0.000 213s Consumption_8 0.000 213s Consumption_9 0.000 213s Consumption_11 0.000 213s Consumption_12 0.000 213s Consumption_13 0.000 213s Consumption_14 0.000 213s Consumption_15 0.000 213s Consumption_16 0.000 213s Consumption_17 0.000 213s Consumption_18 0.000 213s Consumption_19 0.000 213s Consumption_20 0.000 213s Consumption_21 0.000 213s Consumption_22 0.000 213s Investment_2 0.000 213s Investment_3 0.000 213s Investment_4 0.000 213s Investment_5 0.000 213s Investment_6 0.000 213s Investment_8 0.000 213s Investment_9 0.000 213s Investment_10 0.000 213s Investment_11 0.000 213s Investment_12 0.000 213s Investment_13 0.000 213s Investment_14 0.000 213s Investment_15 0.000 213s Investment_16 0.000 213s Investment_17 0.000 213s Investment_18 0.000 213s Investment_19 0.000 213s Investment_20 0.000 213s Investment_21 0.000 213s Investment_22 0.000 213s PrivateWages_2 19.924 213s PrivateWages_3 -4.214 213s PrivateWages_4 -11.227 213s PrivateWages_5 12.509 213s PrivateWages_6 2.176 213s PrivateWages_8 -4.652 213s PrivateWages_9 -3.820 213s PrivateWages_10 -4.428 213s PrivateWages_11 1.291 213s PrivateWages_12 0.000 213s PrivateWages_13 -1.044 213s PrivateWages_14 3.603 213s PrivateWages_15 -1.114 213s PrivateWages_16 -1.562 213s PrivateWages_17 7.467 213s PrivateWages_18 0.168 213s PrivateWages_19 -26.760 213s PrivateWages_20 6.296 213s PrivateWages_21 -6.674 213s PrivateWages_22 12.062 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_(Intercept) 99.763 -0.8715 213s Consumption_corpProf -0.872 0.7621 213s Consumption_corpProfLag -0.479 -0.4940 213s Consumption_wages -1.807 -0.0927 213s Investment_(Intercept) 0.000 0.0000 213s Investment_corpProf 0.000 0.0000 213s Investment_corpProfLag 0.000 0.0000 213s Investment_capitalLag 0.000 0.0000 213s PrivateWages_(Intercept) 0.000 0.0000 213s PrivateWages_gnp 0.000 0.0000 213s PrivateWages_gnpLag 0.000 0.0000 213s PrivateWages_trend 0.000 0.0000 213s Consumption_corpProfLag Consumption_wages 213s Consumption_(Intercept) -0.4786 -1.8068 213s Consumption_corpProf -0.4940 -0.0927 213s Consumption_corpProfLag 0.6462 -0.0403 213s Consumption_wages -0.0403 0.0963 213s Investment_(Intercept) 0.0000 0.0000 213s Investment_corpProf 0.0000 0.0000 213s Investment_corpProfLag 0.0000 0.0000 213s Investment_capitalLag 0.0000 0.0000 213s PrivateWages_(Intercept) 0.0000 0.0000 213s PrivateWages_gnp 0.0000 0.0000 213s PrivateWages_gnpLag 0.0000 0.0000 213s PrivateWages_trend 0.0000 0.0000 213s Investment_(Intercept) Investment_corpProf 213s Consumption_(Intercept) 0.0 0.000 213s Consumption_corpProf 0.0 0.000 213s Consumption_corpProfLag 0.0 0.000 213s Consumption_wages 0.0 0.000 213s Investment_(Intercept) 2405.5 -38.269 213s Investment_corpProf -38.3 1.231 213s Investment_corpProfLag 32.8 -1.072 213s Investment_capitalLag -11.4 0.174 213s PrivateWages_(Intercept) 0.0 0.000 213s PrivateWages_gnp 0.0 0.000 213s PrivateWages_gnpLag 0.0 0.000 213s PrivateWages_trend 0.0 0.000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_(Intercept) 0.000 0.0000 213s Consumption_corpProf 0.000 0.0000 213s Consumption_corpProfLag 0.000 0.0000 213s Consumption_wages 0.000 0.0000 213s Investment_(Intercept) 32.828 -11.4279 213s Investment_corpProf -1.072 0.1744 213s Investment_corpProfLag 1.129 -0.1652 213s Investment_capitalLag -0.165 0.0557 213s PrivateWages_(Intercept) 0.000 0.0000 213s PrivateWages_gnp 0.000 0.0000 213s PrivateWages_gnpLag 0.000 0.0000 213s PrivateWages_trend 0.000 0.0000 213s PrivateWages_(Intercept) PrivateWages_gnp 213s Consumption_(Intercept) 0.000 0.0000 213s Consumption_corpProf 0.000 0.0000 213s Consumption_corpProfLag 0.000 0.0000 213s Consumption_wages 0.000 0.0000 213s Investment_(Intercept) 0.000 0.0000 213s Investment_corpProf 0.000 0.0000 213s Investment_corpProfLag 0.000 0.0000 213s Investment_capitalLag 0.000 0.0000 213s PrivateWages_(Intercept) 167.869 -0.9135 213s PrivateWages_gnp -0.913 0.1554 213s PrivateWages_gnpLag -1.915 -0.1448 213s PrivateWages_trend 2.128 -0.0417 213s PrivateWages_gnpLag PrivateWages_trend 213s Consumption_(Intercept) 0.0000 0.0000 213s Consumption_corpProf 0.0000 0.0000 213s Consumption_corpProfLag 0.0000 0.0000 213s Consumption_wages 0.0000 0.0000 213s Investment_(Intercept) 0.0000 0.0000 213s Investment_corpProf 0.0000 0.0000 213s Investment_corpProfLag 0.0000 0.0000 213s Investment_capitalLag 0.0000 0.0000 213s PrivateWages_(Intercept) -1.9153 2.1280 213s PrivateWages_gnp -0.1448 -0.0417 213s PrivateWages_gnpLag 0.1830 0.0059 213s PrivateWages_trend 0.0059 0.1132 213s > 213s > # SUR 213s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: SUR 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 61 49 45.4 0.151 0.977 0.992 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 20 16 17.6 1.102 1.050 0.981 0.977 213s Investment 21 17 17.5 1.029 1.015 0.931 0.918 213s PrivateWages 20 16 10.3 0.643 0.802 0.987 0.985 213s 213s The covariance matrix of the residuals used for estimation 213s Consumption Investment PrivateWages 213s Consumption 0.8871 0.0268 -0.349 213s Investment 0.0268 0.7328 0.103 213s PrivateWages -0.3492 0.1029 0.444 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 0.8852 0.0508 -0.406 213s Investment 0.0508 0.7313 0.161 213s PrivateWages -0.4063 0.1609 0.467 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.000 0.065 -0.635 213s Investment 0.065 1.000 0.262 213s PrivateWages -0.635 0.262 1.000 213s 213s 213s SUR estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 16.0876 1.2010 13.39 4.1e-10 *** 213s corpProf 0.2173 0.0799 2.72 0.015 * 213s corpProfLag 0.0694 0.0793 0.88 0.394 213s wages 0.7975 0.0360 22.15 2.0e-13 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.05 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 17.63 MSE: 1.102 Root MSE: 1.05 213s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 213s 213s 213s SUR estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 12.3518 4.5615 2.71 0.01493 * 213s corpProf 0.4511 0.0814 5.54 3.6e-05 *** 213s corpProfLag 0.3570 0.0846 4.22 0.00058 *** 213s capitalLag -0.1225 0.0223 -5.49 4.0e-05 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.015 on 17 degrees of freedom 213s Number of observations: 21 Degrees of Freedom: 17 213s SSR: 17.5 MSE: 1.029 Root MSE: 1.015 213s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 213s 213s 213s SUR estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 1.3964 1.0825 1.29 0.22 213s gnp 0.4177 0.0269 15.55 4.4e-11 *** 213s gnpLag 0.1709 0.0306 5.59 4.0e-05 *** 213s trend 0.1467 0.0272 5.40 5.9e-05 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.802 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 10.284 MSE: 0.643 Root MSE: 0.802 213s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 213s 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.2529 -0.2920 -1.15193 213s 3 -1.2998 -0.1392 0.50193 213s 4 -1.5662 1.1106 1.42026 213s 5 -0.4876 -1.4391 -0.09801 213s 6 0.0149 0.3556 -0.35678 213s 7 0.9002 1.4558 NA 213s 8 1.3535 0.8299 -0.74964 213s 9 1.0406 -0.5136 0.29355 213s 10 NA 1.2191 1.18544 213s 11 0.4417 0.2810 -0.36558 213s 12 -0.0892 0.0754 0.33733 213s 13 -0.1541 0.3429 -0.17490 213s 14 0.2984 0.3597 0.39941 213s 15 -0.0260 -0.1602 0.29441 213s 16 -0.0250 0.0130 -0.00177 213s 17 1.5671 1.0231 -0.81891 213s 18 -0.4089 0.0306 0.85516 213s 19 0.2819 -2.6153 -0.77184 213s 20 0.9257 -0.6030 -0.41040 213s 21 0.7415 -0.7118 -1.21679 213s 22 -2.2437 -0.5398 0.57166 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.2 0.092 26.7 213s 3 46.3 2.039 28.8 213s 4 50.8 4.089 32.7 213s 5 51.1 4.439 34.0 213s 6 52.6 4.744 35.8 213s 7 54.2 4.144 NA 213s 8 54.8 3.370 38.6 213s 9 56.3 3.514 38.9 213s 10 NA 3.881 40.1 213s 11 54.6 0.719 38.3 213s 12 51.0 -3.475 34.2 213s 13 45.8 -6.543 29.2 213s 14 46.2 -5.460 28.1 213s 15 48.7 -2.840 30.3 213s 16 51.3 -1.313 33.2 213s 17 56.1 1.077 37.6 213s 18 59.1 1.969 40.1 213s 19 57.2 0.715 39.0 213s 20 60.7 1.903 42.0 213s 21 64.3 4.012 46.2 213s 22 71.9 5.440 52.7 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.2 0.422 41.3 43.0 213s 3 46.3 0.462 45.4 47.2 213s 4 50.8 0.309 50.1 51.4 213s 5 51.1 0.359 50.4 51.8 213s 6 52.6 0.362 51.9 53.3 213s 7 54.2 0.328 53.5 54.9 213s 8 54.8 0.300 54.2 55.4 213s 9 56.3 0.323 55.6 56.9 213s 10 NA NA NA NA 213s 11 54.6 0.531 53.5 55.6 213s 12 51.0 0.427 50.1 51.8 213s 13 45.8 0.564 44.6 46.9 213s 14 46.2 0.543 45.1 47.3 213s 15 48.7 0.341 48.0 49.4 213s 16 51.3 0.302 50.7 51.9 213s 17 56.1 0.328 55.5 56.8 213s 18 59.1 0.294 58.5 59.7 213s 19 57.2 0.332 56.6 57.9 213s 20 60.7 0.392 59.9 61.5 213s 21 64.3 0.394 63.5 65.0 213s 22 71.9 0.615 70.7 73.2 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 0.092 0.508 -0.929 1.113 213s 3 2.039 0.421 1.193 2.885 213s 4 4.089 0.376 3.333 4.846 213s 5 4.439 0.311 3.813 5.065 213s 6 4.744 0.294 4.154 5.335 213s 7 4.144 0.277 3.587 4.701 213s 8 3.370 0.247 2.873 3.867 213s 9 3.514 0.328 2.855 4.172 213s 10 3.881 0.376 3.126 4.636 213s 11 0.719 0.508 -0.301 1.739 213s 12 -3.475 0.428 -4.336 -2.615 213s 13 -6.543 0.521 -7.590 -5.496 213s 14 -5.460 0.583 -6.632 -4.288 213s 15 -2.840 0.316 -3.474 -2.205 213s 16 -1.313 0.271 -1.857 -0.769 213s 17 1.077 0.293 0.488 1.666 213s 18 1.969 0.205 1.557 2.382 213s 19 0.715 0.263 0.187 1.244 213s 20 1.903 0.309 1.283 2.523 213s 21 4.012 0.280 3.449 4.574 213s 22 5.440 0.389 4.659 6.221 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.7 0.306 26.0 27.3 213s 3 28.8 0.305 28.2 29.4 213s 4 32.7 0.302 32.1 33.3 213s 5 34.0 0.231 33.5 34.5 213s 6 35.8 0.230 35.3 36.2 213s 7 NA NA NA NA 213s 8 38.6 0.233 38.2 39.1 213s 9 38.9 0.222 38.5 39.4 213s 10 40.1 0.213 39.7 40.5 213s 11 38.3 0.292 37.7 38.9 213s 12 34.2 0.300 33.6 34.8 213s 13 29.2 0.361 28.4 29.9 213s 14 28.1 0.322 27.5 28.7 213s 15 30.3 0.314 29.7 30.9 213s 16 33.2 0.263 32.7 33.7 213s 17 37.6 0.256 37.1 38.1 213s 18 40.1 0.204 39.7 40.6 213s 19 39.0 0.298 38.4 39.6 213s 20 42.0 0.272 41.5 42.6 213s 21 46.2 0.288 45.6 46.8 213s 22 52.7 0.431 51.9 53.6 213s > model.frame 213s [1] TRUE 213s > model.matrix 213s [1] TRUE 213s > nobs 213s [1] 61 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 50 213s 2 49 1 1.01 0.32 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 50 213s 2 49 1 1.3 0.26 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 50 213s 2 49 1 1.3 0.25 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 51 213s 2 49 2 0.53 0.59 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 51 213s 2 49 2 0.69 0.51 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 51 213s 2 49 2 1.38 0.5 213s > logLik 213s 'log Lik.' -69.6 (df=18) 213s 'log Lik.' -76.9 (df=18) 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -0.42417 -5.2597 213s Consumption_3 -2.17982 -36.8390 213s Consumption_4 -2.62648 -48.3271 213s Consumption_5 -0.81768 -15.8630 213s Consumption_6 0.02500 0.5025 213s Consumption_7 1.50966 29.5894 213s Consumption_8 2.26980 44.9421 213s Consumption_9 1.74517 36.8231 213s Consumption_11 0.74077 11.5559 213s Consumption_12 -0.14959 -1.7053 213s Consumption_13 -0.25842 -1.8090 213s Consumption_14 0.50036 5.6040 213s Consumption_15 -0.04361 -0.5363 213s Consumption_16 -0.04189 -0.5865 213s Consumption_17 2.62802 46.2532 213s Consumption_18 -0.68580 -11.8643 213s Consumption_19 0.47280 7.2339 213s Consumption_20 1.55235 29.4946 213s Consumption_21 1.24350 26.2379 213s Consumption_22 -3.76279 -88.4255 213s Investment_2 0.07441 0.9227 213s Investment_3 0.03547 0.5995 213s Investment_4 -0.28298 -5.2069 213s Investment_5 0.36669 7.1139 213s Investment_6 -0.09061 -1.8212 213s Investment_7 -0.37095 -7.2706 213s Investment_8 -0.21146 -4.1868 213s Investment_9 0.13086 2.7611 213s Investment_10 0.00000 0.0000 213s Investment_11 -0.07161 -1.1172 213s Investment_12 -0.01921 -0.2190 213s Investment_13 -0.08737 -0.6116 213s Investment_14 -0.09166 -1.0266 213s Investment_15 0.04082 0.5021 213s Investment_16 -0.00330 -0.0462 213s Investment_17 -0.26069 -4.5882 213s Investment_18 -0.00779 -0.1348 213s Investment_19 0.66639 10.1958 213s Investment_20 0.15365 2.9194 213s Investment_21 0.18136 3.8268 213s Investment_22 0.13754 3.2323 213s PrivateWages_2 -1.58616 -19.6684 213s PrivateWages_3 0.69114 11.6803 213s PrivateWages_4 1.95564 35.9837 213s PrivateWages_5 -0.13496 -2.6181 213s PrivateWages_6 -0.49127 -9.8746 213s PrivateWages_8 -1.03222 -20.4380 213s PrivateWages_9 0.40421 8.5288 213s PrivateWages_10 0.00000 0.0000 213s PrivateWages_11 -0.50339 -7.8529 213s PrivateWages_12 0.46449 5.2952 213s PrivateWages_13 -0.24083 -1.6858 213s PrivateWages_14 0.54997 6.1596 213s PrivateWages_15 0.40539 4.9863 213s PrivateWages_16 -0.00244 -0.0342 213s PrivateWages_17 -1.12761 -19.8459 213s PrivateWages_18 1.17751 20.3710 213s PrivateWages_19 -1.06279 -16.2607 213s PrivateWages_20 -0.56511 -10.7371 213s PrivateWages_21 -1.67547 -35.3524 213s PrivateWages_22 0.78715 18.4981 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -5.3870 -11.962 213s Consumption_3 -27.0298 -70.190 213s Consumption_4 -44.3874 -97.180 213s Consumption_5 -15.0453 -30.254 213s Consumption_6 0.4850 0.965 213s Consumption_7 30.3442 61.443 213s Consumption_8 44.4881 94.197 213s Consumption_9 34.5544 74.868 213s Consumption_11 16.0746 31.186 213s Consumption_12 -2.3336 -5.879 213s Consumption_13 -2.9460 -8.864 213s Consumption_14 3.5025 17.062 213s Consumption_15 -0.4884 -1.596 213s Consumption_16 -0.5153 -1.646 213s Consumption_17 36.7923 116.159 213s Consumption_18 -12.0701 -32.713 213s Consumption_19 8.1795 21.702 213s Consumption_20 23.7509 76.686 213s Consumption_21 23.6265 65.906 213s Consumption_22 -79.3948 -232.540 213s Investment_2 0.9450 2.098 213s Investment_3 0.4399 1.142 213s Investment_4 -4.7824 -10.470 213s Investment_5 6.7472 13.568 213s Investment_6 -1.7577 -3.497 213s Investment_7 -7.4561 -15.098 213s Investment_8 -4.1445 -8.775 213s Investment_9 2.5910 5.614 213s Investment_10 0.0000 0.000 213s Investment_11 -1.5540 -3.015 213s Investment_12 -0.2997 -0.755 213s Investment_13 -0.9961 -2.997 213s Investment_14 -0.6416 -3.126 213s Investment_15 0.4572 1.494 213s Investment_16 -0.0406 -0.130 213s Investment_17 -3.6497 -11.523 213s Investment_18 -0.1371 -0.372 213s Investment_19 11.5286 30.587 213s Investment_20 2.3509 7.590 213s Investment_21 3.4459 9.612 213s Investment_22 2.9022 8.500 213s PrivateWages_2 -20.1442 -44.730 213s PrivateWages_3 8.5702 22.255 213s PrivateWages_4 33.0503 72.359 213s PrivateWages_5 -2.4832 -4.993 213s PrivateWages_6 -9.5307 -18.963 213s PrivateWages_8 -20.2315 -42.837 213s PrivateWages_9 8.0034 17.341 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 -10.9235 -21.193 213s PrivateWages_12 7.2461 18.254 213s PrivateWages_13 -2.7454 -8.260 213s PrivateWages_14 3.8498 18.754 213s PrivateWages_15 4.5404 14.837 213s PrivateWages_16 -0.0300 -0.096 213s PrivateWages_17 -15.7865 -49.840 213s PrivateWages_18 20.7242 56.167 213s PrivateWages_19 -18.3863 -48.782 213s PrivateWages_20 -8.6462 -27.916 213s PrivateWages_21 -31.8339 -88.800 213s PrivateWages_22 16.6089 48.646 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0.064449 0.7992 213s Consumption_3 0.331201 5.5973 213s Consumption_4 0.399066 7.3428 213s Consumption_5 0.124238 2.4102 213s Consumption_6 -0.003798 -0.0763 213s Consumption_7 -0.229378 -4.4958 213s Consumption_8 -0.344873 -6.8285 213s Consumption_9 -0.265161 -5.5949 213s Consumption_11 -0.112552 -1.7558 213s Consumption_12 0.022729 0.2591 213s Consumption_13 0.039265 0.2749 213s Consumption_14 -0.076024 -0.8515 213s Consumption_15 0.006625 0.0815 213s Consumption_16 0.006365 0.0891 213s Consumption_17 -0.399301 -7.0277 213s Consumption_18 0.104200 1.8027 213s Consumption_19 -0.071838 -1.0991 213s Consumption_20 -0.235863 -4.4814 213s Consumption_21 -0.188937 -3.9866 213s Consumption_22 0.571717 13.4353 213s Investment_2 -0.423201 -5.2477 213s Investment_3 -0.201766 -3.4098 213s Investment_4 1.609495 29.6147 213s Investment_5 -2.085613 -40.4609 213s Investment_6 0.515327 10.3581 213s Investment_7 2.109824 41.3526 213s Investment_8 1.202679 23.8131 213s Investment_9 -0.744277 -15.7042 213s Investment_10 1.766841 38.3405 213s Investment_11 0.407303 6.3539 213s Investment_12 0.109258 1.2455 213s Investment_13 0.496948 3.4786 213s Investment_14 0.521347 5.8391 213s Investment_15 -0.232156 -2.8555 213s Investment_16 0.018782 0.2630 213s Investment_17 1.482721 26.0959 213s Investment_18 0.044303 0.7664 213s Investment_19 -3.790179 -57.9897 213s Investment_20 -0.873905 -16.6042 213s Investment_21 -1.031520 -21.7651 213s Investment_22 -0.782292 -18.3839 213s PrivateWages_2 0.617327 7.6549 213s PrivateWages_3 -0.268990 -4.5459 213s PrivateWages_4 -0.761128 -14.0048 213s PrivateWages_5 0.052525 1.0190 213s PrivateWages_6 0.191202 3.8432 213s PrivateWages_8 0.401737 7.9544 213s PrivateWages_9 -0.157317 -3.3194 213s PrivateWages_10 -0.635285 -13.7857 213s PrivateWages_11 0.195917 3.0563 213s PrivateWages_12 -0.180778 -2.0609 213s PrivateWages_13 0.093729 0.6561 213s PrivateWages_14 -0.214045 -2.3973 213s PrivateWages_15 -0.157776 -1.9406 213s PrivateWages_16 0.000951 0.0133 213s PrivateWages_17 0.438862 7.7240 213s PrivateWages_18 -0.458284 -7.9283 213s PrivateWages_19 0.413636 6.3286 213s PrivateWages_20 0.219939 4.1788 213s PrivateWages_21 0.652086 13.7590 213s PrivateWages_22 -0.306358 -7.1994 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.8185 11.781 213s Consumption_3 4.1069 60.477 213s Consumption_4 6.7442 73.628 213s Consumption_5 2.2860 23.568 213s Consumption_6 -0.0737 -0.732 213s Consumption_7 -4.6105 -45.371 213s Consumption_8 -6.7595 -70.147 213s Consumption_9 -5.2502 -55.047 213s Consumption_11 -2.4424 -24.277 213s Consumption_12 0.3546 4.925 213s Consumption_13 0.4476 8.375 213s Consumption_14 -0.5322 -15.745 213s Consumption_15 0.0742 1.338 213s Consumption_16 0.0783 1.267 213s Consumption_17 -5.5902 -78.942 213s Consumption_18 1.8339 20.819 213s Consumption_19 -1.2428 -14.497 213s Consumption_20 -3.6087 -47.149 213s Consumption_21 -3.5898 -38.014 213s Consumption_22 12.0632 116.916 213s Investment_2 -5.3746 -77.361 213s Investment_3 -2.5019 -36.842 213s Investment_4 27.2005 296.952 213s Investment_5 -38.3753 -395.641 213s Investment_6 9.9974 99.304 213s Investment_7 42.4075 417.323 213s Investment_8 23.5725 244.625 213s Investment_9 -14.7367 -154.512 213s Investment_10 37.2803 372.097 213s Investment_11 8.8385 87.855 213s Investment_12 1.7044 23.676 213s Investment_13 5.6652 105.999 213s Investment_14 3.6494 107.971 213s Investment_15 -2.6002 -46.896 213s Investment_16 0.2310 3.738 213s Investment_17 20.7581 293.134 213s Investment_18 0.7797 8.852 213s Investment_19 -65.5701 -764.858 213s Investment_20 -13.3707 -174.694 213s Investment_21 -19.5989 -207.542 213s Investment_22 -16.5064 -159.979 213s PrivateWages_2 7.8401 112.847 213s PrivateWages_3 -3.3355 -49.118 213s PrivateWages_4 -12.8631 -140.428 213s PrivateWages_5 0.9665 9.964 213s PrivateWages_6 3.7093 36.845 213s PrivateWages_8 7.8740 81.713 213s PrivateWages_9 -3.1149 -32.659 213s PrivateWages_10 -13.4045 -133.791 213s PrivateWages_11 4.2514 42.259 213s PrivateWages_12 -2.8201 -39.175 213s PrivateWages_13 1.0685 19.992 213s PrivateWages_14 -1.4983 -44.329 213s PrivateWages_15 -1.7671 -31.871 213s PrivateWages_16 0.0117 0.189 213s PrivateWages_17 6.1441 86.763 213s PrivateWages_18 -8.0658 -91.565 213s PrivateWages_19 7.1559 83.472 213s PrivateWages_20 3.3651 43.966 213s PrivateWages_21 12.3896 131.200 213s PrivateWages_22 -6.4641 -62.650 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 -0.34828 -15.881 -15.638 213s Consumption_3 -1.78978 -89.668 -81.614 213s Consumption_4 -2.15652 -123.353 -108.042 213s Consumption_5 -0.67137 -38.335 -38.402 213s Consumption_6 0.02052 1.252 1.172 213s Consumption_7 0.00000 0.000 0.000 213s Consumption_8 1.86367 120.020 119.275 213s Consumption_9 1.43291 92.422 92.279 213s Consumption_11 0.60822 37.223 40.751 213s Consumption_12 -0.12282 -6.559 -7.517 213s Consumption_13 -0.21218 -9.400 -11.331 213s Consumption_14 0.41083 18.528 18.200 213s Consumption_15 -0.03580 -1.779 -1.615 213s Consumption_16 -0.03440 -1.871 -1.710 213s Consumption_17 2.15779 135.293 117.384 213s Consumption_18 -0.56309 -36.601 -35.306 213s Consumption_19 0.38821 23.642 25.233 213s Consumption_20 1.27458 88.584 77.622 213s Consumption_21 1.02100 77.290 70.960 213s Consumption_22 -3.08951 -273.113 -233.876 213s Investment_2 0.15649 7.136 7.027 213s Investment_3 0.07461 3.738 3.402 213s Investment_4 -0.59517 -34.043 -29.818 213s Investment_5 0.77123 44.037 44.114 213s Investment_6 -0.19056 -11.624 -10.881 213s Investment_7 0.00000 0.000 0.000 213s Investment_8 -0.44473 -28.641 -28.463 213s Investment_9 0.27522 17.752 17.724 213s Investment_10 -0.65335 -43.774 -42.141 213s Investment_11 -0.15061 -9.218 -10.091 213s Investment_12 -0.04040 -2.157 -2.473 213s Investment_13 -0.18376 -8.141 -9.813 213s Investment_14 -0.19279 -8.695 -8.540 213s Investment_15 0.08585 4.267 3.872 213s Investment_16 -0.00695 -0.378 -0.345 213s Investment_17 -0.54829 -34.378 -29.827 213s Investment_18 -0.01638 -1.065 -1.027 213s Investment_19 1.40155 85.354 91.101 213s Investment_20 0.32316 22.459 19.680 213s Investment_21 0.38144 28.875 26.510 213s Investment_22 0.28928 25.572 21.898 213s PrivateWages_2 -3.98191 -181.575 -178.788 213s PrivateWages_3 1.73505 86.926 79.118 213s PrivateWages_4 4.90946 280.821 245.964 213s PrivateWages_5 -0.33880 -19.345 -19.379 213s PrivateWages_6 -1.23330 -75.231 -70.421 213s PrivateWages_8 -2.59130 -166.880 -165.843 213s PrivateWages_9 1.01473 65.450 65.349 213s PrivateWages_10 4.09774 274.549 264.304 213s PrivateWages_11 -1.26371 -77.339 -84.669 213s PrivateWages_12 1.16606 62.268 71.363 213s PrivateWages_13 -0.60457 -26.783 -32.284 213s PrivateWages_14 1.38064 62.267 61.163 213s PrivateWages_15 1.01769 50.579 45.898 213s PrivateWages_16 -0.00613 -0.334 -0.305 213s PrivateWages_17 -2.83076 -177.489 -153.993 213s PrivateWages_18 2.95604 192.143 185.344 213s PrivateWages_19 -2.66805 -162.484 -173.423 213s PrivateWages_20 -1.41866 -98.597 -86.396 213s PrivateWages_21 -4.20611 -318.403 -292.325 213s PrivateWages_22 1.97608 174.686 149.589 213s PrivateWages_trend 213s Consumption_2 3.4828 213s Consumption_3 16.1081 213s Consumption_4 17.2522 213s Consumption_5 4.6996 213s Consumption_6 -0.1231 213s Consumption_7 0.0000 213s Consumption_8 -7.4547 213s Consumption_9 -4.2987 213s Consumption_11 -0.6082 213s Consumption_12 0.0000 213s Consumption_13 -0.2122 213s Consumption_14 0.8217 213s Consumption_15 -0.1074 213s Consumption_16 -0.1376 213s Consumption_17 10.7889 213s Consumption_18 -3.3785 213s Consumption_19 2.7174 213s Consumption_20 10.1967 213s Consumption_21 9.1890 213s Consumption_22 -30.8951 213s Investment_2 -1.5649 213s Investment_3 -0.6715 213s Investment_4 4.7613 213s Investment_5 -5.3986 213s Investment_6 1.1434 213s Investment_7 0.0000 213s Investment_8 1.7789 213s Investment_9 -0.8257 213s Investment_10 1.3067 213s Investment_11 0.1506 213s Investment_12 0.0000 213s Investment_13 -0.1838 213s Investment_14 -0.3856 213s Investment_15 0.2575 213s Investment_16 -0.0278 213s Investment_17 -2.7414 213s Investment_18 -0.0983 213s Investment_19 9.8108 213s Investment_20 2.5853 213s Investment_21 3.4330 213s Investment_22 2.8928 213s PrivateWages_2 39.8191 213s PrivateWages_3 -15.6154 213s PrivateWages_4 -39.2757 213s PrivateWages_5 2.3716 213s PrivateWages_6 7.3998 213s PrivateWages_8 10.3652 213s PrivateWages_9 -3.0442 213s PrivateWages_10 -8.1955 213s PrivateWages_11 1.2637 213s PrivateWages_12 0.0000 213s PrivateWages_13 -0.6046 213s PrivateWages_14 2.7613 213s PrivateWages_15 3.0531 213s PrivateWages_16 -0.0245 213s PrivateWages_17 -14.1538 213s PrivateWages_18 17.7363 213s PrivateWages_19 -18.6764 213s PrivateWages_20 -11.3493 213s PrivateWages_21 -37.8550 213s PrivateWages_22 19.7608 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 213s [1,] 87.9904 -0.088084 -0.91416 213s [2,] -0.0881 0.389639 -0.23612 213s [3,] -0.9142 -0.236125 0.38341 213s [4,] -1.6692 -0.062952 -0.03326 213s [5,] 2.6851 -0.188961 0.72342 213s [6,] -0.0355 0.023370 -0.02643 213s [7,] -0.0563 -0.020038 0.03196 213s [8,] -0.0054 0.000618 -0.00397 213s [9,] -33.1687 0.063156 1.54217 213s [10,] 0.3665 -0.059172 0.03813 213s [11,] 0.1741 0.060188 -0.06574 213s [12,] 0.1831 0.029476 0.02425 213s Consumption_wages Investment_(Intercept) Investment_corpProf 213s [1,] -1.669236 2.685 -0.03549 213s [2,] -0.062952 -0.189 0.02337 213s [3,] -0.033257 0.723 -0.02643 213s [4,] 0.079061 -0.248 0.00151 213s [5,] -0.248317 1269.247 -12.23080 213s [6,] 0.001506 -12.231 0.40462 213s [7,] -0.002778 9.884 -0.34614 213s [8,] 0.001327 -6.097 0.05519 213s [9,] 0.134743 17.903 -0.13872 213s [10,] 0.000196 0.262 0.01397 213s [11,] -0.002616 -0.581 -0.01197 213s [12,] -0.026193 -0.551 0.00355 213s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 213s [1,] -0.05628 -0.005396 -33.1687 213s [2,] -0.02004 0.000618 0.0632 213s [3,] 0.03196 -0.003967 1.5422 213s [4,] -0.00278 0.001327 0.1347 213s [5,] 9.88435 -6.096982 17.9032 213s [6,] -0.34614 0.055190 -0.1387 213s [7,] 0.43632 -0.055785 -0.4000 213s [8,] -0.05578 0.030317 -0.0433 213s [9,] -0.40000 -0.043343 71.4840 213s [10,] -0.00786 -0.001844 -0.3085 213s [11,] 0.01493 0.002686 -0.8909 213s [12,] -0.01033 0.003295 0.8146 213s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 213s [1,] 0.366465 0.17405 0.18311 213s [2,] -0.059172 0.06019 0.02948 213s [3,] 0.038129 -0.06574 0.02425 213s [4,] 0.000196 -0.00262 -0.02619 213s [5,] 0.262390 -0.58123 -0.55064 213s [6,] 0.013966 -0.01197 0.00355 213s [7,] -0.007857 0.01493 -0.01033 213s [8,] -0.001844 0.00269 0.00330 213s [9,] -0.308484 -0.89087 0.81461 213s [10,] 0.044017 -0.04022 -0.01158 213s [11,] -0.040216 0.05696 -0.00212 213s [12,] -0.011575 -0.00212 0.04506 213s > 213s > # 3SLS 213s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: 3SLS 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 59 47 59.5 0.241 0.97 0.994 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 19 15 18.1 1.203 1.097 0.980 0.977 213s Investment 20 16 31.1 1.945 1.395 0.866 0.841 213s PrivateWages 20 16 10.3 0.645 0.803 0.987 0.985 213s 213s The covariance matrix of the residuals used for estimation 213s Consumption Investment PrivateWages 213s Consumption 1.079 0.354 -0.383 213s Investment 0.354 1.047 0.107 213s PrivateWages -0.383 0.107 0.445 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 0.950 0.324 -0.395 213s Investment 0.324 1.385 0.242 213s PrivateWages -0.395 0.242 0.475 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.000 0.293 -0.582 213s Investment 0.293 1.000 0.292 213s PrivateWages -0.582 0.292 1.000 213s 213s 213s 3SLS estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 16.5606 1.3295 12.46 2.6e-09 *** 213s corpProf 0.1100 0.1098 1.00 0.33 213s corpProfLag 0.1155 0.1007 1.15 0.27 213s wages 0.8086 0.0401 20.18 2.8e-12 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.097 on 15 degrees of freedom 213s Number of observations: 19 Degrees of Freedom: 15 213s SSR: 18.051 MSE: 1.203 Root MSE: 1.097 213s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 213s 213s 213s 3SLS estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 23.6871 6.1159 3.87 0.00135 ** 213s corpProf 0.1072 0.1414 0.76 0.45918 213s corpProfLag 0.6278 0.1361 4.61 0.00029 *** 213s capitalLag -0.1726 0.0295 -5.85 2.5e-05 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.395 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 31.126 MSE: 1.945 Root MSE: 1.395 213s Multiple R-Squared: 0.866 Adjusted R-Squared: 0.841 213s 213s 213s 3SLS estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 1.3603 1.0927 1.24 0.23109 213s gnp 0.4117 0.0315 13.06 6.0e-10 *** 213s gnpLag 0.1782 0.0336 5.31 7.1e-05 *** 213s trend 0.1370 0.0280 4.89 0.00016 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.803 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 10.318 MSE: 0.645 Root MSE: 0.803 213s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 213s 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.29542 -1.636 -1.2658 213s 3 -0.89033 0.135 0.4198 213s 4 -1.25669 0.777 1.3578 213s 5 -0.14000 -1.574 -0.2036 213s 6 0.37365 0.341 -0.4283 213s 7 NA NA NA 213s 8 1.63850 1.194 -0.8319 213s 9 1.44030 0.454 0.2186 213s 10 NA 2.192 1.1346 213s 11 0.17274 -0.750 -0.4603 213s 12 -0.49629 -0.698 0.2476 213s 13 -0.78384 -0.976 -0.2528 213s 14 0.32420 1.365 0.4028 213s 15 -0.10364 -0.170 0.3295 213s 16 -0.00105 0.140 0.0377 213s 17 1.84421 1.862 -0.7540 213s 18 -0.36893 -0.103 0.8827 213s 19 0.14129 -3.255 -0.7764 213s 20 1.23511 0.475 -0.3230 213s 21 1.06553 0.152 -1.1453 213s 22 -1.85709 0.746 0.6843 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.2 1.436 26.8 213s 3 45.9 1.765 28.9 213s 4 50.5 4.423 32.7 213s 5 50.7 4.574 34.1 213s 6 52.2 4.759 35.8 213s 7 NA NA NA 213s 8 54.6 3.006 38.7 213s 9 55.9 2.546 39.0 213s 10 NA 2.908 40.2 213s 11 54.8 1.750 38.4 213s 12 51.4 -2.702 34.3 213s 13 46.4 -5.224 29.3 213s 14 46.2 -6.465 28.1 213s 15 48.8 -2.830 30.3 213s 16 51.3 -1.440 33.2 213s 17 55.9 0.238 37.6 213s 18 59.1 2.103 40.1 213s 19 57.4 1.355 39.0 213s 20 60.4 0.825 41.9 213s 21 63.9 3.148 46.1 213s 22 71.6 4.154 52.6 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.2 0.475 39.6 44.7 213s 3 45.9 0.557 43.3 48.5 213s 4 50.5 0.372 48.0 52.9 213s 5 50.7 0.433 48.2 53.3 213s 6 52.2 0.438 49.7 54.7 213s 7 NA NA NA NA 213s 8 54.6 0.362 52.1 57.0 213s 9 55.9 0.401 53.4 58.3 213s 10 NA NA NA NA 213s 11 54.8 0.684 52.1 57.6 213s 12 51.4 0.563 48.8 54.0 213s 13 46.4 0.733 43.6 49.2 213s 14 46.2 0.612 43.5 48.9 213s 15 48.8 0.379 46.3 51.3 213s 16 51.3 0.334 48.9 53.7 213s 17 55.9 0.394 53.4 58.3 213s 18 59.1 0.322 56.6 61.5 213s 19 57.4 0.392 54.9 59.8 213s 20 60.4 0.462 57.8 62.9 213s 21 63.9 0.448 61.4 66.5 213s 22 71.6 0.686 68.8 74.3 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 1.436 0.709 -1.8811 4.754 213s 3 1.765 0.512 -1.3848 4.915 213s 4 4.423 0.470 1.3027 7.543 213s 5 4.574 0.392 1.5029 7.645 213s 6 4.759 0.370 1.7000 7.818 213s 7 NA NA NA NA 213s 8 3.006 0.306 -0.0214 6.033 213s 9 2.546 0.444 -0.5575 5.649 213s 10 2.908 0.488 -0.2245 6.041 213s 11 1.750 0.738 -1.5953 5.096 213s 12 -2.702 0.583 -5.9068 0.503 213s 13 -5.224 0.743 -8.5738 -1.874 213s 14 -6.465 0.780 -9.8530 -3.077 213s 15 -2.830 0.378 -5.8936 0.233 213s 16 -1.440 0.326 -4.4762 1.597 213s 17 0.238 0.426 -2.8533 3.329 213s 18 2.103 0.268 -0.9077 5.114 213s 19 1.355 0.399 -1.7201 4.431 213s 20 0.825 0.474 -2.2981 3.947 213s 21 3.148 0.393 0.0761 6.220 213s 22 4.154 0.555 0.9719 7.336 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.8 0.309 24.9 28.6 213s 3 28.9 0.315 27.1 30.7 213s 4 32.7 0.326 30.9 34.6 213s 5 34.1 0.236 32.3 35.9 213s 6 35.8 0.244 34.0 37.6 213s 7 NA NA NA NA 213s 8 38.7 0.237 37.0 40.5 213s 9 39.0 0.225 37.2 40.7 213s 10 40.2 0.219 38.4 41.9 213s 11 38.4 0.309 36.5 40.2 213s 12 34.3 0.336 32.4 36.1 213s 13 29.3 0.411 27.3 31.2 213s 14 28.1 0.326 26.3 29.9 213s 15 30.3 0.313 28.4 32.1 213s 16 33.2 0.262 31.4 35.0 213s 17 37.6 0.265 35.8 39.3 213s 18 40.1 0.205 38.4 41.9 213s 19 39.0 0.323 37.1 40.8 213s 20 41.9 0.282 40.1 43.7 213s 21 46.1 0.293 44.3 48.0 213s 22 52.6 0.463 50.7 54.6 213s > model.frame 213s [1] TRUE 213s > model.matrix 213s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 213s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 213s [3] "Numeric: lengths (732, 708) differ" 213s > nobs 213s [1] 59 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.23 0.64 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.31 0.58 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 48 213s 2 47 1 0.31 0.58 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.5 0.61 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.68 0.51 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 49 213s 2 47 2 1.37 0.5 213s > logLik 213s 'log Lik.' -71 (df=18) 213s 'log Lik.' -81.1 (df=18) 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -2.7455 -36.891 213s Consumption_3 -1.0626 -17.729 213s Consumption_4 -0.0885 -1.678 213s Consumption_5 -3.0649 -63.238 213s Consumption_6 0.7553 14.561 213s Consumption_8 5.9278 102.010 213s Consumption_9 4.6365 88.027 213s Consumption_11 -1.1219 -18.435 213s Consumption_12 -1.0756 -13.439 213s Consumption_13 -3.1243 -28.309 213s Consumption_14 2.5683 23.826 213s Consumption_15 -1.2839 -16.033 213s Consumption_16 -1.2479 -17.951 213s Consumption_17 7.5868 111.454 213s Consumption_18 -1.1010 -21.581 213s Consumption_19 -5.4018 -103.426 213s Consumption_20 3.8300 67.171 213s Consumption_21 1.5068 30.633 213s Consumption_22 -1.8041 -41.092 213s Investment_2 1.3384 17.984 213s Investment_3 -0.1231 -2.053 213s Investment_4 -0.5511 -10.444 213s Investment_5 1.3722 28.313 213s Investment_6 -0.3224 -6.215 213s Investment_8 -1.1676 -20.092 213s Investment_9 -0.4950 -9.397 213s Investment_10 0.0000 0.000 213s Investment_11 0.6975 11.462 213s Investment_12 0.6591 8.235 213s Investment_13 0.9331 8.455 213s Investment_14 -1.2380 -11.485 213s Investment_15 0.1758 2.195 213s Investment_16 -0.0882 -1.269 213s Investment_17 -1.7103 -25.126 213s Investment_18 0.2715 5.322 213s Investment_19 2.9123 55.761 213s Investment_20 -0.5118 -8.975 213s Investment_21 -0.2046 -4.160 213s Investment_22 -0.6426 -14.637 213s PrivateWages_2 -3.2663 -43.888 213s PrivateWages_3 1.1062 18.456 213s PrivateWages_4 2.8429 53.880 213s PrivateWages_5 -2.9330 -60.515 213s PrivateWages_6 -0.4678 -9.018 213s PrivateWages_8 1.7117 29.456 213s PrivateWages_9 1.9856 37.698 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 -2.6089 -42.870 213s PrivateWages_12 -0.5972 -7.462 213s PrivateWages_13 -2.3655 -21.434 213s PrivateWages_14 2.8394 26.341 213s PrivateWages_15 -0.5146 -6.427 213s PrivateWages_16 -0.6088 -8.757 213s PrivateWages_17 2.4972 36.686 213s PrivateWages_18 -0.0214 -0.419 213s PrivateWages_19 -6.8265 -130.705 213s PrivateWages_20 1.3447 23.584 213s PrivateWages_21 -1.4002 -28.468 213s PrivateWages_22 2.2878 52.110 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -34.868 -81.19 213s Consumption_3 -13.177 -33.85 213s Consumption_4 -1.496 -3.14 213s Consumption_5 -56.394 -118.79 213s Consumption_6 14.654 29.20 213s Consumption_8 116.186 236.05 213s Consumption_9 91.802 193.78 213s Consumption_11 -24.345 -48.21 213s Consumption_12 -16.779 -42.24 213s Consumption_13 -35.617 -109.94 213s Consumption_14 17.978 84.77 213s Consumption_15 -14.380 -47.92 213s Consumption_16 -15.349 -50.04 213s Consumption_17 106.215 316.24 213s Consumption_18 -19.377 -52.50 213s Consumption_19 -93.451 -266.03 213s Consumption_20 58.598 185.77 213s Consumption_21 28.629 80.45 213s Consumption_22 -38.066 -109.75 213s Investment_2 16.998 39.58 213s Investment_3 -1.526 -3.92 213s Investment_4 -9.313 -19.52 213s Investment_5 25.249 53.18 213s Investment_6 -6.254 -12.46 213s Investment_8 -22.884 -46.49 213s Investment_9 -9.800 -20.69 213s Investment_10 0.000 0.00 213s Investment_11 15.136 29.97 213s Investment_12 10.282 25.88 213s Investment_13 10.638 32.84 213s Investment_14 -8.666 -40.86 213s Investment_15 1.969 6.56 213s Investment_16 -1.085 -3.54 213s Investment_17 -23.945 -71.29 213s Investment_18 4.779 12.95 213s Investment_19 50.383 143.43 213s Investment_20 -7.830 -24.82 213s Investment_21 -3.888 -10.92 213s Investment_22 -13.559 -39.09 213s PrivateWages_2 -41.482 -96.59 213s PrivateWages_3 13.717 35.24 213s PrivateWages_4 48.044 100.73 213s PrivateWages_5 -53.966 -113.67 213s PrivateWages_6 -9.075 -18.08 213s PrivateWages_8 33.550 68.16 213s PrivateWages_9 39.314 82.99 213s PrivateWages_10 0.000 0.00 213s PrivateWages_11 -56.613 -112.10 213s PrivateWages_12 -9.317 -23.46 213s PrivateWages_13 -26.967 -83.24 213s PrivateWages_14 19.876 93.71 213s PrivateWages_15 -5.764 -19.21 213s PrivateWages_16 -7.488 -24.41 213s PrivateWages_17 34.961 104.09 213s PrivateWages_18 -0.376 -1.02 213s PrivateWages_19 -118.099 -336.20 213s PrivateWages_20 20.574 65.22 213s PrivateWages_21 -26.605 -74.76 213s PrivateWages_22 48.272 139.18 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 1.1993 15.540 213s Consumption_3 0.4642 7.754 213s Consumption_4 0.0387 0.740 213s Consumption_5 1.3388 28.029 213s Consumption_6 -0.3299 -6.424 213s Consumption_8 -2.5893 -44.384 213s Consumption_9 -2.0252 -39.469 213s Consumption_11 0.4900 8.255 213s Consumption_12 0.4698 5.957 213s Consumption_13 1.3647 12.176 213s Consumption_14 -1.1219 -10.434 213s Consumption_15 0.5608 7.176 213s Consumption_16 0.5451 7.773 213s Consumption_17 -3.3140 -48.887 213s Consumption_18 0.4809 9.399 213s Consumption_19 2.3595 45.678 213s Consumption_20 -1.6729 -29.086 213s Consumption_21 -0.6582 -13.228 213s Consumption_22 0.7880 18.015 213s Investment_2 -2.2459 -29.102 213s Investment_3 0.2065 3.450 213s Investment_4 0.9247 17.694 213s Investment_5 -2.3026 -48.209 213s Investment_6 0.5410 10.532 213s Investment_8 1.9592 33.583 213s Investment_9 0.8306 16.187 213s Investment_10 3.0781 62.986 213s Investment_11 -1.1704 -19.716 213s Investment_12 -1.1059 -14.023 213s Investment_13 -1.5658 -13.970 213s Investment_14 2.0775 19.321 213s Investment_15 -0.2950 -3.775 213s Investment_16 0.1480 2.111 213s Investment_17 2.8700 42.338 213s Investment_18 -0.4556 -8.905 213s Investment_19 -4.8870 -94.607 213s Investment_20 0.8587 14.930 213s Investment_21 0.3434 6.901 213s Investment_22 1.0783 24.652 213s PrivateWages_2 1.8660 24.179 213s PrivateWages_3 -0.6320 -10.557 213s PrivateWages_4 -1.6241 -31.077 213s PrivateWages_5 1.6755 35.080 213s PrivateWages_6 0.2672 5.203 213s PrivateWages_8 -0.9779 -16.762 213s PrivateWages_9 -1.1343 -22.106 213s PrivateWages_10 -2.1296 -43.576 213s PrivateWages_11 1.4904 25.106 213s PrivateWages_12 0.3412 4.326 213s PrivateWages_13 1.3514 12.057 213s PrivateWages_14 -1.6221 -15.086 213s PrivateWages_15 0.2940 3.762 213s PrivateWages_16 0.3478 4.959 213s PrivateWages_17 -1.4266 -21.045 213s PrivateWages_18 0.0122 0.239 213s PrivateWages_19 3.8998 75.496 213s PrivateWages_20 -0.7682 -13.356 213s PrivateWages_21 0.7999 16.078 213s PrivateWages_22 -1.3070 -29.879 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 15.231 219.22 213s Consumption_3 5.756 84.76 213s Consumption_4 0.654 7.13 213s Consumption_5 24.633 253.96 213s Consumption_6 -6.401 -63.58 213s Consumption_8 -50.751 -526.67 213s Consumption_9 -40.100 -420.44 213s Consumption_11 10.634 105.70 213s Consumption_12 7.329 101.81 213s Consumption_13 15.558 291.09 213s Consumption_14 -7.853 -232.34 213s Consumption_15 6.281 113.29 213s Consumption_16 6.705 108.47 213s Consumption_17 -46.395 -655.17 213s Consumption_18 8.464 96.09 213s Consumption_19 40.820 476.15 213s Consumption_20 -25.596 -334.42 213s Consumption_21 -12.505 -132.42 213s Consumption_22 16.627 161.15 213s Investment_2 -28.522 -410.54 213s Investment_3 2.561 37.71 213s Investment_4 15.627 170.61 213s Investment_5 -42.368 -436.81 213s Investment_6 10.495 104.25 213s Investment_8 38.400 398.50 213s Investment_9 16.445 172.43 213s Investment_10 64.949 648.26 213s Investment_11 -25.398 -252.46 213s Investment_12 -17.253 -239.66 213s Investment_13 -17.850 -333.99 213s Investment_14 14.542 430.24 213s Investment_15 -3.304 -59.59 213s Investment_16 1.821 29.46 213s Investment_17 40.180 567.40 213s Investment_18 -8.019 -91.03 213s Investment_19 -84.545 -986.19 213s Investment_20 13.139 171.66 213s Investment_21 6.524 69.08 213s Investment_22 22.753 220.52 213s PrivateWages_2 23.698 341.10 213s PrivateWages_3 -7.836 -115.39 213s PrivateWages_4 -27.446 -299.64 213s PrivateWages_5 30.830 317.85 213s PrivateWages_6 5.185 51.50 213s PrivateWages_8 -19.166 -198.90 213s PrivateWages_9 -22.459 -235.48 213s PrivateWages_10 -44.934 -448.49 213s PrivateWages_11 32.341 321.48 213s PrivateWages_12 5.323 73.94 213s PrivateWages_13 15.406 288.25 213s PrivateWages_14 -11.355 -335.93 213s PrivateWages_15 3.293 59.39 213s PrivateWages_16 4.278 69.21 213s PrivateWages_17 -19.973 -282.04 213s PrivateWages_18 0.215 2.44 213s PrivateWages_19 67.467 786.98 213s PrivateWages_20 -11.753 -153.56 213s PrivateWages_21 15.199 160.94 213s PrivateWages_22 -27.577 -267.27 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 -2.6531 -124.88 -119.13 213s Consumption_3 -1.0269 -50.91 -46.83 213s Consumption_4 -0.0856 -4.84 -4.29 213s Consumption_5 -2.9618 -179.74 -169.41 213s Consumption_6 0.7299 44.24 41.68 213s Consumption_8 5.7284 343.69 366.62 213s Consumption_9 4.4804 278.99 288.54 213s Consumption_11 -1.0841 -69.07 -72.64 213s Consumption_12 -1.0394 -56.99 -63.61 213s Consumption_13 -3.0192 -141.83 -161.22 213s Consumption_14 2.4819 104.56 109.95 213s Consumption_15 -1.2407 -63.55 -55.96 213s Consumption_16 -1.2059 -66.73 -59.93 213s Consumption_17 7.3315 420.78 398.83 213s Consumption_18 -1.0639 -71.47 -66.71 213s Consumption_19 -5.2200 -357.64 -339.30 213s Consumption_20 3.7011 247.40 225.40 213s Consumption_21 1.4561 109.01 101.20 213s Consumption_22 -1.7434 -151.46 -131.97 213s Investment_2 1.6915 79.62 75.95 213s Investment_3 -0.1555 -7.71 -7.09 213s Investment_4 -0.6965 -39.38 -34.89 213s Investment_5 1.7343 105.25 99.20 213s Investment_6 -0.4074 -24.70 -23.26 213s Investment_8 -1.4756 -88.53 -94.44 213s Investment_9 -0.6256 -38.95 -40.29 213s Investment_10 -2.3184 -149.69 -149.53 213s Investment_11 0.8815 56.16 59.06 213s Investment_12 0.8330 45.67 50.98 213s Investment_13 1.1793 55.40 62.98 213s Investment_14 -1.5647 -65.92 -69.32 213s Investment_15 0.2222 11.38 10.02 213s Investment_16 -0.1115 -6.17 -5.54 213s Investment_17 -2.1616 -124.06 -117.59 213s Investment_18 0.3432 23.05 21.52 213s Investment_19 3.6807 252.18 239.25 213s Investment_20 -0.6468 -43.23 -39.39 213s Investment_21 -0.2586 -19.36 -17.97 213s Investment_22 -0.8122 -70.56 -61.48 213s PrivateWages_2 -7.4676 -351.50 -335.29 213s PrivateWages_3 2.5291 125.39 115.33 213s PrivateWages_4 6.4995 367.50 325.62 213s PrivateWages_5 -6.7054 -406.93 -383.55 213s PrivateWages_6 -1.0695 -64.82 -61.07 213s PrivateWages_8 3.9134 234.79 250.46 213s PrivateWages_9 4.5395 282.67 292.34 213s PrivateWages_10 8.5226 550.30 549.71 213s PrivateWages_11 -5.9646 -380.01 -399.63 213s PrivateWages_12 -1.3654 -74.87 -83.57 213s PrivateWages_13 -5.4082 -254.06 -288.80 213s PrivateWages_14 6.4916 273.48 287.58 213s PrivateWages_15 -1.1766 -60.26 -53.06 213s PrivateWages_16 -1.3918 -77.02 -69.17 213s PrivateWages_17 5.7093 327.68 310.59 213s PrivateWages_18 -0.0489 -3.28 -3.07 213s PrivateWages_19 -15.6071 -1069.28 -1014.46 213s PrivateWages_20 3.0743 205.50 187.22 213s PrivateWages_21 -3.2013 -239.67 -222.49 213s PrivateWages_22 5.2304 454.42 395.94 213s PrivateWages_trend 213s Consumption_2 26.531 213s Consumption_3 9.242 213s Consumption_4 0.684 213s Consumption_5 20.732 213s Consumption_6 -4.380 213s Consumption_8 -22.913 213s Consumption_9 -13.441 213s Consumption_11 1.084 213s Consumption_12 0.000 213s Consumption_13 -3.019 213s Consumption_14 4.964 213s Consumption_15 -3.722 213s Consumption_16 -4.824 213s Consumption_17 36.658 213s Consumption_18 -6.384 213s Consumption_19 -36.540 213s Consumption_20 29.609 213s Consumption_21 13.105 213s Consumption_22 -17.434 213s Investment_2 -16.915 213s Investment_3 1.400 213s Investment_4 5.572 213s Investment_5 -12.140 213s Investment_6 2.445 213s Investment_8 5.902 213s Investment_9 1.877 213s Investment_10 4.637 213s Investment_11 -0.882 213s Investment_12 0.000 213s Investment_13 1.179 213s Investment_14 -3.129 213s Investment_15 0.667 213s Investment_16 -0.446 213s Investment_17 -10.808 213s Investment_18 2.059 213s Investment_19 25.765 213s Investment_20 -5.174 213s Investment_21 -2.327 213s Investment_22 -8.122 213s PrivateWages_2 74.676 213s PrivateWages_3 -22.762 213s PrivateWages_4 -51.996 213s PrivateWages_5 46.938 213s PrivateWages_6 6.417 213s PrivateWages_8 -15.654 213s PrivateWages_9 -13.618 213s PrivateWages_10 -17.045 213s PrivateWages_11 5.965 213s PrivateWages_12 0.000 213s PrivateWages_13 -5.408 213s PrivateWages_14 12.983 213s PrivateWages_15 -3.530 213s PrivateWages_16 -5.567 213s PrivateWages_17 28.547 213s PrivateWages_18 -0.293 213s PrivateWages_19 -109.250 213s PrivateWages_20 24.594 213s PrivateWages_21 -28.812 213s PrivateWages_22 52.304 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 213s [1,] 104.28657 -1.0082 -0.4696 213s [2,] -1.00824 0.7107 -0.4494 213s [3,] -0.46959 -0.4494 0.5979 213s [4,] -1.85053 -0.0857 -0.0409 213s [5,] 80.53000 1.3241 3.0428 213s [6,] -1.81359 0.2334 -0.2583 213s [7,] 0.54047 -0.1847 0.2826 213s [8,] -0.28778 -0.0112 -0.0165 213s [9,] -35.77159 0.2050 1.7044 213s [10,] 0.58031 -0.0870 0.0510 213s [11,] -0.00461 0.0862 -0.0821 213s [12,] 0.19369 0.0416 0.0268 213s Consumption_wages Investment_(Intercept) Investment_corpProf 213s [1,] -1.850529 80.530 -1.81359 213s [2,] -0.085701 1.324 0.23344 213s [3,] -0.040883 3.043 -0.25828 213s [4,] 0.094773 -3.542 0.04931 213s [5,] -3.542001 2206.842 -34.41529 213s [6,] 0.049311 -34.415 1.17951 213s [7,] -0.048133 29.517 -1.02562 213s [8,] 0.017421 -10.487 0.15573 213s [9,] 0.083728 18.025 -0.14810 213s [10,] 0.000958 1.156 0.00386 213s [11,] -0.002304 -1.519 -0.00126 213s [12,] -0.031989 -0.955 0.01443 213s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 213s [1,] 0.54047 -0.28778 -35.7716 213s [2,] -0.18475 -0.01117 0.2050 213s [3,] 0.28258 -0.01647 1.7044 213s [4,] -0.04813 0.01742 0.0837 213s [5,] 29.51706 -10.48672 18.0248 213s [6,] -1.02562 0.15573 -0.1481 213s [7,] 1.09362 -0.14971 -0.4803 213s [8,] -0.14971 0.05132 -0.0381 213s [9,] -0.48030 -0.03806 70.4425 213s [10,] 0.00353 -0.00637 -0.4681 213s [11,] 0.00471 0.00732 -0.7110 213s [12,] -0.02247 0.00534 0.8424 213s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 213s [1,] 0.580315 -0.00461 0.19369 213s [2,] -0.086985 0.08623 0.04160 213s [3,] 0.051027 -0.08213 0.02678 213s [4,] 0.000958 -0.00230 -0.03199 213s [5,] 1.156385 -1.51874 -0.95497 213s [6,] 0.003856 -0.00126 0.01443 213s [7,] 0.003528 0.00471 -0.02247 213s [8,] -0.006374 0.00732 0.00534 213s [9,] -0.468096 -0.71104 0.84245 213s [10,] 0.058634 -0.05251 -0.01709 213s [11,] -0.052508 0.06655 0.00301 213s [12,] -0.017087 0.00301 0.04635 213s > 213s > # I3SLS 213s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: iterated 3SLS 213s 213s convergence achieved after 15 iterations 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 59 47 81.3 0.349 0.958 0.995 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 19 15 18.1 1.209 1.100 0.980 0.976 213s Investment 20 16 52.0 3.250 1.803 0.776 0.735 213s PrivateWages 20 16 11.2 0.699 0.836 0.986 0.983 213s 213s The covariance matrix of the residuals used for estimation 213s Consumption Investment PrivateWages 213s Consumption 0.955 0.456 -0.421 213s Investment 0.456 2.294 0.375 213s PrivateWages -0.421 0.375 0.522 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 0.955 0.456 -0.421 213s Investment 0.456 2.294 0.375 213s PrivateWages -0.421 0.375 0.522 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.000 0.322 -0.582 213s Investment 0.322 1.000 0.341 213s PrivateWages -0.582 0.341 1.000 213s 213s 213s 3SLS estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 16.8311 1.2489 13.48 8.7e-10 *** 213s corpProf 0.1468 0.0991 1.48 0.16 213s corpProfLag 0.0924 0.0906 1.02 0.32 213s wages 0.7945 0.0371 21.43 1.2e-12 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.1 on 15 degrees of freedom 213s Number of observations: 19 Degrees of Freedom: 15 213s SSR: 18.14 MSE: 1.209 Root MSE: 1.1 213s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 213s 213s 213s 3SLS estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 32.4128 8.2695 3.92 0.00122 ** 213s corpProf -0.0799 0.1934 -0.41 0.68498 213s corpProfLag 0.7607 0.1878 4.05 0.00093 *** 213s capitalLag -0.2114 0.0400 -5.29 7.4e-05 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.803 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 51.999 MSE: 3.25 Root MSE: 1.803 213s Multiple R-Squared: 0.776 Adjusted R-Squared: 0.735 213s 213s 213s 3SLS estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 1.5421 1.1496 1.34 0.19852 213s gnp 0.3936 0.0313 12.57 1.0e-09 *** 213s gnpLag 0.1945 0.0328 5.93 2.1e-05 *** 213s trend 0.1416 0.0286 4.95 0.00014 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.836 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 11.181 MSE: 0.699 Root MSE: 0.836 213s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.983 213s 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.3309 -2.6308 -1.3061 213s 3 -1.0419 0.0146 0.4450 213s 4 -1.2918 0.4128 1.4338 213s 5 -0.1772 -1.7488 -0.2494 213s 6 0.3563 0.2807 -0.4066 213s 7 NA NA NA 213s 8 1.6778 1.4671 -0.8700 213s 9 1.4561 1.1068 0.1712 213s 10 NA 2.9002 1.1262 213s 11 0.4237 -1.0652 -0.6189 213s 12 -0.2711 -0.9488 0.0375 213s 13 -0.5643 -1.6241 -0.5055 213s 14 0.2845 1.8477 0.3080 213s 15 -0.0514 -0.2379 0.3003 213s 16 0.0521 0.1268 0.0141 213s 17 1.8733 2.2462 -0.7083 213s 18 -0.1962 -0.1724 0.8305 213s 19 0.3553 -3.5810 -0.9448 213s 20 1.3161 1.0343 -0.2738 213s 21 1.2055 0.6622 -1.1283 213s 22 -1.6327 1.5541 0.8257 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.2 2.431 26.8 213s 3 46.0 1.885 28.9 213s 4 50.5 4.787 32.7 213s 5 50.8 4.749 34.1 213s 6 52.2 4.819 35.8 213s 7 NA NA NA 213s 8 54.5 2.733 38.8 213s 9 55.8 1.893 39.0 213s 10 NA 2.200 40.2 213s 11 54.6 2.065 38.5 213s 12 51.2 -2.451 34.5 213s 13 46.2 -4.576 29.5 213s 14 46.2 -6.948 28.2 213s 15 48.8 -2.762 30.3 213s 16 51.2 -1.427 33.2 213s 17 55.8 -0.146 37.5 213s 18 58.9 2.172 40.2 213s 19 57.1 1.681 39.1 213s 20 60.3 0.266 41.9 213s 21 63.8 2.638 46.1 213s 22 71.3 3.346 52.5 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.2 0.446 41.3 43.1 213s 3 46.0 0.511 45.0 47.1 213s 4 50.5 0.340 49.8 51.2 213s 5 50.8 0.393 50.0 51.6 213s 6 52.2 0.396 51.4 53.0 213s 7 NA NA NA NA 213s 8 54.5 0.326 53.9 55.2 213s 9 55.8 0.362 55.1 56.6 213s 10 NA NA NA NA 213s 11 54.6 0.612 53.3 55.8 213s 12 51.2 0.511 50.1 52.2 213s 13 46.2 0.671 44.8 47.5 213s 14 46.2 0.563 45.1 47.3 213s 15 48.8 0.354 48.0 49.5 213s 16 51.2 0.311 50.6 51.9 213s 17 55.8 0.362 55.1 56.6 213s 18 58.9 0.297 58.3 59.5 213s 19 57.1 0.357 56.4 57.9 213s 20 60.3 0.427 59.4 61.1 213s 21 63.8 0.416 63.0 64.6 213s 22 71.3 0.640 70.0 72.6 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 2.431 0.970 0.4798 4.382 213s 3 1.885 0.745 0.3859 3.385 213s 4 4.787 0.664 3.4506 6.124 213s 5 4.749 0.562 3.6174 5.880 213s 6 4.819 0.537 3.7391 5.900 213s 7 NA NA NA NA 213s 8 2.733 0.446 1.8351 3.631 213s 9 1.893 0.620 0.6455 3.141 213s 10 2.200 0.684 0.8232 3.576 213s 11 2.065 1.055 -0.0569 4.187 213s 12 -2.451 0.845 -4.1517 -0.751 213s 13 -4.576 1.070 -6.7293 -2.423 213s 14 -6.948 1.103 -9.1676 -4.728 213s 15 -2.762 0.556 -3.8806 -1.644 213s 16 -1.427 0.480 -2.3919 -0.462 213s 17 -0.146 0.603 -1.3588 1.066 213s 18 2.172 0.390 1.3869 2.958 213s 19 1.681 0.563 0.5476 2.815 213s 20 0.266 0.661 -1.0634 1.595 213s 21 2.638 0.558 1.5144 3.761 213s 22 3.346 0.778 1.7808 4.911 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.8 0.326 26.2 27.5 213s 3 28.9 0.328 28.2 29.5 213s 4 32.7 0.334 32.0 33.3 213s 5 34.1 0.242 33.7 34.6 213s 6 35.8 0.252 35.3 36.3 213s 7 NA NA NA NA 213s 8 38.8 0.244 38.3 39.3 213s 9 39.0 0.232 38.6 39.5 213s 10 40.2 0.230 39.7 40.6 213s 11 38.5 0.308 37.9 39.1 213s 12 34.5 0.336 33.8 35.1 213s 13 29.5 0.420 28.7 30.4 213s 14 28.2 0.345 27.5 28.9 213s 15 30.3 0.325 29.6 31.0 213s 16 33.2 0.271 32.6 33.7 213s 17 37.5 0.267 37.0 38.0 213s 18 40.2 0.218 39.7 40.6 213s 19 39.1 0.331 38.5 39.8 213s 20 41.9 0.289 41.3 42.5 213s 21 46.1 0.311 45.5 46.8 213s 22 52.5 0.485 51.5 53.5 213s > model.frame 213s [1] TRUE 213s > model.matrix 213s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 213s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 213s [3] "Numeric: lengths (732, 708) differ" 213s > nobs 213s [1] 59 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.28 0.6 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.37 0.55 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 48 213s 2 47 1 0.37 0.54 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 1.25 0.3 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 1.64 0.21 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 49 213s 2 47 2 3.28 0.19 213s > logLik 213s 'log Lik.' -74.5 (df=18) 213s 'log Lik.' -87.1 (df=18) 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -4.75944 -63.951 213s Consumption_3 -2.22772 -37.167 213s Consumption_4 -0.38275 -7.254 213s Consumption_5 -5.30482 -109.454 213s Consumption_6 1.30597 25.176 213s Consumption_8 10.25777 176.523 213s Consumption_9 7.99665 151.823 213s Consumption_11 -1.17443 -19.299 213s Consumption_12 -1.24242 -15.523 213s Consumption_13 -4.75716 -43.103 213s Consumption_14 4.34635 40.320 213s Consumption_15 -1.98107 -24.739 213s Consumption_16 -1.93670 -27.859 213s Consumption_17 13.00314 191.023 213s Consumption_18 -1.57749 -30.922 213s Consumption_19 -8.67959 -166.185 213s Consumption_20 6.77999 118.909 213s Consumption_21 3.04771 61.962 213s Consumption_22 -2.30170 -52.427 213s Investment_2 2.92832 39.347 213s Investment_3 0.00114 0.019 213s Investment_4 -0.53396 -10.120 213s Investment_5 1.84118 37.989 213s Investment_6 -0.26074 -5.026 213s Investment_8 -1.42063 -24.447 213s Investment_9 -1.10750 -21.027 213s Investment_10 0.00000 0.000 213s Investment_11 1.09344 17.968 213s Investment_12 0.95848 11.975 213s Investment_13 1.66503 15.086 213s Investment_14 -1.92032 -17.814 213s Investment_15 0.22458 2.804 213s Investment_16 -0.16698 -2.402 213s Investment_17 -2.28568 -33.578 213s Investment_18 -0.00785 -0.154 213s Investment_19 3.68757 70.604 213s Investment_20 -1.02511 -17.979 213s Investment_21 -0.65919 -13.402 213s Investment_22 -1.70192 -38.765 213s PrivateWages_2 -6.13297 -82.407 213s PrivateWages_3 2.11354 35.262 213s PrivateWages_4 5.50774 104.386 213s PrivateWages_5 -5.40526 -111.526 213s PrivateWages_6 -0.82424 -15.889 213s PrivateWages_8 2.80754 48.314 213s PrivateWages_9 3.41557 64.847 213s PrivateWages_10 0.00000 0.000 213s PrivateWages_11 -5.23135 -85.964 213s PrivateWages_12 -1.71264 -21.398 213s PrivateWages_13 -5.07393 -45.974 213s PrivateWages_14 4.80915 44.613 213s PrivateWages_15 -0.96519 -12.053 213s PrivateWages_16 -1.15621 -16.632 213s PrivateWages_17 4.49108 65.976 213s PrivateWages_18 -0.08188 -1.605 213s PrivateWages_19 -12.82495 -245.555 213s PrivateWages_20 2.51036 44.027 213s PrivateWages_21 -2.60385 -52.938 213s PrivateWages_22 4.63537 105.582 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -60.4449 -140.7509 213s Consumption_3 -27.6237 -70.9657 213s Consumption_4 -6.4685 -13.5614 213s Consumption_5 -97.6087 -205.5997 213s Consumption_6 25.3358 50.4846 213s Consumption_8 201.0522 408.4748 213s Consumption_9 158.3336 334.2197 213s Consumption_11 -25.4852 -50.4634 213s Consumption_12 -19.3817 -48.7944 213s Consumption_13 -54.2317 -167.3998 213s Consumption_14 30.4244 143.4489 213s Consumption_15 -22.1880 -73.9440 213s Consumption_16 -23.8214 -77.6627 213s Consumption_17 182.0440 542.0110 213s Consumption_18 -27.7639 -75.2217 213s Consumption_19 -150.1568 -427.4616 213s Consumption_20 103.7339 328.8605 213s Consumption_21 57.9064 162.7199 213s Consumption_22 -48.5659 -140.0278 213s Investment_2 37.1896 86.5991 213s Investment_3 0.0141 0.0362 213s Investment_4 -9.0240 -18.9190 213s Investment_5 33.8777 71.3589 213s Investment_6 -5.0583 -10.0793 213s Investment_8 -27.8443 -56.5709 213s Investment_9 -21.9285 -46.2880 213s Investment_10 0.0000 0.0000 213s Investment_11 23.7276 46.9832 213s Investment_12 14.9524 37.6432 213s Investment_13 18.9813 58.5907 213s Investment_14 -13.4423 -63.3793 213s Investment_15 2.5153 8.3824 213s Investment_16 -2.0538 -6.6959 213s Investment_17 -31.9996 -95.2743 213s Investment_18 -0.1382 -0.3745 213s Investment_19 63.7949 181.6093 213s Investment_20 -15.6841 -49.7224 213s Investment_21 -12.5246 -35.1949 213s Investment_22 -35.9105 -103.5390 213s PrivateWages_2 -77.8887 -181.3703 213s PrivateWages_3 26.2079 67.3285 213s PrivateWages_4 93.0807 195.1464 213s PrivateWages_5 -99.4568 -209.4924 213s PrivateWages_6 -15.9902 -31.8624 213s PrivateWages_8 55.0278 111.7991 213s PrivateWages_9 67.6282 142.7536 213s PrivateWages_10 0.0000 0.0000 213s PrivateWages_11 -113.5202 -224.7822 213s PrivateWages_12 -26.7172 -67.2617 213s PrivateWages_13 -57.8428 -178.5466 213s PrivateWages_14 33.6641 158.7235 213s PrivateWages_15 -10.8101 -36.0260 213s PrivateWages_16 -14.2214 -46.3646 213s PrivateWages_17 62.8751 187.2021 213s PrivateWages_18 -1.4410 -3.9043 213s PrivateWages_19 -221.8716 -631.6170 213s PrivateWages_20 38.4085 121.7638 213s PrivateWages_21 -49.4732 -139.0222 213s PrivateWages_22 97.8064 282.0006 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 1.782157 23.0934 213s Consumption_3 0.834162 13.9344 213s Consumption_4 0.143320 2.7425 213s Consumption_5 1.986375 41.5880 213s Consumption_6 -0.489016 -9.5207 213s Consumption_8 -3.840991 -65.8399 213s Consumption_9 -2.994321 -58.3554 213s Consumption_11 0.439763 7.4080 213s Consumption_12 0.465220 5.8989 213s Consumption_13 1.781306 15.8927 213s Consumption_14 -1.627477 -15.1363 213s Consumption_15 0.741807 9.4914 213s Consumption_16 0.725191 10.3407 213s Consumption_17 -4.868989 -71.8262 213s Consumption_18 0.590688 11.5449 213s Consumption_19 3.250046 62.9174 213s Consumption_20 -2.538748 -44.1394 213s Consumption_21 -1.141204 -22.9368 213s Consumption_22 0.861865 19.7035 213s Investment_2 -2.373514 -30.7562 213s Investment_3 -0.000921 -0.0154 213s Investment_4 0.432798 8.2817 213s Investment_5 -1.492349 -31.2447 213s Investment_6 0.211337 4.1146 213s Investment_8 1.151475 19.7379 213s Investment_9 0.897673 17.4945 213s Investment_10 2.570865 52.6054 213s Investment_11 -0.886274 -14.9297 213s Investment_12 -0.776889 -9.8508 213s Investment_13 -1.349570 -12.0408 213s Investment_14 1.556498 14.4761 213s Investment_15 -0.182029 -2.3291 213s Investment_16 0.135342 1.9299 213s Investment_17 1.852635 27.3297 213s Investment_18 0.006366 0.1244 213s Investment_19 -2.988917 -57.8622 213s Investment_20 0.830890 14.4461 213s Investment_21 0.534301 10.7388 213s Investment_22 1.379471 31.5367 213s PrivateWages_2 2.964495 38.4142 213s PrivateWages_3 -1.021623 -17.0659 213s PrivateWages_4 -2.662277 -50.9436 213s PrivateWages_5 2.612743 54.7020 213s PrivateWages_6 0.398411 7.7567 213s PrivateWages_8 -1.357082 -23.2623 213s PrivateWages_9 -1.650985 -32.1755 213s PrivateWages_10 -3.276467 -67.0436 213s PrivateWages_11 2.528678 42.5968 213s PrivateWages_12 0.827840 10.4968 213s PrivateWages_13 2.452590 21.8819 213s PrivateWages_14 -2.324602 -21.6199 213s PrivateWages_15 0.466545 5.9694 213s PrivateWages_16 0.558877 7.9692 213s PrivateWages_17 -2.170857 -32.0240 213s PrivateWages_18 0.039577 0.7735 213s PrivateWages_19 6.199203 120.0098 213s PrivateWages_20 -1.213433 -21.0971 213s PrivateWages_21 1.258626 25.2969 213s PrivateWages_22 -2.240603 -51.2233 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 22.6334 325.778 213s Consumption_3 10.3436 152.318 213s Consumption_4 2.4221 26.443 213s Consumption_5 36.5493 376.815 213s Consumption_6 -9.4869 -94.233 213s Consumption_8 -75.2834 -781.258 213s Consumption_9 -59.2876 -621.621 213s Consumption_11 9.5429 94.857 213s Consumption_12 7.2574 100.813 213s Consumption_13 20.3069 379.952 213s Consumption_14 -11.3923 -337.050 213s Consumption_15 8.3082 149.845 213s Consumption_16 8.9199 144.313 213s Consumption_17 -68.1658 -962.599 213s Consumption_18 10.3961 118.019 213s Consumption_19 56.2258 655.859 213s Consumption_20 -38.8428 -507.496 213s Consumption_21 -21.6829 -229.610 213s Consumption_22 18.1854 176.251 213s Investment_2 -30.1436 -433.878 213s Investment_3 -0.0114 -0.168 213s Investment_4 7.3143 79.851 213s Investment_5 -27.4592 -283.099 213s Investment_6 4.0999 40.725 213s Investment_8 22.5689 234.210 213s Investment_9 17.7739 186.357 213s Investment_10 54.2453 541.424 213s Investment_11 -19.2321 -191.169 213s Investment_12 -12.1195 -168.352 213s Investment_13 -15.3851 -287.863 213s Investment_14 10.8955 322.351 213s Investment_15 -2.0387 -36.770 213s Investment_16 1.6647 26.933 213s Investment_17 25.9369 366.266 213s Investment_18 0.1120 1.272 213s Investment_19 -51.7083 -603.163 213s Investment_20 12.7126 166.095 213s Investment_21 10.1517 107.501 213s Investment_22 29.1068 282.102 213s PrivateWages_2 37.6491 541.910 213s PrivateWages_3 -12.6681 -186.548 213s PrivateWages_4 -44.9925 -491.190 213s PrivateWages_5 48.0745 495.637 213s PrivateWages_6 7.7292 76.774 213s PrivateWages_8 -26.5988 -276.031 213s PrivateWages_9 -32.6895 -342.744 213s PrivateWages_10 -69.1335 -690.024 213s PrivateWages_11 54.8723 545.436 213s PrivateWages_12 12.9143 179.393 213s PrivateWages_13 27.9595 523.137 213s PrivateWages_14 -16.2722 -481.425 213s PrivateWages_15 5.2253 94.242 213s PrivateWages_16 6.8742 111.217 213s PrivateWages_17 -30.3920 -429.178 213s PrivateWages_18 0.6966 7.908 213s PrivateWages_19 107.2462 1250.999 213s PrivateWages_20 -18.5655 -242.565 213s PrivateWages_21 23.9139 253.236 213s PrivateWages_22 -47.2767 -458.203 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 -5.12212 -2.41e+02 -229.983 213s Consumption_3 -2.39748 -1.19e+02 -109.325 213s Consumption_4 -0.41192 -2.33e+01 -20.637 213s Consumption_5 -5.70906 -3.46e+02 -326.558 213s Consumption_6 1.40549 8.52e+01 80.253 213s Consumption_8 11.03944 6.62e+02 706.524 213s Consumption_9 8.60601 5.36e+02 554.227 213s Consumption_11 -1.26393 -8.05e+01 -84.683 213s Consumption_12 -1.33709 -7.33e+01 -81.830 213s Consumption_13 -5.11967 -2.41e+02 -273.390 213s Consumption_14 4.67755 1.97e+02 207.216 213s Consumption_15 -2.13204 -1.09e+02 -96.155 213s Consumption_16 -2.08428 -1.15e+02 -103.589 213s Consumption_17 13.99402 8.03e+02 761.275 213s Consumption_18 -1.69770 -1.14e+02 -106.446 213s Consumption_19 -9.34099 -6.40e+02 -607.165 213s Consumption_20 7.29665 4.88e+02 444.366 213s Consumption_21 3.27995 2.46e+02 227.957 213s Consumption_22 -2.47710 -2.15e+02 -187.516 213s Investment_2 4.06820 1.91e+02 182.662 213s Investment_3 0.00158 7.83e-02 0.072 213s Investment_4 -0.74181 -4.19e+01 -37.165 213s Investment_5 2.55788 1.55e+02 146.311 213s Investment_6 -0.36223 -2.20e+01 -20.683 213s Investment_8 -1.97362 -1.18e+02 -126.312 213s Investment_9 -1.53861 -9.58e+01 -99.086 213s Investment_10 -4.40645 -2.85e+02 -284.216 213s Investment_11 1.51907 9.68e+01 101.778 213s Investment_12 1.33159 7.30e+01 81.493 213s Investment_13 2.31316 1.09e+02 123.523 213s Investment_14 -2.66783 -1.12e+02 -118.185 213s Investment_15 0.31200 1.60e+01 14.071 213s Investment_16 -0.23198 -1.28e+01 -11.529 213s Investment_17 -3.17541 -1.82e+02 -172.742 213s Investment_18 -0.01091 -7.33e-01 -0.684 213s Investment_19 5.12299 3.51e+02 332.995 213s Investment_20 -1.42414 -9.52e+01 -86.730 213s Investment_21 -0.91579 -6.86e+01 -63.647 213s Investment_22 -2.36441 -2.05e+02 -178.986 213s PrivateWages_2 -10.69229 -5.03e+02 -480.084 213s PrivateWages_3 3.68477 1.83e+02 168.026 213s PrivateWages_4 9.60226 5.43e+02 481.073 213s PrivateWages_5 -9.42360 -5.72e+02 -539.030 213s PrivateWages_6 -1.43698 -8.71e+01 -82.052 213s PrivateWages_8 4.89470 2.94e+02 313.261 213s PrivateWages_9 5.95474 3.71e+02 383.486 213s PrivateWages_10 11.81751 7.63e+02 762.229 213s PrivateWages_11 -9.12040 -5.81e+02 -611.067 213s PrivateWages_12 -2.98584 -1.64e+02 -182.733 213s PrivateWages_13 -8.84596 -4.16e+02 -472.374 213s PrivateWages_14 8.38434 3.53e+02 371.426 213s PrivateWages_15 -1.68273 -8.62e+01 -75.891 213s PrivateWages_16 -2.01575 -1.12e+02 -100.183 213s PrivateWages_17 7.82981 4.49e+02 425.942 213s PrivateWages_18 -0.14275 -9.59e+00 -8.950 213s PrivateWages_19 -22.35918 -1.53e+03 -1453.347 213s PrivateWages_20 4.37659 2.93e+02 266.534 213s PrivateWages_21 -4.53959 -3.40e+02 -315.502 213s PrivateWages_22 8.08137 7.02e+02 611.760 213s PrivateWages_trend 213s Consumption_2 51.2212 213s Consumption_3 21.5773 213s Consumption_4 3.2953 213s Consumption_5 39.9635 213s Consumption_6 -8.4329 213s Consumption_8 -44.1578 213s Consumption_9 -25.8180 213s Consumption_11 1.2639 213s Consumption_12 0.0000 213s Consumption_13 -5.1197 213s Consumption_14 9.3551 213s Consumption_15 -6.3961 213s Consumption_16 -8.3371 213s Consumption_17 69.9701 213s Consumption_18 -10.1862 213s Consumption_19 -65.3870 213s Consumption_20 58.3732 213s Consumption_21 29.5195 213s Consumption_22 -24.7710 213s Investment_2 -40.6819 213s Investment_3 -0.0142 213s Investment_4 5.9345 213s Investment_5 -17.9052 213s Investment_6 2.1734 213s Investment_8 7.8945 213s Investment_9 4.6158 213s Investment_10 8.8129 213s Investment_11 -1.5191 213s Investment_12 0.0000 213s Investment_13 2.3132 213s Investment_14 -5.3357 213s Investment_15 0.9360 213s Investment_16 -0.9279 213s Investment_17 -15.8771 213s Investment_18 -0.0655 213s Investment_19 35.8610 213s Investment_20 -11.3931 213s Investment_21 -8.2421 213s Investment_22 -23.6441 213s PrivateWages_2 106.9229 213s PrivateWages_3 -33.1629 213s PrivateWages_4 -76.8181 213s PrivateWages_5 65.9652 213s PrivateWages_6 8.6219 213s PrivateWages_8 -19.5788 213s PrivateWages_9 -17.8642 213s PrivateWages_10 -23.6350 213s PrivateWages_11 9.1204 213s PrivateWages_12 0.0000 213s PrivateWages_13 -8.8460 213s PrivateWages_14 16.7687 213s PrivateWages_15 -5.0482 213s PrivateWages_16 -8.0630 213s PrivateWages_17 39.1491 213s PrivateWages_18 -0.8565 213s PrivateWages_19 -156.5143 213s PrivateWages_20 35.0127 213s PrivateWages_21 -40.8563 213s PrivateWages_22 80.8137 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 213s [1,] 92.02523 -0.8883 -0.3567 213s [2,] -0.88834 0.5799 -0.3635 213s [3,] -0.35667 -0.3635 0.4840 213s [4,] -1.65059 -0.0695 -0.0345 213s [5,] 87.30345 -0.4940 5.6093 213s [6,] -2.09669 0.4100 -0.4129 213s [7,] 0.52353 -0.3352 0.4397 213s [8,] -0.29441 -0.0047 -0.0291 213s [9,] -39.25694 0.2930 1.5879 213s [10,] 0.63395 -0.0766 0.0444 213s [11,] -0.00377 0.0739 -0.0730 213s [12,] 0.26412 0.0450 0.0239 213s Consumption_wages Investment_(Intercept) Investment_corpProf 213s [1,] -1.650593 87.303 -2.09669 213s [2,] -0.069509 -0.494 0.41001 213s [3,] -0.034488 5.609 -0.41285 213s [4,] 0.081060 -3.868 0.04419 213s [5,] -3.867758 4034.682 -59.45928 213s [6,] 0.044186 -59.459 2.20583 213s [7,] -0.048017 50.679 -1.90719 213s [8,] 0.019469 -19.184 0.26586 213s [9,] 0.172081 52.203 -0.49762 213s [10,] -0.001839 2.943 0.01728 213s [11,] -0.000946 -3.971 -0.00883 213s [12,] -0.034168 -2.641 0.03741 213s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 213s [1,] 0.52353 -0.2944 -39.2569 213s [2,] -0.33517 -0.0047 0.2930 213s [3,] 0.43972 -0.0291 1.5879 213s [4,] -0.04802 0.0195 0.1721 213s [5,] 50.67914 -19.1839 52.2027 213s [6,] -1.90719 0.2659 -0.4976 213s [7,] 2.08136 -0.2612 -1.5286 213s [8,] -0.26125 0.0944 -0.0914 213s [9,] -1.52864 -0.0914 77.9751 213s [10,] 0.00872 -0.0168 -0.5909 213s [11,] 0.01756 0.0191 -0.7086 213s [12,] -0.06267 0.0150 0.8675 213s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 213s [1,] 0.63395 -0.003771 0.26412 213s [2,] -0.07661 0.073937 0.04500 213s [3,] 0.04435 -0.072979 0.02395 213s [4,] -0.00184 -0.000946 -0.03417 213s [5,] 2.94321 -3.971150 -2.64074 213s [6,] 0.01728 -0.008829 0.03741 213s [7,] 0.00872 0.017559 -0.06267 213s [8,] -0.01682 0.019146 0.01504 213s [9,] -0.59094 -0.708614 0.86750 213s [10,] 0.05781 -0.049542 -0.01891 213s [11,] -0.04954 0.063408 0.00453 213s [12,] -0.01891 0.004534 0.04825 213s > 213s > # OLS 213s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: OLS 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 59 47 44.2 0.453 0.976 0.99 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 213s Investment 20 16 17.11 1.069 1.03 0.912 0.895 213s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.1939 0.0559 -0.474 213s Investment 0.0559 0.9839 0.140 213s PrivateWages -0.4745 0.1403 0.602 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.0000 0.0447 -0.568 213s Investment 0.0447 1.0000 0.169 213s PrivateWages -0.5680 0.1689 1.000 213s 213s 213s OLS estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 16.2957 1.4879 10.95 1.5e-08 *** 213s corpProf 0.1796 0.1162 1.55 0.14 213s corpProfLag 0.1032 0.0994 1.04 0.32 213s wages 0.7962 0.0433 18.39 1.1e-11 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.076 on 15 degrees of freedom 213s Number of observations: 19 Degrees of Freedom: 15 213s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 213s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 213s 213s 213s OLS estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 10.1813 5.3720 1.90 0.07627 . 213s corpProf 0.5003 0.1052 4.75 0.00022 *** 213s corpProfLag 0.3259 0.1003 3.25 0.00502 ** 213s capitalLag -0.1134 0.0265 -4.28 0.00057 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.034 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 17.109 MSE: 1.069 Root MSE: 1.034 213s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.895 213s 213s 213s OLS estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 1.3550 1.3021 1.04 0.3135 213s gnp 0.4417 0.0330 13.40 4.1e-10 *** 213s gnpLag 0.1466 0.0379 3.87 0.0013 ** 213s trend 0.1244 0.0335 3.72 0.0019 ** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.78 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 213s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 213s 213s compare coef with single-equation OLS 213s [1] TRUE 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.3863 -0.000301 -1.3389 213s 3 -1.2484 -0.076489 0.2462 213s 4 -1.6040 1.221792 1.1255 213s 5 -0.5384 -1.377872 -0.1959 213s 6 -0.0413 0.386104 -0.5284 213s 7 0.8043 1.486279 NA 213s 8 1.2830 0.784055 -0.7909 213s 9 1.0142 -0.655354 0.2819 213s 10 NA 1.060871 1.1384 213s 11 0.1429 0.395249 -0.1904 213s 12 -0.3439 0.198005 0.5813 213s 13 NA NA 0.1206 213s 14 0.3199 0.312725 0.4773 213s 15 -0.1016 -0.084685 0.3035 213s 16 -0.0702 0.066194 0.0284 213s 17 1.6064 0.963697 -0.8517 213s 18 -0.4980 0.078506 0.9908 213s 19 0.1253 -2.496401 -0.4597 213s 20 0.9805 -0.711004 -0.3819 213s 21 0.7551 -0.820172 -1.1062 213s 22 -2.1992 -0.731199 0.5501 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.3 -0.200 26.8 213s 3 46.2 1.976 29.1 213s 4 50.8 3.978 33.0 213s 5 51.1 4.378 34.1 213s 6 52.6 4.714 35.9 213s 7 54.3 4.114 NA 213s 8 54.9 3.416 38.7 213s 9 56.3 3.655 38.9 213s 10 NA 4.039 40.2 213s 11 54.9 0.605 38.1 213s 12 51.2 -3.598 33.9 213s 13 NA NA 28.9 213s 14 46.2 -5.413 28.0 213s 15 48.8 -2.915 30.3 213s 16 51.4 -1.366 33.2 213s 17 56.1 1.136 37.7 213s 18 59.2 1.921 40.0 213s 19 57.4 0.596 38.7 213s 20 60.6 2.011 42.0 213s 21 64.2 4.120 46.1 213s 22 71.9 5.631 52.7 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.3 0.523 39.9 44.7 213s 3 46.2 0.560 43.8 48.7 213s 4 50.8 0.379 48.5 53.1 213s 5 51.1 0.448 48.8 53.5 213s 6 52.6 0.457 50.3 55.0 213s 7 54.3 0.408 52.0 56.6 213s 8 54.9 0.375 52.6 57.2 213s 9 56.3 0.418 54.0 58.6 213s 10 NA NA NA NA 213s 11 54.9 0.701 52.3 57.4 213s 12 51.2 0.638 48.7 53.8 213s 13 NA NA NA NA 213s 14 46.2 0.673 43.6 48.7 213s 15 48.8 0.453 46.5 51.2 213s 16 51.4 0.384 49.1 53.7 213s 17 56.1 0.391 53.8 58.4 213s 18 59.2 0.361 56.9 61.5 213s 19 57.4 0.449 55.0 59.7 213s 20 60.6 0.465 58.3 63.0 213s 21 64.2 0.468 61.9 66.6 213s 22 71.9 0.728 69.3 74.5 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 -0.200 0.613 -2.618 2.219 213s 3 1.976 0.494 -0.329 4.282 213s 4 3.978 0.444 1.714 6.242 213s 5 4.378 0.369 2.169 6.587 213s 6 4.714 0.349 2.519 6.909 213s 7 4.114 0.323 1.934 6.293 213s 8 3.416 0.287 1.257 5.575 213s 9 3.655 0.386 1.435 5.876 213s 10 4.039 0.441 1.777 6.301 213s 11 0.605 0.641 -1.843 3.053 213s 12 -3.598 0.606 -6.010 -1.186 213s 13 NA NA NA NA 213s 14 -5.413 0.708 -7.934 -2.892 213s 15 -2.915 0.412 -5.155 -0.676 213s 16 -1.366 0.336 -3.554 0.821 213s 17 1.136 0.342 -1.055 3.327 213s 18 1.921 0.246 -0.217 4.060 213s 19 0.596 0.341 -1.594 2.787 213s 20 2.011 0.364 -0.194 4.216 213s 21 4.120 0.337 1.932 6.308 213s 22 5.631 0.477 3.341 7.922 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.8 0.364 25.1 28.6 213s 3 29.1 0.367 27.3 30.8 213s 4 33.0 0.370 31.2 34.7 213s 5 34.1 0.286 32.4 35.8 213s 6 35.9 0.285 34.3 37.6 213s 7 NA NA NA NA 213s 8 38.7 0.292 37.0 40.4 213s 9 38.9 0.277 37.3 40.6 213s 10 40.2 0.264 38.5 41.8 213s 11 38.1 0.363 36.4 39.8 213s 12 33.9 0.367 32.2 35.7 213s 13 28.9 0.435 27.1 30.7 213s 14 28.0 0.383 26.3 29.8 213s 15 30.3 0.377 28.6 32.0 213s 16 33.2 0.315 31.5 34.9 213s 17 37.7 0.308 36.0 39.3 213s 18 40.0 0.241 38.4 41.7 213s 19 38.7 0.361 36.9 40.4 213s 20 42.0 0.324 40.3 43.7 213s 21 46.1 0.339 44.4 47.8 213s 22 52.7 0.511 50.9 54.6 213s > model.frame 213s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 213s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 213s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 213s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 213s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 213s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 213s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 213s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 213s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 213s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 213s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 213s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 213s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 213s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 213s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 213s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 213s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 213s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 213s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 213s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 213s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 213s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 213s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 213s trend 213s 1 -11 213s 2 -10 213s 3 -9 213s 4 -8 213s 5 -7 213s 6 -6 213s 7 -5 213s 8 -4 213s 9 -3 213s 10 -2 213s 11 -1 213s 12 0 213s 13 1 213s 14 2 213s 15 3 213s 16 4 213s 17 5 213s 18 6 213s 19 7 213s 20 8 213s 21 9 213s 22 10 213s > model.matrix 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 1 12.4 213s Consumption_3 1 16.9 213s Consumption_4 1 18.4 213s Consumption_5 1 19.4 213s Consumption_6 1 20.1 213s Consumption_7 1 19.6 213s Consumption_8 1 19.8 213s Consumption_9 1 21.1 213s Consumption_11 1 15.6 213s Consumption_12 1 11.4 213s Consumption_14 1 11.2 213s Consumption_15 1 12.3 213s Consumption_16 1 14.0 213s Consumption_17 1 17.6 213s Consumption_18 1 17.3 213s Consumption_19 1 15.3 213s Consumption_20 1 19.0 213s Consumption_21 1 21.1 213s Consumption_22 1 23.5 213s Investment_2 0 0.0 213s Investment_3 0 0.0 213s Investment_4 0 0.0 213s Investment_5 0 0.0 213s Investment_6 0 0.0 213s Investment_7 0 0.0 213s Investment_8 0 0.0 213s Investment_9 0 0.0 213s Investment_10 0 0.0 213s Investment_11 0 0.0 213s Investment_12 0 0.0 213s Investment_14 0 0.0 213s Investment_15 0 0.0 213s Investment_16 0 0.0 213s Investment_17 0 0.0 213s Investment_18 0 0.0 213s Investment_19 0 0.0 213s Investment_20 0 0.0 213s Investment_21 0 0.0 213s Investment_22 0 0.0 213s PrivateWages_2 0 0.0 213s PrivateWages_3 0 0.0 213s PrivateWages_4 0 0.0 213s PrivateWages_5 0 0.0 213s PrivateWages_6 0 0.0 213s PrivateWages_8 0 0.0 213s PrivateWages_9 0 0.0 213s PrivateWages_10 0 0.0 213s PrivateWages_11 0 0.0 213s PrivateWages_12 0 0.0 213s PrivateWages_13 0 0.0 213s PrivateWages_14 0 0.0 213s PrivateWages_15 0 0.0 213s PrivateWages_16 0 0.0 213s PrivateWages_17 0 0.0 213s PrivateWages_18 0 0.0 213s PrivateWages_19 0 0.0 213s PrivateWages_20 0 0.0 213s PrivateWages_21 0 0.0 213s PrivateWages_22 0 0.0 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 12.7 28.2 213s Consumption_3 12.4 32.2 213s Consumption_4 16.9 37.0 213s Consumption_5 18.4 37.0 213s Consumption_6 19.4 38.6 213s Consumption_7 20.1 40.7 213s Consumption_8 19.6 41.5 213s Consumption_9 19.8 42.9 213s Consumption_11 21.7 42.1 213s Consumption_12 15.6 39.3 213s Consumption_14 7.0 34.1 213s Consumption_15 11.2 36.6 213s Consumption_16 12.3 39.3 213s Consumption_17 14.0 44.2 213s Consumption_18 17.6 47.7 213s Consumption_19 17.3 45.9 213s Consumption_20 15.3 49.4 213s Consumption_21 19.0 53.0 213s Consumption_22 21.1 61.8 213s Investment_2 0.0 0.0 213s Investment_3 0.0 0.0 213s Investment_4 0.0 0.0 213s Investment_5 0.0 0.0 213s Investment_6 0.0 0.0 213s Investment_7 0.0 0.0 213s Investment_8 0.0 0.0 213s Investment_9 0.0 0.0 213s Investment_10 0.0 0.0 213s Investment_11 0.0 0.0 213s Investment_12 0.0 0.0 213s Investment_14 0.0 0.0 213s Investment_15 0.0 0.0 213s Investment_16 0.0 0.0 213s Investment_17 0.0 0.0 213s Investment_18 0.0 0.0 213s Investment_19 0.0 0.0 213s Investment_20 0.0 0.0 213s Investment_21 0.0 0.0 213s Investment_22 0.0 0.0 213s PrivateWages_2 0.0 0.0 213s PrivateWages_3 0.0 0.0 213s PrivateWages_4 0.0 0.0 213s PrivateWages_5 0.0 0.0 213s PrivateWages_6 0.0 0.0 213s PrivateWages_8 0.0 0.0 213s PrivateWages_9 0.0 0.0 213s PrivateWages_10 0.0 0.0 213s PrivateWages_11 0.0 0.0 213s PrivateWages_12 0.0 0.0 213s PrivateWages_13 0.0 0.0 213s PrivateWages_14 0.0 0.0 213s PrivateWages_15 0.0 0.0 213s PrivateWages_16 0.0 0.0 213s PrivateWages_17 0.0 0.0 213s PrivateWages_18 0.0 0.0 213s PrivateWages_19 0.0 0.0 213s PrivateWages_20 0.0 0.0 213s PrivateWages_21 0.0 0.0 213s PrivateWages_22 0.0 0.0 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0 0.0 213s Consumption_3 0 0.0 213s Consumption_4 0 0.0 213s Consumption_5 0 0.0 213s Consumption_6 0 0.0 213s Consumption_7 0 0.0 213s Consumption_8 0 0.0 213s Consumption_9 0 0.0 213s Consumption_11 0 0.0 213s Consumption_12 0 0.0 213s Consumption_14 0 0.0 213s Consumption_15 0 0.0 213s Consumption_16 0 0.0 213s Consumption_17 0 0.0 213s Consumption_18 0 0.0 213s Consumption_19 0 0.0 213s Consumption_20 0 0.0 213s Consumption_21 0 0.0 213s Consumption_22 0 0.0 213s Investment_2 1 12.4 213s Investment_3 1 16.9 213s Investment_4 1 18.4 213s Investment_5 1 19.4 213s Investment_6 1 20.1 213s Investment_7 1 19.6 213s Investment_8 1 19.8 213s Investment_9 1 21.1 213s Investment_10 1 21.7 213s Investment_11 1 15.6 213s Investment_12 1 11.4 213s Investment_14 1 11.2 213s Investment_15 1 12.3 213s Investment_16 1 14.0 213s Investment_17 1 17.6 213s Investment_18 1 17.3 213s Investment_19 1 15.3 213s Investment_20 1 19.0 213s Investment_21 1 21.1 213s Investment_22 1 23.5 213s PrivateWages_2 0 0.0 213s PrivateWages_3 0 0.0 213s PrivateWages_4 0 0.0 213s PrivateWages_5 0 0.0 213s PrivateWages_6 0 0.0 213s PrivateWages_8 0 0.0 213s PrivateWages_9 0 0.0 213s PrivateWages_10 0 0.0 213s PrivateWages_11 0 0.0 213s PrivateWages_12 0 0.0 213s PrivateWages_13 0 0.0 213s PrivateWages_14 0 0.0 213s PrivateWages_15 0 0.0 213s PrivateWages_16 0 0.0 213s PrivateWages_17 0 0.0 213s PrivateWages_18 0 0.0 213s PrivateWages_19 0 0.0 213s PrivateWages_20 0 0.0 213s PrivateWages_21 0 0.0 213s PrivateWages_22 0 0.0 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.0 0 213s Consumption_3 0.0 0 213s Consumption_4 0.0 0 213s Consumption_5 0.0 0 213s Consumption_6 0.0 0 213s Consumption_7 0.0 0 213s Consumption_8 0.0 0 213s Consumption_9 0.0 0 213s Consumption_11 0.0 0 213s Consumption_12 0.0 0 213s Consumption_14 0.0 0 213s Consumption_15 0.0 0 213s Consumption_16 0.0 0 213s Consumption_17 0.0 0 213s Consumption_18 0.0 0 213s Consumption_19 0.0 0 213s Consumption_20 0.0 0 213s Consumption_21 0.0 0 213s Consumption_22 0.0 0 213s Investment_2 12.7 183 213s Investment_3 12.4 183 213s Investment_4 16.9 184 213s Investment_5 18.4 190 213s Investment_6 19.4 193 213s Investment_7 20.1 198 213s Investment_8 19.6 203 213s Investment_9 19.8 208 213s Investment_10 21.1 211 213s Investment_11 21.7 216 213s Investment_12 15.6 217 213s Investment_14 7.0 207 213s Investment_15 11.2 202 213s Investment_16 12.3 199 213s Investment_17 14.0 198 213s Investment_18 17.6 200 213s Investment_19 17.3 202 213s Investment_20 15.3 200 213s Investment_21 19.0 201 213s Investment_22 21.1 204 213s PrivateWages_2 0.0 0 213s PrivateWages_3 0.0 0 213s PrivateWages_4 0.0 0 213s PrivateWages_5 0.0 0 213s PrivateWages_6 0.0 0 213s PrivateWages_8 0.0 0 213s PrivateWages_9 0.0 0 213s PrivateWages_10 0.0 0 213s PrivateWages_11 0.0 0 213s PrivateWages_12 0.0 0 213s PrivateWages_13 0.0 0 213s PrivateWages_14 0.0 0 213s PrivateWages_15 0.0 0 213s PrivateWages_16 0.0 0 213s PrivateWages_17 0.0 0 213s PrivateWages_18 0.0 0 213s PrivateWages_19 0.0 0 213s PrivateWages_20 0.0 0 213s PrivateWages_21 0.0 0 213s PrivateWages_22 0.0 0 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 0 0.0 0.0 213s Consumption_3 0 0.0 0.0 213s Consumption_4 0 0.0 0.0 213s Consumption_5 0 0.0 0.0 213s Consumption_6 0 0.0 0.0 213s Consumption_7 0 0.0 0.0 213s Consumption_8 0 0.0 0.0 213s Consumption_9 0 0.0 0.0 213s Consumption_11 0 0.0 0.0 213s Consumption_12 0 0.0 0.0 213s Consumption_14 0 0.0 0.0 213s Consumption_15 0 0.0 0.0 213s Consumption_16 0 0.0 0.0 213s Consumption_17 0 0.0 0.0 213s Consumption_18 0 0.0 0.0 213s Consumption_19 0 0.0 0.0 213s Consumption_20 0 0.0 0.0 213s Consumption_21 0 0.0 0.0 213s Consumption_22 0 0.0 0.0 213s Investment_2 0 0.0 0.0 213s Investment_3 0 0.0 0.0 213s Investment_4 0 0.0 0.0 213s Investment_5 0 0.0 0.0 213s Investment_6 0 0.0 0.0 213s Investment_7 0 0.0 0.0 213s Investment_8 0 0.0 0.0 213s Investment_9 0 0.0 0.0 213s Investment_10 0 0.0 0.0 213s Investment_11 0 0.0 0.0 213s Investment_12 0 0.0 0.0 213s Investment_14 0 0.0 0.0 213s Investment_15 0 0.0 0.0 213s Investment_16 0 0.0 0.0 213s Investment_17 0 0.0 0.0 213s Investment_18 0 0.0 0.0 213s Investment_19 0 0.0 0.0 213s Investment_20 0 0.0 0.0 213s Investment_21 0 0.0 0.0 213s Investment_22 0 0.0 0.0 213s PrivateWages_2 1 45.6 44.9 213s PrivateWages_3 1 50.1 45.6 213s PrivateWages_4 1 57.2 50.1 213s PrivateWages_5 1 57.1 57.2 213s PrivateWages_6 1 61.0 57.1 213s PrivateWages_8 1 64.4 64.0 213s PrivateWages_9 1 64.5 64.4 213s PrivateWages_10 1 67.0 64.5 213s PrivateWages_11 1 61.2 67.0 213s PrivateWages_12 1 53.4 61.2 213s PrivateWages_13 1 44.3 53.4 213s PrivateWages_14 1 45.1 44.3 213s PrivateWages_15 1 49.7 45.1 213s PrivateWages_16 1 54.4 49.7 213s PrivateWages_17 1 62.7 54.4 213s PrivateWages_18 1 65.0 62.7 213s PrivateWages_19 1 60.9 65.0 213s PrivateWages_20 1 69.5 60.9 213s PrivateWages_21 1 75.7 69.5 213s PrivateWages_22 1 88.4 75.7 213s PrivateWages_trend 213s Consumption_2 0 213s Consumption_3 0 213s Consumption_4 0 213s Consumption_5 0 213s Consumption_6 0 213s Consumption_7 0 213s Consumption_8 0 213s Consumption_9 0 213s Consumption_11 0 213s Consumption_12 0 213s Consumption_14 0 213s Consumption_15 0 213s Consumption_16 0 213s Consumption_17 0 213s Consumption_18 0 213s Consumption_19 0 213s Consumption_20 0 213s Consumption_21 0 213s Consumption_22 0 213s Investment_2 0 213s Investment_3 0 213s Investment_4 0 213s Investment_5 0 213s Investment_6 0 213s Investment_7 0 213s Investment_8 0 213s Investment_9 0 213s Investment_10 0 213s Investment_11 0 213s Investment_12 0 213s Investment_14 0 213s Investment_15 0 213s Investment_16 0 213s Investment_17 0 213s Investment_18 0 213s Investment_19 0 213s Investment_20 0 213s Investment_21 0 213s Investment_22 0 213s PrivateWages_2 -10 213s PrivateWages_3 -9 213s PrivateWages_4 -8 213s PrivateWages_5 -7 213s PrivateWages_6 -6 213s PrivateWages_8 -4 213s PrivateWages_9 -3 213s PrivateWages_10 -2 213s PrivateWages_11 -1 213s PrivateWages_12 0 213s PrivateWages_13 1 213s PrivateWages_14 2 213s PrivateWages_15 3 213s PrivateWages_16 4 213s PrivateWages_17 5 213s PrivateWages_18 6 213s PrivateWages_19 7 213s PrivateWages_20 8 213s PrivateWages_21 9 213s PrivateWages_22 10 213s > nobs 213s [1] 59 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.33 0.57 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.31 0.58 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 48 213s 2 47 1 0.31 0.58 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.17 0.84 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.16 0.85 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 49 213s 2 47 2 0.33 0.85 213s > logLik 213s 'log Lik.' -69.6 (df=13) 213s 'log Lik.' -74.2 (df=13) 213s compare log likelihood value with single-equation OLS 213s [1] "Mean relative difference: 0.00099" 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -0.3863 -4.791 213s Consumption_3 -1.2484 -21.098 213s Consumption_4 -1.6040 -29.514 213s Consumption_5 -0.5384 -10.446 213s Consumption_6 -0.0413 -0.830 213s Consumption_7 0.8043 15.763 213s Consumption_8 1.2830 25.403 213s Consumption_9 1.0142 21.399 213s Consumption_11 0.1429 2.229 213s Consumption_12 -0.3439 -3.920 213s Consumption_14 0.3199 3.583 213s Consumption_15 -0.1016 -1.250 213s Consumption_16 -0.0702 -0.983 213s Consumption_17 1.6064 28.272 213s Consumption_18 -0.4980 -8.616 213s Consumption_19 0.1253 1.917 213s Consumption_20 0.9805 18.629 213s Consumption_21 0.7551 15.933 213s Consumption_22 -2.1992 -51.681 213s Investment_2 0.0000 0.000 213s Investment_3 0.0000 0.000 213s Investment_4 0.0000 0.000 213s Investment_5 0.0000 0.000 213s Investment_6 0.0000 0.000 213s Investment_7 0.0000 0.000 213s Investment_8 0.0000 0.000 213s Investment_9 0.0000 0.000 213s Investment_10 0.0000 0.000 213s Investment_11 0.0000 0.000 213s Investment_12 0.0000 0.000 213s Investment_14 0.0000 0.000 213s Investment_15 0.0000 0.000 213s Investment_16 0.0000 0.000 213s Investment_17 0.0000 0.000 213s Investment_18 0.0000 0.000 213s Investment_19 0.0000 0.000 213s Investment_20 0.0000 0.000 213s Investment_21 0.0000 0.000 213s Investment_22 0.0000 0.000 213s PrivateWages_2 0.0000 0.000 213s PrivateWages_3 0.0000 0.000 213s PrivateWages_4 0.0000 0.000 213s PrivateWages_5 0.0000 0.000 213s PrivateWages_6 0.0000 0.000 213s PrivateWages_8 0.0000 0.000 213s PrivateWages_9 0.0000 0.000 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 0.0000 0.000 213s PrivateWages_12 0.0000 0.000 213s PrivateWages_13 0.0000 0.000 213s PrivateWages_14 0.0000 0.000 213s PrivateWages_15 0.0000 0.000 213s PrivateWages_16 0.0000 0.000 213s PrivateWages_17 0.0000 0.000 213s PrivateWages_18 0.0000 0.000 213s PrivateWages_19 0.0000 0.000 213s PrivateWages_20 0.0000 0.000 213s PrivateWages_21 0.0000 0.000 213s PrivateWages_22 0.0000 0.000 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -4.907 -10.90 213s Consumption_3 -15.480 -40.20 213s Consumption_4 -27.108 -59.35 213s Consumption_5 -9.907 -19.92 213s Consumption_6 -0.801 -1.59 213s Consumption_7 16.166 32.73 213s Consumption_8 25.146 53.24 213s Consumption_9 20.081 43.51 213s Consumption_11 3.100 6.01 213s Consumption_12 -5.364 -13.51 213s Consumption_14 2.239 10.91 213s Consumption_15 -1.138 -3.72 213s Consumption_16 -0.864 -2.76 213s Consumption_17 22.489 71.00 213s Consumption_18 -8.765 -23.76 213s Consumption_19 2.168 5.75 213s Consumption_20 15.002 48.44 213s Consumption_21 14.348 40.02 213s Consumption_22 -46.403 -135.91 213s Investment_2 0.000 0.00 213s Investment_3 0.000 0.00 213s Investment_4 0.000 0.00 213s Investment_5 0.000 0.00 213s Investment_6 0.000 0.00 213s Investment_7 0.000 0.00 213s Investment_8 0.000 0.00 213s Investment_9 0.000 0.00 213s Investment_10 0.000 0.00 213s Investment_11 0.000 0.00 213s Investment_12 0.000 0.00 213s Investment_14 0.000 0.00 213s Investment_15 0.000 0.00 213s Investment_16 0.000 0.00 213s Investment_17 0.000 0.00 213s Investment_18 0.000 0.00 213s Investment_19 0.000 0.00 213s Investment_20 0.000 0.00 213s Investment_21 0.000 0.00 213s Investment_22 0.000 0.00 213s PrivateWages_2 0.000 0.00 213s PrivateWages_3 0.000 0.00 213s PrivateWages_4 0.000 0.00 213s PrivateWages_5 0.000 0.00 213s PrivateWages_6 0.000 0.00 213s PrivateWages_8 0.000 0.00 213s PrivateWages_9 0.000 0.00 213s PrivateWages_10 0.000 0.00 213s PrivateWages_11 0.000 0.00 213s PrivateWages_12 0.000 0.00 213s PrivateWages_13 0.000 0.00 213s PrivateWages_14 0.000 0.00 213s PrivateWages_15 0.000 0.00 213s PrivateWages_16 0.000 0.00 213s PrivateWages_17 0.000 0.00 213s PrivateWages_18 0.000 0.00 213s PrivateWages_19 0.000 0.00 213s PrivateWages_20 0.000 0.00 213s PrivateWages_21 0.000 0.00 213s PrivateWages_22 0.000 0.00 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0.000000 0.00000 213s Consumption_3 0.000000 0.00000 213s Consumption_4 0.000000 0.00000 213s Consumption_5 0.000000 0.00000 213s Consumption_6 0.000000 0.00000 213s Consumption_7 0.000000 0.00000 213s Consumption_8 0.000000 0.00000 213s Consumption_9 0.000000 0.00000 213s Consumption_11 0.000000 0.00000 213s Consumption_12 0.000000 0.00000 213s Consumption_14 0.000000 0.00000 213s Consumption_15 0.000000 0.00000 213s Consumption_16 0.000000 0.00000 213s Consumption_17 0.000000 0.00000 213s Consumption_18 0.000000 0.00000 213s Consumption_19 0.000000 0.00000 213s Consumption_20 0.000000 0.00000 213s Consumption_21 0.000000 0.00000 213s Consumption_22 0.000000 0.00000 213s Investment_2 -0.000301 -0.00373 213s Investment_3 -0.076489 -1.29266 213s Investment_4 1.221792 22.48097 213s Investment_5 -1.377872 -26.73071 213s Investment_6 0.386104 7.76068 213s Investment_7 1.486279 29.13107 213s Investment_8 0.784055 15.52429 213s Investment_9 -0.655354 -13.82796 213s Investment_10 1.060871 23.02091 213s Investment_11 0.395249 6.16588 213s Investment_12 0.198005 2.25726 213s Investment_14 0.312725 3.50252 213s Investment_15 -0.084685 -1.04163 213s Investment_16 0.066194 0.92672 213s Investment_17 0.963697 16.96106 213s Investment_18 0.078506 1.35816 213s Investment_19 -2.496401 -38.19494 213s Investment_20 -0.711004 -13.50907 213s Investment_21 -0.820172 -17.30564 213s Investment_22 -0.731199 -17.18317 213s PrivateWages_2 0.000000 0.00000 213s PrivateWages_3 0.000000 0.00000 213s PrivateWages_4 0.000000 0.00000 213s PrivateWages_5 0.000000 0.00000 213s PrivateWages_6 0.000000 0.00000 213s PrivateWages_8 0.000000 0.00000 213s PrivateWages_9 0.000000 0.00000 213s PrivateWages_10 0.000000 0.00000 213s PrivateWages_11 0.000000 0.00000 213s PrivateWages_12 0.000000 0.00000 213s PrivateWages_13 0.000000 0.00000 213s PrivateWages_14 0.000000 0.00000 213s PrivateWages_15 0.000000 0.00000 213s PrivateWages_16 0.000000 0.00000 213s PrivateWages_17 0.000000 0.00000 213s PrivateWages_18 0.000000 0.00000 213s PrivateWages_19 0.000000 0.00000 213s PrivateWages_20 0.000000 0.00000 213s PrivateWages_21 0.000000 0.00000 213s PrivateWages_22 0.000000 0.00000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.00000 0.000 213s Consumption_3 0.00000 0.000 213s Consumption_4 0.00000 0.000 213s Consumption_5 0.00000 0.000 213s Consumption_6 0.00000 0.000 213s Consumption_7 0.00000 0.000 213s Consumption_8 0.00000 0.000 213s Consumption_9 0.00000 0.000 213s Consumption_11 0.00000 0.000 213s Consumption_12 0.00000 0.000 213s Consumption_14 0.00000 0.000 213s Consumption_15 0.00000 0.000 213s Consumption_16 0.00000 0.000 213s Consumption_17 0.00000 0.000 213s Consumption_18 0.00000 0.000 213s Consumption_19 0.00000 0.000 213s Consumption_20 0.00000 0.000 213s Consumption_21 0.00000 0.000 213s Consumption_22 0.00000 0.000 213s Investment_2 -0.00382 -0.055 213s Investment_3 -0.94846 -13.967 213s Investment_4 20.64828 225.421 213s Investment_5 -25.35284 -261.382 213s Investment_6 7.49041 74.402 213s Investment_7 29.87421 293.986 213s Investment_8 15.36748 159.477 213s Investment_9 -12.97600 -136.051 213s Investment_10 22.38438 223.419 213s Investment_11 8.57690 85.255 213s Investment_12 3.08888 42.908 213s Investment_14 2.18907 64.765 213s Investment_15 -0.94848 -17.106 213s Investment_16 0.81419 13.173 213s Investment_17 13.49175 190.523 213s Investment_18 1.38171 15.686 213s Investment_19 -43.18774 -503.774 213s Investment_20 -10.87836 -142.130 213s Investment_21 -15.58327 -165.019 213s Investment_22 -15.42829 -149.530 213s PrivateWages_2 0.00000 0.000 213s PrivateWages_3 0.00000 0.000 213s PrivateWages_4 0.00000 0.000 213s PrivateWages_5 0.00000 0.000 213s PrivateWages_6 0.00000 0.000 213s PrivateWages_8 0.00000 0.000 213s PrivateWages_9 0.00000 0.000 213s PrivateWages_10 0.00000 0.000 213s PrivateWages_11 0.00000 0.000 213s PrivateWages_12 0.00000 0.000 213s PrivateWages_13 0.00000 0.000 213s PrivateWages_14 0.00000 0.000 213s PrivateWages_15 0.00000 0.000 213s PrivateWages_16 0.00000 0.000 213s PrivateWages_17 0.00000 0.000 213s PrivateWages_18 0.00000 0.000 213s PrivateWages_19 0.00000 0.000 213s PrivateWages_20 0.00000 0.000 213s PrivateWages_21 0.00000 0.000 213s PrivateWages_22 0.00000 0.000 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 0.0000 0.00 0.00 213s Consumption_3 0.0000 0.00 0.00 213s Consumption_4 0.0000 0.00 0.00 213s Consumption_5 0.0000 0.00 0.00 213s Consumption_6 0.0000 0.00 0.00 213s Consumption_7 0.0000 0.00 0.00 213s Consumption_8 0.0000 0.00 0.00 213s Consumption_9 0.0000 0.00 0.00 213s Consumption_11 0.0000 0.00 0.00 213s Consumption_12 0.0000 0.00 0.00 213s Consumption_14 0.0000 0.00 0.00 213s Consumption_15 0.0000 0.00 0.00 213s Consumption_16 0.0000 0.00 0.00 213s Consumption_17 0.0000 0.00 0.00 213s Consumption_18 0.0000 0.00 0.00 213s Consumption_19 0.0000 0.00 0.00 213s Consumption_20 0.0000 0.00 0.00 213s Consumption_21 0.0000 0.00 0.00 213s Consumption_22 0.0000 0.00 0.00 213s Investment_2 0.0000 0.00 0.00 213s Investment_3 0.0000 0.00 0.00 213s Investment_4 0.0000 0.00 0.00 213s Investment_5 0.0000 0.00 0.00 213s Investment_6 0.0000 0.00 0.00 213s Investment_7 0.0000 0.00 0.00 213s Investment_8 0.0000 0.00 0.00 213s Investment_9 0.0000 0.00 0.00 213s Investment_10 0.0000 0.00 0.00 213s Investment_11 0.0000 0.00 0.00 213s Investment_12 0.0000 0.00 0.00 213s Investment_14 0.0000 0.00 0.00 213s Investment_15 0.0000 0.00 0.00 213s Investment_16 0.0000 0.00 0.00 213s Investment_17 0.0000 0.00 0.00 213s Investment_18 0.0000 0.00 0.00 213s Investment_19 0.0000 0.00 0.00 213s Investment_20 0.0000 0.00 0.00 213s Investment_21 0.0000 0.00 0.00 213s Investment_22 0.0000 0.00 0.00 213s PrivateWages_2 -1.3389 -61.06 -60.12 213s PrivateWages_3 0.2462 12.33 11.23 213s PrivateWages_4 1.1255 64.38 56.39 213s PrivateWages_5 -0.1959 -11.18 -11.20 213s PrivateWages_6 -0.5284 -32.23 -30.17 213s PrivateWages_8 -0.7909 -50.94 -50.62 213s PrivateWages_9 0.2819 18.18 18.15 213s PrivateWages_10 1.1384 76.28 73.43 213s PrivateWages_11 -0.1904 -11.65 -12.76 213s PrivateWages_12 0.5813 31.04 35.58 213s PrivateWages_13 0.1206 5.34 6.44 213s PrivateWages_14 0.4773 21.53 21.14 213s PrivateWages_15 0.3035 15.09 13.69 213s PrivateWages_16 0.0284 1.55 1.41 213s PrivateWages_17 -0.8517 -53.40 -46.33 213s PrivateWages_18 0.9908 64.40 62.12 213s PrivateWages_19 -0.4597 -28.00 -29.88 213s PrivateWages_20 -0.3819 -26.54 -23.26 213s PrivateWages_21 -1.1062 -83.74 -76.88 213s PrivateWages_22 0.5501 48.63 41.64 213s PrivateWages_trend 213s Consumption_2 0.000 213s Consumption_3 0.000 213s Consumption_4 0.000 213s Consumption_5 0.000 213s Consumption_6 0.000 213s Consumption_7 0.000 213s Consumption_8 0.000 213s Consumption_9 0.000 213s Consumption_11 0.000 213s Consumption_12 0.000 213s Consumption_14 0.000 213s Consumption_15 0.000 213s Consumption_16 0.000 213s Consumption_17 0.000 213s Consumption_18 0.000 213s Consumption_19 0.000 213s Consumption_20 0.000 213s Consumption_21 0.000 213s Consumption_22 0.000 213s Investment_2 0.000 213s Investment_3 0.000 213s Investment_4 0.000 213s Investment_5 0.000 213s Investment_6 0.000 213s Investment_7 0.000 213s Investment_8 0.000 213s Investment_9 0.000 213s Investment_10 0.000 213s Investment_11 0.000 213s Investment_12 0.000 213s Investment_14 0.000 213s Investment_15 0.000 213s Investment_16 0.000 213s Investment_17 0.000 213s Investment_18 0.000 213s Investment_19 0.000 213s Investment_20 0.000 213s Investment_21 0.000 213s Investment_22 0.000 213s PrivateWages_2 13.389 213s PrivateWages_3 -2.216 213s PrivateWages_4 -9.004 213s PrivateWages_5 1.371 213s PrivateWages_6 3.170 213s PrivateWages_8 3.164 213s PrivateWages_9 -0.846 213s PrivateWages_10 -2.277 213s PrivateWages_11 0.190 213s PrivateWages_12 0.000 213s PrivateWages_13 0.121 213s PrivateWages_14 0.955 213s PrivateWages_15 0.911 213s PrivateWages_16 0.114 213s PrivateWages_17 -4.258 213s PrivateWages_18 5.945 213s PrivateWages_19 -3.218 213s PrivateWages_20 -3.055 213s PrivateWages_21 -9.956 213s PrivateWages_22 5.501 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_(Intercept) 109.396 -1.6401 213s Consumption_corpProf -1.640 0.6675 213s Consumption_corpProfLag -0.598 -0.3509 213s Consumption_wages -1.641 -0.0975 213s Investment_(Intercept) 0.000 0.0000 213s Investment_corpProf 0.000 0.0000 213s Investment_corpProfLag 0.000 0.0000 213s Investment_capitalLag 0.000 0.0000 213s PrivateWages_(Intercept) 0.000 0.0000 213s PrivateWages_gnp 0.000 0.0000 213s PrivateWages_gnpLag 0.000 0.0000 213s PrivateWages_trend 0.000 0.0000 213s Consumption_corpProfLag Consumption_wages 213s Consumption_(Intercept) -0.5979 -1.6408 213s Consumption_corpProf -0.3509 -0.0975 213s Consumption_corpProfLag 0.4880 -0.0331 213s Consumption_wages -0.0331 0.0926 213s Investment_(Intercept) 0.0000 0.0000 213s Investment_corpProf 0.0000 0.0000 213s Investment_corpProfLag 0.0000 0.0000 213s Investment_capitalLag 0.0000 0.0000 213s PrivateWages_(Intercept) 0.0000 0.0000 213s PrivateWages_gnp 0.0000 0.0000 213s PrivateWages_gnpLag 0.0000 0.0000 213s PrivateWages_trend 0.0000 0.0000 213s Investment_(Intercept) Investment_corpProf 213s Consumption_(Intercept) 0.00 0.0000 213s Consumption_corpProf 0.00 0.0000 213s Consumption_corpProfLag 0.00 0.0000 213s Consumption_wages 0.00 0.0000 213s Investment_(Intercept) 1730.48 -16.5126 213s Investment_corpProf -16.51 0.6641 213s Investment_corpProfLag 13.63 -0.5096 213s Investment_capitalLag -8.34 0.0672 213s PrivateWages_(Intercept) 0.00 0.0000 213s PrivateWages_gnp 0.00 0.0000 213s PrivateWages_gnpLag 0.00 0.0000 213s PrivateWages_trend 0.00 0.0000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_(Intercept) 0.000 0.0000 213s Consumption_corpProf 0.000 0.0000 213s Consumption_corpProfLag 0.000 0.0000 213s Consumption_wages 0.000 0.0000 213s Investment_(Intercept) 13.633 -8.3416 213s Investment_corpProf -0.510 0.0672 213s Investment_corpProfLag 0.603 -0.0740 213s Investment_capitalLag -0.074 0.0420 213s PrivateWages_(Intercept) 0.000 0.0000 213s PrivateWages_gnp 0.000 0.0000 213s PrivateWages_gnpLag 0.000 0.0000 213s PrivateWages_trend 0.000 0.0000 213s PrivateWages_(Intercept) PrivateWages_gnp 213s Consumption_(Intercept) 0.000 0.0000 213s Consumption_corpProf 0.000 0.0000 213s Consumption_corpProfLag 0.000 0.0000 213s Consumption_wages 0.000 0.0000 213s Investment_(Intercept) 0.000 0.0000 213s Investment_corpProf 0.000 0.0000 213s Investment_corpProfLag 0.000 0.0000 213s Investment_capitalLag 0.000 0.0000 213s PrivateWages_(Intercept) 166.178 -0.6258 213s PrivateWages_gnp -0.626 0.1064 213s PrivateWages_gnpLag -2.183 -0.0992 213s PrivateWages_trend 2.051 -0.0286 213s PrivateWages_gnpLag PrivateWages_trend 213s Consumption_(Intercept) 0.00000 0.00000 213s Consumption_corpProf 0.00000 0.00000 213s Consumption_corpProfLag 0.00000 0.00000 213s Consumption_wages 0.00000 0.00000 213s Investment_(Intercept) 0.00000 0.00000 213s Investment_corpProf 0.00000 0.00000 213s Investment_corpProfLag 0.00000 0.00000 213s Investment_capitalLag 0.00000 0.00000 213s PrivateWages_(Intercept) -2.18348 2.05079 213s PrivateWages_gnp -0.09921 -0.02859 213s PrivateWages_gnpLag 0.14047 -0.00635 213s PrivateWages_trend -0.00635 0.10969 213s > 213s > # 2SLS 213s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: 2SLS 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 57 45 58.2 0.333 0.968 0.991 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 213s Investment 19 15 26.21 1.748 1.32 0.852 0.823 213s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.237 0.518 -0.408 213s Investment 0.518 1.263 0.113 213s PrivateWages -0.408 0.113 0.468 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.000 0.416 -0.538 213s Investment 0.416 1.000 0.139 213s PrivateWages -0.538 0.139 1.000 213s 213s 213s 2SLS estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 17.2849 1.6018 10.79 3.6e-08 *** 213s corpProf -0.0770 0.1637 -0.47 0.645 213s corpProfLag 0.2327 0.1242 1.87 0.082 . 213s wages 0.8259 0.0459 17.98 4.5e-11 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.261 on 14 degrees of freedom 213s Number of observations: 18 Degrees of Freedom: 14 213s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 213s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 213s 213s 213s 2SLS estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 18.4005 7.1627 2.57 0.02138 * 213s corpProf 0.1507 0.1905 0.79 0.44118 213s corpProfLag 0.5757 0.1634 3.52 0.00307 ** 213s capitalLag -0.1452 0.0339 -4.28 0.00065 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.322 on 15 degrees of freedom 213s Number of observations: 19 Degrees of Freedom: 15 213s SSR: 26.213 MSE: 1.748 Root MSE: 1.322 213s Multiple R-Squared: 0.852 Adjusted R-Squared: 0.823 213s 213s 213s 2SLS estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 1.3431 1.1544 1.16 0.26172 213s gnp 0.4438 0.0351 12.64 9.7e-10 *** 213s gnpLag 0.1447 0.0381 3.80 0.00158 ** 213s trend 0.1238 0.0300 4.13 0.00078 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.78 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 213s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 213s 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.6754 -1.23599 -1.3401 213s 3 -0.4627 0.32957 0.2378 213s 4 -1.1585 1.08894 1.1117 213s 5 -0.0305 -1.37017 -0.1954 213s 6 0.4693 0.48431 -0.5355 213s 7 NA NA NA 213s 8 1.6045 1.06811 -0.7908 213s 9 1.6018 0.16695 0.2831 213s 10 NA 1.86380 1.1353 213s 11 -0.9031 -0.92183 -0.1765 213s 12 -1.5948 -1.03217 0.6007 213s 13 NA NA 0.1443 213s 14 0.2854 0.85468 0.4826 213s 15 -0.4718 -0.36943 0.3016 213s 16 -0.2268 0.00554 0.0261 213s 17 2.0079 1.69566 -0.8614 213s 18 -0.7434 -0.12659 0.9927 213s 19 -0.5410 -3.26209 -0.4446 213s 20 1.4186 0.25579 -0.3914 213s 21 1.1462 -0.00185 -1.1115 213s 22 -1.7256 0.50679 0.5312 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.6 1.036 26.8 213s 3 45.5 1.570 29.1 213s 4 50.4 4.111 33.0 213s 5 50.6 4.370 34.1 213s 6 52.1 4.616 35.9 213s 7 NA NA NA 213s 8 54.6 3.132 38.7 213s 9 55.7 2.833 38.9 213s 10 NA 3.236 40.2 213s 11 55.9 1.922 38.1 213s 12 52.5 -2.368 33.9 213s 13 NA NA 28.9 213s 14 46.2 -5.955 28.0 213s 15 49.2 -2.631 30.3 213s 16 51.5 -1.306 33.2 213s 17 55.7 0.404 37.7 213s 18 59.4 2.127 40.0 213s 19 58.0 1.362 38.6 213s 20 60.2 1.044 42.0 213s 21 63.9 3.302 46.1 213s 22 71.4 4.393 52.8 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.6 0.571 41.4 43.8 213s 3 45.5 0.656 44.1 46.9 213s 4 50.4 0.431 49.4 51.3 213s 5 50.6 0.510 49.5 51.7 213s 6 52.1 0.521 51.0 53.2 213s 7 NA NA NA NA 213s 8 54.6 0.419 53.7 55.5 213s 9 55.7 0.496 54.6 56.8 213s 10 NA NA NA NA 213s 11 55.9 0.910 54.0 57.9 213s 12 52.5 0.869 50.6 54.4 213s 13 NA NA NA NA 213s 14 46.2 0.694 44.7 47.7 213s 15 49.2 0.487 48.1 50.2 213s 16 51.5 0.396 50.7 52.4 213s 17 55.7 0.445 54.7 56.6 213s 18 59.4 0.386 58.6 60.3 213s 19 58.0 0.548 56.9 59.2 213s 20 60.2 0.528 59.0 61.3 213s 21 63.9 0.515 62.8 65.0 213s 22 71.4 0.786 69.7 73.1 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 1.036 0.892 -0.865 2.937 213s 3 1.570 0.579 0.335 2.805 213s 4 4.111 0.531 2.979 5.243 213s 5 4.370 0.440 3.432 5.308 213s 6 4.616 0.416 3.729 5.502 213s 7 NA NA NA NA 213s 8 3.132 0.344 2.398 3.866 213s 9 2.833 0.533 1.696 3.970 213s 10 3.236 0.580 2.000 4.473 213s 11 1.922 0.959 -0.122 3.966 213s 12 -2.368 0.860 -4.201 -0.534 213s 13 NA NA NA NA 213s 14 -5.955 0.865 -7.799 -4.110 213s 15 -2.631 0.479 -3.652 -1.610 213s 16 -1.306 0.382 -2.120 -0.491 213s 17 0.404 0.487 -0.635 1.443 213s 18 2.127 0.319 1.447 2.806 213s 19 1.362 0.537 0.218 2.506 213s 20 1.044 0.566 -0.162 2.250 213s 21 3.302 0.486 2.265 4.339 213s 22 4.393 0.713 2.874 5.912 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.8 0.321 26.2 27.5 213s 3 29.1 0.334 28.4 29.8 213s 4 33.0 0.353 32.2 33.7 213s 5 34.1 0.253 33.6 34.6 213s 6 35.9 0.261 35.4 36.5 213s 7 NA NA NA NA 213s 8 38.7 0.257 38.1 39.2 213s 9 38.9 0.245 38.4 39.4 213s 10 40.2 0.235 39.7 40.7 213s 11 38.1 0.348 37.3 38.8 213s 12 33.9 0.374 33.1 34.7 213s 13 28.9 0.447 27.9 29.8 213s 14 28.0 0.341 27.3 28.7 213s 15 30.3 0.333 29.6 31.0 213s 16 33.2 0.278 32.6 33.8 213s 17 37.7 0.288 37.1 38.3 213s 18 40.0 0.214 39.6 40.5 213s 19 38.6 0.351 37.9 39.4 213s 20 42.0 0.301 41.4 42.6 213s 21 46.1 0.304 45.5 46.8 213s 22 52.8 0.486 51.7 53.8 213s > model.frame 213s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 213s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 213s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 213s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 213s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 213s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 213s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 213s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 213s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 213s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 213s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 213s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 213s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 213s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 213s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 213s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 213s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 213s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 213s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 213s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 213s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 213s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 213s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 213s trend 213s 1 -11 213s 2 -10 213s 3 -9 213s 4 -8 213s 5 -7 213s 6 -6 213s 7 -5 213s 8 -4 213s 9 -3 213s 10 -2 213s 11 -1 213s 12 0 213s 13 1 213s 14 2 213s 15 3 213s 16 4 213s 17 5 213s 18 6 213s 19 7 213s 20 8 213s 21 9 213s 22 10 213s > Frames of instrumental variables 213s govExp taxes govWage trend capitalLag corpProfLag gnpLag 213s 1 2.4 3.4 2.2 -11 180 NA NA 213s 2 3.9 7.7 2.7 -10 183 12.7 44.9 213s 3 3.2 3.9 2.9 -9 183 12.4 45.6 213s 4 2.8 4.7 2.9 -8 184 16.9 50.1 213s 5 3.5 3.8 3.1 -7 190 18.4 57.2 213s 6 3.3 5.5 3.2 -6 193 19.4 57.1 213s 7 3.3 7.0 3.3 -5 198 20.1 NA 213s 8 4.0 6.7 3.6 -4 203 19.6 64.0 213s 9 4.2 4.2 3.7 -3 208 19.8 64.4 213s 10 4.1 4.0 4.0 -2 211 21.1 64.5 213s 11 5.2 7.7 4.2 -1 216 21.7 67.0 213s 12 5.9 7.5 4.8 0 217 15.6 61.2 213s 13 4.9 8.3 5.3 1 213 11.4 53.4 213s 14 3.7 5.4 5.6 2 207 7.0 44.3 213s 15 4.0 6.8 6.0 3 202 11.2 45.1 213s 16 4.4 7.2 6.1 4 199 12.3 49.7 213s 17 2.9 8.3 7.4 5 198 14.0 54.4 213s 18 4.3 6.7 6.7 6 200 17.6 62.7 213s 19 5.3 7.4 7.7 7 202 17.3 65.0 213s 20 6.6 8.9 7.8 8 200 15.3 60.9 213s 21 7.4 9.6 8.0 9 201 19.0 69.5 213s 22 13.8 11.6 8.5 10 204 21.1 75.7 213s govExp taxes govWage trend capitalLag corpProfLag gnpLag 213s 1 2.4 3.4 2.2 -11 180 NA NA 213s 2 3.9 7.7 2.7 -10 183 12.7 44.9 213s 3 3.2 3.9 2.9 -9 183 12.4 45.6 213s 4 2.8 4.7 2.9 -8 184 16.9 50.1 213s 5 3.5 3.8 3.1 -7 190 18.4 57.2 213s 6 3.3 5.5 3.2 -6 193 19.4 57.1 213s 7 3.3 7.0 3.3 -5 198 20.1 NA 213s 8 4.0 6.7 3.6 -4 203 19.6 64.0 213s 9 4.2 4.2 3.7 -3 208 19.8 64.4 213s 10 4.1 4.0 4.0 -2 211 21.1 64.5 213s 11 5.2 7.7 4.2 -1 216 21.7 67.0 213s 12 5.9 7.5 4.8 0 217 15.6 61.2 213s 13 4.9 8.3 5.3 1 213 11.4 53.4 213s 14 3.7 5.4 5.6 2 207 7.0 44.3 213s 15 4.0 6.8 6.0 3 202 11.2 45.1 213s 16 4.4 7.2 6.1 4 199 12.3 49.7 213s 17 2.9 8.3 7.4 5 198 14.0 54.4 213s 18 4.3 6.7 6.7 6 200 17.6 62.7 213s 19 5.3 7.4 7.7 7 202 17.3 65.0 213s 20 6.6 8.9 7.8 8 200 15.3 60.9 213s 21 7.4 9.6 8.0 9 201 19.0 69.5 213s 22 13.8 11.6 8.5 10 204 21.1 75.7 213s govExp taxes govWage trend capitalLag corpProfLag gnpLag 213s 1 2.4 3.4 2.2 -11 180 NA NA 213s 2 3.9 7.7 2.7 -10 183 12.7 44.9 213s 3 3.2 3.9 2.9 -9 183 12.4 45.6 213s 4 2.8 4.7 2.9 -8 184 16.9 50.1 213s 5 3.5 3.8 3.1 -7 190 18.4 57.2 213s 6 3.3 5.5 3.2 -6 193 19.4 57.1 213s 7 3.3 7.0 3.3 -5 198 20.1 NA 213s 8 4.0 6.7 3.6 -4 203 19.6 64.0 213s 9 4.2 4.2 3.7 -3 208 19.8 64.4 213s 10 4.1 4.0 4.0 -2 211 21.1 64.5 213s 11 5.2 7.7 4.2 -1 216 21.7 67.0 213s 12 5.9 7.5 4.8 0 217 15.6 61.2 213s 13 4.9 8.3 5.3 1 213 11.4 53.4 213s 14 3.7 5.4 5.6 2 207 7.0 44.3 213s 15 4.0 6.8 6.0 3 202 11.2 45.1 213s 16 4.4 7.2 6.1 4 199 12.3 49.7 213s 17 2.9 8.3 7.4 5 198 14.0 54.4 213s 18 4.3 6.7 6.7 6 200 17.6 62.7 213s 19 5.3 7.4 7.7 7 202 17.3 65.0 213s 20 6.6 8.9 7.8 8 200 15.3 60.9 213s 21 7.4 9.6 8.0 9 201 19.0 69.5 213s 22 13.8 11.6 8.5 10 204 21.1 75.7 213s > model.matrix 213s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 213s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 213s [3] "Numeric: lengths (708, 684) differ" 213s > matrix of instrumental variables 213s Consumption_(Intercept) Consumption_govExp Consumption_taxes 213s Consumption_2 1 3.9 7.7 213s Consumption_3 1 3.2 3.9 213s Consumption_4 1 2.8 4.7 213s Consumption_5 1 3.5 3.8 213s Consumption_6 1 3.3 5.5 213s Consumption_8 1 4.0 6.7 213s Consumption_9 1 4.2 4.2 213s Consumption_11 1 5.2 7.7 213s Consumption_12 1 5.9 7.5 213s Consumption_14 1 3.7 5.4 213s Consumption_15 1 4.0 6.8 213s Consumption_16 1 4.4 7.2 213s Consumption_17 1 2.9 8.3 213s Consumption_18 1 4.3 6.7 213s Consumption_19 1 5.3 7.4 213s Consumption_20 1 6.6 8.9 213s Consumption_21 1 7.4 9.6 213s Consumption_22 1 13.8 11.6 213s Investment_2 0 0.0 0.0 213s Investment_3 0 0.0 0.0 213s Investment_4 0 0.0 0.0 213s Investment_5 0 0.0 0.0 213s Investment_6 0 0.0 0.0 213s Investment_8 0 0.0 0.0 213s Investment_9 0 0.0 0.0 213s Investment_10 0 0.0 0.0 213s Investment_11 0 0.0 0.0 213s Investment_12 0 0.0 0.0 213s Investment_14 0 0.0 0.0 213s Investment_15 0 0.0 0.0 213s Investment_16 0 0.0 0.0 213s Investment_17 0 0.0 0.0 213s Investment_18 0 0.0 0.0 213s Investment_19 0 0.0 0.0 213s Investment_20 0 0.0 0.0 213s Investment_21 0 0.0 0.0 213s Investment_22 0 0.0 0.0 213s PrivateWages_2 0 0.0 0.0 213s PrivateWages_3 0 0.0 0.0 213s PrivateWages_4 0 0.0 0.0 213s PrivateWages_5 0 0.0 0.0 213s PrivateWages_6 0 0.0 0.0 213s PrivateWages_8 0 0.0 0.0 213s PrivateWages_9 0 0.0 0.0 213s PrivateWages_10 0 0.0 0.0 213s PrivateWages_11 0 0.0 0.0 213s PrivateWages_12 0 0.0 0.0 213s PrivateWages_13 0 0.0 0.0 213s PrivateWages_14 0 0.0 0.0 213s PrivateWages_15 0 0.0 0.0 213s PrivateWages_16 0 0.0 0.0 213s PrivateWages_17 0 0.0 0.0 213s PrivateWages_18 0 0.0 0.0 213s PrivateWages_19 0 0.0 0.0 213s PrivateWages_20 0 0.0 0.0 213s PrivateWages_21 0 0.0 0.0 213s PrivateWages_22 0 0.0 0.0 213s Consumption_govWage Consumption_trend Consumption_capitalLag 213s Consumption_2 2.7 -10 183 213s Consumption_3 2.9 -9 183 213s Consumption_4 2.9 -8 184 213s Consumption_5 3.1 -7 190 213s Consumption_6 3.2 -6 193 213s Consumption_8 3.6 -4 203 213s Consumption_9 3.7 -3 208 213s Consumption_11 4.2 -1 216 213s Consumption_12 4.8 0 217 213s Consumption_14 5.6 2 207 213s Consumption_15 6.0 3 202 213s Consumption_16 6.1 4 199 213s Consumption_17 7.4 5 198 213s Consumption_18 6.7 6 200 213s Consumption_19 7.7 7 202 213s Consumption_20 7.8 8 200 213s Consumption_21 8.0 9 201 213s Consumption_22 8.5 10 204 213s Investment_2 0.0 0 0 213s Investment_3 0.0 0 0 213s Investment_4 0.0 0 0 213s Investment_5 0.0 0 0 213s Investment_6 0.0 0 0 213s Investment_8 0.0 0 0 213s Investment_9 0.0 0 0 213s Investment_10 0.0 0 0 213s Investment_11 0.0 0 0 213s Investment_12 0.0 0 0 213s Investment_14 0.0 0 0 213s Investment_15 0.0 0 0 213s Investment_16 0.0 0 0 213s Investment_17 0.0 0 0 213s Investment_18 0.0 0 0 213s Investment_19 0.0 0 0 213s Investment_20 0.0 0 0 213s Investment_21 0.0 0 0 213s Investment_22 0.0 0 0 213s PrivateWages_2 0.0 0 0 213s PrivateWages_3 0.0 0 0 213s PrivateWages_4 0.0 0 0 213s PrivateWages_5 0.0 0 0 213s PrivateWages_6 0.0 0 0 213s PrivateWages_8 0.0 0 0 213s PrivateWages_9 0.0 0 0 213s PrivateWages_10 0.0 0 0 213s PrivateWages_11 0.0 0 0 213s PrivateWages_12 0.0 0 0 213s PrivateWages_13 0.0 0 0 213s PrivateWages_14 0.0 0 0 213s PrivateWages_15 0.0 0 0 213s PrivateWages_16 0.0 0 0 213s PrivateWages_17 0.0 0 0 213s PrivateWages_18 0.0 0 0 213s PrivateWages_19 0.0 0 0 213s PrivateWages_20 0.0 0 0 213s PrivateWages_21 0.0 0 0 213s PrivateWages_22 0.0 0 0 213s Consumption_corpProfLag Consumption_gnpLag 213s Consumption_2 12.7 44.9 213s Consumption_3 12.4 45.6 213s Consumption_4 16.9 50.1 213s Consumption_5 18.4 57.2 213s Consumption_6 19.4 57.1 213s Consumption_8 19.6 64.0 213s Consumption_9 19.8 64.4 213s Consumption_11 21.7 67.0 213s Consumption_12 15.6 61.2 213s Consumption_14 7.0 44.3 213s Consumption_15 11.2 45.1 213s Consumption_16 12.3 49.7 213s Consumption_17 14.0 54.4 213s Consumption_18 17.6 62.7 213s Consumption_19 17.3 65.0 213s Consumption_20 15.3 60.9 213s Consumption_21 19.0 69.5 213s Consumption_22 21.1 75.7 213s Investment_2 0.0 0.0 213s Investment_3 0.0 0.0 213s Investment_4 0.0 0.0 213s Investment_5 0.0 0.0 213s Investment_6 0.0 0.0 213s Investment_8 0.0 0.0 213s Investment_9 0.0 0.0 213s Investment_10 0.0 0.0 213s Investment_11 0.0 0.0 213s Investment_12 0.0 0.0 213s Investment_14 0.0 0.0 213s Investment_15 0.0 0.0 213s Investment_16 0.0 0.0 213s Investment_17 0.0 0.0 213s Investment_18 0.0 0.0 213s Investment_19 0.0 0.0 213s Investment_20 0.0 0.0 213s Investment_21 0.0 0.0 213s Investment_22 0.0 0.0 213s PrivateWages_2 0.0 0.0 213s PrivateWages_3 0.0 0.0 213s PrivateWages_4 0.0 0.0 213s PrivateWages_5 0.0 0.0 213s PrivateWages_6 0.0 0.0 213s PrivateWages_8 0.0 0.0 213s PrivateWages_9 0.0 0.0 213s PrivateWages_10 0.0 0.0 213s PrivateWages_11 0.0 0.0 213s PrivateWages_12 0.0 0.0 213s PrivateWages_13 0.0 0.0 213s PrivateWages_14 0.0 0.0 213s PrivateWages_15 0.0 0.0 213s PrivateWages_16 0.0 0.0 213s PrivateWages_17 0.0 0.0 213s PrivateWages_18 0.0 0.0 213s PrivateWages_19 0.0 0.0 213s PrivateWages_20 0.0 0.0 213s PrivateWages_21 0.0 0.0 213s PrivateWages_22 0.0 0.0 213s Investment_(Intercept) Investment_govExp Investment_taxes 213s Consumption_2 0 0.0 0.0 213s Consumption_3 0 0.0 0.0 213s Consumption_4 0 0.0 0.0 213s Consumption_5 0 0.0 0.0 213s Consumption_6 0 0.0 0.0 213s Consumption_8 0 0.0 0.0 213s Consumption_9 0 0.0 0.0 213s Consumption_11 0 0.0 0.0 213s Consumption_12 0 0.0 0.0 213s Consumption_14 0 0.0 0.0 213s Consumption_15 0 0.0 0.0 213s Consumption_16 0 0.0 0.0 213s Consumption_17 0 0.0 0.0 213s Consumption_18 0 0.0 0.0 213s Consumption_19 0 0.0 0.0 213s Consumption_20 0 0.0 0.0 213s Consumption_21 0 0.0 0.0 213s Consumption_22 0 0.0 0.0 213s Investment_2 1 3.9 7.7 213s Investment_3 1 3.2 3.9 213s Investment_4 1 2.8 4.7 213s Investment_5 1 3.5 3.8 213s Investment_6 1 3.3 5.5 213s Investment_8 1 4.0 6.7 213s Investment_9 1 4.2 4.2 213s Investment_10 1 4.1 4.0 213s Investment_11 1 5.2 7.7 213s Investment_12 1 5.9 7.5 213s Investment_14 1 3.7 5.4 213s Investment_15 1 4.0 6.8 213s Investment_16 1 4.4 7.2 213s Investment_17 1 2.9 8.3 213s Investment_18 1 4.3 6.7 213s Investment_19 1 5.3 7.4 213s Investment_20 1 6.6 8.9 213s Investment_21 1 7.4 9.6 213s Investment_22 1 13.8 11.6 213s PrivateWages_2 0 0.0 0.0 213s PrivateWages_3 0 0.0 0.0 213s PrivateWages_4 0 0.0 0.0 213s PrivateWages_5 0 0.0 0.0 213s PrivateWages_6 0 0.0 0.0 213s PrivateWages_8 0 0.0 0.0 213s PrivateWages_9 0 0.0 0.0 213s PrivateWages_10 0 0.0 0.0 213s PrivateWages_11 0 0.0 0.0 213s PrivateWages_12 0 0.0 0.0 213s PrivateWages_13 0 0.0 0.0 213s PrivateWages_14 0 0.0 0.0 213s PrivateWages_15 0 0.0 0.0 213s PrivateWages_16 0 0.0 0.0 213s PrivateWages_17 0 0.0 0.0 213s PrivateWages_18 0 0.0 0.0 213s PrivateWages_19 0 0.0 0.0 213s PrivateWages_20 0 0.0 0.0 213s PrivateWages_21 0 0.0 0.0 213s PrivateWages_22 0 0.0 0.0 213s Investment_govWage Investment_trend Investment_capitalLag 213s Consumption_2 0.0 0 0 213s Consumption_3 0.0 0 0 213s Consumption_4 0.0 0 0 213s Consumption_5 0.0 0 0 213s Consumption_6 0.0 0 0 213s Consumption_8 0.0 0 0 213s Consumption_9 0.0 0 0 213s Consumption_11 0.0 0 0 213s Consumption_12 0.0 0 0 213s Consumption_14 0.0 0 0 213s Consumption_15 0.0 0 0 213s Consumption_16 0.0 0 0 213s Consumption_17 0.0 0 0 213s Consumption_18 0.0 0 0 213s Consumption_19 0.0 0 0 213s Consumption_20 0.0 0 0 213s Consumption_21 0.0 0 0 213s Consumption_22 0.0 0 0 213s Investment_2 2.7 -10 183 213s Investment_3 2.9 -9 183 213s Investment_4 2.9 -8 184 213s Investment_5 3.1 -7 190 213s Investment_6 3.2 -6 193 213s Investment_8 3.6 -4 203 213s Investment_9 3.7 -3 208 213s Investment_10 4.0 -2 211 213s Investment_11 4.2 -1 216 213s Investment_12 4.8 0 217 213s Investment_14 5.6 2 207 213s Investment_15 6.0 3 202 213s Investment_16 6.1 4 199 213s Investment_17 7.4 5 198 213s Investment_18 6.7 6 200 213s Investment_19 7.7 7 202 213s Investment_20 7.8 8 200 213s Investment_21 8.0 9 201 213s Investment_22 8.5 10 204 213s PrivateWages_2 0.0 0 0 213s PrivateWages_3 0.0 0 0 213s PrivateWages_4 0.0 0 0 213s PrivateWages_5 0.0 0 0 213s PrivateWages_6 0.0 0 0 213s PrivateWages_8 0.0 0 0 213s PrivateWages_9 0.0 0 0 213s PrivateWages_10 0.0 0 0 213s PrivateWages_11 0.0 0 0 213s PrivateWages_12 0.0 0 0 213s PrivateWages_13 0.0 0 0 213s PrivateWages_14 0.0 0 0 213s PrivateWages_15 0.0 0 0 213s PrivateWages_16 0.0 0 0 213s PrivateWages_17 0.0 0 0 213s PrivateWages_18 0.0 0 0 213s PrivateWages_19 0.0 0 0 213s PrivateWages_20 0.0 0 0 213s PrivateWages_21 0.0 0 0 213s PrivateWages_22 0.0 0 0 213s Investment_corpProfLag Investment_gnpLag 213s Consumption_2 0.0 0.0 213s Consumption_3 0.0 0.0 213s Consumption_4 0.0 0.0 213s Consumption_5 0.0 0.0 213s Consumption_6 0.0 0.0 213s Consumption_8 0.0 0.0 213s Consumption_9 0.0 0.0 213s Consumption_11 0.0 0.0 213s Consumption_12 0.0 0.0 213s Consumption_14 0.0 0.0 213s Consumption_15 0.0 0.0 213s Consumption_16 0.0 0.0 213s Consumption_17 0.0 0.0 213s Consumption_18 0.0 0.0 213s Consumption_19 0.0 0.0 213s Consumption_20 0.0 0.0 213s Consumption_21 0.0 0.0 213s Consumption_22 0.0 0.0 213s Investment_2 12.7 44.9 213s Investment_3 12.4 45.6 213s Investment_4 16.9 50.1 213s Investment_5 18.4 57.2 213s Investment_6 19.4 57.1 213s Investment_8 19.6 64.0 213s Investment_9 19.8 64.4 213s Investment_10 21.1 64.5 213s Investment_11 21.7 67.0 213s Investment_12 15.6 61.2 213s Investment_14 7.0 44.3 213s Investment_15 11.2 45.1 213s Investment_16 12.3 49.7 213s Investment_17 14.0 54.4 213s Investment_18 17.6 62.7 213s Investment_19 17.3 65.0 213s Investment_20 15.3 60.9 213s Investment_21 19.0 69.5 213s Investment_22 21.1 75.7 213s PrivateWages_2 0.0 0.0 213s PrivateWages_3 0.0 0.0 213s PrivateWages_4 0.0 0.0 213s PrivateWages_5 0.0 0.0 213s PrivateWages_6 0.0 0.0 213s PrivateWages_8 0.0 0.0 213s PrivateWages_9 0.0 0.0 213s PrivateWages_10 0.0 0.0 213s PrivateWages_11 0.0 0.0 213s PrivateWages_12 0.0 0.0 213s PrivateWages_13 0.0 0.0 213s PrivateWages_14 0.0 0.0 213s PrivateWages_15 0.0 0.0 213s PrivateWages_16 0.0 0.0 213s PrivateWages_17 0.0 0.0 213s PrivateWages_18 0.0 0.0 213s PrivateWages_19 0.0 0.0 213s PrivateWages_20 0.0 0.0 213s PrivateWages_21 0.0 0.0 213s PrivateWages_22 0.0 0.0 213s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 213s Consumption_2 0 0.0 0.0 213s Consumption_3 0 0.0 0.0 213s Consumption_4 0 0.0 0.0 213s Consumption_5 0 0.0 0.0 213s Consumption_6 0 0.0 0.0 213s Consumption_8 0 0.0 0.0 213s Consumption_9 0 0.0 0.0 213s Consumption_11 0 0.0 0.0 213s Consumption_12 0 0.0 0.0 213s Consumption_14 0 0.0 0.0 213s Consumption_15 0 0.0 0.0 213s Consumption_16 0 0.0 0.0 213s Consumption_17 0 0.0 0.0 213s Consumption_18 0 0.0 0.0 213s Consumption_19 0 0.0 0.0 213s Consumption_20 0 0.0 0.0 213s Consumption_21 0 0.0 0.0 213s Consumption_22 0 0.0 0.0 213s Investment_2 0 0.0 0.0 213s Investment_3 0 0.0 0.0 213s Investment_4 0 0.0 0.0 213s Investment_5 0 0.0 0.0 213s Investment_6 0 0.0 0.0 213s Investment_8 0 0.0 0.0 213s Investment_9 0 0.0 0.0 213s Investment_10 0 0.0 0.0 213s Investment_11 0 0.0 0.0 213s Investment_12 0 0.0 0.0 213s Investment_14 0 0.0 0.0 213s Investment_15 0 0.0 0.0 213s Investment_16 0 0.0 0.0 213s Investment_17 0 0.0 0.0 213s Investment_18 0 0.0 0.0 213s Investment_19 0 0.0 0.0 213s Investment_20 0 0.0 0.0 213s Investment_21 0 0.0 0.0 213s Investment_22 0 0.0 0.0 213s PrivateWages_2 1 3.9 7.7 213s PrivateWages_3 1 3.2 3.9 213s PrivateWages_4 1 2.8 4.7 213s PrivateWages_5 1 3.5 3.8 213s PrivateWages_6 1 3.3 5.5 213s PrivateWages_8 1 4.0 6.7 213s PrivateWages_9 1 4.2 4.2 213s PrivateWages_10 1 4.1 4.0 213s PrivateWages_11 1 5.2 7.7 213s PrivateWages_12 1 5.9 7.5 213s PrivateWages_13 1 4.9 8.3 213s PrivateWages_14 1 3.7 5.4 213s PrivateWages_15 1 4.0 6.8 213s PrivateWages_16 1 4.4 7.2 213s PrivateWages_17 1 2.9 8.3 213s PrivateWages_18 1 4.3 6.7 213s PrivateWages_19 1 5.3 7.4 213s PrivateWages_20 1 6.6 8.9 213s PrivateWages_21 1 7.4 9.6 213s PrivateWages_22 1 13.8 11.6 213s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 213s Consumption_2 0.0 0 0 213s Consumption_3 0.0 0 0 213s Consumption_4 0.0 0 0 213s Consumption_5 0.0 0 0 213s Consumption_6 0.0 0 0 213s Consumption_8 0.0 0 0 213s Consumption_9 0.0 0 0 213s Consumption_11 0.0 0 0 213s Consumption_12 0.0 0 0 213s Consumption_14 0.0 0 0 213s Consumption_15 0.0 0 0 213s Consumption_16 0.0 0 0 213s Consumption_17 0.0 0 0 213s Consumption_18 0.0 0 0 213s Consumption_19 0.0 0 0 213s Consumption_20 0.0 0 0 213s Consumption_21 0.0 0 0 213s Consumption_22 0.0 0 0 213s Investment_2 0.0 0 0 213s Investment_3 0.0 0 0 213s Investment_4 0.0 0 0 213s Investment_5 0.0 0 0 213s Investment_6 0.0 0 0 213s Investment_8 0.0 0 0 213s Investment_9 0.0 0 0 213s Investment_10 0.0 0 0 213s Investment_11 0.0 0 0 213s Investment_12 0.0 0 0 213s Investment_14 0.0 0 0 213s Investment_15 0.0 0 0 213s Investment_16 0.0 0 0 213s Investment_17 0.0 0 0 213s Investment_18 0.0 0 0 213s Investment_19 0.0 0 0 213s Investment_20 0.0 0 0 213s Investment_21 0.0 0 0 213s Investment_22 0.0 0 0 213s PrivateWages_2 2.7 -10 183 213s PrivateWages_3 2.9 -9 183 213s PrivateWages_4 2.9 -8 184 213s PrivateWages_5 3.1 -7 190 213s PrivateWages_6 3.2 -6 193 213s PrivateWages_8 3.6 -4 203 213s PrivateWages_9 3.7 -3 208 213s PrivateWages_10 4.0 -2 211 213s PrivateWages_11 4.2 -1 216 213s PrivateWages_12 4.8 0 217 213s PrivateWages_13 5.3 1 213 213s PrivateWages_14 5.6 2 207 213s PrivateWages_15 6.0 3 202 213s PrivateWages_16 6.1 4 199 213s PrivateWages_17 7.4 5 198 213s PrivateWages_18 6.7 6 200 213s PrivateWages_19 7.7 7 202 213s PrivateWages_20 7.8 8 200 213s PrivateWages_21 8.0 9 201 213s PrivateWages_22 8.5 10 204 213s PrivateWages_corpProfLag PrivateWages_gnpLag 213s Consumption_2 0.0 0.0 213s Consumption_3 0.0 0.0 213s Consumption_4 0.0 0.0 213s Consumption_5 0.0 0.0 213s Consumption_6 0.0 0.0 213s Consumption_8 0.0 0.0 213s Consumption_9 0.0 0.0 213s Consumption_11 0.0 0.0 213s Consumption_12 0.0 0.0 213s Consumption_14 0.0 0.0 213s Consumption_15 0.0 0.0 213s Consumption_16 0.0 0.0 213s Consumption_17 0.0 0.0 213s Consumption_18 0.0 0.0 213s Consumption_19 0.0 0.0 213s Consumption_20 0.0 0.0 213s Consumption_21 0.0 0.0 213s Consumption_22 0.0 0.0 213s Investment_2 0.0 0.0 213s Investment_3 0.0 0.0 213s Investment_4 0.0 0.0 213s Investment_5 0.0 0.0 213s Investment_6 0.0 0.0 213s Investment_8 0.0 0.0 213s Investment_9 0.0 0.0 213s Investment_10 0.0 0.0 213s Investment_11 0.0 0.0 213s Investment_12 0.0 0.0 213s Investment_14 0.0 0.0 213s Investment_15 0.0 0.0 213s Investment_16 0.0 0.0 213s Investment_17 0.0 0.0 213s Investment_18 0.0 0.0 213s Investment_19 0.0 0.0 213s Investment_20 0.0 0.0 213s Investment_21 0.0 0.0 213s Investment_22 0.0 0.0 213s PrivateWages_2 12.7 44.9 213s PrivateWages_3 12.4 45.6 213s PrivateWages_4 16.9 50.1 213s PrivateWages_5 18.4 57.2 213s PrivateWages_6 19.4 57.1 213s PrivateWages_8 19.6 64.0 213s PrivateWages_9 19.8 64.4 213s PrivateWages_10 21.1 64.5 213s PrivateWages_11 21.7 67.0 213s PrivateWages_12 15.6 61.2 213s PrivateWages_13 11.4 53.4 213s PrivateWages_14 7.0 44.3 213s PrivateWages_15 11.2 45.1 213s PrivateWages_16 12.3 49.7 213s PrivateWages_17 14.0 54.4 213s PrivateWages_18 17.6 62.7 213s PrivateWages_19 17.3 65.0 213s PrivateWages_20 15.3 60.9 213s PrivateWages_21 19.0 69.5 213s PrivateWages_22 21.1 75.7 213s > matrix of fitted regressors 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 1 14.0 213s Consumption_3 1 16.7 213s Consumption_4 1 18.5 213s Consumption_5 1 20.3 213s Consumption_6 1 19.0 213s Consumption_8 1 17.6 213s Consumption_9 1 18.9 213s Consumption_11 1 16.7 213s Consumption_12 1 13.4 213s Consumption_14 1 10.0 213s Consumption_15 1 12.5 213s Consumption_16 1 14.5 213s Consumption_17 1 14.9 213s Consumption_18 1 19.4 213s Consumption_19 1 19.1 213s Consumption_20 1 17.7 213s Consumption_21 1 20.4 213s Consumption_22 1 22.7 213s Investment_2 0 0.0 213s Investment_3 0 0.0 213s Investment_4 0 0.0 213s Investment_5 0 0.0 213s Investment_6 0 0.0 213s Investment_8 0 0.0 213s Investment_9 0 0.0 213s Investment_10 0 0.0 213s Investment_11 0 0.0 213s Investment_12 0 0.0 213s Investment_14 0 0.0 213s Investment_15 0 0.0 213s Investment_16 0 0.0 213s Investment_17 0 0.0 213s Investment_18 0 0.0 213s Investment_19 0 0.0 213s Investment_20 0 0.0 213s Investment_21 0 0.0 213s Investment_22 0 0.0 213s PrivateWages_2 0 0.0 213s PrivateWages_3 0 0.0 213s PrivateWages_4 0 0.0 213s PrivateWages_5 0 0.0 213s PrivateWages_6 0 0.0 213s PrivateWages_8 0 0.0 213s PrivateWages_9 0 0.0 213s PrivateWages_10 0 0.0 213s PrivateWages_11 0 0.0 213s PrivateWages_12 0 0.0 213s PrivateWages_13 0 0.0 213s PrivateWages_14 0 0.0 213s PrivateWages_15 0 0.0 213s PrivateWages_16 0 0.0 213s PrivateWages_17 0 0.0 213s PrivateWages_18 0 0.0 213s PrivateWages_19 0 0.0 213s PrivateWages_20 0 0.0 213s PrivateWages_21 0 0.0 213s PrivateWages_22 0 0.0 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 12.7 29.8 213s Consumption_3 12.4 31.8 213s Consumption_4 16.9 35.3 213s Consumption_5 18.4 38.6 213s Consumption_6 19.4 38.5 213s Consumption_8 19.6 40.0 213s Consumption_9 19.8 41.8 213s Consumption_11 21.7 43.1 213s Consumption_12 15.6 39.7 213s Consumption_14 7.0 33.3 213s Consumption_15 11.2 37.3 213s Consumption_16 12.3 40.1 213s Consumption_17 14.0 41.8 213s Consumption_18 17.6 47.6 213s Consumption_19 17.3 49.2 213s Consumption_20 15.3 48.6 213s Consumption_21 19.0 53.4 213s Consumption_22 21.1 60.8 213s Investment_2 0.0 0.0 213s Investment_3 0.0 0.0 213s Investment_4 0.0 0.0 213s Investment_5 0.0 0.0 213s Investment_6 0.0 0.0 213s Investment_8 0.0 0.0 213s Investment_9 0.0 0.0 213s Investment_10 0.0 0.0 213s Investment_11 0.0 0.0 213s Investment_12 0.0 0.0 213s Investment_14 0.0 0.0 213s Investment_15 0.0 0.0 213s Investment_16 0.0 0.0 213s Investment_17 0.0 0.0 213s Investment_18 0.0 0.0 213s Investment_19 0.0 0.0 213s Investment_20 0.0 0.0 213s Investment_21 0.0 0.0 213s Investment_22 0.0 0.0 213s PrivateWages_2 0.0 0.0 213s PrivateWages_3 0.0 0.0 213s PrivateWages_4 0.0 0.0 213s PrivateWages_5 0.0 0.0 213s PrivateWages_6 0.0 0.0 213s PrivateWages_8 0.0 0.0 213s PrivateWages_9 0.0 0.0 213s PrivateWages_10 0.0 0.0 213s PrivateWages_11 0.0 0.0 213s PrivateWages_12 0.0 0.0 213s PrivateWages_13 0.0 0.0 213s PrivateWages_14 0.0 0.0 213s PrivateWages_15 0.0 0.0 213s PrivateWages_16 0.0 0.0 213s PrivateWages_17 0.0 0.0 213s PrivateWages_18 0.0 0.0 213s PrivateWages_19 0.0 0.0 213s PrivateWages_20 0.0 0.0 213s PrivateWages_21 0.0 0.0 213s PrivateWages_22 0.0 0.0 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0 0.00 213s Consumption_3 0 0.00 213s Consumption_4 0 0.00 213s Consumption_5 0 0.00 213s Consumption_6 0 0.00 213s Consumption_8 0 0.00 213s Consumption_9 0 0.00 213s Consumption_11 0 0.00 213s Consumption_12 0 0.00 213s Consumption_14 0 0.00 213s Consumption_15 0 0.00 213s Consumption_16 0 0.00 213s Consumption_17 0 0.00 213s Consumption_18 0 0.00 213s Consumption_19 0 0.00 213s Consumption_20 0 0.00 213s Consumption_21 0 0.00 213s Consumption_22 0 0.00 213s Investment_2 1 13.41 213s Investment_3 1 16.69 213s Investment_4 1 18.79 213s Investment_5 1 20.65 213s Investment_6 1 19.26 213s Investment_8 1 17.53 213s Investment_9 1 19.53 213s Investment_10 1 20.27 213s Investment_11 1 17.19 213s Investment_12 1 13.52 213s Investment_14 1 9.99 213s Investment_15 1 12.86 213s Investment_16 1 14.33 213s Investment_17 1 14.97 213s Investment_18 1 19.37 213s Investment_19 1 19.36 213s Investment_20 1 17.47 213s Investment_21 1 20.12 213s Investment_22 1 22.78 213s PrivateWages_2 0 0.00 213s PrivateWages_3 0 0.00 213s PrivateWages_4 0 0.00 213s PrivateWages_5 0 0.00 213s PrivateWages_6 0 0.00 213s PrivateWages_8 0 0.00 213s PrivateWages_9 0 0.00 213s PrivateWages_10 0 0.00 213s PrivateWages_11 0 0.00 213s PrivateWages_12 0 0.00 213s PrivateWages_13 0 0.00 213s PrivateWages_14 0 0.00 213s PrivateWages_15 0 0.00 213s PrivateWages_16 0 0.00 213s PrivateWages_17 0 0.00 213s PrivateWages_18 0 0.00 213s PrivateWages_19 0 0.00 213s PrivateWages_20 0 0.00 213s PrivateWages_21 0 0.00 213s PrivateWages_22 0 0.00 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.0 0 213s Consumption_3 0.0 0 213s Consumption_4 0.0 0 213s Consumption_5 0.0 0 213s Consumption_6 0.0 0 213s Consumption_8 0.0 0 213s Consumption_9 0.0 0 213s Consumption_11 0.0 0 213s Consumption_12 0.0 0 213s Consumption_14 0.0 0 213s Consumption_15 0.0 0 213s Consumption_16 0.0 0 213s Consumption_17 0.0 0 213s Consumption_18 0.0 0 213s Consumption_19 0.0 0 213s Consumption_20 0.0 0 213s Consumption_21 0.0 0 213s Consumption_22 0.0 0 213s Investment_2 12.7 183 213s Investment_3 12.4 183 213s Investment_4 16.9 184 213s Investment_5 18.4 190 213s Investment_6 19.4 193 213s Investment_8 19.6 203 213s Investment_9 19.8 208 213s Investment_10 21.1 211 213s Investment_11 21.7 216 213s Investment_12 15.6 217 213s Investment_14 7.0 207 213s Investment_15 11.2 202 213s Investment_16 12.3 199 213s Investment_17 14.0 198 213s Investment_18 17.6 200 213s Investment_19 17.3 202 213s Investment_20 15.3 200 213s Investment_21 19.0 201 213s Investment_22 21.1 204 213s PrivateWages_2 0.0 0 213s PrivateWages_3 0.0 0 213s PrivateWages_4 0.0 0 213s PrivateWages_5 0.0 0 213s PrivateWages_6 0.0 0 213s PrivateWages_8 0.0 0 213s PrivateWages_9 0.0 0 213s PrivateWages_10 0.0 0 213s PrivateWages_11 0.0 0 213s PrivateWages_12 0.0 0 213s PrivateWages_13 0.0 0 213s PrivateWages_14 0.0 0 213s PrivateWages_15 0.0 0 213s PrivateWages_16 0.0 0 213s PrivateWages_17 0.0 0 213s PrivateWages_18 0.0 0 213s PrivateWages_19 0.0 0 213s PrivateWages_20 0.0 0 213s PrivateWages_21 0.0 0 213s PrivateWages_22 0.0 0 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 0 0.0 0.0 213s Consumption_3 0 0.0 0.0 213s Consumption_4 0 0.0 0.0 213s Consumption_5 0 0.0 0.0 213s Consumption_6 0 0.0 0.0 213s Consumption_8 0 0.0 0.0 213s Consumption_9 0 0.0 0.0 213s Consumption_11 0 0.0 0.0 213s Consumption_12 0 0.0 0.0 213s Consumption_14 0 0.0 0.0 213s Consumption_15 0 0.0 0.0 213s Consumption_16 0 0.0 0.0 213s Consumption_17 0 0.0 0.0 213s Consumption_18 0 0.0 0.0 213s Consumption_19 0 0.0 0.0 213s Consumption_20 0 0.0 0.0 213s Consumption_21 0 0.0 0.0 213s Consumption_22 0 0.0 0.0 213s Investment_2 0 0.0 0.0 213s Investment_3 0 0.0 0.0 213s Investment_4 0 0.0 0.0 213s Investment_5 0 0.0 0.0 213s Investment_6 0 0.0 0.0 213s Investment_8 0 0.0 0.0 213s Investment_9 0 0.0 0.0 213s Investment_10 0 0.0 0.0 213s Investment_11 0 0.0 0.0 213s Investment_12 0 0.0 0.0 213s Investment_14 0 0.0 0.0 213s Investment_15 0 0.0 0.0 213s Investment_16 0 0.0 0.0 213s Investment_17 0 0.0 0.0 213s Investment_18 0 0.0 0.0 213s Investment_19 0 0.0 0.0 213s Investment_20 0 0.0 0.0 213s Investment_21 0 0.0 0.0 213s Investment_22 0 0.0 0.0 213s PrivateWages_2 1 47.1 44.9 213s PrivateWages_3 1 49.6 45.6 213s PrivateWages_4 1 56.5 50.1 213s PrivateWages_5 1 60.7 57.2 213s PrivateWages_6 1 60.6 57.1 213s PrivateWages_8 1 60.0 64.0 213s PrivateWages_9 1 62.3 64.4 213s PrivateWages_10 1 64.6 64.5 213s PrivateWages_11 1 63.7 67.0 213s PrivateWages_12 1 54.8 61.2 213s PrivateWages_13 1 47.0 53.4 213s PrivateWages_14 1 42.1 44.3 213s PrivateWages_15 1 51.2 45.1 213s PrivateWages_16 1 55.3 49.7 213s PrivateWages_17 1 57.4 54.4 213s PrivateWages_18 1 67.2 62.7 213s PrivateWages_19 1 68.5 65.0 213s PrivateWages_20 1 66.8 60.9 213s PrivateWages_21 1 74.9 69.5 213s PrivateWages_22 1 86.9 75.7 213s PrivateWages_trend 213s Consumption_2 0 213s Consumption_3 0 213s Consumption_4 0 213s Consumption_5 0 213s Consumption_6 0 213s Consumption_8 0 213s Consumption_9 0 213s Consumption_11 0 213s Consumption_12 0 213s Consumption_14 0 213s Consumption_15 0 213s Consumption_16 0 213s Consumption_17 0 213s Consumption_18 0 213s Consumption_19 0 213s Consumption_20 0 213s Consumption_21 0 213s Consumption_22 0 213s Investment_2 0 213s Investment_3 0 213s Investment_4 0 213s Investment_5 0 213s Investment_6 0 213s Investment_8 0 213s Investment_9 0 213s Investment_10 0 213s Investment_11 0 213s Investment_12 0 213s Investment_14 0 213s Investment_15 0 213s Investment_16 0 213s Investment_17 0 213s Investment_18 0 213s Investment_19 0 213s Investment_20 0 213s Investment_21 0 213s Investment_22 0 213s PrivateWages_2 -10 213s PrivateWages_3 -9 213s PrivateWages_4 -8 213s PrivateWages_5 -7 213s PrivateWages_6 -6 213s PrivateWages_8 -4 213s PrivateWages_9 -3 213s PrivateWages_10 -2 213s PrivateWages_11 -1 213s PrivateWages_12 0 213s PrivateWages_13 1 213s PrivateWages_14 2 213s PrivateWages_15 3 213s PrivateWages_16 4 213s PrivateWages_17 5 213s PrivateWages_18 6 213s PrivateWages_19 7 213s PrivateWages_20 8 213s PrivateWages_21 9 213s PrivateWages_22 10 213s > nobs 213s [1] 57 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 46 213s 2 45 1 1.37 0.25 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 46 213s 2 45 1 1.77 0.19 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 46 213s 2 45 1 1.77 0.18 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 47 213s 2 45 2 0.69 0.51 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 47 213s 2 45 2 0.89 0.42 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 47 213s 2 45 2 1.78 0.41 213s > logLik 213s 'log Lik.' -70.6 (df=13) 213s 'log Lik.' -78.7 (df=13) 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -1.891 -26.49 213s Consumption_3 -0.190 -3.16 213s Consumption_4 0.294 5.45 213s Consumption_5 -1.285 -26.05 213s Consumption_6 0.431 8.19 213s Consumption_8 2.670 47.11 213s Consumption_9 2.363 44.77 213s Consumption_11 -1.642 -27.49 213s Consumption_12 -1.735 -23.21 213s Consumption_14 0.834 8.35 213s Consumption_15 -1.061 -13.27 213s Consumption_16 -0.885 -12.82 213s Consumption_17 3.801 56.68 213s Consumption_18 -0.502 -9.76 213s Consumption_19 -3.000 -57.33 213s Consumption_20 2.012 35.52 213s Consumption_21 0.746 15.21 213s Consumption_22 -0.957 -21.70 213s Investment_2 0.000 0.00 213s Investment_3 0.000 0.00 213s Investment_4 0.000 0.00 213s Investment_5 0.000 0.00 213s Investment_6 0.000 0.00 213s Investment_8 0.000 0.00 213s Investment_9 0.000 0.00 213s Investment_10 0.000 0.00 213s Investment_11 0.000 0.00 213s Investment_12 0.000 0.00 213s Investment_14 0.000 0.00 213s Investment_15 0.000 0.00 213s Investment_16 0.000 0.00 213s Investment_17 0.000 0.00 213s Investment_18 0.000 0.00 213s Investment_19 0.000 0.00 213s Investment_20 0.000 0.00 213s Investment_21 0.000 0.00 213s Investment_22 0.000 0.00 213s PrivateWages_2 0.000 0.00 213s PrivateWages_3 0.000 0.00 213s PrivateWages_4 0.000 0.00 213s PrivateWages_5 0.000 0.00 213s PrivateWages_6 0.000 0.00 213s PrivateWages_8 0.000 0.00 213s PrivateWages_9 0.000 0.00 213s PrivateWages_10 0.000 0.00 213s PrivateWages_11 0.000 0.00 213s PrivateWages_12 0.000 0.00 213s PrivateWages_13 0.000 0.00 213s PrivateWages_14 0.000 0.00 213s PrivateWages_15 0.000 0.00 213s PrivateWages_16 0.000 0.00 213s PrivateWages_17 0.000 0.00 213s PrivateWages_18 0.000 0.00 213s PrivateWages_19 0.000 0.00 213s PrivateWages_20 0.000 0.00 213s PrivateWages_21 0.000 0.00 213s PrivateWages_22 0.000 0.00 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -24.01 -56.38 213s Consumption_3 -2.35 -6.04 213s Consumption_4 4.96 10.35 213s Consumption_5 -23.65 -49.61 213s Consumption_6 8.35 16.60 213s Consumption_8 52.33 106.81 213s Consumption_9 46.80 98.74 213s Consumption_11 -35.64 -70.78 213s Consumption_12 -27.07 -68.81 213s Consumption_14 5.83 27.78 213s Consumption_15 -11.88 -39.61 213s Consumption_16 -10.89 -35.54 213s Consumption_17 53.21 158.79 213s Consumption_18 -8.84 -23.92 213s Consumption_19 -51.90 -147.70 213s Consumption_20 30.78 97.67 213s Consumption_21 14.17 39.83 213s Consumption_22 -20.20 -58.19 213s Investment_2 0.00 0.00 213s Investment_3 0.00 0.00 213s Investment_4 0.00 0.00 213s Investment_5 0.00 0.00 213s Investment_6 0.00 0.00 213s Investment_8 0.00 0.00 213s Investment_9 0.00 0.00 213s Investment_10 0.00 0.00 213s Investment_11 0.00 0.00 213s Investment_12 0.00 0.00 213s Investment_14 0.00 0.00 213s Investment_15 0.00 0.00 213s Investment_16 0.00 0.00 213s Investment_17 0.00 0.00 213s Investment_18 0.00 0.00 213s Investment_19 0.00 0.00 213s Investment_20 0.00 0.00 213s Investment_21 0.00 0.00 213s Investment_22 0.00 0.00 213s PrivateWages_2 0.00 0.00 213s PrivateWages_3 0.00 0.00 213s PrivateWages_4 0.00 0.00 213s PrivateWages_5 0.00 0.00 213s PrivateWages_6 0.00 0.00 213s PrivateWages_8 0.00 0.00 213s PrivateWages_9 0.00 0.00 213s PrivateWages_10 0.00 0.00 213s PrivateWages_11 0.00 0.00 213s PrivateWages_12 0.00 0.00 213s PrivateWages_13 0.00 0.00 213s PrivateWages_14 0.00 0.00 213s PrivateWages_15 0.00 0.00 213s PrivateWages_16 0.00 0.00 213s PrivateWages_17 0.00 0.00 213s PrivateWages_18 0.00 0.00 213s PrivateWages_19 0.00 0.00 213s PrivateWages_20 0.00 0.00 213s PrivateWages_21 0.00 0.00 213s PrivateWages_22 0.00 0.00 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0.000 0.000 213s Consumption_3 0.000 0.000 213s Consumption_4 0.000 0.000 213s Consumption_5 0.000 0.000 213s Consumption_6 0.000 0.000 213s Consumption_8 0.000 0.000 213s Consumption_9 0.000 0.000 213s Consumption_11 0.000 0.000 213s Consumption_12 0.000 0.000 213s Consumption_14 0.000 0.000 213s Consumption_15 0.000 0.000 213s Consumption_16 0.000 0.000 213s Consumption_17 0.000 0.000 213s Consumption_18 0.000 0.000 213s Consumption_19 0.000 0.000 213s Consumption_20 0.000 0.000 213s Consumption_21 0.000 0.000 213s Consumption_22 0.000 0.000 213s Investment_2 -1.389 -18.632 213s Investment_3 0.361 6.028 213s Investment_4 1.031 19.362 213s Investment_5 -1.558 -32.177 213s Investment_6 0.610 11.759 213s Investment_8 1.410 24.716 213s Investment_9 0.404 7.885 213s Investment_10 2.080 42.149 213s Investment_11 -1.162 -19.982 213s Investment_12 -1.352 -18.282 213s Investment_14 1.037 10.359 213s Investment_15 -0.454 -5.832 213s Investment_16 -0.044 -0.631 213s Investment_17 2.093 31.318 213s Investment_18 -0.438 -8.488 213s Investment_19 -3.873 -74.977 213s Investment_20 0.486 8.486 213s Investment_21 0.145 2.925 213s Investment_22 0.615 14.015 213s PrivateWages_2 0.000 0.000 213s PrivateWages_3 0.000 0.000 213s PrivateWages_4 0.000 0.000 213s PrivateWages_5 0.000 0.000 213s PrivateWages_6 0.000 0.000 213s PrivateWages_8 0.000 0.000 213s PrivateWages_9 0.000 0.000 213s PrivateWages_10 0.000 0.000 213s PrivateWages_11 0.000 0.000 213s PrivateWages_12 0.000 0.000 213s PrivateWages_13 0.000 0.000 213s PrivateWages_14 0.000 0.000 213s PrivateWages_15 0.000 0.000 213s PrivateWages_16 0.000 0.000 213s PrivateWages_17 0.000 0.000 213s PrivateWages_18 0.000 0.000 213s PrivateWages_19 0.000 0.000 213s PrivateWages_20 0.000 0.000 213s PrivateWages_21 0.000 0.000 213s PrivateWages_22 0.000 0.000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 0.000 0.00 213s Consumption_3 0.000 0.00 213s Consumption_4 0.000 0.00 213s Consumption_5 0.000 0.00 213s Consumption_6 0.000 0.00 213s Consumption_8 0.000 0.00 213s Consumption_9 0.000 0.00 213s Consumption_11 0.000 0.00 213s Consumption_12 0.000 0.00 213s Consumption_14 0.000 0.00 213s Consumption_15 0.000 0.00 213s Consumption_16 0.000 0.00 213s Consumption_17 0.000 0.00 213s Consumption_18 0.000 0.00 213s Consumption_19 0.000 0.00 213s Consumption_20 0.000 0.00 213s Consumption_21 0.000 0.00 213s Consumption_22 0.000 0.00 213s Investment_2 -17.639 -253.89 213s Investment_3 4.479 65.95 213s Investment_4 17.417 190.14 213s Investment_5 -28.673 -295.61 213s Investment_6 11.843 117.63 213s Investment_8 27.629 286.73 213s Investment_9 7.995 83.82 213s Investment_10 43.878 437.95 213s Investment_11 -25.218 -250.67 213s Investment_12 -21.091 -292.97 213s Investment_14 7.256 214.68 213s Investment_15 -5.080 -91.62 213s Investment_16 -0.541 -8.76 213s Investment_17 29.296 413.70 213s Investment_18 -7.713 -87.56 213s Investment_19 -67.010 -781.66 213s Investment_20 7.430 97.07 213s Investment_21 2.762 29.24 213s Investment_22 12.981 125.81 213s PrivateWages_2 0.000 0.00 213s PrivateWages_3 0.000 0.00 213s PrivateWages_4 0.000 0.00 213s PrivateWages_5 0.000 0.00 213s PrivateWages_6 0.000 0.00 213s PrivateWages_8 0.000 0.00 213s PrivateWages_9 0.000 0.00 213s PrivateWages_10 0.000 0.00 213s PrivateWages_11 0.000 0.00 213s PrivateWages_12 0.000 0.00 213s PrivateWages_13 0.000 0.00 213s PrivateWages_14 0.000 0.00 213s PrivateWages_15 0.000 0.00 213s PrivateWages_16 0.000 0.00 213s PrivateWages_17 0.000 0.00 213s PrivateWages_18 0.000 0.00 213s PrivateWages_19 0.000 0.00 213s PrivateWages_20 0.000 0.00 213s PrivateWages_21 0.000 0.00 213s PrivateWages_22 0.000 0.00 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 0.0000 0.00 0.00 213s Consumption_3 0.0000 0.00 0.00 213s Consumption_4 0.0000 0.00 0.00 213s Consumption_5 0.0000 0.00 0.00 213s Consumption_6 0.0000 0.00 0.00 213s Consumption_8 0.0000 0.00 0.00 213s Consumption_9 0.0000 0.00 0.00 213s Consumption_11 0.0000 0.00 0.00 213s Consumption_12 0.0000 0.00 0.00 213s Consumption_14 0.0000 0.00 0.00 213s Consumption_15 0.0000 0.00 0.00 213s Consumption_16 0.0000 0.00 0.00 213s Consumption_17 0.0000 0.00 0.00 213s Consumption_18 0.0000 0.00 0.00 213s Consumption_19 0.0000 0.00 0.00 213s Consumption_20 0.0000 0.00 0.00 213s Consumption_21 0.0000 0.00 0.00 213s Consumption_22 0.0000 0.00 0.00 213s Investment_2 0.0000 0.00 0.00 213s Investment_3 0.0000 0.00 0.00 213s Investment_4 0.0000 0.00 0.00 213s Investment_5 0.0000 0.00 0.00 213s Investment_6 0.0000 0.00 0.00 213s Investment_8 0.0000 0.00 0.00 213s Investment_9 0.0000 0.00 0.00 213s Investment_10 0.0000 0.00 0.00 213s Investment_11 0.0000 0.00 0.00 213s Investment_12 0.0000 0.00 0.00 213s Investment_14 0.0000 0.00 0.00 213s Investment_15 0.0000 0.00 0.00 213s Investment_16 0.0000 0.00 0.00 213s Investment_17 0.0000 0.00 0.00 213s Investment_18 0.0000 0.00 0.00 213s Investment_19 0.0000 0.00 0.00 213s Investment_20 0.0000 0.00 0.00 213s Investment_21 0.0000 0.00 0.00 213s Investment_22 0.0000 0.00 0.00 213s PrivateWages_2 -1.9924 -93.78 -89.46 213s PrivateWages_3 0.4683 23.22 21.35 213s PrivateWages_4 1.4034 79.35 70.31 213s PrivateWages_5 -1.7870 -108.45 -102.22 213s PrivateWages_6 -0.3627 -21.98 -20.71 213s PrivateWages_8 1.1629 69.77 74.43 213s PrivateWages_9 1.2735 79.30 82.01 213s PrivateWages_10 2.2141 142.96 142.81 213s PrivateWages_11 -1.2912 -82.26 -86.51 213s PrivateWages_12 -0.0350 -1.92 -2.14 213s PrivateWages_13 -1.0438 -49.04 -55.74 213s PrivateWages_14 1.8016 75.90 79.81 213s PrivateWages_15 -0.3714 -19.02 -16.75 213s PrivateWages_16 -0.3904 -21.61 -19.40 213s PrivateWages_17 1.4934 85.71 81.24 213s PrivateWages_18 0.0279 1.88 1.75 213s PrivateWages_19 -3.8229 -261.91 -248.49 213s PrivateWages_20 0.7870 52.61 47.93 213s PrivateWages_21 -0.7415 -55.52 -51.54 213s PrivateWages_22 1.2062 104.79 91.31 213s PrivateWages_trend 213s Consumption_2 0.000 213s Consumption_3 0.000 213s Consumption_4 0.000 213s Consumption_5 0.000 213s Consumption_6 0.000 213s Consumption_8 0.000 213s Consumption_9 0.000 213s Consumption_11 0.000 213s Consumption_12 0.000 213s Consumption_14 0.000 213s Consumption_15 0.000 213s Consumption_16 0.000 213s Consumption_17 0.000 213s Consumption_18 0.000 213s Consumption_19 0.000 213s Consumption_20 0.000 213s Consumption_21 0.000 213s Consumption_22 0.000 213s Investment_2 0.000 213s Investment_3 0.000 213s Investment_4 0.000 213s Investment_5 0.000 213s Investment_6 0.000 213s Investment_8 0.000 213s Investment_9 0.000 213s Investment_10 0.000 213s Investment_11 0.000 213s Investment_12 0.000 213s Investment_14 0.000 213s Investment_15 0.000 213s Investment_16 0.000 213s Investment_17 0.000 213s Investment_18 0.000 213s Investment_19 0.000 213s Investment_20 0.000 213s Investment_21 0.000 213s Investment_22 0.000 213s PrivateWages_2 19.924 213s PrivateWages_3 -4.214 213s PrivateWages_4 -11.227 213s PrivateWages_5 12.509 213s PrivateWages_6 2.176 213s PrivateWages_8 -4.652 213s PrivateWages_9 -3.820 213s PrivateWages_10 -4.428 213s PrivateWages_11 1.291 213s PrivateWages_12 0.000 213s PrivateWages_13 -1.044 213s PrivateWages_14 3.603 213s PrivateWages_15 -1.114 213s PrivateWages_16 -1.562 213s PrivateWages_17 7.467 213s PrivateWages_18 0.168 213s PrivateWages_19 -26.760 213s PrivateWages_20 6.296 213s PrivateWages_21 -6.674 213s PrivateWages_22 12.062 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_(Intercept) 118.21 -4.213 213s Consumption_corpProf -4.21 1.235 213s Consumption_corpProfLag 1.03 -0.689 213s Consumption_wages -1.44 -0.136 213s Investment_(Intercept) 0.00 0.000 213s Investment_corpProf 0.00 0.000 213s Investment_corpProfLag 0.00 0.000 213s Investment_capitalLag 0.00 0.000 213s PrivateWages_(Intercept) 0.00 0.000 213s PrivateWages_gnp 0.00 0.000 213s PrivateWages_gnpLag 0.00 0.000 213s PrivateWages_trend 0.00 0.000 213s Consumption_corpProfLag Consumption_wages 213s Consumption_(Intercept) 1.0298 -1.4384 213s Consumption_corpProf -0.6891 -0.1356 213s Consumption_corpProfLag 0.7104 -0.0191 213s Consumption_wages -0.0191 0.0972 213s Investment_(Intercept) 0.0000 0.0000 213s Investment_corpProf 0.0000 0.0000 213s Investment_corpProfLag 0.0000 0.0000 213s Investment_capitalLag 0.0000 0.0000 213s PrivateWages_(Intercept) 0.0000 0.0000 213s PrivateWages_gnp 0.0000 0.0000 213s PrivateWages_gnpLag 0.0000 0.0000 213s PrivateWages_trend 0.0000 0.0000 213s Investment_(Intercept) Investment_corpProf 213s Consumption_(Intercept) 0.0 0.000 213s Consumption_corpProf 0.0 0.000 213s Consumption_corpProfLag 0.0 0.000 213s Consumption_wages 0.0 0.000 213s Investment_(Intercept) 2314.8 -41.107 213s Investment_corpProf -41.1 1.637 213s Investment_corpProfLag 33.2 -1.272 213s Investment_capitalLag -10.7 0.169 213s PrivateWages_(Intercept) 0.0 0.000 213s PrivateWages_gnp 0.0 0.000 213s PrivateWages_gnpLag 0.0 0.000 213s PrivateWages_trend 0.0 0.000 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_(Intercept) 0.000 0.0000 213s Consumption_corpProf 0.000 0.0000 213s Consumption_corpProfLag 0.000 0.0000 213s Consumption_wages 0.000 0.0000 213s Investment_(Intercept) 33.159 -10.7377 213s Investment_corpProf -1.272 0.1688 213s Investment_corpProfLag 1.204 -0.1550 213s Investment_capitalLag -0.155 0.0519 213s PrivateWages_(Intercept) 0.000 0.0000 213s PrivateWages_gnp 0.000 0.0000 213s PrivateWages_gnpLag 0.000 0.0000 213s PrivateWages_trend 0.000 0.0000 213s PrivateWages_(Intercept) PrivateWages_gnp 213s Consumption_(Intercept) 0.000 0.0000 213s Consumption_corpProf 0.000 0.0000 213s Consumption_corpProfLag 0.000 0.0000 213s Consumption_wages 0.000 0.0000 213s Investment_(Intercept) 0.000 0.0000 213s Investment_corpProf 0.000 0.0000 213s Investment_corpProfLag 0.000 0.0000 213s Investment_capitalLag 0.000 0.0000 213s PrivateWages_(Intercept) 162.179 -0.8825 213s PrivateWages_gnp -0.882 0.1501 213s PrivateWages_gnpLag -1.850 -0.1399 213s PrivateWages_trend 2.056 -0.0403 213s PrivateWages_gnpLag PrivateWages_trend 213s Consumption_(Intercept) 0.0000 0.0000 213s Consumption_corpProf 0.0000 0.0000 213s Consumption_corpProfLag 0.0000 0.0000 213s Consumption_wages 0.0000 0.0000 213s Investment_(Intercept) 0.0000 0.0000 213s Investment_corpProf 0.0000 0.0000 213s Investment_corpProfLag 0.0000 0.0000 213s Investment_capitalLag 0.0000 0.0000 213s PrivateWages_(Intercept) -1.8504 2.0559 213s PrivateWages_gnp -0.1399 -0.0403 213s PrivateWages_gnpLag 0.1768 0.0057 213s PrivateWages_trend 0.0057 0.1094 213s > 213s > # SUR 213s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: SUR 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 59 47 45.1 0.168 0.976 0.992 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 213s Investment 20 16 17.3 1.083 1.041 0.911 0.894 213s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 213s 213s The covariance matrix of the residuals used for estimation 213s Consumption Investment PrivateWages 213s Consumption 0.9286 0.0435 -0.369 213s Investment 0.0435 0.7653 0.109 213s PrivateWages -0.3690 0.1091 0.468 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 0.9251 0.0748 -0.427 213s Investment 0.0748 0.7653 0.171 213s PrivateWages -0.4268 0.1706 0.492 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.0000 0.0888 -0.636 213s Investment 0.0888 1.0000 0.268 213s PrivateWages -0.6364 0.2678 1.000 213s 213s 213s SUR estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 16.2684 1.2781 12.73 1.9e-09 *** 213s corpProf 0.1942 0.0927 2.10 0.054 . 213s corpProfLag 0.0746 0.0819 0.91 0.377 213s wages 0.8011 0.0372 21.53 1.1e-12 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.08 on 15 degrees of freedom 213s Number of observations: 19 Degrees of Freedom: 15 213s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 213s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 213s 213s 213s SUR estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 12.6462 4.6500 2.72 0.01515 * 213s corpProf 0.4707 0.0916 5.14 9.9e-05 *** 213s corpProfLag 0.3519 0.0874 4.03 0.00097 *** 213s capitalLag -0.1253 0.0229 -5.47 5.1e-05 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.041 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 17.325 MSE: 1.083 Root MSE: 1.041 213s Multiple R-Squared: 0.911 Adjusted R-Squared: 0.894 213s 213s 213s SUR estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 1.3245 1.0946 1.21 0.24 213s gnp 0.4184 0.0260 16.08 2.7e-11 *** 213s gnpLag 0.1714 0.0307 5.59 4.1e-05 *** 213s trend 0.1455 0.0276 5.27 7.6e-05 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.801 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 10.265 MSE: 0.642 Root MSE: 0.801 213s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 213s 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.3146 -0.2419 -1.1439 213s 3 -1.2707 -0.1795 0.5080 213s 4 -1.5428 1.0691 1.4208 213s 5 -0.4489 -1.4778 -0.1000 213s 6 0.0588 0.3168 -0.3599 213s 7 0.9215 1.4450 NA 213s 8 1.3791 0.8287 -0.7561 213s 9 1.0901 -0.5272 0.2880 213s 10 NA 1.2089 1.1795 213s 11 0.3577 0.4081 -0.3681 213s 12 -0.2286 0.2569 0.3439 213s 13 NA NA -0.1574 213s 14 0.2172 0.4743 0.4225 213s 15 -0.1124 -0.0607 0.3154 213s 16 -0.0876 0.0761 0.0151 213s 17 1.5611 1.0205 -0.8084 213s 18 -0.4529 0.0580 0.8611 213s 19 0.1999 -2.5444 -0.7635 213s 20 0.9266 -0.6202 -0.4039 213s 21 0.7589 -0.7478 -1.2175 213s 22 -2.2135 -0.6029 0.5611 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.2 0.0419 26.6 213s 3 46.3 2.0795 28.8 213s 4 50.7 4.1309 32.7 213s 5 51.0 4.4778 34.0 213s 6 52.5 4.7832 35.8 213s 7 54.2 4.1550 NA 213s 8 54.8 3.3713 38.7 213s 9 56.2 3.5272 38.9 213s 10 NA 3.8911 40.1 213s 11 54.6 0.5919 38.3 213s 12 51.1 -3.6569 34.2 213s 13 NA NA 29.2 213s 14 46.3 -5.5743 28.1 213s 15 48.8 -2.9393 30.3 213s 16 51.4 -1.3761 33.2 213s 17 56.1 1.0795 37.6 213s 18 59.2 1.9420 40.1 213s 19 57.3 0.6444 39.0 213s 20 60.7 1.9202 42.0 213s 21 64.2 4.0478 46.2 213s 22 71.9 5.5029 52.7 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.2 0.448 41.3 43.1 213s 3 46.3 0.476 45.3 47.2 213s 4 50.7 0.318 50.1 51.4 213s 5 51.0 0.373 50.3 51.8 213s 6 52.5 0.378 51.8 53.3 213s 7 54.2 0.337 53.5 54.9 213s 8 54.8 0.310 54.2 55.4 213s 9 56.2 0.343 55.5 56.9 213s 10 NA NA NA NA 213s 11 54.6 0.567 53.5 55.8 213s 12 51.1 0.509 50.1 52.2 213s 13 NA NA NA NA 213s 14 46.3 0.573 45.1 47.4 213s 15 48.8 0.382 48.0 49.6 213s 16 51.4 0.328 50.7 52.0 213s 17 56.1 0.336 55.5 56.8 213s 18 59.2 0.309 58.5 59.8 213s 19 57.3 0.370 56.6 58.0 213s 20 60.7 0.401 59.9 61.5 213s 21 64.2 0.405 63.4 65.1 213s 22 71.9 0.633 70.6 73.2 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 0.0419 0.533 -1.0309 1.115 213s 3 2.0795 0.433 1.2082 2.951 213s 4 4.1309 0.387 3.3532 4.909 213s 5 4.4778 0.322 3.8307 5.125 213s 6 4.7832 0.305 4.1700 5.396 213s 7 4.1550 0.283 3.5852 4.725 213s 8 3.3713 0.253 2.8630 3.880 213s 9 3.5272 0.337 2.8488 4.206 213s 10 3.8911 0.386 3.1149 4.667 213s 11 0.5919 0.561 -0.5376 1.722 213s 12 -3.6569 0.530 -4.7223 -2.591 213s 13 NA NA NA NA 213s 14 -5.5743 0.618 -6.8176 -4.331 213s 15 -2.9393 0.362 -3.6671 -2.212 213s 16 -1.3761 0.296 -1.9710 -0.781 213s 17 1.0795 0.300 0.4763 1.683 213s 18 1.9420 0.216 1.5081 2.376 213s 19 0.6444 0.298 0.0451 1.244 213s 20 1.9202 0.318 1.2798 2.561 213s 21 4.0478 0.295 3.4537 4.642 213s 22 5.5029 0.417 4.6638 6.342 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.6 0.312 26.0 27.3 213s 3 28.8 0.312 28.2 29.4 213s 4 32.7 0.307 32.1 33.3 213s 5 34.0 0.237 33.5 34.5 213s 6 35.8 0.235 35.3 36.2 213s 7 NA NA NA NA 213s 8 38.7 0.239 38.2 39.1 213s 9 38.9 0.228 38.5 39.4 213s 10 40.1 0.218 39.7 40.6 213s 11 38.3 0.293 37.7 38.9 213s 12 34.2 0.290 33.6 34.7 213s 13 29.2 0.343 28.5 29.8 213s 14 28.1 0.321 27.4 28.7 213s 15 30.3 0.320 29.6 30.9 213s 16 33.2 0.268 32.6 33.7 213s 17 37.6 0.263 37.1 38.1 213s 18 40.1 0.207 39.7 40.6 213s 19 39.0 0.293 38.4 39.6 213s 20 42.0 0.279 41.4 42.6 213s 21 46.2 0.295 45.6 46.8 213s 22 52.7 0.435 51.9 53.6 213s > model.frame 213s [1] TRUE 213s > model.matrix 213s [1] TRUE 213s > nobs 213s [1] 59 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.41 0.52 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 48 213s 2 47 1 0.52 0.47 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 48 213s 2 47 1 0.52 0.47 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.31 0.73 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 49 213s 2 47 2 0.4 0.67 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 49 213s 2 47 2 0.79 0.67 213s > logLik 213s 'log Lik.' -67.3 (df=18) 213s 'log Lik.' -74.9 (df=18) 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -0.5115 -6.342 213s Consumption_3 -2.0659 -34.913 213s Consumption_4 -2.5083 -46.152 213s Consumption_5 -0.7298 -14.158 213s Consumption_6 0.0957 1.923 213s Consumption_7 1.4982 29.364 213s Consumption_8 2.2421 44.394 213s Consumption_9 1.7723 37.396 213s Consumption_11 0.5815 9.072 213s Consumption_12 -0.3716 -4.237 213s Consumption_14 0.3531 3.954 213s Consumption_15 -0.1827 -2.248 213s Consumption_16 -0.1424 -1.993 213s Consumption_17 2.5380 44.669 213s Consumption_18 -0.7363 -12.738 213s Consumption_19 0.3251 4.973 213s Consumption_20 1.5064 28.622 213s Consumption_21 1.2337 26.032 213s Consumption_22 -3.5987 -84.568 213s Investment_2 0.0688 0.854 213s Investment_3 0.0511 0.863 213s Investment_4 -0.3043 -5.599 213s Investment_5 0.4206 8.160 213s Investment_6 -0.0902 -1.813 213s Investment_7 -0.4113 -8.061 213s Investment_8 -0.2359 -4.670 213s Investment_9 0.1501 3.166 213s Investment_10 0.0000 0.000 213s Investment_11 -0.1161 -1.812 213s Investment_12 -0.0731 -0.834 213s Investment_14 -0.1350 -1.512 213s Investment_15 0.0173 0.212 213s Investment_16 -0.0217 -0.303 213s Investment_17 -0.2904 -5.112 213s Investment_18 -0.0165 -0.286 213s Investment_19 0.7242 11.080 213s Investment_20 0.1765 3.354 213s Investment_21 0.2128 4.491 213s Investment_22 0.1716 4.032 213s PrivateWages_2 -1.5418 -19.118 213s PrivateWages_3 0.6847 11.571 213s PrivateWages_4 1.9149 35.234 213s PrivateWages_5 -0.1348 -2.615 213s PrivateWages_6 -0.4851 -9.750 213s PrivateWages_8 -1.0191 -20.178 213s PrivateWages_9 0.3882 8.190 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 -0.4961 -7.739 213s PrivateWages_12 0.4635 5.284 213s PrivateWages_13 0.0000 0.000 213s PrivateWages_14 0.5694 6.377 213s PrivateWages_15 0.4251 5.229 213s PrivateWages_16 0.0204 0.286 213s PrivateWages_17 -1.0895 -19.175 213s PrivateWages_18 1.1605 20.077 213s PrivateWages_19 -1.0290 -15.743 213s PrivateWages_20 -0.5443 -10.343 213s PrivateWages_21 -1.6408 -34.622 213s PrivateWages_22 0.7563 17.772 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -6.496 -14.423 213s Consumption_3 -25.617 -66.521 213s Consumption_4 -42.390 -92.806 213s Consumption_5 -13.428 -27.003 213s Consumption_6 1.856 3.693 213s Consumption_7 30.114 60.976 213s Consumption_8 43.945 93.047 213s Consumption_9 35.092 76.033 213s Consumption_11 12.619 24.482 213s Consumption_12 -5.798 -14.606 213s Consumption_14 2.471 12.039 213s Consumption_15 -2.047 -6.688 213s Consumption_16 -1.751 -5.595 213s Consumption_17 35.532 112.180 213s Consumption_18 -12.959 -35.121 213s Consumption_19 5.624 14.920 213s Consumption_20 23.048 74.417 213s Consumption_21 23.441 65.389 213s Consumption_22 -75.932 -222.397 213s Investment_2 0.874 1.941 213s Investment_3 0.633 1.645 213s Investment_4 -5.142 -11.258 213s Investment_5 7.739 15.562 213s Investment_6 -1.749 -3.481 213s Investment_7 -8.267 -16.739 213s Investment_8 -4.623 -9.788 213s Investment_9 2.971 6.437 213s Investment_10 0.000 0.000 213s Investment_11 -2.520 -4.889 213s Investment_12 -1.141 -2.873 213s Investment_14 -0.945 -4.603 213s Investment_15 0.193 0.632 213s Investment_16 -0.266 -0.851 213s Investment_17 -4.066 -12.838 213s Investment_18 -0.291 -0.787 213s Investment_19 12.528 33.240 213s Investment_20 2.701 8.720 213s Investment_21 4.044 11.280 213s Investment_22 3.620 10.604 213s PrivateWages_2 -19.580 -43.478 213s PrivateWages_3 8.490 22.046 213s PrivateWages_4 32.362 70.851 213s PrivateWages_5 -2.480 -4.987 213s PrivateWages_6 -9.410 -18.724 213s PrivateWages_8 -19.974 -42.291 213s PrivateWages_9 7.686 16.652 213s PrivateWages_10 0.000 0.000 213s PrivateWages_11 -10.765 -20.886 213s PrivateWages_12 7.230 18.215 213s PrivateWages_13 0.000 0.000 213s PrivateWages_14 3.986 19.417 213s PrivateWages_15 4.762 15.560 213s PrivateWages_16 0.251 0.802 213s PrivateWages_17 -15.253 -48.156 213s PrivateWages_18 20.425 55.356 213s PrivateWages_19 -17.801 -47.230 213s PrivateWages_20 -8.329 -26.891 213s PrivateWages_21 -31.176 -86.965 213s PrivateWages_22 15.957 46.737 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 0.08954 1.110 213s Consumption_3 0.36165 6.112 213s Consumption_4 0.43910 8.079 213s Consumption_5 0.12776 2.479 213s Consumption_6 -0.01675 -0.337 213s Consumption_7 -0.26227 -5.141 213s Consumption_8 -0.39250 -7.772 213s Consumption_9 -0.31026 -6.547 213s Consumption_11 -0.10180 -1.588 213s Consumption_12 0.06506 0.742 213s Consumption_14 -0.06181 -0.692 213s Consumption_15 0.03199 0.393 213s Consumption_16 0.02492 0.349 213s Consumption_17 -0.44431 -7.820 213s Consumption_18 0.12890 2.230 213s Consumption_19 -0.05691 -0.871 213s Consumption_20 -0.26372 -5.011 213s Consumption_21 -0.21598 -4.557 213s Consumption_22 0.62998 14.805 213s Investment_2 -0.33900 -4.204 213s Investment_3 -0.25149 -4.250 213s Investment_4 1.49825 27.568 213s Investment_5 -2.07104 -40.178 213s Investment_6 0.44402 8.925 213s Investment_7 2.02512 39.692 213s Investment_8 1.16134 22.995 213s Investment_9 -0.73888 -15.590 213s Investment_10 1.69419 36.764 213s Investment_11 0.57188 8.921 213s Investment_12 0.36002 4.104 213s Investment_14 0.66469 7.445 213s Investment_15 -0.08500 -1.046 213s Investment_16 0.10666 1.493 213s Investment_17 1.43016 25.171 213s Investment_18 0.08129 1.406 213s Investment_19 -3.56588 -54.558 213s Investment_20 -0.86923 -16.515 213s Investment_21 -1.04801 -22.113 213s Investment_22 -0.84488 -19.855 213s PrivateWages_2 0.63026 7.815 213s PrivateWages_3 -0.27988 -4.730 213s PrivateWages_4 -0.78278 -14.403 213s PrivateWages_5 0.05510 1.069 213s PrivateWages_6 0.19829 3.986 213s PrivateWages_8 0.41658 8.248 213s PrivateWages_9 -0.15868 -3.348 213s PrivateWages_10 -0.64985 -14.102 213s PrivateWages_11 0.20280 3.164 213s PrivateWages_12 -0.18947 -2.160 213s PrivateWages_13 0.00000 0.000 213s PrivateWages_14 -0.23276 -2.607 213s PrivateWages_15 -0.17379 -2.138 213s PrivateWages_16 -0.00834 -0.117 213s PrivateWages_17 0.44538 7.839 213s PrivateWages_18 -0.47440 -8.207 213s PrivateWages_19 0.42063 6.436 213s PrivateWages_20 0.22252 4.228 213s PrivateWages_21 0.67076 14.153 213s PrivateWages_22 -0.30915 -7.265 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 1.137 16.37 213s Consumption_3 4.484 66.04 213s Consumption_4 7.421 81.01 213s Consumption_5 2.351 24.24 213s Consumption_6 -0.325 -3.23 213s Consumption_7 -5.272 -51.88 213s Consumption_8 -7.693 -79.84 213s Consumption_9 -6.143 -64.41 213s Consumption_11 -2.209 -21.96 213s Consumption_12 1.015 14.10 213s Consumption_14 -0.433 -12.80 213s Consumption_15 0.358 6.46 213s Consumption_16 0.307 4.96 213s Consumption_17 -6.220 -87.84 213s Consumption_18 2.269 25.75 213s Consumption_19 -0.984 -11.48 213s Consumption_20 -4.035 -52.72 213s Consumption_21 -4.104 -43.46 213s Consumption_22 13.293 128.83 213s Investment_2 -4.305 -61.97 213s Investment_3 -3.118 -45.92 213s Investment_4 25.320 276.43 213s Investment_5 -38.107 -392.88 213s Investment_6 8.614 85.56 213s Investment_7 40.705 400.57 213s Investment_8 22.762 236.22 213s Investment_9 -14.630 -153.39 213s Investment_10 35.747 356.80 213s Investment_11 12.410 123.35 213s Investment_12 5.616 78.02 213s Investment_14 4.653 137.66 213s Investment_15 -0.952 -17.17 213s Investment_16 1.312 21.22 213s Investment_17 20.022 282.74 213s Investment_18 1.431 16.24 213s Investment_19 -61.690 -719.59 213s Investment_20 -13.299 -173.76 213s Investment_21 -19.912 -210.86 213s Investment_22 -17.827 -172.78 213s PrivateWages_2 8.004 115.21 213s PrivateWages_3 -3.471 -51.11 213s PrivateWages_4 -13.229 -144.42 213s PrivateWages_5 1.014 10.45 213s PrivateWages_6 3.847 38.21 213s PrivateWages_8 8.165 84.73 213s PrivateWages_9 -3.142 -32.94 213s PrivateWages_10 -13.712 -136.86 213s PrivateWages_11 4.401 43.74 213s PrivateWages_12 -2.956 -41.06 213s PrivateWages_13 0.000 0.00 213s PrivateWages_14 -1.629 -48.21 213s PrivateWages_15 -1.946 -35.11 213s PrivateWages_16 -0.103 -1.66 213s PrivateWages_17 6.235 88.05 213s PrivateWages_18 -8.349 -94.78 213s PrivateWages_19 7.277 84.88 213s PrivateWages_20 3.405 44.48 213s PrivateWages_21 12.744 134.96 213s PrivateWages_22 -6.523 -63.22 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 -0.4240 -19.33 -19.04 213s Consumption_3 -1.7126 -85.80 -78.09 213s Consumption_4 -2.0793 -118.94 -104.17 213s Consumption_5 -0.6050 -34.54 -34.61 213s Consumption_6 0.0793 4.84 4.53 213s Consumption_7 0.0000 0.00 0.00 213s Consumption_8 1.8587 119.70 118.95 213s Consumption_9 1.4692 94.76 94.62 213s Consumption_11 0.4821 29.50 32.30 213s Consumption_12 -0.3081 -16.45 -18.85 213s Consumption_14 0.2927 13.20 12.97 213s Consumption_15 -0.1515 -7.53 -6.83 213s Consumption_16 -0.1180 -6.42 -5.87 213s Consumption_17 2.1040 131.92 114.46 213s Consumption_18 -0.6104 -39.67 -38.27 213s Consumption_19 0.2695 16.41 17.52 213s Consumption_20 1.2488 86.79 76.05 213s Consumption_21 1.0228 77.42 71.08 213s Consumption_22 -2.9832 -263.72 -225.83 213s Investment_2 0.1333 6.08 5.98 213s Investment_3 0.0989 4.95 4.51 213s Investment_4 -0.5890 -33.69 -29.51 213s Investment_5 0.8142 46.49 46.57 213s Investment_6 -0.1746 -10.65 -9.97 213s Investment_7 0.0000 0.00 0.00 213s Investment_8 -0.4566 -29.40 -29.22 213s Investment_9 0.2905 18.74 18.71 213s Investment_10 -0.6660 -44.62 -42.96 213s Investment_11 -0.2248 -13.76 -15.06 213s Investment_12 -0.1415 -7.56 -8.66 213s Investment_14 -0.2613 -11.79 -11.58 213s Investment_15 0.0334 1.66 1.51 213s Investment_16 -0.0419 -2.28 -2.08 213s Investment_17 -0.5622 -35.25 -30.59 213s Investment_18 -0.0320 -2.08 -2.00 213s Investment_19 1.4018 85.37 91.12 213s Investment_20 0.3417 23.75 20.81 213s Investment_21 0.4120 31.19 28.63 213s Investment_22 0.3321 29.36 25.14 213s PrivateWages_2 -3.8052 -173.52 -170.85 213s PrivateWages_3 1.6898 84.66 77.06 213s PrivateWages_4 4.7261 270.33 236.78 213s PrivateWages_5 -0.3327 -19.00 -19.03 213s PrivateWages_6 -1.1972 -73.03 -68.36 213s PrivateWages_8 -2.5152 -161.98 -160.97 213s PrivateWages_9 0.9580 61.79 61.70 213s PrivateWages_10 3.9235 262.88 253.07 213s PrivateWages_11 -1.2244 -74.93 -82.04 213s PrivateWages_12 1.1439 61.09 70.01 213s PrivateWages_13 -0.5236 -23.19 -27.96 213s PrivateWages_14 1.4053 63.38 62.26 213s PrivateWages_15 1.0493 52.15 47.32 213s PrivateWages_16 0.0503 2.74 2.50 213s PrivateWages_17 -2.6890 -168.60 -146.28 213s PrivateWages_18 2.8642 186.17 179.59 213s PrivateWages_19 -2.5396 -154.66 -165.07 213s PrivateWages_20 -1.3435 -93.37 -81.82 213s PrivateWages_21 -4.0497 -306.57 -281.46 213s PrivateWages_22 1.8665 165.00 141.30 213s PrivateWages_trend 213s Consumption_2 4.240 213s Consumption_3 15.413 213s Consumption_4 16.634 213s Consumption_5 4.235 213s Consumption_6 -0.476 213s Consumption_7 0.000 213s Consumption_8 -7.435 213s Consumption_9 -4.408 213s Consumption_11 -0.482 213s Consumption_12 0.000 213s Consumption_14 0.585 213s Consumption_15 -0.454 213s Consumption_16 -0.472 213s Consumption_17 10.520 213s Consumption_18 -3.662 213s Consumption_19 1.886 213s Consumption_20 9.990 213s Consumption_21 9.205 213s Consumption_22 -29.832 213s Investment_2 -1.333 213s Investment_3 -0.890 213s Investment_4 4.712 213s Investment_5 -5.699 213s Investment_6 1.047 213s Investment_7 0.000 213s Investment_8 1.826 213s Investment_9 -0.871 213s Investment_10 1.332 213s Investment_11 0.225 213s Investment_12 0.000 213s Investment_14 -0.523 213s Investment_15 0.100 213s Investment_16 -0.168 213s Investment_17 -2.811 213s Investment_18 -0.192 213s Investment_19 9.813 213s Investment_20 2.734 213s Investment_21 3.708 213s Investment_22 3.321 213s PrivateWages_2 38.052 213s PrivateWages_3 -15.208 213s PrivateWages_4 -37.809 213s PrivateWages_5 2.329 213s PrivateWages_6 7.183 213s PrivateWages_8 10.061 213s PrivateWages_9 -2.874 213s PrivateWages_10 -7.847 213s PrivateWages_11 1.224 213s PrivateWages_12 0.000 213s PrivateWages_13 -0.524 213s PrivateWages_14 2.811 213s PrivateWages_15 3.148 213s PrivateWages_16 0.201 213s PrivateWages_17 -13.445 213s PrivateWages_18 17.185 213s PrivateWages_19 -17.777 213s PrivateWages_20 -10.748 213s PrivateWages_21 -36.448 213s PrivateWages_22 18.665 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 213s [1,] 9.64e+01 -1.01207 -0.67760 213s [2,] -1.01e+00 0.50717 -0.26912 213s [3,] -6.78e-01 -0.26912 0.39547 213s [4,] -1.57e+00 -0.07816 -0.02960 213s [5,] 4.72e+00 -0.06998 0.78589 213s [6,] -2.60e-01 0.05062 -0.04147 213s [7,] 5.84e-03 -0.03341 0.04369 213s [8,] -2.63e-04 -0.00132 -0.00391 213s [9,] -3.35e+01 0.06371 1.58512 213s [10,] 2.97e-01 -0.05279 0.03618 213s [11,] 2.54e-01 0.05334 -0.06435 213s [12,] 1.92e-01 0.03084 0.02478 213s Consumption_wages Investment_(Intercept) Investment_corpProf 213s [1,] -1.566759 4.725 -0.25994 213s [2,] -0.078160 -0.070 0.05062 213s [3,] -0.029602 0.786 -0.04147 213s [4,] 0.081697 -0.368 0.00116 213s [5,] -0.368191 1275.706 -12.07893 213s [6,] 0.001158 -12.079 0.49514 213s [7,] -0.003210 9.845 -0.37888 213s [8,] 0.001998 -6.140 0.04890 213s [9,] 0.126305 19.264 -0.14904 213s [10,] -0.000206 0.266 0.01283 213s [11,] -0.002055 -0.608 -0.01053 213s [12,] -0.027162 -0.549 0.00394 213s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 213s [1,] 0.00584 -0.000263 -33.5037 213s [2,] -0.03341 -0.001318 0.0637 213s [3,] 0.04369 -0.003914 1.5851 213s [4,] -0.00321 0.001998 0.1263 213s [5,] 9.84516 -6.139910 19.2637 213s [6,] -0.37888 0.048897 -0.1490 213s [7,] 0.45026 -0.053769 -0.4040 213s [8,] -0.05377 0.030940 -0.0490 213s [9,] -0.40395 -0.049007 70.6849 213s [10,] -0.00755 -0.001777 -0.2111 213s [11,] 0.01465 0.002709 -0.9817 213s [12,] -0.01065 0.003278 0.7839 213s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 213s [1,] 0.297134 0.25379 0.19157 213s [2,] -0.052789 0.05334 0.03084 213s [3,] 0.036177 -0.06435 0.02478 213s [4,] -0.000206 -0.00206 -0.02716 213s [5,] 0.265808 -0.60808 -0.54935 213s [6,] 0.012829 -0.01053 0.00394 213s [7,] -0.007548 0.01465 -0.01065 213s [8,] -0.001777 0.00271 0.00328 213s [9,] -0.211061 -0.98166 0.78387 213s [10,] 0.039911 -0.03744 -0.00955 213s [11,] -0.037441 0.05550 -0.00377 213s [12,] -0.009553 -0.00377 0.04488 213s > 213s > # 3SLS 213s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 213s > summary 213s 213s systemfit results 213s method: 3SLS 213s 213s N DF SSR detRCov OLS-R2 McElroy-R2 213s system 57 45 66.8 0.361 0.963 0.993 213s 213s N DF SSR MSE RMSE R2 Adj R2 213s Consumption 18 14 22.6 1.616 1.271 0.974 0.968 213s Investment 19 15 34.1 2.277 1.509 0.807 0.769 213s PrivateWages 20 16 10.1 0.628 0.793 0.987 0.985 213s 213s The covariance matrix of the residuals used for estimation 213s Consumption Investment PrivateWages 213s Consumption 1.237 0.518 -0.408 213s Investment 0.518 1.263 0.113 213s PrivateWages -0.408 0.113 0.468 213s 213s The covariance matrix of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.257 0.601 -0.421 213s Investment 0.601 1.601 0.214 213s PrivateWages -0.421 0.214 0.491 213s 213s The correlations of the residuals 213s Consumption Investment PrivateWages 213s Consumption 1.000 0.425 -0.537 213s Investment 0.425 1.000 0.239 213s PrivateWages -0.537 0.239 1.000 213s 213s 213s 3SLS estimates for 'Consumption' (equation 1) 213s Model Formula: consump ~ corpProf + corpProfLag + wages 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 18.2100 1.5273 11.92 1e-08 *** 213s corpProf -0.0639 0.1461 -0.44 0.67 213s corpProfLag 0.1687 0.1125 1.50 0.16 213s wages 0.8230 0.0431 19.07 2e-11 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.271 on 14 degrees of freedom 213s Number of observations: 18 Degrees of Freedom: 14 213s SSR: 22.626 MSE: 1.616 Root MSE: 1.271 213s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 213s 213s 213s 3SLS estimates for 'Investment' (equation 2) 213s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 24.7534 6.5548 3.78 0.00183 ** 213s corpProf 0.0524 0.1807 0.29 0.77600 213s corpProfLag 0.6584 0.1551 4.24 0.00071 *** 213s capitalLag -0.1756 0.0311 -5.64 4.7e-05 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 1.509 on 15 degrees of freedom 213s Number of observations: 19 Degrees of Freedom: 15 213s SSR: 34.149 MSE: 2.277 Root MSE: 1.509 213s Multiple R-Squared: 0.807 Adjusted R-Squared: 0.769 213s 213s 213s 3SLS estimates for 'PrivateWages' (equation 3) 213s Model Formula: privWage ~ gnp + gnpLag + trend 213s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 213s gnpLag 213s 213s Estimate Std. Error t value Pr(>|t|) 213s (Intercept) 0.8154 1.0961 0.74 0.46772 213s gnp 0.4250 0.0299 14.19 1.7e-10 *** 213s gnpLag 0.1731 0.0331 5.23 8.3e-05 *** 213s trend 0.1255 0.0283 4.43 0.00042 *** 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s 213s Residual standard error: 0.793 on 16 degrees of freedom 213s Number of observations: 20 Degrees of Freedom: 16 213s SSR: 10.054 MSE: 0.628 Root MSE: 0.793 213s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 213s 213s > residuals 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 -0.8680 -1.857 -1.21010 213s 3 -0.7217 0.170 0.43075 213s 4 -1.1353 0.762 1.30899 213s 5 0.0755 -1.565 -0.20270 213s 6 0.6348 0.367 -0.46842 213s 7 NA NA NA 213s 8 1.7953 1.230 -0.85853 213s 9 1.7924 0.568 0.20422 213s 10 NA 2.308 1.09889 213s 11 -0.5211 -0.972 -0.39427 213s 12 -1.5560 -0.960 0.39889 213s 13 NA NA -0.00934 213s 14 -0.2384 1.327 0.59990 213s 15 -0.7342 -0.292 0.48094 213s 16 -0.4331 0.068 0.16188 213s 17 1.8775 1.932 -0.70448 213s 18 -0.6294 -0.154 0.95616 213s 19 -0.4252 -3.400 -0.62489 213s 20 1.3682 0.589 -0.29589 213s 21 1.3155 0.271 -1.14466 213s 22 -1.4276 0.942 0.55941 213s > fitted 213s Consumption Investment PrivateWages 213s 1 NA NA NA 213s 2 42.8 1.657 26.7 213s 3 45.7 1.730 28.9 213s 4 50.3 4.438 32.8 213s 5 50.5 4.565 34.1 213s 6 52.0 4.733 35.9 213s 7 NA NA NA 213s 8 54.4 2.970 38.8 213s 9 55.5 2.432 39.0 213s 10 NA 2.792 40.2 213s 11 55.5 1.972 38.3 213s 12 52.5 -2.440 34.1 213s 13 NA NA 29.0 213s 14 46.7 -6.427 27.9 213s 15 49.4 -2.708 30.1 213s 16 51.7 -1.368 33.0 213s 17 55.8 0.168 37.5 213s 18 59.3 2.154 40.0 213s 19 57.9 1.500 38.8 213s 20 60.2 0.711 41.9 213s 21 63.7 3.029 46.1 213s 22 71.1 3.958 52.7 213s > predict 213s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 213s 1 NA NA NA NA 213s 2 42.8 0.542 39.8 45.7 213s 3 45.7 0.612 42.7 48.7 213s 4 50.3 0.407 47.5 53.2 213s 5 50.5 0.478 47.6 53.4 213s 6 52.0 0.488 49.0 54.9 213s 7 NA NA NA NA 213s 8 54.4 0.394 51.5 57.3 213s 9 55.5 0.464 52.6 58.4 213s 10 NA NA NA NA 213s 11 55.5 0.811 52.3 58.8 213s 12 52.5 0.773 49.3 55.6 213s 13 NA NA NA NA 213s 14 46.7 0.666 43.7 49.8 213s 15 49.4 0.463 46.5 52.3 213s 16 51.7 0.381 48.9 54.6 213s 17 55.8 0.424 52.9 58.7 213s 18 59.3 0.359 56.5 62.2 213s 19 57.9 0.492 55.0 60.8 213s 20 60.2 0.501 57.3 63.2 213s 21 63.7 0.491 60.8 66.6 213s 22 71.1 0.749 68.0 74.3 213s Investment.pred Investment.se.fit Investment.lwr Investment.upr 213s 1 NA NA NA NA 213s 2 1.657 0.831 -2.015 5.329 213s 3 1.730 0.574 -1.711 5.171 213s 4 4.438 0.507 1.045 7.831 213s 5 4.565 0.426 1.223 7.907 213s 6 4.733 0.406 1.402 8.064 213s 7 NA NA NA NA 213s 8 2.970 0.334 -0.324 6.263 213s 9 2.432 0.501 -0.957 5.820 213s 10 2.792 0.544 -0.627 6.211 213s 11 1.972 0.937 -1.814 5.757 213s 12 -2.440 0.849 -6.131 1.250 213s 13 NA NA NA NA 213s 14 -6.427 0.836 -10.104 -2.750 213s 15 -2.708 0.477 -6.081 0.665 213s 16 -1.368 0.381 -4.685 1.949 213s 17 0.168 0.473 -3.202 3.538 213s 18 2.154 0.311 -1.130 5.438 213s 19 1.500 0.518 -1.900 4.900 213s 20 0.711 0.541 -2.705 4.127 213s 21 3.029 0.467 -0.338 6.395 213s 22 3.958 0.677 0.432 7.483 213s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 213s 1 NA NA NA NA 213s 2 26.7 0.315 24.9 28.5 213s 3 28.9 0.322 27.1 30.7 213s 4 32.8 0.330 31.0 34.6 213s 5 34.1 0.241 32.3 35.9 213s 6 35.9 0.249 34.1 37.6 213s 7 NA NA NA NA 213s 8 38.8 0.243 37.0 40.5 213s 9 39.0 0.231 37.2 40.7 213s 10 40.2 0.225 38.5 41.9 213s 11 38.3 0.305 36.5 40.1 213s 12 34.1 0.317 32.3 35.9 213s 13 29.0 0.382 27.1 30.9 213s 14 27.9 0.321 26.1 29.7 213s 15 30.1 0.316 28.3 31.9 213s 16 33.0 0.265 31.3 34.8 213s 17 37.5 0.270 35.7 39.3 213s 18 40.0 0.207 38.3 41.8 213s 19 38.8 0.311 37.0 40.6 213s 20 41.9 0.287 40.1 43.7 213s 21 46.1 0.300 44.3 47.9 213s 22 52.7 0.463 50.8 54.7 213s > model.frame 213s [1] TRUE 213s > model.matrix 213s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 213s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 213s [3] "Numeric: lengths (708, 684) differ" 213s > nobs 213s [1] 57 213s > linearHypothesis 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 46 213s 2 45 1 1.95 0.17 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 46 213s 2 45 1 2.71 0.11 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 46 213s 2 45 1 2.71 0.1 . 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s Linear hypothesis test (Theil's F test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 47 213s 2 45 2 1.78 0.18 213s Linear hypothesis test (F statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df F Pr(>F) 213s 1 47 213s 2 45 2 2.48 0.095 . 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s Linear hypothesis test (Chi^2 statistic of a Wald test) 213s 213s Hypothesis: 213s Consumption_corpProf + Investment_capitalLag = 0 213s Consumption_corpProfLag - PrivateWages_trend = 0 213s 213s Model 1: restricted model 213s Model 2: kleinModel 213s 213s Res.Df Df Chisq Pr(>Chisq) 213s 1 47 213s 2 45 2 4.95 0.084 . 213s --- 213s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 213s > logLik 213s 'log Lik.' -71.2 (df=18) 213s 'log Lik.' -81.7 (df=18) 213s Estimating function 213s Consumption_(Intercept) Consumption_corpProf 213s Consumption_2 -3.6474 -51.112 213s Consumption_3 -0.7759 -12.930 213s Consumption_4 0.5383 9.982 213s Consumption_5 -2.0601 -41.756 213s Consumption_6 1.0597 20.157 213s Consumption_8 5.0108 88.416 213s Consumption_9 4.4804 84.874 213s Consumption_11 -2.2103 -37.003 213s Consumption_12 -2.9903 -39.999 213s Consumption_14 0.5609 5.622 213s Consumption_15 -2.2997 -28.756 213s Consumption_16 -1.9032 -27.562 213s Consumption_17 6.4249 95.811 213s Consumption_18 -0.7235 -14.050 213s Consumption_19 -5.0805 -97.079 213s Consumption_20 3.4333 60.632 213s Consumption_21 1.6077 32.791 213s Consumption_22 -1.1313 -25.654 213s Investment_2 1.6537 23.174 213s Investment_3 -0.1564 -2.607 213s Investment_4 -0.6420 -11.906 213s Investment_5 1.4113 28.605 213s Investment_6 -0.3557 -6.767 213s Investment_8 -1.1680 -20.610 213s Investment_9 -0.5634 -10.672 213s Investment_10 0.0000 0.000 213s Investment_11 0.9137 15.295 213s Investment_12 0.9272 12.402 213s Investment_14 -1.2036 -12.064 213s Investment_15 0.2779 3.475 213s Investment_16 -0.0439 -0.636 213s Investment_17 -1.7918 -26.720 213s Investment_18 0.2271 4.411 213s Investment_19 3.1278 59.767 213s Investment_20 -0.5790 -10.225 213s Investment_21 -0.2789 -5.690 213s Investment_22 -0.8484 -19.238 213s PrivateWages_2 -3.1568 -44.237 213s PrivateWages_3 1.1209 18.679 213s PrivateWages_4 2.7328 50.677 213s PrivateWages_5 -2.9712 -60.223 213s PrivateWages_6 -0.5212 -9.913 213s PrivateWages_8 1.7420 30.738 213s PrivateWages_9 1.9832 37.569 213s PrivateWages_10 0.0000 0.000 213s PrivateWages_11 -2.5151 -42.105 213s PrivateWages_12 -0.3611 -4.830 213s PrivateWages_13 0.0000 0.000 213s PrivateWages_14 3.2055 32.130 213s PrivateWages_15 -0.2814 -3.519 213s PrivateWages_16 -0.4078 -5.906 213s PrivateWages_17 2.6678 39.784 213s PrivateWages_18 0.0554 1.076 213s PrivateWages_19 -6.6416 -126.909 213s PrivateWages_20 1.4327 25.301 213s PrivateWages_21 -1.3598 -27.735 213s PrivateWages_22 2.0747 47.044 213s Consumption_corpProfLag Consumption_wages 213s Consumption_2 -46.322 -108.77 213s Consumption_3 -9.621 -24.71 213s Consumption_4 9.097 18.98 213s Consumption_5 -37.905 -79.52 213s Consumption_6 20.558 40.85 213s Consumption_8 98.211 200.48 213s Consumption_9 88.711 187.18 213s Consumption_11 -47.964 -95.27 213s Consumption_12 -46.648 -118.58 213s Consumption_14 3.926 18.69 213s Consumption_15 -25.757 -85.85 213s Consumption_16 -23.410 -76.40 213s Consumption_17 89.949 268.43 213s Consumption_18 -12.733 -34.44 213s Consumption_19 -87.892 -250.13 213s Consumption_20 52.529 166.71 213s Consumption_21 30.546 85.88 213s Consumption_22 -23.871 -68.78 213s Investment_2 21.002 49.32 213s Investment_3 -1.940 -4.98 213s Investment_4 -10.851 -22.64 213s Investment_5 25.967 54.47 213s Investment_6 -6.901 -13.71 213s Investment_8 -22.893 -46.73 213s Investment_9 -11.154 -23.53 213s Investment_10 0.000 0.00 213s Investment_11 19.827 39.38 213s Investment_12 14.464 36.77 213s Investment_14 -8.425 -40.11 213s Investment_15 3.113 10.38 213s Investment_16 -0.540 -1.76 213s Investment_17 -25.085 -74.86 213s Investment_18 3.997 10.81 213s Investment_19 54.111 153.99 213s Investment_20 -8.858 -28.11 213s Investment_21 -5.300 -14.90 213s Investment_22 -17.901 -51.58 213s PrivateWages_2 -40.091 -94.14 213s PrivateWages_3 13.899 35.70 213s PrivateWages_4 46.184 96.34 213s PrivateWages_5 -54.670 -114.69 213s PrivateWages_6 -10.110 -20.09 213s PrivateWages_8 34.144 69.70 213s PrivateWages_9 39.267 82.85 213s PrivateWages_10 0.000 0.00 213s PrivateWages_11 -54.578 -108.40 213s PrivateWages_12 -5.633 -14.32 213s PrivateWages_13 0.000 0.00 213s PrivateWages_14 22.438 106.83 213s PrivateWages_15 -3.152 -10.51 213s PrivateWages_16 -5.016 -16.37 213s PrivateWages_17 37.350 111.46 213s PrivateWages_18 0.975 2.64 213s PrivateWages_19 -114.899 -326.98 213s PrivateWages_20 21.920 69.57 213s PrivateWages_21 -25.836 -72.64 213s PrivateWages_22 43.775 126.12 213s Investment_(Intercept) Investment_corpProf 213s Consumption_2 1.8176 24.384 213s Consumption_3 0.3867 6.453 213s Consumption_4 -0.2682 -5.040 213s Consumption_5 1.0266 21.198 213s Consumption_6 -0.5281 -10.172 213s Consumption_8 -2.4970 -43.782 213s Consumption_9 -2.2327 -43.602 213s Consumption_11 1.1015 18.940 213s Consumption_12 1.4902 20.151 213s Consumption_14 -0.2795 -2.793 213s Consumption_15 1.1460 14.736 213s Consumption_16 0.9485 13.590 213s Consumption_17 -3.2018 -47.918 213s Consumption_18 0.3605 6.983 213s Consumption_19 2.5318 49.008 213s Consumption_20 -1.7109 -29.898 213s Consumption_21 -0.8012 -16.122 213s Consumption_22 0.5638 12.844 213s Investment_2 -2.3696 -31.787 213s Investment_3 0.2241 3.741 213s Investment_4 0.9200 17.284 213s Investment_5 -2.0221 -41.754 213s Investment_6 0.5097 9.819 213s Investment_8 1.6736 29.344 213s Investment_9 0.8072 15.764 213s Investment_10 2.9560 59.913 213s Investment_11 -1.3092 -22.510 213s Investment_12 -1.3285 -17.964 213s Investment_14 1.7246 17.233 213s Investment_15 -0.3982 -5.120 213s Investment_16 0.0630 0.902 213s Investment_17 2.5674 38.424 213s Investment_18 -0.3254 -6.303 213s Investment_19 -4.4817 -86.752 213s Investment_20 0.8296 14.497 213s Investment_21 0.3997 8.043 213s Investment_22 1.2156 27.693 213s PrivateWages_2 1.9315 25.910 213s PrivateWages_3 -0.6858 -11.446 213s PrivateWages_4 -1.6720 -31.413 213s PrivateWages_5 1.8179 37.537 213s PrivateWages_6 0.3189 6.142 213s PrivateWages_8 -1.0659 -18.688 213s PrivateWages_9 -1.2134 -23.696 213s PrivateWages_10 -2.2443 -45.488 213s PrivateWages_11 1.5389 26.460 213s PrivateWages_12 0.2209 2.988 213s PrivateWages_13 0.0000 0.000 213s PrivateWages_14 -1.9613 -19.598 213s PrivateWages_15 0.1722 2.214 213s PrivateWages_16 0.2495 3.576 213s PrivateWages_17 -1.6323 -24.429 213s PrivateWages_18 -0.0339 -0.657 213s PrivateWages_19 4.0636 78.659 213s PrivateWages_20 -0.8766 -15.318 213s PrivateWages_21 0.8320 16.742 213s PrivateWages_22 -1.2694 -28.917 213s Investment_corpProfLag Investment_capitalLag 213s Consumption_2 23.084 332.27 213s Consumption_3 4.795 70.60 213s Consumption_4 -4.533 -49.49 213s Consumption_5 18.890 194.75 213s Consumption_6 -10.245 -101.76 213s Consumption_8 -48.942 -507.90 213s Consumption_9 -44.208 -463.52 213s Consumption_11 23.902 237.59 213s Consumption_12 23.247 322.92 213s Consumption_14 -1.957 -57.89 213s Consumption_15 12.836 231.50 213s Consumption_16 11.666 188.74 213s Consumption_17 -44.825 -632.99 213s Consumption_18 6.345 72.04 213s Consumption_19 43.800 510.92 213s Consumption_20 -26.177 -342.01 213s Consumption_21 -15.222 -161.20 213s Consumption_22 11.896 115.30 213s Investment_2 -30.093 -433.16 213s Investment_3 2.779 40.93 213s Investment_4 15.547 169.73 213s Investment_5 -37.208 -383.60 213s Investment_6 9.888 98.22 213s Investment_8 32.803 340.41 213s Investment_9 15.983 167.58 213s Investment_10 62.371 622.53 213s Investment_11 -28.409 -282.39 213s Investment_12 -20.724 -287.88 213s Investment_14 12.072 357.16 213s Investment_15 -4.460 -80.44 213s Investment_16 0.774 12.53 213s Investment_17 35.944 507.58 213s Investment_18 -5.727 -65.02 213s Investment_19 -77.534 -904.41 213s Investment_20 12.693 165.84 213s Investment_21 7.594 80.42 213s Investment_22 25.650 248.60 213s PrivateWages_2 24.530 353.07 213s PrivateWages_3 -8.504 -125.23 213s PrivateWages_4 -28.257 -308.49 213s PrivateWages_5 33.450 344.86 213s PrivateWages_6 6.186 61.45 213s PrivateWages_8 -20.891 -216.79 213s PrivateWages_9 -24.025 -251.90 213s PrivateWages_10 -47.355 -472.65 213s PrivateWages_11 33.393 331.93 213s PrivateWages_12 3.447 47.88 213s PrivateWages_13 0.000 0.00 213s PrivateWages_14 -13.729 -406.18 213s PrivateWages_15 1.929 34.78 213s PrivateWages_16 3.069 49.66 213s PrivateWages_17 -22.852 -322.71 213s PrivateWages_18 -0.597 -6.77 213s PrivateWages_19 70.300 820.04 213s PrivateWages_20 -13.412 -175.23 213s PrivateWages_21 15.807 167.39 213s PrivateWages_22 -26.784 -259.59 213s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 213s Consumption_2 -3.6123 -170.03 -162.19 213s Consumption_3 -0.7684 -38.10 -35.04 213s Consumption_4 0.5331 30.14 26.71 213s Consumption_5 -2.0403 -123.82 -116.70 213s Consumption_6 1.0495 63.61 59.93 213s Consumption_8 4.9625 297.74 317.60 213s Consumption_9 4.4373 276.30 285.76 213s Consumption_11 -2.1891 -139.47 -146.67 213s Consumption_12 -2.9615 -162.39 -181.24 213s Consumption_14 0.5555 23.40 24.61 213s Consumption_15 -2.2776 -116.65 -102.72 213s Consumption_16 -1.8849 -104.31 -93.68 213s Consumption_17 6.3631 365.20 346.15 213s Consumption_18 -0.7165 -48.13 -44.93 213s Consumption_19 -5.0316 -344.73 -327.05 213s Consumption_20 3.4002 227.29 207.07 213s Consumption_21 1.5922 119.20 110.66 213s Consumption_22 -1.1205 -97.34 -84.82 213s Investment_2 2.0108 94.65 90.29 213s Investment_3 -0.1902 -9.43 -8.67 213s Investment_4 -0.7807 -44.14 -39.11 213s Investment_5 1.7160 104.14 98.16 213s Investment_6 -0.4326 -26.22 -24.70 213s Investment_8 -1.4203 -85.21 -90.90 213s Investment_9 -0.6850 -42.65 -44.11 213s Investment_10 -2.5085 -161.97 -161.80 213s Investment_11 1.1110 70.78 74.44 213s Investment_12 1.1274 61.82 69.00 213s Investment_14 -1.4635 -61.65 -64.83 213s Investment_15 0.3379 17.31 15.24 213s Investment_16 -0.0534 -2.96 -2.66 213s Investment_17 -2.1788 -125.05 -118.52 213s Investment_18 0.2762 18.55 17.32 213s Investment_19 3.8033 260.57 247.21 213s Investment_20 -0.7040 -47.06 -42.87 213s Investment_21 -0.3392 -25.39 -23.57 213s Investment_22 -1.0316 -89.62 -78.09 213s PrivateWages_2 -7.1301 -335.61 -320.14 213s PrivateWages_3 2.5317 125.52 115.44 213s PrivateWages_4 6.1723 349.00 309.23 213s PrivateWages_5 -6.7109 -407.26 -383.86 213s PrivateWages_6 -1.1771 -71.34 -67.21 213s PrivateWages_8 3.9346 236.07 251.82 213s PrivateWages_9 4.4793 278.92 288.47 213s PrivateWages_10 8.2849 534.95 534.38 213s PrivateWages_11 -5.6807 -361.93 -380.61 213s PrivateWages_12 -0.8156 -44.72 -49.92 213s PrivateWages_13 -4.4579 -209.42 -238.05 213s PrivateWages_14 7.2401 305.01 320.74 213s PrivateWages_15 -0.6357 -32.56 -28.67 213s PrivateWages_16 -0.9212 -50.98 -45.78 213s PrivateWages_17 6.0257 345.84 327.80 213s PrivateWages_18 0.1252 8.41 7.85 213s PrivateWages_19 -15.0009 -1027.75 -975.06 213s PrivateWages_20 3.2360 216.31 197.07 213s PrivateWages_21 -3.0713 -229.93 -213.45 213s PrivateWages_22 4.6859 407.11 354.72 213s PrivateWages_trend 213s Consumption_2 36.123 213s Consumption_3 6.916 213s Consumption_4 -4.265 213s Consumption_5 14.282 213s Consumption_6 -6.297 213s Consumption_8 -19.850 213s Consumption_9 -13.312 213s Consumption_11 2.189 213s Consumption_12 0.000 213s Consumption_14 1.111 213s Consumption_15 -6.833 213s Consumption_16 -7.540 213s Consumption_17 31.815 213s Consumption_18 -4.299 213s Consumption_19 -35.221 213s Consumption_20 27.202 213s Consumption_21 14.330 213s Consumption_22 -11.205 213s Investment_2 -20.108 213s Investment_3 1.712 213s Investment_4 6.246 213s Investment_5 -12.012 213s Investment_6 2.595 213s Investment_8 5.681 213s Investment_9 2.055 213s Investment_10 5.017 213s Investment_11 -1.111 213s Investment_12 0.000 213s Investment_14 -2.927 213s Investment_15 1.014 213s Investment_16 -0.214 213s Investment_17 -10.894 213s Investment_18 1.657 213s Investment_19 26.623 213s Investment_20 -5.632 213s Investment_21 -3.053 213s Investment_22 -10.316 213s PrivateWages_2 71.301 213s PrivateWages_3 -22.785 213s PrivateWages_4 -49.379 213s PrivateWages_5 46.976 213s PrivateWages_6 7.063 213s PrivateWages_8 -15.738 213s PrivateWages_9 -13.438 213s PrivateWages_10 -16.570 213s PrivateWages_11 5.681 213s PrivateWages_12 0.000 213s PrivateWages_13 -4.458 213s PrivateWages_14 14.480 213s PrivateWages_15 -1.907 213s PrivateWages_16 -3.685 213s PrivateWages_17 30.129 213s PrivateWages_18 0.751 213s PrivateWages_19 -105.007 213s PrivateWages_20 25.888 213s PrivateWages_21 -27.641 213s PrivateWages_22 46.859 213s [1] TRUE 213s > Bread 213s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 213s [1,] 132.9647 -4.1876 0.7762 213s [2,] -4.1876 1.2160 -0.6687 213s [3,] 0.7762 -0.6687 0.7219 213s [4,] -1.6897 -0.1344 -0.0278 213s [5,] 101.6483 3.2473 3.4997 213s [6,] -4.3150 0.5140 -0.4474 213s [7,] 1.5566 -0.3374 0.4240 213s [8,] -0.2539 -0.0329 -0.0138 213s [9,] -35.7522 0.3296 1.6708 213s [10,] 0.5355 -0.0797 0.0478 213s [11,] 0.0459 0.0759 -0.0780 213s [12,] 0.1973 0.0481 0.0250 213s Consumption_wages Investment_(Intercept) Investment_corpProf 213s [1,] -1.689687 101.65 -4.32e+00 213s [2,] -0.134421 3.25 5.14e-01 213s [3,] -0.027837 3.50 -4.47e-01 213s [4,] 0.106098 -5.00 6.63e-02 213s [5,] -4.996393 2449.02 -4.26e+01 213s [6,] 0.066338 -42.57 1.86e+00 213s [7,] -0.064579 34.21 -1.44e+00 213s [8,] 0.024569 -11.36 1.70e-01 213s [9,] 0.047220 27.91 -2.66e-01 213s [10,] 0.000172 1.31 3.12e-04 213s [11,] -0.000827 -1.84 4.41e-03 213s [12,] -0.034079 -0.80 1.58e-02 213s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 213s [1,] 1.55659 -0.25392 -35.7522 213s [2,] -0.33742 -0.03292 0.3296 213s [3,] 0.42396 -0.01383 1.6708 213s [4,] -0.06458 0.02457 0.0472 213s [5,] 34.20897 -11.35519 27.9136 213s [6,] -1.43523 0.17002 -0.2656 213s [7,] 1.37137 -0.15991 -0.3976 213s [8,] -0.15991 0.05521 -0.0847 213s [9,] -0.39759 -0.08475 68.4821 213s [10,] 0.00601 -0.00701 -0.3279 213s [11,] 0.00088 0.00875 -0.8283 213s [12,] -0.02279 0.00445 0.7887 213s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 213s [1,] 0.535460 0.045866 0.197271 213s [2,] -0.079666 0.075947 0.048142 213s [3,] 0.047829 -0.078006 0.025001 213s [4,] 0.000172 -0.000827 -0.034079 213s [5,] 1.306914 -1.841775 -0.800037 213s [6,] 0.000312 0.004408 0.015824 213s [7,] 0.006007 0.000880 -0.022790 213s [8,] -0.007006 0.008751 0.004448 213s [9,] -0.327909 -0.828330 0.788744 213s [10,] 0.051096 -0.046839 -0.013933 213s [11,] -0.046839 0.062505 0.000532 213s [12,] -0.013933 0.000532 0.045663 213s > 213s > # I3SLS 213s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 213s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 214s > summary 214s 214s systemfit results 214s method: iterated 3SLS 214s 214s convergence achieved after 9 iterations 214s 214s N DF SSR detRCov OLS-R2 McElroy-R2 214s system 57 45 75 0.422 0.959 0.993 214s 214s N DF SSR MSE RMSE R2 Adj R2 214s Consumption 18 14 22.7 1.622 1.273 0.973 0.968 214s Investment 19 15 42.1 2.809 1.676 0.762 0.715 214s PrivateWages 20 16 10.2 0.638 0.799 0.987 0.985 214s 214s The covariance matrix of the residuals used for estimation 214s Consumption Investment PrivateWages 214s Consumption 1.261 0.675 -0.439 214s Investment 0.675 1.949 0.237 214s PrivateWages -0.439 0.237 0.503 214s 214s The covariance matrix of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.261 0.675 -0.439 214s Investment 0.675 1.949 0.237 214s PrivateWages -0.439 0.237 0.503 214s 214s The correlations of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.000 0.431 -0.550 214s Investment 0.431 1.000 0.239 214s PrivateWages -0.550 0.239 1.000 214s 214s 214s 3SLS estimates for 'Consumption' (equation 1) 214s Model Formula: consump ~ corpProf + corpProfLag + wages 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 18.5887 1.5250 12.19 7.6e-09 *** 214s corpProf -0.0438 0.1441 -0.30 0.77 214s corpProfLag 0.1456 0.1109 1.31 0.21 214s wages 0.8141 0.0428 19.01 2.1e-11 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.273 on 14 degrees of freedom 214s Number of observations: 18 Degrees of Freedom: 14 214s SSR: 22.704 MSE: 1.622 Root MSE: 1.273 214s Multiple R-Squared: 0.973 Adjusted R-Squared: 0.968 214s 214s 214s 3SLS estimates for 'Investment' (equation 2) 214s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 29.4725 7.6857 3.83 0.0016 ** 214s corpProf -0.0183 0.2154 -0.09 0.9333 214s corpProfLag 0.7195 0.1850 3.89 0.0015 ** 214s capitalLag -0.1985 0.0366 -5.43 6.9e-05 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.676 on 15 degrees of freedom 214s Number of observations: 19 Degrees of Freedom: 15 214s SSR: 42.136 MSE: 2.809 Root MSE: 1.676 214s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.715 214s 214s 214s 3SLS estimates for 'PrivateWages' (equation 3) 214s Model Formula: privWage ~ gnp + gnpLag + trend 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 0.5385 1.1055 0.49 0.63277 214s gnp 0.4251 0.0287 14.80 9.3e-11 *** 214s gnpLag 0.1776 0.0322 5.51 4.7e-05 *** 214s trend 0.1211 0.0283 4.28 0.00057 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 0.799 on 16 degrees of freedom 214s Number of observations: 20 Degrees of Freedom: 16 214s SSR: 10.204 MSE: 0.638 Root MSE: 0.799 214s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 214s 214s > residuals 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 -0.9524 -2.2888 -1.1837 214s 3 -0.8681 0.0698 0.4581 214s 4 -1.1653 0.5368 1.3199 214s 5 0.0601 -1.6917 -0.2194 214s 6 0.6426 0.2972 -0.4805 214s 7 NA NA NA 214s 8 1.8394 1.3723 -0.8931 214s 9 1.8275 0.8861 0.1723 214s 10 NA 2.6574 1.0707 214s 11 -0.3387 -0.9736 -0.4288 214s 12 -1.4550 -0.8630 0.3956 214s 13 NA NA 0.0277 214s 14 -0.3782 1.7151 0.6823 214s 15 -0.7768 -0.1993 0.5638 214s 16 -0.4606 0.1448 0.2281 214s 17 1.8605 2.1295 -0.6557 214s 18 -0.5262 -0.1493 0.9718 214s 19 -0.3047 -3.4730 -0.6148 214s 20 1.3992 0.8566 -0.2636 214s 21 1.4216 0.4910 -1.1472 214s 22 -1.2431 1.2792 0.5323 214s > fitted 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 42.9 2.0888 26.7 214s 3 45.9 1.8302 28.8 214s 4 50.4 4.6632 32.8 214s 5 50.5 4.6917 34.1 214s 6 52.0 4.8028 35.9 214s 7 NA NA NA 214s 8 54.4 2.8277 38.8 214s 9 55.5 2.1139 39.0 214s 10 NA 2.4426 40.2 214s 11 55.3 1.9736 38.3 214s 12 52.4 -2.5370 34.1 214s 13 NA NA 29.0 214s 14 46.9 -6.8151 27.8 214s 15 49.5 -2.8007 30.0 214s 16 51.8 -1.4448 33.0 214s 17 55.8 -0.0295 37.5 214s 18 59.2 2.1493 40.0 214s 19 57.8 1.5730 38.8 214s 20 60.2 0.4434 41.9 214s 21 63.6 2.8090 46.1 214s 22 70.9 3.6208 52.8 214s > predict 214s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 214s 1 NA NA NA NA 214s 2 42.9 0.541 41.8 43.9 214s 3 45.9 0.608 44.6 47.1 214s 4 50.4 0.403 49.6 51.2 214s 5 50.5 0.472 49.6 51.5 214s 6 52.0 0.481 51.0 52.9 214s 7 NA NA NA NA 214s 8 54.4 0.388 53.6 55.1 214s 9 55.5 0.458 54.6 56.4 214s 10 NA NA NA NA 214s 11 55.3 0.795 53.7 56.9 214s 12 52.4 0.762 50.8 53.9 214s 13 NA NA NA NA 214s 14 46.9 0.663 45.5 48.2 214s 15 49.5 0.462 48.5 50.4 214s 16 51.8 0.381 51.0 52.5 214s 17 55.8 0.423 55.0 56.7 214s 18 59.2 0.355 58.5 59.9 214s 19 57.8 0.484 56.8 58.8 214s 20 60.2 0.500 59.2 61.2 214s 21 63.6 0.490 62.6 64.6 214s 22 70.9 0.747 69.4 72.4 214s Investment.pred Investment.se.fit Investment.lwr Investment.upr 214s 1 NA NA NA NA 214s 2 2.0888 0.985 0.105 4.072 214s 3 1.8302 0.708 0.404 3.257 214s 4 4.6632 0.612 3.430 5.897 214s 5 4.6917 0.519 3.645 5.738 214s 6 4.8028 0.498 3.800 5.806 214s 7 NA NA NA NA 214s 8 2.8277 0.410 2.003 3.653 214s 9 2.1139 0.599 0.908 3.320 214s 10 2.4426 0.651 1.131 3.754 214s 11 1.9736 1.138 -0.320 4.267 214s 12 -2.5370 1.038 -4.627 -0.447 214s 13 NA NA NA NA 214s 14 -6.8151 1.011 -8.851 -4.779 214s 15 -2.8007 0.587 -3.984 -1.617 214s 16 -1.4448 0.470 -2.392 -0.498 214s 17 -0.0295 0.573 -1.183 1.124 214s 18 2.1493 0.380 1.384 2.915 214s 19 1.5730 0.624 0.315 2.831 214s 20 0.4434 0.649 -0.864 1.751 214s 21 2.8090 0.565 1.671 3.947 214s 22 3.6208 0.814 1.982 5.260 214s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 214s 1 NA NA NA NA 214s 2 26.7 0.322 26.0 27.3 214s 3 28.8 0.328 28.2 29.5 214s 4 32.8 0.332 32.1 33.4 214s 5 34.1 0.244 33.6 34.6 214s 6 35.9 0.252 35.4 36.4 214s 7 NA NA NA NA 214s 8 38.8 0.246 38.3 39.3 214s 9 39.0 0.234 38.6 39.5 214s 10 40.2 0.230 39.8 40.7 214s 11 38.3 0.299 37.7 38.9 214s 12 34.1 0.304 33.5 34.7 214s 13 29.0 0.366 28.2 29.7 214s 14 27.8 0.321 27.2 28.5 214s 15 30.0 0.317 29.4 30.7 214s 16 33.0 0.266 32.4 33.5 214s 17 37.5 0.270 36.9 38.0 214s 18 40.0 0.211 39.6 40.5 214s 19 38.8 0.305 38.2 39.4 214s 20 41.9 0.290 41.3 42.4 214s 21 46.1 0.309 45.5 46.8 214s 22 52.8 0.468 51.8 53.7 214s > model.frame 214s [1] TRUE 214s > model.matrix 214s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 214s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 214s [3] "Numeric: lengths (708, 684) differ" 214s > nobs 214s [1] 57 214s > linearHypothesis 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 45 1 2.17 0.15 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 45 1 2.84 0.099 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 46 214s 2 45 1 2.84 0.092 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 47 214s 2 45 2 2.45 0.098 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 47 214s 2 45 2 3.2 0.05 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 47 214s 2 45 2 6.4 0.041 * 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s > logLik 214s 'log Lik.' -72.7 (df=18) 214s 'log Lik.' -83.9 (df=18) 214s Estimating function 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 -4.8293 -67.67 214s Consumption_3 -1.2969 -21.61 214s Consumption_4 0.5735 10.64 214s Consumption_5 -2.6416 -53.54 214s Consumption_6 1.4014 26.66 214s Consumption_8 6.4885 114.49 214s Consumption_9 5.8062 109.99 214s Consumption_11 -2.4210 -40.53 214s Consumption_12 -3.6335 -48.60 214s Consumption_14 0.4385 4.39 214s Consumption_15 -2.9914 -37.40 214s Consumption_16 -2.4677 -35.74 214s Consumption_17 8.1448 121.46 214s Consumption_18 -0.7823 -15.19 214s Consumption_19 -6.2524 -119.47 214s Consumption_20 4.4447 78.49 214s Consumption_21 2.3016 46.94 214s Consumption_22 -1.0069 -22.83 214s Investment_2 2.3888 33.48 214s Investment_3 -0.0694 -1.16 214s Investment_4 -0.5723 -10.61 214s Investment_5 1.7561 35.59 214s Investment_6 -0.2966 -5.64 214s Investment_8 -1.4003 -24.71 214s Investment_9 -0.9021 -17.09 214s Investment_10 0.0000 0.00 214s Investment_11 0.9937 16.63 214s Investment_12 0.8671 11.60 214s Investment_14 -1.7814 -17.86 214s Investment_15 0.1989 2.49 214s Investment_16 -0.1587 -2.30 214s Investment_17 -2.1900 -32.66 214s Investment_18 0.1172 2.28 214s Investment_19 3.5762 68.34 214s Investment_20 -0.8719 -15.40 214s Investment_21 -0.4978 -10.15 214s Investment_22 -1.3322 -30.21 214s PrivateWages_2 -4.3522 -60.99 214s PrivateWages_3 1.6337 27.22 214s PrivateWages_4 3.8487 71.37 214s PrivateWages_5 -4.1966 -85.06 214s PrivateWages_6 -0.7579 -14.42 214s PrivateWages_8 2.3542 41.54 214s PrivateWages_9 2.6975 51.10 214s PrivateWages_10 0.0000 0.00 214s PrivateWages_11 -3.6015 -60.29 214s PrivateWages_12 -0.5133 -6.87 214s PrivateWages_13 0.0000 0.00 214s PrivateWages_14 4.6825 46.94 214s PrivateWages_15 -0.1944 -2.43 214s PrivateWages_16 -0.4112 -5.96 214s PrivateWages_17 3.8500 57.41 214s PrivateWages_18 0.1148 2.23 214s PrivateWages_19 -9.2669 -177.08 214s PrivateWages_20 2.0821 36.77 214s PrivateWages_21 -1.9079 -38.91 214s PrivateWages_22 2.8370 64.33 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 -61.332 -144.02 214s Consumption_3 -16.082 -41.30 214s Consumption_4 9.693 20.22 214s Consumption_5 -48.605 -101.97 214s Consumption_6 27.187 54.02 214s Consumption_8 127.174 259.60 214s Consumption_9 114.963 242.56 214s Consumption_11 -52.537 -104.35 214s Consumption_12 -56.683 -144.08 214s Consumption_14 3.069 14.61 214s Consumption_15 -33.504 -111.68 214s Consumption_16 -30.352 -99.06 214s Consumption_17 114.027 340.28 214s Consumption_18 -13.768 -37.24 214s Consumption_19 -108.167 -307.82 214s Consumption_20 68.004 215.82 214s Consumption_21 43.729 122.95 214s Consumption_22 -21.245 -61.21 214s Investment_2 30.338 71.24 214s Investment_3 -0.861 -2.21 214s Investment_4 -9.672 -20.18 214s Investment_5 32.311 67.78 214s Investment_6 -5.754 -11.43 214s Investment_8 -27.445 -56.02 214s Investment_9 -17.861 -37.69 214s Investment_10 0.000 0.00 214s Investment_11 21.563 42.83 214s Investment_12 13.527 34.39 214s Investment_14 -12.470 -59.37 214s Investment_15 2.228 7.43 214s Investment_16 -1.952 -6.37 214s Investment_17 -30.659 -91.49 214s Investment_18 2.063 5.58 214s Investment_19 61.869 176.07 214s Investment_20 -13.340 -42.34 214s Investment_21 -9.458 -26.59 214s Investment_22 -28.109 -80.99 214s PrivateWages_2 -55.273 -129.79 214s PrivateWages_3 20.257 52.03 214s PrivateWages_4 65.044 135.69 214s PrivateWages_5 -77.218 -161.99 214s PrivateWages_6 -14.704 -29.21 214s PrivateWages_8 46.143 94.19 214s PrivateWages_9 53.410 112.69 214s PrivateWages_10 0.000 0.00 214s PrivateWages_11 -78.152 -155.23 214s PrivateWages_12 -8.008 -20.36 214s PrivateWages_13 0.000 0.00 214s PrivateWages_14 32.778 156.05 214s PrivateWages_15 -2.178 -7.26 214s PrivateWages_16 -5.058 -16.51 214s PrivateWages_17 53.901 160.85 214s PrivateWages_18 2.020 5.46 214s PrivateWages_19 -160.318 -456.23 214s PrivateWages_20 31.857 101.10 214s PrivateWages_21 -36.250 -101.92 214s PrivateWages_22 59.861 172.47 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 2.3171 31.08 214s Consumption_3 0.6223 10.39 214s Consumption_4 -0.2752 -5.17 214s Consumption_5 1.2675 26.17 214s Consumption_6 -0.6724 -12.95 214s Consumption_8 -3.1132 -54.59 214s Consumption_9 -2.7858 -54.40 214s Consumption_11 1.1616 19.97 214s Consumption_12 1.7434 23.57 214s Consumption_14 -0.2104 -2.10 214s Consumption_15 1.4353 18.46 214s Consumption_16 1.1840 16.97 214s Consumption_17 -3.9079 -58.49 214s Consumption_18 0.3753 7.27 214s Consumption_19 2.9999 58.07 214s Consumption_20 -2.1326 -37.27 214s Consumption_21 -1.1043 -22.22 214s Consumption_22 0.4831 11.01 214s Investment_2 -2.3817 -31.95 214s Investment_3 0.0692 1.16 214s Investment_4 0.5706 10.72 214s Investment_5 -1.7509 -36.15 214s Investment_6 0.2957 5.70 214s Investment_8 1.3961 24.48 214s Investment_9 0.8994 17.56 214s Investment_10 2.7604 55.95 214s Investment_11 -0.9907 -17.04 214s Investment_12 -0.8646 -11.69 214s Investment_14 1.7761 17.75 214s Investment_15 -0.1983 -2.55 214s Investment_16 0.1582 2.27 214s Investment_17 2.1835 32.68 214s Investment_18 -0.1169 -2.26 214s Investment_19 -3.5657 -69.02 214s Investment_20 0.8693 15.19 214s Investment_21 0.4963 9.99 214s Investment_22 1.3282 30.26 214s PrivateWages_2 2.5510 34.22 214s PrivateWages_3 -0.9575 -15.98 214s PrivateWages_4 -2.2559 -42.38 214s PrivateWages_5 2.4598 50.79 214s PrivateWages_6 0.4442 8.56 214s PrivateWages_8 -1.3799 -24.19 214s PrivateWages_9 -1.5811 -30.88 214s PrivateWages_10 -2.9678 -60.15 214s PrivateWages_11 2.1109 36.30 214s PrivateWages_12 0.3009 4.07 214s PrivateWages_13 0.0000 0.00 214s PrivateWages_14 -2.7446 -27.43 214s PrivateWages_15 0.1140 1.47 214s PrivateWages_16 0.2410 3.45 214s PrivateWages_17 -2.2567 -33.77 214s PrivateWages_18 -0.0673 -1.30 214s PrivateWages_19 5.4317 105.14 214s PrivateWages_20 -1.2204 -21.33 214s PrivateWages_21 1.1183 22.50 214s PrivateWages_22 -1.6629 -37.88 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 29.428 423.6 214s Consumption_3 7.716 113.6 214s Consumption_4 -4.651 -50.8 214s Consumption_5 23.321 240.4 214s Consumption_6 -13.045 -129.6 214s Consumption_8 -61.019 -633.2 214s Consumption_9 -55.160 -578.3 214s Consumption_11 25.207 250.6 214s Consumption_12 27.197 377.8 214s Consumption_14 -1.473 -43.6 214s Consumption_15 16.075 289.9 214s Consumption_16 14.563 235.6 214s Consumption_17 -54.711 -772.6 214s Consumption_18 6.606 75.0 214s Consumption_19 51.899 605.4 214s Consumption_20 -32.629 -426.3 214s Consumption_21 -20.982 -222.2 214s Consumption_22 10.194 98.8 214s Investment_2 -30.248 -435.4 214s Investment_3 0.858 12.6 214s Investment_4 9.643 105.3 214s Investment_5 -32.216 -332.1 214s Investment_6 5.737 57.0 214s Investment_8 27.364 284.0 214s Investment_9 17.808 186.7 214s Investment_10 58.244 581.3 214s Investment_11 -21.499 -213.7 214s Investment_12 -13.487 -187.4 214s Investment_14 12.433 367.8 214s Investment_15 -2.221 -40.1 214s Investment_16 1.946 31.5 214s Investment_17 30.569 431.7 214s Investment_18 -2.057 -23.4 214s Investment_19 -61.686 -719.5 214s Investment_20 13.301 173.8 214s Investment_21 9.430 99.9 214s Investment_22 28.026 271.6 214s PrivateWages_2 32.397 466.3 214s PrivateWages_3 -11.874 -174.8 214s PrivateWages_4 -38.124 -416.2 214s PrivateWages_5 45.260 466.6 214s PrivateWages_6 8.618 85.6 214s PrivateWages_8 -27.046 -280.7 214s PrivateWages_9 -31.306 -328.2 214s PrivateWages_10 -62.621 -625.0 214s PrivateWages_11 45.808 455.3 214s PrivateWages_12 4.694 65.2 214s PrivateWages_13 0.000 0.0 214s PrivateWages_14 -19.212 -568.4 214s PrivateWages_15 1.276 23.0 214s PrivateWages_16 2.965 48.0 214s PrivateWages_17 -31.593 -446.1 214s PrivateWages_18 -1.184 -13.4 214s PrivateWages_19 93.968 1096.1 214s PrivateWages_20 -18.672 -244.0 214s PrivateWages_21 21.247 225.0 214s PrivateWages_22 -35.087 -340.1 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 -5.2993 -249.44 -237.94 214s Consumption_3 -1.4232 -70.56 -64.90 214s Consumption_4 0.6293 35.58 31.53 214s Consumption_5 -2.8987 -175.91 -165.80 214s Consumption_6 1.5378 93.21 87.81 214s Consumption_8 7.1199 427.18 455.67 214s Consumption_9 6.3712 396.73 410.31 214s Consumption_11 -2.6567 -169.26 -178.00 214s Consumption_12 -3.9871 -218.62 -244.01 214s Consumption_14 0.4811 20.27 21.31 214s Consumption_15 -3.2826 -168.12 -148.04 214s Consumption_16 -2.7078 -149.85 -134.58 214s Consumption_17 8.9374 512.95 486.20 214s Consumption_18 -0.8584 -57.66 -53.82 214s Consumption_19 -6.8609 -470.06 -445.96 214s Consumption_20 4.8772 326.02 297.02 214s Consumption_21 2.5255 189.08 175.52 214s Consumption_22 -1.1049 -95.99 -83.64 214s Investment_2 3.2022 150.73 143.78 214s Investment_3 -0.0931 -4.61 -4.24 214s Investment_4 -0.7671 -43.38 -38.43 214s Investment_5 2.3540 142.85 134.65 214s Investment_6 -0.3976 -24.10 -22.70 214s Investment_8 -1.8770 -112.62 -120.13 214s Investment_9 -1.2092 -75.30 -77.87 214s Investment_10 -3.7113 -239.64 -239.38 214s Investment_11 1.3320 84.87 89.25 214s Investment_12 1.1624 63.74 71.14 214s Investment_14 -2.3880 -100.60 -105.79 214s Investment_15 0.2667 13.66 12.03 214s Investment_16 -0.2127 -11.77 -10.57 214s Investment_17 -2.9356 -168.49 -159.70 214s Investment_18 0.1571 10.56 9.85 214s Investment_19 4.7939 328.45 311.61 214s Investment_20 -1.1688 -78.13 -71.18 214s Investment_21 -0.6673 -49.96 -46.38 214s Investment_22 -1.7858 -155.15 -135.18 214s PrivateWages_2 -8.5877 -404.22 -385.59 214s PrivateWages_3 3.2235 159.82 146.99 214s PrivateWages_4 7.5943 429.40 380.48 214s PrivateWages_5 -8.2808 -502.53 -473.66 214s PrivateWages_6 -1.4955 -90.64 -85.39 214s PrivateWages_8 4.6454 278.71 297.31 214s PrivateWages_9 5.3226 331.43 342.78 214s PrivateWages_10 9.9910 645.11 644.42 214s PrivateWages_11 -7.1064 -452.76 -476.13 214s PrivateWages_12 -1.0129 -55.54 -61.99 214s PrivateWages_13 -5.2725 -247.69 -281.55 214s PrivateWages_14 9.2395 389.24 409.31 214s PrivateWages_15 -0.3837 -19.65 -17.30 214s PrivateWages_16 -0.8115 -44.91 -40.33 214s PrivateWages_17 7.5969 436.02 413.27 214s PrivateWages_18 0.2264 15.21 14.20 214s PrivateWages_19 -18.2855 -1252.79 -1188.56 214s PrivateWages_20 4.1085 274.63 250.21 214s PrivateWages_21 -3.7647 -281.85 -261.64 214s PrivateWages_22 5.5980 486.35 423.77 214s PrivateWages_trend 214s Consumption_2 52.993 214s Consumption_3 12.808 214s Consumption_4 -5.035 214s Consumption_5 20.291 214s Consumption_6 -9.227 214s Consumption_8 -28.480 214s Consumption_9 -19.114 214s Consumption_11 2.657 214s Consumption_12 0.000 214s Consumption_14 0.962 214s Consumption_15 -9.848 214s Consumption_16 -10.831 214s Consumption_17 44.687 214s Consumption_18 -5.151 214s Consumption_19 -48.026 214s Consumption_20 39.018 214s Consumption_21 22.730 214s Consumption_22 -11.049 214s Investment_2 -32.022 214s Investment_3 0.838 214s Investment_4 6.137 214s Investment_5 -16.478 214s Investment_6 2.386 214s Investment_8 7.508 214s Investment_9 3.628 214s Investment_10 7.423 214s Investment_11 -1.332 214s Investment_12 0.000 214s Investment_14 -4.776 214s Investment_15 0.800 214s Investment_16 -0.851 214s Investment_17 -14.678 214s Investment_18 0.943 214s Investment_19 33.558 214s Investment_20 -9.351 214s Investment_21 -6.006 214s Investment_22 -17.858 214s PrivateWages_2 85.877 214s PrivateWages_3 -29.012 214s PrivateWages_4 -60.755 214s PrivateWages_5 57.966 214s PrivateWages_6 8.973 214s PrivateWages_8 -18.582 214s PrivateWages_9 -15.968 214s PrivateWages_10 -19.982 214s PrivateWages_11 7.106 214s PrivateWages_12 0.000 214s PrivateWages_13 -5.272 214s PrivateWages_14 18.479 214s PrivateWages_15 -1.151 214s PrivateWages_16 -3.246 214s PrivateWages_17 37.985 214s PrivateWages_18 1.359 214s PrivateWages_19 -127.998 214s PrivateWages_20 32.868 214s PrivateWages_21 -33.882 214s PrivateWages_22 55.980 214s [1] TRUE 214s > Bread 214s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 214s [1,] 132.5589 -4.1405 0.7711 214s [2,] -4.1405 1.1839 -0.6491 214s [3,] 0.7711 -0.6491 0.7009 214s [4,] -1.6944 -0.1297 -0.0283 214s [5,] 114.8656 3.1837 5.1587 214s [6,] -5.5704 0.7491 -0.6223 214s [7,] 1.9218 -0.4973 0.5817 214s [8,] -0.2370 -0.0398 -0.0201 214s [9,] -36.8131 0.3292 1.6643 214s [10,] 0.5110 -0.0698 0.0440 214s [11,] 0.0898 0.0655 -0.0737 214s [12,] 0.2835 0.0505 0.0244 214s Consumption_wages Investment_(Intercept) Investment_corpProf 214s [1,] -1.694379 114.87 -5.57043 214s [2,] -0.129702 3.18 0.74914 214s [3,] -0.028262 5.16 -0.62232 214s [4,] 0.104489 -5.87 0.06772 214s [5,] -5.874854 3366.95 -56.98587 214s [6,] 0.067720 -56.99 2.64551 214s [7,] -0.069795 45.44 -2.02544 214s [8,] 0.029271 -15.60 0.22292 214s [9,] 0.075832 53.51 -0.48750 214s [10,] -0.001892 2.12 0.00442 214s [11,] 0.000817 -3.12 0.00410 214s [12,] -0.036920 -1.40 0.02820 214s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 214s [1,] 1.92185 -0.23700 -36.8131 214s [2,] -0.49725 -0.03983 0.3292 214s [3,] 0.58170 -0.02007 1.6643 214s [4,] -0.06979 0.02927 0.0758 214s [5,] 45.44092 -15.60143 53.5110 214s [6,] -2.02544 0.22292 -0.4875 214s [7,] 1.95029 -0.21271 -0.7904 214s [8,] -0.21271 0.07616 -0.1618 214s [9,] -0.79038 -0.16180 69.6580 214s [10,] 0.00806 -0.01150 -0.3039 214s [11,] 0.00580 0.01472 -0.8753 214s [12,] -0.04133 0.00782 0.7539 214s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 214s [1,] 0.51104 0.089786 0.283482 214s [2,] -0.06979 0.065456 0.050508 214s [3,] 0.04399 -0.073692 0.024378 214s [4,] -0.00189 0.000817 -0.036920 214s [5,] 2.11576 -3.117775 -1.396100 214s [6,] 0.00442 0.004099 0.028202 214s [7,] 0.00806 0.005798 -0.041335 214s [8,] -0.01150 0.014719 0.007824 214s [9,] -0.30387 -0.875279 0.753905 214s [10,] 0.04699 -0.042862 -0.013049 214s [11,] -0.04286 0.059096 0.000172 214s [12,] -0.01305 0.000172 0.045631 214s > 214s > # OLS 214s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 214s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 214s > summary 214s 214s systemfit results 214s method: OLS 214s 214s N DF SSR detRCov OLS-R2 McElroy-R2 214s system 58 46 44.2 0.565 0.976 0.991 214s 214s N DF SSR MSE RMSE R2 Adj R2 214s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 214s Investment 19 15 17.11 1.140 1.07 0.907 0.889 214s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 214s 214s The covariance matrix of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.285 0.061 -0.511 214s Investment 0.061 1.059 0.151 214s PrivateWages -0.511 0.151 0.648 214s 214s The correlations of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.0000 0.0457 -0.568 214s Investment 0.0457 1.0000 0.168 214s PrivateWages -0.5681 0.1676 1.000 214s 214s 214s OLS estimates for 'Consumption' (equation 1) 214s Model Formula: consump ~ corpProf + corpProfLag + wages 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 16.2957 1.5438 10.56 2.4e-08 *** 214s corpProf 0.1796 0.1206 1.49 0.16 214s corpProfLag 0.1032 0.1031 1.00 0.33 214s wages 0.7962 0.0449 17.73 1.8e-11 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.076 on 15 degrees of freedom 214s Number of observations: 19 Degrees of Freedom: 15 214s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 214s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 214s 214s 214s OLS estimates for 'Investment' (equation 2) 214s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 10.1724 5.5758 1.82 0.08808 . 214s corpProf 0.5004 0.1092 4.58 0.00036 *** 214s corpProfLag 0.3270 0.1052 3.11 0.00718 ** 214s capitalLag -0.1134 0.0275 -4.13 0.00090 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.068 on 15 degrees of freedom 214s Number of observations: 19 Degrees of Freedom: 15 214s SSR: 17.105 MSE: 1.14 Root MSE: 1.068 214s Multiple R-Squared: 0.907 Adjusted R-Squared: 0.889 214s 214s 214s OLS estimates for 'PrivateWages' (equation 3) 214s Model Formula: privWage ~ gnp + gnpLag + trend 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 1.3550 1.3512 1.00 0.3309 214s gnp 0.4417 0.0342 12.92 7e-10 *** 214s gnpLag 0.1466 0.0393 3.73 0.0018 ** 214s trend 0.1244 0.0347 3.58 0.0025 ** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 0.78 on 16 degrees of freedom 214s Number of observations: 20 Degrees of Freedom: 16 214s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 214s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 214s 214s compare coef with single-equation OLS 214s [1] TRUE 214s > residuals 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 -0.3863 0.00693 -1.3389 214s 3 -1.2484 -0.06954 0.2462 214s 4 -1.6040 1.22401 1.1255 214s 5 -0.5384 -1.37697 -0.1959 214s 6 -0.0413 0.38610 -0.5284 214s 7 0.8043 1.48598 NA 214s 8 1.2830 0.78465 -0.7909 214s 9 1.0142 -0.65483 0.2819 214s 10 NA 1.06018 1.1384 214s 11 0.1429 0.39508 -0.1904 214s 12 -0.3439 0.20479 0.5813 214s 13 NA NA 0.1206 214s 14 0.3199 0.32778 0.4773 214s 15 -0.1016 -0.07450 0.3035 214s 16 -0.0702 NA 0.0284 214s 17 1.6064 0.96998 -0.8517 214s 18 -0.4980 0.08124 0.9908 214s 19 0.1253 -2.49295 -0.4597 214s 20 0.9805 -0.70609 -0.3819 214s 21 0.7551 -0.81928 -1.1062 214s 22 -2.1992 -0.73256 0.5501 214s > fitted 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 42.3 -0.207 26.8 214s 3 46.2 1.970 29.1 214s 4 50.8 3.976 33.0 214s 5 51.1 4.377 34.1 214s 6 52.6 4.714 35.9 214s 7 54.3 4.114 NA 214s 8 54.9 3.415 38.7 214s 9 56.3 3.655 38.9 214s 10 NA 4.040 40.2 214s 11 54.9 0.605 38.1 214s 12 51.2 -3.605 33.9 214s 13 NA NA 28.9 214s 14 46.2 -5.428 28.0 214s 15 48.8 -2.926 30.3 214s 16 51.4 NA 33.2 214s 17 56.1 1.130 37.7 214s 18 59.2 1.919 40.0 214s 19 57.4 0.593 38.7 214s 20 60.6 2.006 42.0 214s 21 64.2 4.119 46.1 214s 22 71.9 5.633 52.7 214s > predict 214s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 214s 1 NA NA NA NA 214s 2 42.3 0.543 39.9 44.7 214s 3 46.2 0.581 43.8 48.7 214s 4 50.8 0.394 48.5 53.1 214s 5 51.1 0.465 48.8 53.5 214s 6 52.6 0.474 50.3 55.0 214s 7 54.3 0.423 52.0 56.6 214s 8 54.9 0.389 52.6 57.2 214s 9 56.3 0.434 54.0 58.6 214s 10 NA NA NA NA 214s 11 54.9 0.727 52.2 57.5 214s 12 51.2 0.662 48.7 53.8 214s 13 NA NA NA NA 214s 14 46.2 0.698 43.6 48.8 214s 15 48.8 0.470 46.4 51.2 214s 16 51.4 0.398 49.1 53.7 214s 17 56.1 0.405 53.8 58.4 214s 18 59.2 0.375 56.9 61.5 214s 19 57.4 0.466 55.0 59.7 214s 20 60.6 0.482 58.2 63.0 214s 21 64.2 0.485 61.9 66.6 214s 22 71.9 0.755 69.3 74.5 214s Investment.pred Investment.se.fit Investment.lwr Investment.upr 214s 1 NA NA NA NA 214s 2 -0.207 0.645 -2.718 2.30 214s 3 1.970 0.523 -0.423 4.36 214s 4 3.976 0.462 1.634 6.32 214s 5 4.377 0.383 2.094 6.66 214s 6 4.714 0.362 2.444 6.98 214s 7 4.114 0.336 1.861 6.37 214s 8 3.415 0.298 1.184 5.65 214s 9 3.655 0.400 1.359 5.95 214s 10 4.040 0.458 1.701 6.38 214s 11 0.605 0.666 -1.928 3.14 214s 12 -3.605 0.637 -6.108 -1.10 214s 13 NA NA NA NA 214s 14 -5.428 0.767 -8.074 -2.78 214s 15 -2.926 0.453 -5.261 -0.59 214s 16 NA NA NA NA 214s 17 1.130 0.366 -1.142 3.40 214s 18 1.919 0.258 -0.293 4.13 214s 19 0.593 0.357 -1.674 2.86 214s 20 2.006 0.384 -0.278 4.29 214s 21 4.119 0.350 1.858 6.38 214s 22 5.633 0.495 3.263 8.00 214s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 214s 1 NA NA NA NA 214s 2 26.8 0.378 25.1 28.6 214s 3 29.1 0.381 27.3 30.8 214s 4 33.0 0.384 31.2 34.7 214s 5 34.1 0.297 32.4 35.8 214s 6 35.9 0.296 34.2 37.6 214s 7 NA NA NA NA 214s 8 38.7 0.303 37.0 40.4 214s 9 38.9 0.288 37.2 40.6 214s 10 40.2 0.274 38.5 41.8 214s 11 38.1 0.377 36.3 39.8 214s 12 33.9 0.381 32.2 35.7 214s 13 28.9 0.452 27.1 30.7 214s 14 28.0 0.397 26.3 29.8 214s 15 30.3 0.391 28.5 32.1 214s 16 33.2 0.327 31.5 34.9 214s 17 37.7 0.320 36.0 39.3 214s 18 40.0 0.250 38.4 41.7 214s 19 38.7 0.375 36.9 40.4 214s 20 42.0 0.337 40.3 43.7 214s 21 46.1 0.352 44.4 47.8 214s 22 52.7 0.530 50.9 54.6 214s > model.frame 214s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 214s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 214s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 214s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 214s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 214s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 214s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 214s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 214s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 214s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 214s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 214s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 214s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 214s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 214s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 214s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 214s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 214s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 214s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 214s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 214s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 214s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 214s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 214s trend 214s 1 -11 214s 2 -10 214s 3 -9 214s 4 -8 214s 5 -7 214s 6 -6 214s 7 -5 214s 8 -4 214s 9 -3 214s 10 -2 214s 11 -1 214s 12 0 214s 13 1 214s 14 2 214s 15 3 214s 16 4 214s 17 5 214s 18 6 214s 19 7 214s 20 8 214s 21 9 214s 22 10 214s > model.matrix 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 1 12.4 214s Consumption_3 1 16.9 214s Consumption_4 1 18.4 214s Consumption_5 1 19.4 214s Consumption_6 1 20.1 214s Consumption_7 1 19.6 214s Consumption_8 1 19.8 214s Consumption_9 1 21.1 214s Consumption_11 1 15.6 214s Consumption_12 1 11.4 214s Consumption_14 1 11.2 214s Consumption_15 1 12.3 214s Consumption_16 1 14.0 214s Consumption_17 1 17.6 214s Consumption_18 1 17.3 214s Consumption_19 1 15.3 214s Consumption_20 1 19.0 214s Consumption_21 1 21.1 214s Consumption_22 1 23.5 214s Investment_2 0 0.0 214s Investment_3 0 0.0 214s Investment_4 0 0.0 214s Investment_5 0 0.0 214s Investment_6 0 0.0 214s Investment_7 0 0.0 214s Investment_8 0 0.0 214s Investment_9 0 0.0 214s Investment_10 0 0.0 214s Investment_11 0 0.0 214s Investment_12 0 0.0 214s Investment_14 0 0.0 214s Investment_15 0 0.0 214s Investment_17 0 0.0 214s Investment_18 0 0.0 214s Investment_19 0 0.0 214s Investment_20 0 0.0 214s Investment_21 0 0.0 214s Investment_22 0 0.0 214s PrivateWages_2 0 0.0 214s PrivateWages_3 0 0.0 214s PrivateWages_4 0 0.0 214s PrivateWages_5 0 0.0 214s PrivateWages_6 0 0.0 214s PrivateWages_8 0 0.0 214s PrivateWages_9 0 0.0 214s PrivateWages_10 0 0.0 214s PrivateWages_11 0 0.0 214s PrivateWages_12 0 0.0 214s PrivateWages_13 0 0.0 214s PrivateWages_14 0 0.0 214s PrivateWages_15 0 0.0 214s PrivateWages_16 0 0.0 214s PrivateWages_17 0 0.0 214s PrivateWages_18 0 0.0 214s PrivateWages_19 0 0.0 214s PrivateWages_20 0 0.0 214s PrivateWages_21 0 0.0 214s PrivateWages_22 0 0.0 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 12.7 28.2 214s Consumption_3 12.4 32.2 214s Consumption_4 16.9 37.0 214s Consumption_5 18.4 37.0 214s Consumption_6 19.4 38.6 214s Consumption_7 20.1 40.7 214s Consumption_8 19.6 41.5 214s Consumption_9 19.8 42.9 214s Consumption_11 21.7 42.1 214s Consumption_12 15.6 39.3 214s Consumption_14 7.0 34.1 214s Consumption_15 11.2 36.6 214s Consumption_16 12.3 39.3 214s Consumption_17 14.0 44.2 214s Consumption_18 17.6 47.7 214s Consumption_19 17.3 45.9 214s Consumption_20 15.3 49.4 214s Consumption_21 19.0 53.0 214s Consumption_22 21.1 61.8 214s Investment_2 0.0 0.0 214s Investment_3 0.0 0.0 214s Investment_4 0.0 0.0 214s Investment_5 0.0 0.0 214s Investment_6 0.0 0.0 214s Investment_7 0.0 0.0 214s Investment_8 0.0 0.0 214s Investment_9 0.0 0.0 214s Investment_10 0.0 0.0 214s Investment_11 0.0 0.0 214s Investment_12 0.0 0.0 214s Investment_14 0.0 0.0 214s Investment_15 0.0 0.0 214s Investment_17 0.0 0.0 214s Investment_18 0.0 0.0 214s Investment_19 0.0 0.0 214s Investment_20 0.0 0.0 214s Investment_21 0.0 0.0 214s Investment_22 0.0 0.0 214s PrivateWages_2 0.0 0.0 214s PrivateWages_3 0.0 0.0 214s PrivateWages_4 0.0 0.0 214s PrivateWages_5 0.0 0.0 214s PrivateWages_6 0.0 0.0 214s PrivateWages_8 0.0 0.0 214s PrivateWages_9 0.0 0.0 214s PrivateWages_10 0.0 0.0 214s PrivateWages_11 0.0 0.0 214s PrivateWages_12 0.0 0.0 214s PrivateWages_13 0.0 0.0 214s PrivateWages_14 0.0 0.0 214s PrivateWages_15 0.0 0.0 214s PrivateWages_16 0.0 0.0 214s PrivateWages_17 0.0 0.0 214s PrivateWages_18 0.0 0.0 214s PrivateWages_19 0.0 0.0 214s PrivateWages_20 0.0 0.0 214s PrivateWages_21 0.0 0.0 214s PrivateWages_22 0.0 0.0 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 0 0.0 214s Consumption_3 0 0.0 214s Consumption_4 0 0.0 214s Consumption_5 0 0.0 214s Consumption_6 0 0.0 214s Consumption_7 0 0.0 214s Consumption_8 0 0.0 214s Consumption_9 0 0.0 214s Consumption_11 0 0.0 214s Consumption_12 0 0.0 214s Consumption_14 0 0.0 214s Consumption_15 0 0.0 214s Consumption_16 0 0.0 214s Consumption_17 0 0.0 214s Consumption_18 0 0.0 214s Consumption_19 0 0.0 214s Consumption_20 0 0.0 214s Consumption_21 0 0.0 214s Consumption_22 0 0.0 214s Investment_2 1 12.4 214s Investment_3 1 16.9 214s Investment_4 1 18.4 214s Investment_5 1 19.4 214s Investment_6 1 20.1 214s Investment_7 1 19.6 214s Investment_8 1 19.8 214s Investment_9 1 21.1 214s Investment_10 1 21.7 214s Investment_11 1 15.6 214s Investment_12 1 11.4 214s Investment_14 1 11.2 214s Investment_15 1 12.3 214s Investment_17 1 17.6 214s Investment_18 1 17.3 214s Investment_19 1 15.3 214s Investment_20 1 19.0 214s Investment_21 1 21.1 214s Investment_22 1 23.5 214s PrivateWages_2 0 0.0 214s PrivateWages_3 0 0.0 214s PrivateWages_4 0 0.0 214s PrivateWages_5 0 0.0 214s PrivateWages_6 0 0.0 214s PrivateWages_8 0 0.0 214s PrivateWages_9 0 0.0 214s PrivateWages_10 0 0.0 214s PrivateWages_11 0 0.0 214s PrivateWages_12 0 0.0 214s PrivateWages_13 0 0.0 214s PrivateWages_14 0 0.0 214s PrivateWages_15 0 0.0 214s PrivateWages_16 0 0.0 214s PrivateWages_17 0 0.0 214s PrivateWages_18 0 0.0 214s PrivateWages_19 0 0.0 214s PrivateWages_20 0 0.0 214s PrivateWages_21 0 0.0 214s PrivateWages_22 0 0.0 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 0.0 0 214s Consumption_3 0.0 0 214s Consumption_4 0.0 0 214s Consumption_5 0.0 0 214s Consumption_6 0.0 0 214s Consumption_7 0.0 0 214s Consumption_8 0.0 0 214s Consumption_9 0.0 0 214s Consumption_11 0.0 0 214s Consumption_12 0.0 0 214s Consumption_14 0.0 0 214s Consumption_15 0.0 0 214s Consumption_16 0.0 0 214s Consumption_17 0.0 0 214s Consumption_18 0.0 0 214s Consumption_19 0.0 0 214s Consumption_20 0.0 0 214s Consumption_21 0.0 0 214s Consumption_22 0.0 0 214s Investment_2 12.7 183 214s Investment_3 12.4 183 214s Investment_4 16.9 184 214s Investment_5 18.4 190 214s Investment_6 19.4 193 214s Investment_7 20.1 198 214s Investment_8 19.6 203 214s Investment_9 19.8 208 214s Investment_10 21.1 211 214s Investment_11 21.7 216 214s Investment_12 15.6 217 214s Investment_14 7.0 207 214s Investment_15 11.2 202 214s Investment_17 14.0 198 214s Investment_18 17.6 200 214s Investment_19 17.3 202 214s Investment_20 15.3 200 214s Investment_21 19.0 201 214s Investment_22 21.1 204 214s PrivateWages_2 0.0 0 214s PrivateWages_3 0.0 0 214s PrivateWages_4 0.0 0 214s PrivateWages_5 0.0 0 214s PrivateWages_6 0.0 0 214s PrivateWages_8 0.0 0 214s PrivateWages_9 0.0 0 214s PrivateWages_10 0.0 0 214s PrivateWages_11 0.0 0 214s PrivateWages_12 0.0 0 214s PrivateWages_13 0.0 0 214s PrivateWages_14 0.0 0 214s PrivateWages_15 0.0 0 214s PrivateWages_16 0.0 0 214s PrivateWages_17 0.0 0 214s PrivateWages_18 0.0 0 214s PrivateWages_19 0.0 0 214s PrivateWages_20 0.0 0 214s PrivateWages_21 0.0 0 214s PrivateWages_22 0.0 0 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 0 0.0 0.0 214s Consumption_3 0 0.0 0.0 214s Consumption_4 0 0.0 0.0 214s Consumption_5 0 0.0 0.0 214s Consumption_6 0 0.0 0.0 214s Consumption_7 0 0.0 0.0 214s Consumption_8 0 0.0 0.0 214s Consumption_9 0 0.0 0.0 214s Consumption_11 0 0.0 0.0 214s Consumption_12 0 0.0 0.0 214s Consumption_14 0 0.0 0.0 214s Consumption_15 0 0.0 0.0 214s Consumption_16 0 0.0 0.0 214s Consumption_17 0 0.0 0.0 214s Consumption_18 0 0.0 0.0 214s Consumption_19 0 0.0 0.0 214s Consumption_20 0 0.0 0.0 214s Consumption_21 0 0.0 0.0 214s Consumption_22 0 0.0 0.0 214s Investment_2 0 0.0 0.0 214s Investment_3 0 0.0 0.0 214s Investment_4 0 0.0 0.0 214s Investment_5 0 0.0 0.0 214s Investment_6 0 0.0 0.0 214s Investment_7 0 0.0 0.0 214s Investment_8 0 0.0 0.0 214s Investment_9 0 0.0 0.0 214s Investment_10 0 0.0 0.0 214s Investment_11 0 0.0 0.0 214s Investment_12 0 0.0 0.0 214s Investment_14 0 0.0 0.0 214s Investment_15 0 0.0 0.0 214s Investment_17 0 0.0 0.0 214s Investment_18 0 0.0 0.0 214s Investment_19 0 0.0 0.0 214s Investment_20 0 0.0 0.0 214s Investment_21 0 0.0 0.0 214s Investment_22 0 0.0 0.0 214s PrivateWages_2 1 45.6 44.9 214s PrivateWages_3 1 50.1 45.6 214s PrivateWages_4 1 57.2 50.1 214s PrivateWages_5 1 57.1 57.2 214s PrivateWages_6 1 61.0 57.1 214s PrivateWages_8 1 64.4 64.0 214s PrivateWages_9 1 64.5 64.4 214s PrivateWages_10 1 67.0 64.5 214s PrivateWages_11 1 61.2 67.0 214s PrivateWages_12 1 53.4 61.2 214s PrivateWages_13 1 44.3 53.4 214s PrivateWages_14 1 45.1 44.3 214s PrivateWages_15 1 49.7 45.1 214s PrivateWages_16 1 54.4 49.7 214s PrivateWages_17 1 62.7 54.4 214s PrivateWages_18 1 65.0 62.7 214s PrivateWages_19 1 60.9 65.0 214s PrivateWages_20 1 69.5 60.9 214s PrivateWages_21 1 75.7 69.5 214s PrivateWages_22 1 88.4 75.7 214s PrivateWages_trend 214s Consumption_2 0 214s Consumption_3 0 214s Consumption_4 0 214s Consumption_5 0 214s Consumption_6 0 214s Consumption_7 0 214s Consumption_8 0 214s Consumption_9 0 214s Consumption_11 0 214s Consumption_12 0 214s Consumption_14 0 214s Consumption_15 0 214s Consumption_16 0 214s Consumption_17 0 214s Consumption_18 0 214s Consumption_19 0 214s Consumption_20 0 214s Consumption_21 0 214s Consumption_22 0 214s Investment_2 0 214s Investment_3 0 214s Investment_4 0 214s Investment_5 0 214s Investment_6 0 214s Investment_7 0 214s Investment_8 0 214s Investment_9 0 214s Investment_10 0 214s Investment_11 0 214s Investment_12 0 214s Investment_14 0 214s Investment_15 0 214s Investment_17 0 214s Investment_18 0 214s Investment_19 0 214s Investment_20 0 214s Investment_21 0 214s Investment_22 0 214s PrivateWages_2 -10 214s PrivateWages_3 -9 214s PrivateWages_4 -8 214s PrivateWages_5 -7 214s PrivateWages_6 -6 214s PrivateWages_8 -4 214s PrivateWages_9 -3 214s PrivateWages_10 -2 214s PrivateWages_11 -1 214s PrivateWages_12 0 214s PrivateWages_13 1 214s PrivateWages_14 2 214s PrivateWages_15 3 214s PrivateWages_16 4 214s PrivateWages_17 5 214s PrivateWages_18 6 214s PrivateWages_19 7 214s PrivateWages_20 8 214s PrivateWages_21 9 214s PrivateWages_22 10 214s > nobs 214s [1] 58 214s > linearHypothesis 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 47 214s 2 46 1 0.3 0.59 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 47 214s 2 46 1 0.29 0.6 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 47 214s 2 46 1 0.29 0.59 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 48 214s 2 46 2 0.16 0.85 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 48 214s 2 46 2 0.15 0.86 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 48 214s 2 46 2 0.3 0.86 214s > logLik 214s 'log Lik.' -68.8 (df=13) 214s 'log Lik.' -73.3 (df=13) 214s compare log likelihood value with single-equation OLS 214s [1] "Mean relative difference: 0.0011" 214s Estimating function 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 -0.3863 -4.791 214s Consumption_3 -1.2484 -21.098 214s Consumption_4 -1.6040 -29.514 214s Consumption_5 -0.5384 -10.446 214s Consumption_6 -0.0413 -0.830 214s Consumption_7 0.8043 15.763 214s Consumption_8 1.2830 25.403 214s Consumption_9 1.0142 21.399 214s Consumption_11 0.1429 2.229 214s Consumption_12 -0.3439 -3.920 214s Consumption_14 0.3199 3.583 214s Consumption_15 -0.1016 -1.250 214s Consumption_16 -0.0702 -0.983 214s Consumption_17 1.6064 28.272 214s Consumption_18 -0.4980 -8.616 214s Consumption_19 0.1253 1.917 214s Consumption_20 0.9805 18.629 214s Consumption_21 0.7551 15.933 214s Consumption_22 -2.1992 -51.681 214s Investment_2 0.0000 0.000 214s Investment_3 0.0000 0.000 214s Investment_4 0.0000 0.000 214s Investment_5 0.0000 0.000 214s Investment_6 0.0000 0.000 214s Investment_7 0.0000 0.000 214s Investment_8 0.0000 0.000 214s Investment_9 0.0000 0.000 214s Investment_10 0.0000 0.000 214s Investment_11 0.0000 0.000 214s Investment_12 0.0000 0.000 214s Investment_14 0.0000 0.000 214s Investment_15 0.0000 0.000 214s Investment_17 0.0000 0.000 214s Investment_18 0.0000 0.000 214s Investment_19 0.0000 0.000 214s Investment_20 0.0000 0.000 214s Investment_21 0.0000 0.000 214s Investment_22 0.0000 0.000 214s PrivateWages_2 0.0000 0.000 214s PrivateWages_3 0.0000 0.000 214s PrivateWages_4 0.0000 0.000 214s PrivateWages_5 0.0000 0.000 214s PrivateWages_6 0.0000 0.000 214s PrivateWages_8 0.0000 0.000 214s PrivateWages_9 0.0000 0.000 214s PrivateWages_10 0.0000 0.000 214s PrivateWages_11 0.0000 0.000 214s PrivateWages_12 0.0000 0.000 214s PrivateWages_13 0.0000 0.000 214s PrivateWages_14 0.0000 0.000 214s PrivateWages_15 0.0000 0.000 214s PrivateWages_16 0.0000 0.000 214s PrivateWages_17 0.0000 0.000 214s PrivateWages_18 0.0000 0.000 214s PrivateWages_19 0.0000 0.000 214s PrivateWages_20 0.0000 0.000 214s PrivateWages_21 0.0000 0.000 214s PrivateWages_22 0.0000 0.000 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 -4.907 -10.90 214s Consumption_3 -15.480 -40.20 214s Consumption_4 -27.108 -59.35 214s Consumption_5 -9.907 -19.92 214s Consumption_6 -0.801 -1.59 214s Consumption_7 16.166 32.73 214s Consumption_8 25.146 53.24 214s Consumption_9 20.081 43.51 214s Consumption_11 3.100 6.01 214s Consumption_12 -5.364 -13.51 214s Consumption_14 2.239 10.91 214s Consumption_15 -1.138 -3.72 214s Consumption_16 -0.864 -2.76 214s Consumption_17 22.489 71.00 214s Consumption_18 -8.765 -23.76 214s Consumption_19 2.168 5.75 214s Consumption_20 15.002 48.44 214s Consumption_21 14.348 40.02 214s Consumption_22 -46.403 -135.91 214s Investment_2 0.000 0.00 214s Investment_3 0.000 0.00 214s Investment_4 0.000 0.00 214s Investment_5 0.000 0.00 214s Investment_6 0.000 0.00 214s Investment_7 0.000 0.00 214s Investment_8 0.000 0.00 214s Investment_9 0.000 0.00 214s Investment_10 0.000 0.00 214s Investment_11 0.000 0.00 214s Investment_12 0.000 0.00 214s Investment_14 0.000 0.00 214s Investment_15 0.000 0.00 214s Investment_17 0.000 0.00 214s Investment_18 0.000 0.00 214s Investment_19 0.000 0.00 214s Investment_20 0.000 0.00 214s Investment_21 0.000 0.00 214s Investment_22 0.000 0.00 214s PrivateWages_2 0.000 0.00 214s PrivateWages_3 0.000 0.00 214s PrivateWages_4 0.000 0.00 214s PrivateWages_5 0.000 0.00 214s PrivateWages_6 0.000 0.00 214s PrivateWages_8 0.000 0.00 214s PrivateWages_9 0.000 0.00 214s PrivateWages_10 0.000 0.00 214s PrivateWages_11 0.000 0.00 214s PrivateWages_12 0.000 0.00 214s PrivateWages_13 0.000 0.00 214s PrivateWages_14 0.000 0.00 214s PrivateWages_15 0.000 0.00 214s PrivateWages_16 0.000 0.00 214s PrivateWages_17 0.000 0.00 214s PrivateWages_18 0.000 0.00 214s PrivateWages_19 0.000 0.00 214s PrivateWages_20 0.000 0.00 214s PrivateWages_21 0.000 0.00 214s PrivateWages_22 0.000 0.00 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 0.00000 0.000 214s Consumption_3 0.00000 0.000 214s Consumption_4 0.00000 0.000 214s Consumption_5 0.00000 0.000 214s Consumption_6 0.00000 0.000 214s Consumption_7 0.00000 0.000 214s Consumption_8 0.00000 0.000 214s Consumption_9 0.00000 0.000 214s Consumption_11 0.00000 0.000 214s Consumption_12 0.00000 0.000 214s Consumption_14 0.00000 0.000 214s Consumption_15 0.00000 0.000 214s Consumption_16 0.00000 0.000 214s Consumption_17 0.00000 0.000 214s Consumption_18 0.00000 0.000 214s Consumption_19 0.00000 0.000 214s Consumption_20 0.00000 0.000 214s Consumption_21 0.00000 0.000 214s Consumption_22 0.00000 0.000 214s Investment_2 0.00693 0.086 214s Investment_3 -0.06954 -1.175 214s Investment_4 1.22401 22.522 214s Investment_5 -1.37696 -26.713 214s Investment_6 0.38610 7.761 214s Investment_7 1.48598 29.125 214s Investment_8 0.78465 15.536 214s Investment_9 -0.65483 -13.817 214s Investment_10 1.06018 23.006 214s Investment_11 0.39508 6.163 214s Investment_12 0.20479 2.335 214s Investment_14 0.32778 3.671 214s Investment_15 -0.07450 -0.916 214s Investment_17 0.96998 17.072 214s Investment_18 0.08124 1.405 214s Investment_19 -2.49295 -38.142 214s Investment_20 -0.70609 -13.416 214s Investment_21 -0.81928 -17.287 214s Investment_22 -0.73256 -17.215 214s PrivateWages_2 0.00000 0.000 214s PrivateWages_3 0.00000 0.000 214s PrivateWages_4 0.00000 0.000 214s PrivateWages_5 0.00000 0.000 214s PrivateWages_6 0.00000 0.000 214s PrivateWages_8 0.00000 0.000 214s PrivateWages_9 0.00000 0.000 214s PrivateWages_10 0.00000 0.000 214s PrivateWages_11 0.00000 0.000 214s PrivateWages_12 0.00000 0.000 214s PrivateWages_13 0.00000 0.000 214s PrivateWages_14 0.00000 0.000 214s PrivateWages_15 0.00000 0.000 214s PrivateWages_16 0.00000 0.000 214s PrivateWages_17 0.00000 0.000 214s PrivateWages_18 0.00000 0.000 214s PrivateWages_19 0.00000 0.000 214s PrivateWages_20 0.00000 0.000 214s PrivateWages_21 0.00000 0.000 214s PrivateWages_22 0.00000 0.000 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 0.0000 0.00 214s Consumption_3 0.0000 0.00 214s Consumption_4 0.0000 0.00 214s Consumption_5 0.0000 0.00 214s Consumption_6 0.0000 0.00 214s Consumption_7 0.0000 0.00 214s Consumption_8 0.0000 0.00 214s Consumption_9 0.0000 0.00 214s Consumption_11 0.0000 0.00 214s Consumption_12 0.0000 0.00 214s Consumption_14 0.0000 0.00 214s Consumption_15 0.0000 0.00 214s Consumption_16 0.0000 0.00 214s Consumption_17 0.0000 0.00 214s Consumption_18 0.0000 0.00 214s Consumption_19 0.0000 0.00 214s Consumption_20 0.0000 0.00 214s Consumption_21 0.0000 0.00 214s Consumption_22 0.0000 0.00 214s Investment_2 0.0881 1.27 214s Investment_3 -0.8622 -12.70 214s Investment_4 20.6858 225.83 214s Investment_5 -25.3362 -261.21 214s Investment_6 7.4903 74.40 214s Investment_7 29.8681 293.93 214s Investment_8 15.3791 159.60 214s Investment_9 -12.9657 -135.94 214s Investment_10 22.3698 223.27 214s Investment_11 8.5733 85.22 214s Investment_12 3.1947 44.38 214s Investment_14 2.2945 67.88 214s Investment_15 -0.8344 -15.05 214s Investment_17 13.5797 191.77 214s Investment_18 1.4298 16.23 214s Investment_19 -43.1281 -503.08 214s Investment_20 -10.8032 -141.15 214s Investment_21 -15.5663 -164.84 214s Investment_22 -15.4570 -149.81 214s PrivateWages_2 0.0000 0.00 214s PrivateWages_3 0.0000 0.00 214s PrivateWages_4 0.0000 0.00 214s PrivateWages_5 0.0000 0.00 214s PrivateWages_6 0.0000 0.00 214s PrivateWages_8 0.0000 0.00 214s PrivateWages_9 0.0000 0.00 214s PrivateWages_10 0.0000 0.00 214s PrivateWages_11 0.0000 0.00 214s PrivateWages_12 0.0000 0.00 214s PrivateWages_13 0.0000 0.00 214s PrivateWages_14 0.0000 0.00 214s PrivateWages_15 0.0000 0.00 214s PrivateWages_16 0.0000 0.00 214s PrivateWages_17 0.0000 0.00 214s PrivateWages_18 0.0000 0.00 214s PrivateWages_19 0.0000 0.00 214s PrivateWages_20 0.0000 0.00 214s PrivateWages_21 0.0000 0.00 214s PrivateWages_22 0.0000 0.00 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 0.0000 0.00 0.00 214s Consumption_3 0.0000 0.00 0.00 214s Consumption_4 0.0000 0.00 0.00 214s Consumption_5 0.0000 0.00 0.00 214s Consumption_6 0.0000 0.00 0.00 214s Consumption_7 0.0000 0.00 0.00 214s Consumption_8 0.0000 0.00 0.00 214s Consumption_9 0.0000 0.00 0.00 214s Consumption_11 0.0000 0.00 0.00 214s Consumption_12 0.0000 0.00 0.00 214s Consumption_14 0.0000 0.00 0.00 214s Consumption_15 0.0000 0.00 0.00 214s Consumption_16 0.0000 0.00 0.00 214s Consumption_17 0.0000 0.00 0.00 214s Consumption_18 0.0000 0.00 0.00 214s Consumption_19 0.0000 0.00 0.00 214s Consumption_20 0.0000 0.00 0.00 214s Consumption_21 0.0000 0.00 0.00 214s Consumption_22 0.0000 0.00 0.00 214s Investment_2 0.0000 0.00 0.00 214s Investment_3 0.0000 0.00 0.00 214s Investment_4 0.0000 0.00 0.00 214s Investment_5 0.0000 0.00 0.00 214s Investment_6 0.0000 0.00 0.00 214s Investment_7 0.0000 0.00 0.00 214s Investment_8 0.0000 0.00 0.00 214s Investment_9 0.0000 0.00 0.00 214s Investment_10 0.0000 0.00 0.00 214s Investment_11 0.0000 0.00 0.00 214s Investment_12 0.0000 0.00 0.00 214s Investment_14 0.0000 0.00 0.00 214s Investment_15 0.0000 0.00 0.00 214s Investment_17 0.0000 0.00 0.00 214s Investment_18 0.0000 0.00 0.00 214s Investment_19 0.0000 0.00 0.00 214s Investment_20 0.0000 0.00 0.00 214s Investment_21 0.0000 0.00 0.00 214s Investment_22 0.0000 0.00 0.00 214s PrivateWages_2 -1.3389 -61.06 -60.12 214s PrivateWages_3 0.2462 12.33 11.23 214s PrivateWages_4 1.1255 64.38 56.39 214s PrivateWages_5 -0.1959 -11.18 -11.20 214s PrivateWages_6 -0.5284 -32.23 -30.17 214s PrivateWages_8 -0.7909 -50.94 -50.62 214s PrivateWages_9 0.2819 18.18 18.15 214s PrivateWages_10 1.1384 76.28 73.43 214s PrivateWages_11 -0.1904 -11.65 -12.76 214s PrivateWages_12 0.5813 31.04 35.58 214s PrivateWages_13 0.1206 5.34 6.44 214s PrivateWages_14 0.4773 21.53 21.14 214s PrivateWages_15 0.3035 15.09 13.69 214s PrivateWages_16 0.0284 1.55 1.41 214s PrivateWages_17 -0.8517 -53.40 -46.33 214s PrivateWages_18 0.9908 64.40 62.12 214s PrivateWages_19 -0.4597 -28.00 -29.88 214s PrivateWages_20 -0.3819 -26.54 -23.26 214s PrivateWages_21 -1.1062 -83.74 -76.88 214s PrivateWages_22 0.5501 48.63 41.64 214s PrivateWages_trend 214s Consumption_2 0.000 214s Consumption_3 0.000 214s Consumption_4 0.000 214s Consumption_5 0.000 214s Consumption_6 0.000 214s Consumption_7 0.000 214s Consumption_8 0.000 214s Consumption_9 0.000 214s Consumption_11 0.000 214s Consumption_12 0.000 214s Consumption_14 0.000 214s Consumption_15 0.000 214s Consumption_16 0.000 214s Consumption_17 0.000 214s Consumption_18 0.000 214s Consumption_19 0.000 214s Consumption_20 0.000 214s Consumption_21 0.000 214s Consumption_22 0.000 214s Investment_2 0.000 214s Investment_3 0.000 214s Investment_4 0.000 214s Investment_5 0.000 214s Investment_6 0.000 214s Investment_7 0.000 214s Investment_8 0.000 214s Investment_9 0.000 214s Investment_10 0.000 214s Investment_11 0.000 214s Investment_12 0.000 214s Investment_14 0.000 214s Investment_15 0.000 214s Investment_17 0.000 214s Investment_18 0.000 214s Investment_19 0.000 214s Investment_20 0.000 214s Investment_21 0.000 214s Investment_22 0.000 214s PrivateWages_2 13.389 214s PrivateWages_3 -2.216 214s PrivateWages_4 -9.004 214s PrivateWages_5 1.371 214s PrivateWages_6 3.170 214s PrivateWages_8 3.164 214s PrivateWages_9 -0.846 214s PrivateWages_10 -2.277 214s PrivateWages_11 0.190 214s PrivateWages_12 0.000 214s PrivateWages_13 0.121 214s PrivateWages_14 0.955 214s PrivateWages_15 0.911 214s PrivateWages_16 0.114 214s PrivateWages_17 -4.258 214s PrivateWages_18 5.945 214s PrivateWages_19 -3.218 214s PrivateWages_20 -3.055 214s PrivateWages_21 -9.956 214s PrivateWages_22 5.501 214s [1] TRUE 214s > Bread 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_(Intercept) 107.542 -1.6123 214s Consumption_corpProf -1.612 0.6562 214s Consumption_corpProfLag -0.588 -0.3449 214s Consumption_wages -1.613 -0.0959 214s Investment_(Intercept) 0.000 0.0000 214s Investment_corpProf 0.000 0.0000 214s Investment_corpProfLag 0.000 0.0000 214s Investment_capitalLag 0.000 0.0000 214s PrivateWages_(Intercept) 0.000 0.0000 214s PrivateWages_gnp 0.000 0.0000 214s PrivateWages_gnpLag 0.000 0.0000 214s PrivateWages_trend 0.000 0.0000 214s Consumption_corpProfLag Consumption_wages 214s Consumption_(Intercept) -0.5878 -1.6130 214s Consumption_corpProf -0.3449 -0.0959 214s Consumption_corpProfLag 0.4797 -0.0326 214s Consumption_wages -0.0326 0.0910 214s Investment_(Intercept) 0.0000 0.0000 214s Investment_corpProf 0.0000 0.0000 214s Investment_corpProfLag 0.0000 0.0000 214s Investment_capitalLag 0.0000 0.0000 214s PrivateWages_(Intercept) 0.0000 0.0000 214s PrivateWages_gnp 0.0000 0.0000 214s PrivateWages_gnpLag 0.0000 0.0000 214s PrivateWages_trend 0.0000 0.0000 214s Investment_(Intercept) Investment_corpProf 214s Consumption_(Intercept) 0.00 0.000 214s Consumption_corpProf 0.00 0.000 214s Consumption_corpProfLag 0.00 0.000 214s Consumption_wages 0.00 0.000 214s Investment_(Intercept) 1702.08 -16.246 214s Investment_corpProf -16.25 0.653 214s Investment_corpProfLag 13.29 -0.499 214s Investment_capitalLag -8.19 0.066 214s PrivateWages_(Intercept) 0.00 0.000 214s PrivateWages_gnp 0.00 0.000 214s PrivateWages_gnpLag 0.00 0.000 214s PrivateWages_trend 0.00 0.000 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_(Intercept) 0.0000 0.0000 214s Consumption_corpProf 0.0000 0.0000 214s Consumption_corpProfLag 0.0000 0.0000 214s Consumption_wages 0.0000 0.0000 214s Investment_(Intercept) 13.2940 -8.1927 214s Investment_corpProf -0.4994 0.0660 214s Investment_corpProfLag 0.6054 -0.0737 214s Investment_capitalLag -0.0737 0.0414 214s PrivateWages_(Intercept) 0.0000 0.0000 214s PrivateWages_gnp 0.0000 0.0000 214s PrivateWages_gnpLag 0.0000 0.0000 214s PrivateWages_trend 0.0000 0.0000 214s PrivateWages_(Intercept) PrivateWages_gnp 214s Consumption_(Intercept) 0.000 0.0000 214s Consumption_corpProf 0.000 0.0000 214s Consumption_corpProfLag 0.000 0.0000 214s Consumption_wages 0.000 0.0000 214s Investment_(Intercept) 0.000 0.0000 214s Investment_corpProf 0.000 0.0000 214s Investment_corpProfLag 0.000 0.0000 214s Investment_capitalLag 0.000 0.0000 214s PrivateWages_(Intercept) 163.361 -0.6152 214s PrivateWages_gnp -0.615 0.1046 214s PrivateWages_gnpLag -2.146 -0.0975 214s PrivateWages_trend 2.016 -0.0281 214s PrivateWages_gnpLag PrivateWages_trend 214s Consumption_(Intercept) 0.00000 0.00000 214s Consumption_corpProf 0.00000 0.00000 214s Consumption_corpProfLag 0.00000 0.00000 214s Consumption_wages 0.00000 0.00000 214s Investment_(Intercept) 0.00000 0.00000 214s Investment_corpProf 0.00000 0.00000 214s Investment_corpProfLag 0.00000 0.00000 214s Investment_capitalLag 0.00000 0.00000 214s PrivateWages_(Intercept) -2.14647 2.01603 214s PrivateWages_gnp -0.09753 -0.02810 214s PrivateWages_gnpLag 0.13809 -0.00624 214s PrivateWages_trend -0.00624 0.10783 214s > 214s > # 2SLS 214s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 214s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 214s > summary 214s 214s systemfit results 214s method: 2SLS 214s 214s N DF SSR detRCov OLS-R2 McElroy-R2 214s system 56 44 57.9 0.391 0.968 0.992 214s 214s N DF SSR MSE RMSE R2 Adj R2 214s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 214s Investment 18 14 25.85 1.847 1.36 0.847 0.815 214s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 214s 214s The covariance matrix of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.307 0.540 -0.431 214s Investment 0.540 1.319 0.119 214s PrivateWages -0.431 0.119 0.496 214s 214s The correlations of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.000 0.414 -0.538 214s Investment 0.414 1.000 0.139 214s PrivateWages -0.538 0.139 1.000 214s 214s 214s 2SLS estimates for 'Consumption' (equation 1) 214s Model Formula: consump ~ corpProf + corpProfLag + wages 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 17.2849 1.6463 10.50 5.1e-08 *** 214s corpProf -0.0770 0.1683 -0.46 0.65 214s corpProfLag 0.2327 0.1276 1.82 0.09 . 214s wages 0.8259 0.0472 17.49 6.6e-11 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.261 on 14 degrees of freedom 214s Number of observations: 18 Degrees of Freedom: 14 214s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 214s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 214s 214s 214s 2SLS estimates for 'Investment' (equation 2) 214s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 18.2571 7.3132 2.50 0.02564 * 214s corpProf 0.1564 0.1942 0.81 0.43408 214s corpProfLag 0.5714 0.1672 3.42 0.00417 ** 214s capitalLag -0.1446 0.0346 -4.18 0.00093 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.359 on 14 degrees of freedom 214s Number of observations: 18 Degrees of Freedom: 14 214s SSR: 25.852 MSE: 1.847 Root MSE: 1.359 214s Multiple R-Squared: 0.847 Adjusted R-Squared: 0.815 214s 214s 214s 2SLS estimates for 'PrivateWages' (equation 3) 214s Model Formula: privWage ~ gnp + gnpLag + trend 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 1.3431 1.1879 1.13 0.275 214s gnp 0.4438 0.0361 12.28 1.5e-09 *** 214s gnpLag 0.1447 0.0392 3.69 0.002 ** 214s trend 0.1238 0.0308 4.01 0.001 ** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 0.78 on 16 degrees of freedom 214s Number of observations: 20 Degrees of Freedom: 16 214s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 214s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 214s 214s > residuals 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 -0.6754 -1.214 -1.3401 214s 3 -0.4627 0.325 0.2378 214s 4 -1.1585 1.094 1.1117 214s 5 -0.0305 -1.368 -0.1954 214s 6 0.4693 0.486 -0.5355 214s 7 NA NA NA 214s 8 1.6045 1.066 -0.7908 214s 9 1.6018 0.156 0.2831 214s 10 NA 1.853 1.1353 214s 11 -0.9031 -0.898 -0.1765 214s 12 -1.5948 -1.012 0.6007 214s 13 NA NA 0.1443 214s 14 0.2854 0.845 0.4826 214s 15 -0.4718 -0.365 0.3016 214s 16 -0.2268 NA 0.0261 214s 17 2.0079 1.685 -0.8614 214s 18 -0.7434 -0.121 0.9927 214s 19 -0.5410 -3.248 -0.4446 214s 20 1.4186 0.241 -0.3914 214s 21 1.1462 -0.013 -1.1115 214s 22 -1.7256 0.489 0.5312 214s > fitted 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 42.6 1.014 26.8 214s 3 45.5 1.575 29.1 214s 4 50.4 4.106 33.0 214s 5 50.6 4.368 34.1 214s 6 52.1 4.614 35.9 214s 7 NA NA NA 214s 8 54.6 3.134 38.7 214s 9 55.7 2.844 38.9 214s 10 NA 3.247 40.2 214s 11 55.9 1.898 38.1 214s 12 52.5 -2.388 33.9 214s 13 NA NA 28.9 214s 14 46.2 -5.945 28.0 214s 15 49.2 -2.635 30.3 214s 16 51.5 NA 33.2 214s 17 55.7 0.415 37.7 214s 18 59.4 2.121 40.0 214s 19 58.0 1.348 38.6 214s 20 60.2 1.059 42.0 214s 21 63.9 3.313 46.1 214s 22 71.4 4.411 52.8 214s > predict 214s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 214s 1 NA NA NA NA 214s 2 42.6 0.586 41.3 43.8 214s 3 45.5 0.674 44.0 46.9 214s 4 50.4 0.443 49.4 51.3 214s 5 50.6 0.524 49.5 51.8 214s 6 52.1 0.535 51.0 53.3 214s 7 NA NA NA NA 214s 8 54.6 0.431 53.7 55.5 214s 9 55.7 0.510 54.6 56.8 214s 10 NA NA NA NA 214s 11 55.9 0.936 53.9 57.9 214s 12 52.5 0.893 50.6 54.4 214s 13 NA NA NA NA 214s 14 46.2 0.713 44.7 47.7 214s 15 49.2 0.501 48.1 50.2 214s 16 51.5 0.407 50.7 52.4 214s 17 55.7 0.457 54.7 56.7 214s 18 59.4 0.397 58.6 60.3 214s 19 58.0 0.564 56.8 59.2 214s 20 60.2 0.543 59.0 61.3 214s 21 63.9 0.529 62.7 65.0 214s 22 71.4 0.808 69.7 73.2 214s Investment.pred Investment.se.fit Investment.lwr Investment.upr 214s 1 NA NA NA NA 214s 2 1.014 0.919 -0.957 2.985 214s 3 1.575 0.602 0.284 2.867 214s 4 4.106 0.544 2.940 5.272 214s 5 4.368 0.450 3.402 5.333 214s 6 4.614 0.425 3.703 5.526 214s 7 NA NA NA NA 214s 8 3.134 0.352 2.380 3.889 214s 9 2.844 0.544 1.677 4.012 214s 10 3.247 0.592 1.976 4.518 214s 11 1.898 0.978 -0.200 3.996 214s 12 -2.388 0.886 -4.289 -0.488 214s 13 NA NA NA NA 214s 14 -5.945 0.916 -7.909 -3.980 214s 15 -2.635 0.518 -3.745 -1.525 214s 16 NA NA NA NA 214s 17 0.415 0.507 -0.671 1.501 214s 18 2.121 0.329 1.416 2.826 214s 19 1.348 0.551 0.166 2.529 214s 20 1.059 0.582 -0.189 2.306 214s 21 3.313 0.496 2.248 4.377 214s 22 4.411 0.728 2.850 5.971 214s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 214s 1 NA NA NA NA 214s 2 26.8 0.330 26.1 27.5 214s 3 29.1 0.344 28.3 29.8 214s 4 33.0 0.363 32.2 33.8 214s 5 34.1 0.260 33.5 34.6 214s 6 35.9 0.268 35.4 36.5 214s 7 NA NA NA NA 214s 8 38.7 0.265 38.1 39.3 214s 9 38.9 0.252 38.4 39.5 214s 10 40.2 0.242 39.7 40.7 214s 11 38.1 0.358 37.3 38.8 214s 12 33.9 0.385 33.1 34.7 214s 13 28.9 0.460 27.9 29.8 214s 14 28.0 0.351 27.3 28.8 214s 15 30.3 0.343 29.6 31.0 214s 16 33.2 0.287 32.6 33.8 214s 17 37.7 0.296 37.0 38.3 214s 18 40.0 0.220 39.5 40.5 214s 19 38.6 0.361 37.9 39.4 214s 20 42.0 0.309 41.3 42.6 214s 21 46.1 0.312 45.4 46.8 214s 22 52.8 0.501 51.7 53.8 214s > model.frame 214s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 214s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 214s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 214s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 214s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 214s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 214s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 214s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 214s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 214s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 214s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 214s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 214s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 214s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 214s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 214s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 214s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 214s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 214s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 214s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 214s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 214s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 214s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 214s trend 214s 1 -11 214s 2 -10 214s 3 -9 214s 4 -8 214s 5 -7 214s 6 -6 214s 7 -5 214s 8 -4 214s 9 -3 214s 10 -2 214s 11 -1 214s 12 0 214s 13 1 214s 14 2 214s 15 3 214s 16 4 214s 17 5 214s 18 6 214s 19 7 214s 20 8 214s 21 9 214s 22 10 214s > Frames of instrumental variables 214s govExp taxes govWage trend capitalLag corpProfLag gnpLag 214s 1 2.4 3.4 2.2 -11 180 NA NA 214s 2 3.9 7.7 2.7 -10 183 12.7 44.9 214s 3 3.2 3.9 2.9 -9 183 12.4 45.6 214s 4 2.8 4.7 2.9 -8 184 16.9 50.1 214s 5 3.5 3.8 3.1 -7 190 18.4 57.2 214s 6 3.3 5.5 3.2 -6 193 19.4 57.1 214s 7 3.3 7.0 3.3 -5 198 20.1 NA 214s 8 4.0 6.7 3.6 -4 203 19.6 64.0 214s 9 4.2 4.2 3.7 -3 208 19.8 64.4 214s 10 4.1 4.0 4.0 -2 211 21.1 64.5 214s 11 5.2 7.7 4.2 -1 216 21.7 67.0 214s 12 5.9 7.5 4.8 0 217 15.6 61.2 214s 13 4.9 8.3 5.3 1 213 11.4 53.4 214s 14 3.7 5.4 5.6 2 207 7.0 44.3 214s 15 4.0 6.8 6.0 3 202 11.2 45.1 214s 16 4.4 7.2 6.1 4 199 12.3 49.7 214s 17 2.9 8.3 7.4 5 198 14.0 54.4 214s 18 4.3 6.7 6.7 6 200 17.6 62.7 214s 19 5.3 7.4 7.7 7 202 17.3 65.0 214s 20 6.6 8.9 7.8 8 200 15.3 60.9 214s 21 7.4 9.6 8.0 9 201 19.0 69.5 214s 22 13.8 11.6 8.5 10 204 21.1 75.7 214s govExp taxes govWage trend capitalLag corpProfLag gnpLag 214s 1 2.4 3.4 2.2 -11 180 NA NA 214s 2 3.9 7.7 2.7 -10 183 12.7 44.9 214s 3 3.2 3.9 2.9 -9 183 12.4 45.6 214s 4 2.8 4.7 2.9 -8 184 16.9 50.1 214s 5 3.5 3.8 3.1 -7 190 18.4 57.2 214s 6 3.3 5.5 3.2 -6 193 19.4 57.1 214s 7 3.3 7.0 3.3 -5 198 20.1 NA 214s 8 4.0 6.7 3.6 -4 203 19.6 64.0 214s 9 4.2 4.2 3.7 -3 208 19.8 64.4 214s 10 4.1 4.0 4.0 -2 211 21.1 64.5 214s 11 5.2 7.7 4.2 -1 216 21.7 67.0 214s 12 5.9 7.5 4.8 0 217 15.6 61.2 214s 13 4.9 8.3 5.3 1 213 11.4 53.4 214s 14 3.7 5.4 5.6 2 207 7.0 44.3 214s 15 4.0 6.8 6.0 3 202 11.2 45.1 214s 16 4.4 7.2 6.1 4 199 12.3 49.7 214s 17 2.9 8.3 7.4 5 198 14.0 54.4 214s 18 4.3 6.7 6.7 6 200 17.6 62.7 214s 19 5.3 7.4 7.7 7 202 17.3 65.0 214s 20 6.6 8.9 7.8 8 200 15.3 60.9 214s 21 7.4 9.6 8.0 9 201 19.0 69.5 214s 22 13.8 11.6 8.5 10 204 21.1 75.7 214s govExp taxes govWage trend capitalLag corpProfLag gnpLag 214s 1 2.4 3.4 2.2 -11 180 NA NA 214s 2 3.9 7.7 2.7 -10 183 12.7 44.9 214s 3 3.2 3.9 2.9 -9 183 12.4 45.6 214s 4 2.8 4.7 2.9 -8 184 16.9 50.1 214s 5 3.5 3.8 3.1 -7 190 18.4 57.2 214s 6 3.3 5.5 3.2 -6 193 19.4 57.1 214s 7 3.3 7.0 3.3 -5 198 20.1 NA 214s 8 4.0 6.7 3.6 -4 203 19.6 64.0 214s 9 4.2 4.2 3.7 -3 208 19.8 64.4 214s 10 4.1 4.0 4.0 -2 211 21.1 64.5 214s 11 5.2 7.7 4.2 -1 216 21.7 67.0 214s 12 5.9 7.5 4.8 0 217 15.6 61.2 214s 13 4.9 8.3 5.3 1 213 11.4 53.4 214s 14 3.7 5.4 5.6 2 207 7.0 44.3 214s 15 4.0 6.8 6.0 3 202 11.2 45.1 214s 16 4.4 7.2 6.1 4 199 12.3 49.7 214s 17 2.9 8.3 7.4 5 198 14.0 54.4 214s 18 4.3 6.7 6.7 6 200 17.6 62.7 214s 19 5.3 7.4 7.7 7 202 17.3 65.0 214s 20 6.6 8.9 7.8 8 200 15.3 60.9 214s 21 7.4 9.6 8.0 9 201 19.0 69.5 214s 22 13.8 11.6 8.5 10 204 21.1 75.7 214s > model.matrix 214s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 214s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 214s [3] "Numeric: lengths (696, 672) differ" 214s > matrix of instrumental variables 214s Consumption_(Intercept) Consumption_govExp Consumption_taxes 214s Consumption_2 1 3.9 7.7 214s Consumption_3 1 3.2 3.9 214s Consumption_4 1 2.8 4.7 214s Consumption_5 1 3.5 3.8 214s Consumption_6 1 3.3 5.5 214s Consumption_8 1 4.0 6.7 214s Consumption_9 1 4.2 4.2 214s Consumption_11 1 5.2 7.7 214s Consumption_12 1 5.9 7.5 214s Consumption_14 1 3.7 5.4 214s Consumption_15 1 4.0 6.8 214s Consumption_16 1 4.4 7.2 214s Consumption_17 1 2.9 8.3 214s Consumption_18 1 4.3 6.7 214s Consumption_19 1 5.3 7.4 214s Consumption_20 1 6.6 8.9 214s Consumption_21 1 7.4 9.6 214s Consumption_22 1 13.8 11.6 214s Investment_2 0 0.0 0.0 214s Investment_3 0 0.0 0.0 214s Investment_4 0 0.0 0.0 214s Investment_5 0 0.0 0.0 214s Investment_6 0 0.0 0.0 214s Investment_8 0 0.0 0.0 214s Investment_9 0 0.0 0.0 214s Investment_10 0 0.0 0.0 214s Investment_11 0 0.0 0.0 214s Investment_12 0 0.0 0.0 214s Investment_14 0 0.0 0.0 214s Investment_15 0 0.0 0.0 214s Investment_17 0 0.0 0.0 214s Investment_18 0 0.0 0.0 214s Investment_19 0 0.0 0.0 214s Investment_20 0 0.0 0.0 214s Investment_21 0 0.0 0.0 214s Investment_22 0 0.0 0.0 214s PrivateWages_2 0 0.0 0.0 214s PrivateWages_3 0 0.0 0.0 214s PrivateWages_4 0 0.0 0.0 214s PrivateWages_5 0 0.0 0.0 214s PrivateWages_6 0 0.0 0.0 214s PrivateWages_8 0 0.0 0.0 214s PrivateWages_9 0 0.0 0.0 214s PrivateWages_10 0 0.0 0.0 214s PrivateWages_11 0 0.0 0.0 214s PrivateWages_12 0 0.0 0.0 214s PrivateWages_13 0 0.0 0.0 214s PrivateWages_14 0 0.0 0.0 214s PrivateWages_15 0 0.0 0.0 214s PrivateWages_16 0 0.0 0.0 214s PrivateWages_17 0 0.0 0.0 214s PrivateWages_18 0 0.0 0.0 214s PrivateWages_19 0 0.0 0.0 214s PrivateWages_20 0 0.0 0.0 214s PrivateWages_21 0 0.0 0.0 214s PrivateWages_22 0 0.0 0.0 214s Consumption_govWage Consumption_trend Consumption_capitalLag 214s Consumption_2 2.7 -10 183 214s Consumption_3 2.9 -9 183 214s Consumption_4 2.9 -8 184 214s Consumption_5 3.1 -7 190 214s Consumption_6 3.2 -6 193 214s Consumption_8 3.6 -4 203 214s Consumption_9 3.7 -3 208 214s Consumption_11 4.2 -1 216 214s Consumption_12 4.8 0 217 214s Consumption_14 5.6 2 207 214s Consumption_15 6.0 3 202 214s Consumption_16 6.1 4 199 214s Consumption_17 7.4 5 198 214s Consumption_18 6.7 6 200 214s Consumption_19 7.7 7 202 214s Consumption_20 7.8 8 200 214s Consumption_21 8.0 9 201 214s Consumption_22 8.5 10 204 214s Investment_2 0.0 0 0 214s Investment_3 0.0 0 0 214s Investment_4 0.0 0 0 214s Investment_5 0.0 0 0 214s Investment_6 0.0 0 0 214s Investment_8 0.0 0 0 214s Investment_9 0.0 0 0 214s Investment_10 0.0 0 0 214s Investment_11 0.0 0 0 214s Investment_12 0.0 0 0 214s Investment_14 0.0 0 0 214s Investment_15 0.0 0 0 214s Investment_17 0.0 0 0 214s Investment_18 0.0 0 0 214s Investment_19 0.0 0 0 214s Investment_20 0.0 0 0 214s Investment_21 0.0 0 0 214s Investment_22 0.0 0 0 214s PrivateWages_2 0.0 0 0 214s PrivateWages_3 0.0 0 0 214s PrivateWages_4 0.0 0 0 214s PrivateWages_5 0.0 0 0 214s PrivateWages_6 0.0 0 0 214s PrivateWages_8 0.0 0 0 214s PrivateWages_9 0.0 0 0 214s PrivateWages_10 0.0 0 0 214s PrivateWages_11 0.0 0 0 214s PrivateWages_12 0.0 0 0 214s PrivateWages_13 0.0 0 0 214s PrivateWages_14 0.0 0 0 214s PrivateWages_15 0.0 0 0 214s PrivateWages_16 0.0 0 0 214s PrivateWages_17 0.0 0 0 214s PrivateWages_18 0.0 0 0 214s PrivateWages_19 0.0 0 0 214s PrivateWages_20 0.0 0 0 214s PrivateWages_21 0.0 0 0 214s PrivateWages_22 0.0 0 0 214s Consumption_corpProfLag Consumption_gnpLag 214s Consumption_2 12.7 44.9 214s Consumption_3 12.4 45.6 214s Consumption_4 16.9 50.1 214s Consumption_5 18.4 57.2 214s Consumption_6 19.4 57.1 214s Consumption_8 19.6 64.0 214s Consumption_9 19.8 64.4 214s Consumption_11 21.7 67.0 214s Consumption_12 15.6 61.2 214s Consumption_14 7.0 44.3 214s Consumption_15 11.2 45.1 214s Consumption_16 12.3 49.7 214s Consumption_17 14.0 54.4 214s Consumption_18 17.6 62.7 214s Consumption_19 17.3 65.0 214s Consumption_20 15.3 60.9 214s Consumption_21 19.0 69.5 214s Consumption_22 21.1 75.7 214s Investment_2 0.0 0.0 214s Investment_3 0.0 0.0 214s Investment_4 0.0 0.0 214s Investment_5 0.0 0.0 214s Investment_6 0.0 0.0 214s Investment_8 0.0 0.0 214s Investment_9 0.0 0.0 214s Investment_10 0.0 0.0 214s Investment_11 0.0 0.0 214s Investment_12 0.0 0.0 214s Investment_14 0.0 0.0 214s Investment_15 0.0 0.0 214s Investment_17 0.0 0.0 214s Investment_18 0.0 0.0 214s Investment_19 0.0 0.0 214s Investment_20 0.0 0.0 214s Investment_21 0.0 0.0 214s Investment_22 0.0 0.0 214s PrivateWages_2 0.0 0.0 214s PrivateWages_3 0.0 0.0 214s PrivateWages_4 0.0 0.0 214s PrivateWages_5 0.0 0.0 214s PrivateWages_6 0.0 0.0 214s PrivateWages_8 0.0 0.0 214s PrivateWages_9 0.0 0.0 214s PrivateWages_10 0.0 0.0 214s PrivateWages_11 0.0 0.0 214s PrivateWages_12 0.0 0.0 214s PrivateWages_13 0.0 0.0 214s PrivateWages_14 0.0 0.0 214s PrivateWages_15 0.0 0.0 214s PrivateWages_16 0.0 0.0 214s PrivateWages_17 0.0 0.0 214s PrivateWages_18 0.0 0.0 214s PrivateWages_19 0.0 0.0 214s PrivateWages_20 0.0 0.0 214s PrivateWages_21 0.0 0.0 214s PrivateWages_22 0.0 0.0 214s Investment_(Intercept) Investment_govExp Investment_taxes 214s Consumption_2 0 0.0 0.0 214s Consumption_3 0 0.0 0.0 214s Consumption_4 0 0.0 0.0 214s Consumption_5 0 0.0 0.0 214s Consumption_6 0 0.0 0.0 214s Consumption_8 0 0.0 0.0 214s Consumption_9 0 0.0 0.0 214s Consumption_11 0 0.0 0.0 214s Consumption_12 0 0.0 0.0 214s Consumption_14 0 0.0 0.0 214s Consumption_15 0 0.0 0.0 214s Consumption_16 0 0.0 0.0 214s Consumption_17 0 0.0 0.0 214s Consumption_18 0 0.0 0.0 214s Consumption_19 0 0.0 0.0 214s Consumption_20 0 0.0 0.0 214s Consumption_21 0 0.0 0.0 214s Consumption_22 0 0.0 0.0 214s Investment_2 1 3.9 7.7 214s Investment_3 1 3.2 3.9 214s Investment_4 1 2.8 4.7 214s Investment_5 1 3.5 3.8 214s Investment_6 1 3.3 5.5 214s Investment_8 1 4.0 6.7 214s Investment_9 1 4.2 4.2 214s Investment_10 1 4.1 4.0 214s Investment_11 1 5.2 7.7 214s Investment_12 1 5.9 7.5 214s Investment_14 1 3.7 5.4 214s Investment_15 1 4.0 6.8 214s Investment_17 1 2.9 8.3 214s Investment_18 1 4.3 6.7 214s Investment_19 1 5.3 7.4 214s Investment_20 1 6.6 8.9 214s Investment_21 1 7.4 9.6 214s Investment_22 1 13.8 11.6 214s PrivateWages_2 0 0.0 0.0 214s PrivateWages_3 0 0.0 0.0 214s PrivateWages_4 0 0.0 0.0 214s PrivateWages_5 0 0.0 0.0 214s PrivateWages_6 0 0.0 0.0 214s PrivateWages_8 0 0.0 0.0 214s PrivateWages_9 0 0.0 0.0 214s PrivateWages_10 0 0.0 0.0 214s PrivateWages_11 0 0.0 0.0 214s PrivateWages_12 0 0.0 0.0 214s PrivateWages_13 0 0.0 0.0 214s PrivateWages_14 0 0.0 0.0 214s PrivateWages_15 0 0.0 0.0 214s PrivateWages_16 0 0.0 0.0 214s PrivateWages_17 0 0.0 0.0 214s PrivateWages_18 0 0.0 0.0 214s PrivateWages_19 0 0.0 0.0 214s PrivateWages_20 0 0.0 0.0 214s PrivateWages_21 0 0.0 0.0 214s PrivateWages_22 0 0.0 0.0 214s Investment_govWage Investment_trend Investment_capitalLag 214s Consumption_2 0.0 0 0 214s Consumption_3 0.0 0 0 214s Consumption_4 0.0 0 0 214s Consumption_5 0.0 0 0 214s Consumption_6 0.0 0 0 214s Consumption_8 0.0 0 0 214s Consumption_9 0.0 0 0 214s Consumption_11 0.0 0 0 214s Consumption_12 0.0 0 0 214s Consumption_14 0.0 0 0 214s Consumption_15 0.0 0 0 214s Consumption_16 0.0 0 0 214s Consumption_17 0.0 0 0 214s Consumption_18 0.0 0 0 214s Consumption_19 0.0 0 0 214s Consumption_20 0.0 0 0 214s Consumption_21 0.0 0 0 214s Consumption_22 0.0 0 0 214s Investment_2 2.7 -10 183 214s Investment_3 2.9 -9 183 214s Investment_4 2.9 -8 184 214s Investment_5 3.1 -7 190 214s Investment_6 3.2 -6 193 214s Investment_8 3.6 -4 203 214s Investment_9 3.7 -3 208 214s Investment_10 4.0 -2 211 214s Investment_11 4.2 -1 216 214s Investment_12 4.8 0 217 214s Investment_14 5.6 2 207 214s Investment_15 6.0 3 202 214s Investment_17 7.4 5 198 214s Investment_18 6.7 6 200 214s Investment_19 7.7 7 202 214s Investment_20 7.8 8 200 214s Investment_21 8.0 9 201 214s Investment_22 8.5 10 204 214s PrivateWages_2 0.0 0 0 214s PrivateWages_3 0.0 0 0 214s PrivateWages_4 0.0 0 0 214s PrivateWages_5 0.0 0 0 214s PrivateWages_6 0.0 0 0 214s PrivateWages_8 0.0 0 0 214s PrivateWages_9 0.0 0 0 214s PrivateWages_10 0.0 0 0 214s PrivateWages_11 0.0 0 0 214s PrivateWages_12 0.0 0 0 214s PrivateWages_13 0.0 0 0 214s PrivateWages_14 0.0 0 0 214s PrivateWages_15 0.0 0 0 214s PrivateWages_16 0.0 0 0 214s PrivateWages_17 0.0 0 0 214s PrivateWages_18 0.0 0 0 214s PrivateWages_19 0.0 0 0 214s PrivateWages_20 0.0 0 0 214s PrivateWages_21 0.0 0 0 214s PrivateWages_22 0.0 0 0 214s Investment_corpProfLag Investment_gnpLag 214s Consumption_2 0.0 0.0 214s Consumption_3 0.0 0.0 214s Consumption_4 0.0 0.0 214s Consumption_5 0.0 0.0 214s Consumption_6 0.0 0.0 214s Consumption_8 0.0 0.0 214s Consumption_9 0.0 0.0 214s Consumption_11 0.0 0.0 214s Consumption_12 0.0 0.0 214s Consumption_14 0.0 0.0 214s Consumption_15 0.0 0.0 214s Consumption_16 0.0 0.0 214s Consumption_17 0.0 0.0 214s Consumption_18 0.0 0.0 214s Consumption_19 0.0 0.0 214s Consumption_20 0.0 0.0 214s Consumption_21 0.0 0.0 214s Consumption_22 0.0 0.0 214s Investment_2 12.7 44.9 214s Investment_3 12.4 45.6 214s Investment_4 16.9 50.1 214s Investment_5 18.4 57.2 214s Investment_6 19.4 57.1 214s Investment_8 19.6 64.0 214s Investment_9 19.8 64.4 214s Investment_10 21.1 64.5 214s Investment_11 21.7 67.0 214s Investment_12 15.6 61.2 214s Investment_14 7.0 44.3 214s Investment_15 11.2 45.1 214s Investment_17 14.0 54.4 214s Investment_18 17.6 62.7 214s Investment_19 17.3 65.0 214s Investment_20 15.3 60.9 214s Investment_21 19.0 69.5 214s Investment_22 21.1 75.7 214s PrivateWages_2 0.0 0.0 214s PrivateWages_3 0.0 0.0 214s PrivateWages_4 0.0 0.0 214s PrivateWages_5 0.0 0.0 214s PrivateWages_6 0.0 0.0 214s PrivateWages_8 0.0 0.0 214s PrivateWages_9 0.0 0.0 214s PrivateWages_10 0.0 0.0 214s PrivateWages_11 0.0 0.0 214s PrivateWages_12 0.0 0.0 214s PrivateWages_13 0.0 0.0 214s PrivateWages_14 0.0 0.0 214s PrivateWages_15 0.0 0.0 214s PrivateWages_16 0.0 0.0 214s PrivateWages_17 0.0 0.0 214s PrivateWages_18 0.0 0.0 214s PrivateWages_19 0.0 0.0 214s PrivateWages_20 0.0 0.0 214s PrivateWages_21 0.0 0.0 214s PrivateWages_22 0.0 0.0 214s PrivateWages_(Intercept) PrivateWages_govExp PrivateWages_taxes 214s Consumption_2 0 0.0 0.0 214s Consumption_3 0 0.0 0.0 214s Consumption_4 0 0.0 0.0 214s Consumption_5 0 0.0 0.0 214s Consumption_6 0 0.0 0.0 214s Consumption_8 0 0.0 0.0 214s Consumption_9 0 0.0 0.0 214s Consumption_11 0 0.0 0.0 214s Consumption_12 0 0.0 0.0 214s Consumption_14 0 0.0 0.0 214s Consumption_15 0 0.0 0.0 214s Consumption_16 0 0.0 0.0 214s Consumption_17 0 0.0 0.0 214s Consumption_18 0 0.0 0.0 214s Consumption_19 0 0.0 0.0 214s Consumption_20 0 0.0 0.0 214s Consumption_21 0 0.0 0.0 214s Consumption_22 0 0.0 0.0 214s Investment_2 0 0.0 0.0 214s Investment_3 0 0.0 0.0 214s Investment_4 0 0.0 0.0 214s Investment_5 0 0.0 0.0 214s Investment_6 0 0.0 0.0 214s Investment_8 0 0.0 0.0 214s Investment_9 0 0.0 0.0 214s Investment_10 0 0.0 0.0 214s Investment_11 0 0.0 0.0 214s Investment_12 0 0.0 0.0 214s Investment_14 0 0.0 0.0 214s Investment_15 0 0.0 0.0 214s Investment_17 0 0.0 0.0 214s Investment_18 0 0.0 0.0 214s Investment_19 0 0.0 0.0 214s Investment_20 0 0.0 0.0 214s Investment_21 0 0.0 0.0 214s Investment_22 0 0.0 0.0 214s PrivateWages_2 1 3.9 7.7 214s PrivateWages_3 1 3.2 3.9 214s PrivateWages_4 1 2.8 4.7 214s PrivateWages_5 1 3.5 3.8 214s PrivateWages_6 1 3.3 5.5 214s PrivateWages_8 1 4.0 6.7 214s PrivateWages_9 1 4.2 4.2 214s PrivateWages_10 1 4.1 4.0 214s PrivateWages_11 1 5.2 7.7 214s PrivateWages_12 1 5.9 7.5 214s PrivateWages_13 1 4.9 8.3 214s PrivateWages_14 1 3.7 5.4 214s PrivateWages_15 1 4.0 6.8 214s PrivateWages_16 1 4.4 7.2 214s PrivateWages_17 1 2.9 8.3 214s PrivateWages_18 1 4.3 6.7 214s PrivateWages_19 1 5.3 7.4 214s PrivateWages_20 1 6.6 8.9 214s PrivateWages_21 1 7.4 9.6 214s PrivateWages_22 1 13.8 11.6 214s PrivateWages_govWage PrivateWages_trend PrivateWages_capitalLag 214s Consumption_2 0.0 0 0 214s Consumption_3 0.0 0 0 214s Consumption_4 0.0 0 0 214s Consumption_5 0.0 0 0 214s Consumption_6 0.0 0 0 214s Consumption_8 0.0 0 0 214s Consumption_9 0.0 0 0 214s Consumption_11 0.0 0 0 214s Consumption_12 0.0 0 0 214s Consumption_14 0.0 0 0 214s Consumption_15 0.0 0 0 214s Consumption_16 0.0 0 0 214s Consumption_17 0.0 0 0 214s Consumption_18 0.0 0 0 214s Consumption_19 0.0 0 0 214s Consumption_20 0.0 0 0 214s Consumption_21 0.0 0 0 214s Consumption_22 0.0 0 0 214s Investment_2 0.0 0 0 214s Investment_3 0.0 0 0 214s Investment_4 0.0 0 0 214s Investment_5 0.0 0 0 214s Investment_6 0.0 0 0 214s Investment_8 0.0 0 0 214s Investment_9 0.0 0 0 214s Investment_10 0.0 0 0 214s Investment_11 0.0 0 0 214s Investment_12 0.0 0 0 214s Investment_14 0.0 0 0 214s Investment_15 0.0 0 0 214s Investment_17 0.0 0 0 214s Investment_18 0.0 0 0 214s Investment_19 0.0 0 0 214s Investment_20 0.0 0 0 214s Investment_21 0.0 0 0 214s Investment_22 0.0 0 0 214s PrivateWages_2 2.7 -10 183 214s PrivateWages_3 2.9 -9 183 214s PrivateWages_4 2.9 -8 184 214s PrivateWages_5 3.1 -7 190 214s PrivateWages_6 3.2 -6 193 214s PrivateWages_8 3.6 -4 203 214s PrivateWages_9 3.7 -3 208 214s PrivateWages_10 4.0 -2 211 214s PrivateWages_11 4.2 -1 216 214s PrivateWages_12 4.8 0 217 214s PrivateWages_13 5.3 1 213 214s PrivateWages_14 5.6 2 207 214s PrivateWages_15 6.0 3 202 214s PrivateWages_16 6.1 4 199 214s PrivateWages_17 7.4 5 198 214s PrivateWages_18 6.7 6 200 214s PrivateWages_19 7.7 7 202 214s PrivateWages_20 7.8 8 200 214s PrivateWages_21 8.0 9 201 214s PrivateWages_22 8.5 10 204 214s PrivateWages_corpProfLag PrivateWages_gnpLag 214s Consumption_2 0.0 0.0 214s Consumption_3 0.0 0.0 214s Consumption_4 0.0 0.0 214s Consumption_5 0.0 0.0 214s Consumption_6 0.0 0.0 214s Consumption_8 0.0 0.0 214s Consumption_9 0.0 0.0 214s Consumption_11 0.0 0.0 214s Consumption_12 0.0 0.0 214s Consumption_14 0.0 0.0 214s Consumption_15 0.0 0.0 214s Consumption_16 0.0 0.0 214s Consumption_17 0.0 0.0 214s Consumption_18 0.0 0.0 214s Consumption_19 0.0 0.0 214s Consumption_20 0.0 0.0 214s Consumption_21 0.0 0.0 214s Consumption_22 0.0 0.0 214s Investment_2 0.0 0.0 214s Investment_3 0.0 0.0 214s Investment_4 0.0 0.0 214s Investment_5 0.0 0.0 214s Investment_6 0.0 0.0 214s Investment_8 0.0 0.0 214s Investment_9 0.0 0.0 214s Investment_10 0.0 0.0 214s Investment_11 0.0 0.0 214s Investment_12 0.0 0.0 214s Investment_14 0.0 0.0 214s Investment_15 0.0 0.0 214s Investment_17 0.0 0.0 214s Investment_18 0.0 0.0 214s Investment_19 0.0 0.0 214s Investment_20 0.0 0.0 214s Investment_21 0.0 0.0 214s Investment_22 0.0 0.0 214s PrivateWages_2 12.7 44.9 214s PrivateWages_3 12.4 45.6 214s PrivateWages_4 16.9 50.1 214s PrivateWages_5 18.4 57.2 214s PrivateWages_6 19.4 57.1 214s PrivateWages_8 19.6 64.0 214s PrivateWages_9 19.8 64.4 214s PrivateWages_10 21.1 64.5 214s PrivateWages_11 21.7 67.0 214s PrivateWages_12 15.6 61.2 214s PrivateWages_13 11.4 53.4 214s PrivateWages_14 7.0 44.3 214s PrivateWages_15 11.2 45.1 214s PrivateWages_16 12.3 49.7 214s PrivateWages_17 14.0 54.4 214s PrivateWages_18 17.6 62.7 214s PrivateWages_19 17.3 65.0 214s PrivateWages_20 15.3 60.9 214s PrivateWages_21 19.0 69.5 214s PrivateWages_22 21.1 75.7 214s > matrix of fitted regressors 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 1 14.0 214s Consumption_3 1 16.7 214s Consumption_4 1 18.5 214s Consumption_5 1 20.3 214s Consumption_6 1 19.0 214s Consumption_8 1 17.6 214s Consumption_9 1 18.9 214s Consumption_11 1 16.7 214s Consumption_12 1 13.4 214s Consumption_14 1 10.0 214s Consumption_15 1 12.5 214s Consumption_16 1 14.5 214s Consumption_17 1 14.9 214s Consumption_18 1 19.4 214s Consumption_19 1 19.1 214s Consumption_20 1 17.7 214s Consumption_21 1 20.4 214s Consumption_22 1 22.7 214s Investment_2 0 0.0 214s Investment_3 0 0.0 214s Investment_4 0 0.0 214s Investment_5 0 0.0 214s Investment_6 0 0.0 214s Investment_8 0 0.0 214s Investment_9 0 0.0 214s Investment_10 0 0.0 214s Investment_11 0 0.0 214s Investment_12 0 0.0 214s Investment_14 0 0.0 214s Investment_15 0 0.0 214s Investment_17 0 0.0 214s Investment_18 0 0.0 214s Investment_19 0 0.0 214s Investment_20 0 0.0 214s Investment_21 0 0.0 214s Investment_22 0 0.0 214s PrivateWages_2 0 0.0 214s PrivateWages_3 0 0.0 214s PrivateWages_4 0 0.0 214s PrivateWages_5 0 0.0 214s PrivateWages_6 0 0.0 214s PrivateWages_8 0 0.0 214s PrivateWages_9 0 0.0 214s PrivateWages_10 0 0.0 214s PrivateWages_11 0 0.0 214s PrivateWages_12 0 0.0 214s PrivateWages_13 0 0.0 214s PrivateWages_14 0 0.0 214s PrivateWages_15 0 0.0 214s PrivateWages_16 0 0.0 214s PrivateWages_17 0 0.0 214s PrivateWages_18 0 0.0 214s PrivateWages_19 0 0.0 214s PrivateWages_20 0 0.0 214s PrivateWages_21 0 0.0 214s PrivateWages_22 0 0.0 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 12.7 29.8 214s Consumption_3 12.4 31.8 214s Consumption_4 16.9 35.3 214s Consumption_5 18.4 38.6 214s Consumption_6 19.4 38.5 214s Consumption_8 19.6 40.0 214s Consumption_9 19.8 41.8 214s Consumption_11 21.7 43.1 214s Consumption_12 15.6 39.7 214s Consumption_14 7.0 33.3 214s Consumption_15 11.2 37.3 214s Consumption_16 12.3 40.1 214s Consumption_17 14.0 41.8 214s Consumption_18 17.6 47.6 214s Consumption_19 17.3 49.2 214s Consumption_20 15.3 48.6 214s Consumption_21 19.0 53.4 214s Consumption_22 21.1 60.8 214s Investment_2 0.0 0.0 214s Investment_3 0.0 0.0 214s Investment_4 0.0 0.0 214s Investment_5 0.0 0.0 214s Investment_6 0.0 0.0 214s Investment_8 0.0 0.0 214s Investment_9 0.0 0.0 214s Investment_10 0.0 0.0 214s Investment_11 0.0 0.0 214s Investment_12 0.0 0.0 214s Investment_14 0.0 0.0 214s Investment_15 0.0 0.0 214s Investment_17 0.0 0.0 214s Investment_18 0.0 0.0 214s Investment_19 0.0 0.0 214s Investment_20 0.0 0.0 214s Investment_21 0.0 0.0 214s Investment_22 0.0 0.0 214s PrivateWages_2 0.0 0.0 214s PrivateWages_3 0.0 0.0 214s PrivateWages_4 0.0 0.0 214s PrivateWages_5 0.0 0.0 214s PrivateWages_6 0.0 0.0 214s PrivateWages_8 0.0 0.0 214s PrivateWages_9 0.0 0.0 214s PrivateWages_10 0.0 0.0 214s PrivateWages_11 0.0 0.0 214s PrivateWages_12 0.0 0.0 214s PrivateWages_13 0.0 0.0 214s PrivateWages_14 0.0 0.0 214s PrivateWages_15 0.0 0.0 214s PrivateWages_16 0.0 0.0 214s PrivateWages_17 0.0 0.0 214s PrivateWages_18 0.0 0.0 214s PrivateWages_19 0.0 0.0 214s PrivateWages_20 0.0 0.0 214s PrivateWages_21 0.0 0.0 214s PrivateWages_22 0.0 0.0 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 0 0.0 214s Consumption_3 0 0.0 214s Consumption_4 0 0.0 214s Consumption_5 0 0.0 214s Consumption_6 0 0.0 214s Consumption_8 0 0.0 214s Consumption_9 0 0.0 214s Consumption_11 0 0.0 214s Consumption_12 0 0.0 214s Consumption_14 0 0.0 214s Consumption_15 0 0.0 214s Consumption_16 0 0.0 214s Consumption_17 0 0.0 214s Consumption_18 0 0.0 214s Consumption_19 0 0.0 214s Consumption_20 0 0.0 214s Consumption_21 0 0.0 214s Consumption_22 0 0.0 214s Investment_2 1 13.4 214s Investment_3 1 16.7 214s Investment_4 1 18.8 214s Investment_5 1 20.6 214s Investment_6 1 19.3 214s Investment_8 1 17.5 214s Investment_9 1 19.5 214s Investment_10 1 20.2 214s Investment_11 1 17.2 214s Investment_12 1 13.5 214s Investment_14 1 10.1 214s Investment_15 1 13.0 214s Investment_17 1 14.9 214s Investment_18 1 19.5 214s Investment_19 1 19.3 214s Investment_20 1 17.5 214s Investment_21 1 20.2 214s Investment_22 1 22.8 214s PrivateWages_2 0 0.0 214s PrivateWages_3 0 0.0 214s PrivateWages_4 0 0.0 214s PrivateWages_5 0 0.0 214s PrivateWages_6 0 0.0 214s PrivateWages_8 0 0.0 214s PrivateWages_9 0 0.0 214s PrivateWages_10 0 0.0 214s PrivateWages_11 0 0.0 214s PrivateWages_12 0 0.0 214s PrivateWages_13 0 0.0 214s PrivateWages_14 0 0.0 214s PrivateWages_15 0 0.0 214s PrivateWages_16 0 0.0 214s PrivateWages_17 0 0.0 214s PrivateWages_18 0 0.0 214s PrivateWages_19 0 0.0 214s PrivateWages_20 0 0.0 214s PrivateWages_21 0 0.0 214s PrivateWages_22 0 0.0 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 0.0 0 214s Consumption_3 0.0 0 214s Consumption_4 0.0 0 214s Consumption_5 0.0 0 214s Consumption_6 0.0 0 214s Consumption_8 0.0 0 214s Consumption_9 0.0 0 214s Consumption_11 0.0 0 214s Consumption_12 0.0 0 214s Consumption_14 0.0 0 214s Consumption_15 0.0 0 214s Consumption_16 0.0 0 214s Consumption_17 0.0 0 214s Consumption_18 0.0 0 214s Consumption_19 0.0 0 214s Consumption_20 0.0 0 214s Consumption_21 0.0 0 214s Consumption_22 0.0 0 214s Investment_2 12.7 183 214s Investment_3 12.4 183 214s Investment_4 16.9 184 214s Investment_5 18.4 190 214s Investment_6 19.4 193 214s Investment_8 19.6 203 214s Investment_9 19.8 208 214s Investment_10 21.1 211 214s Investment_11 21.7 216 214s Investment_12 15.6 217 214s Investment_14 7.0 207 214s Investment_15 11.2 202 214s Investment_17 14.0 198 214s Investment_18 17.6 200 214s Investment_19 17.3 202 214s Investment_20 15.3 200 214s Investment_21 19.0 201 214s Investment_22 21.1 204 214s PrivateWages_2 0.0 0 214s PrivateWages_3 0.0 0 214s PrivateWages_4 0.0 0 214s PrivateWages_5 0.0 0 214s PrivateWages_6 0.0 0 214s PrivateWages_8 0.0 0 214s PrivateWages_9 0.0 0 214s PrivateWages_10 0.0 0 214s PrivateWages_11 0.0 0 214s PrivateWages_12 0.0 0 214s PrivateWages_13 0.0 0 214s PrivateWages_14 0.0 0 214s PrivateWages_15 0.0 0 214s PrivateWages_16 0.0 0 214s PrivateWages_17 0.0 0 214s PrivateWages_18 0.0 0 214s PrivateWages_19 0.0 0 214s PrivateWages_20 0.0 0 214s PrivateWages_21 0.0 0 214s PrivateWages_22 0.0 0 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 0 0.0 0.0 214s Consumption_3 0 0.0 0.0 214s Consumption_4 0 0.0 0.0 214s Consumption_5 0 0.0 0.0 214s Consumption_6 0 0.0 0.0 214s Consumption_8 0 0.0 0.0 214s Consumption_9 0 0.0 0.0 214s Consumption_11 0 0.0 0.0 214s Consumption_12 0 0.0 0.0 214s Consumption_14 0 0.0 0.0 214s Consumption_15 0 0.0 0.0 214s Consumption_16 0 0.0 0.0 214s Consumption_17 0 0.0 0.0 214s Consumption_18 0 0.0 0.0 214s Consumption_19 0 0.0 0.0 214s Consumption_20 0 0.0 0.0 214s Consumption_21 0 0.0 0.0 214s Consumption_22 0 0.0 0.0 214s Investment_2 0 0.0 0.0 214s Investment_3 0 0.0 0.0 214s Investment_4 0 0.0 0.0 214s Investment_5 0 0.0 0.0 214s Investment_6 0 0.0 0.0 214s Investment_8 0 0.0 0.0 214s Investment_9 0 0.0 0.0 214s Investment_10 0 0.0 0.0 214s Investment_11 0 0.0 0.0 214s Investment_12 0 0.0 0.0 214s Investment_14 0 0.0 0.0 214s Investment_15 0 0.0 0.0 214s Investment_17 0 0.0 0.0 214s Investment_18 0 0.0 0.0 214s Investment_19 0 0.0 0.0 214s Investment_20 0 0.0 0.0 214s Investment_21 0 0.0 0.0 214s Investment_22 0 0.0 0.0 214s PrivateWages_2 1 47.1 44.9 214s PrivateWages_3 1 49.6 45.6 214s PrivateWages_4 1 56.5 50.1 214s PrivateWages_5 1 60.7 57.2 214s PrivateWages_6 1 60.6 57.1 214s PrivateWages_8 1 60.0 64.0 214s PrivateWages_9 1 62.3 64.4 214s PrivateWages_10 1 64.6 64.5 214s PrivateWages_11 1 63.7 67.0 214s PrivateWages_12 1 54.8 61.2 214s PrivateWages_13 1 47.0 53.4 214s PrivateWages_14 1 42.1 44.3 214s PrivateWages_15 1 51.2 45.1 214s PrivateWages_16 1 55.3 49.7 214s PrivateWages_17 1 57.4 54.4 214s PrivateWages_18 1 67.2 62.7 214s PrivateWages_19 1 68.5 65.0 214s PrivateWages_20 1 66.8 60.9 214s PrivateWages_21 1 74.9 69.5 214s PrivateWages_22 1 86.9 75.7 214s PrivateWages_trend 214s Consumption_2 0 214s Consumption_3 0 214s Consumption_4 0 214s Consumption_5 0 214s Consumption_6 0 214s Consumption_8 0 214s Consumption_9 0 214s Consumption_11 0 214s Consumption_12 0 214s Consumption_14 0 214s Consumption_15 0 214s Consumption_16 0 214s Consumption_17 0 214s Consumption_18 0 214s Consumption_19 0 214s Consumption_20 0 214s Consumption_21 0 214s Consumption_22 0 214s Investment_2 0 214s Investment_3 0 214s Investment_4 0 214s Investment_5 0 214s Investment_6 0 214s Investment_8 0 214s Investment_9 0 214s Investment_10 0 214s Investment_11 0 214s Investment_12 0 214s Investment_14 0 214s Investment_15 0 214s Investment_17 0 214s Investment_18 0 214s Investment_19 0 214s Investment_20 0 214s Investment_21 0 214s Investment_22 0 214s PrivateWages_2 -10 214s PrivateWages_3 -9 214s PrivateWages_4 -8 214s PrivateWages_5 -7 214s PrivateWages_6 -6 214s PrivateWages_8 -4 214s PrivateWages_9 -3 214s PrivateWages_10 -2 214s PrivateWages_11 -1 214s PrivateWages_12 0 214s PrivateWages_13 1 214s PrivateWages_14 2 214s PrivateWages_15 3 214s PrivateWages_16 4 214s PrivateWages_17 5 214s PrivateWages_18 6 214s PrivateWages_19 7 214s PrivateWages_20 8 214s PrivateWages_21 9 214s PrivateWages_22 10 214s > nobs 214s [1] 56 214s > linearHypothesis 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 45 214s 2 44 1 1.27 0.27 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 45 214s 2 44 1 1.66 0.2 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 45 214s 2 44 1 1.66 0.2 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 44 2 0.64 0.53 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 44 2 0.84 0.44 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 46 214s 2 44 2 1.68 0.43 214s > logLik 214s 'log Lik.' -69.5 (df=13) 214s 'log Lik.' -77.5 (df=13) 214s Estimating function 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 -1.891 -26.49 214s Consumption_3 -0.190 -3.16 214s Consumption_4 0.294 5.45 214s Consumption_5 -1.285 -26.05 214s Consumption_6 0.431 8.19 214s Consumption_8 2.670 47.11 214s Consumption_9 2.363 44.77 214s Consumption_11 -1.642 -27.49 214s Consumption_12 -1.735 -23.21 214s Consumption_14 0.834 8.35 214s Consumption_15 -1.061 -13.27 214s Consumption_16 -0.885 -12.82 214s Consumption_17 3.801 56.68 214s Consumption_18 -0.502 -9.76 214s Consumption_19 -3.000 -57.33 214s Consumption_20 2.012 35.52 214s Consumption_21 0.746 15.21 214s Consumption_22 -0.957 -21.70 214s Investment_2 0.000 0.00 214s Investment_3 0.000 0.00 214s Investment_4 0.000 0.00 214s Investment_5 0.000 0.00 214s Investment_6 0.000 0.00 214s Investment_8 0.000 0.00 214s Investment_9 0.000 0.00 214s Investment_10 0.000 0.00 214s Investment_11 0.000 0.00 214s Investment_12 0.000 0.00 214s Investment_14 0.000 0.00 214s Investment_15 0.000 0.00 214s Investment_17 0.000 0.00 214s Investment_18 0.000 0.00 214s Investment_19 0.000 0.00 214s Investment_20 0.000 0.00 214s Investment_21 0.000 0.00 214s Investment_22 0.000 0.00 214s PrivateWages_2 0.000 0.00 214s PrivateWages_3 0.000 0.00 214s PrivateWages_4 0.000 0.00 214s PrivateWages_5 0.000 0.00 214s PrivateWages_6 0.000 0.00 214s PrivateWages_8 0.000 0.00 214s PrivateWages_9 0.000 0.00 214s PrivateWages_10 0.000 0.00 214s PrivateWages_11 0.000 0.00 214s PrivateWages_12 0.000 0.00 214s PrivateWages_13 0.000 0.00 214s PrivateWages_14 0.000 0.00 214s PrivateWages_15 0.000 0.00 214s PrivateWages_16 0.000 0.00 214s PrivateWages_17 0.000 0.00 214s PrivateWages_18 0.000 0.00 214s PrivateWages_19 0.000 0.00 214s PrivateWages_20 0.000 0.00 214s PrivateWages_21 0.000 0.00 214s PrivateWages_22 0.000 0.00 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 -24.01 -56.38 214s Consumption_3 -2.35 -6.04 214s Consumption_4 4.96 10.35 214s Consumption_5 -23.65 -49.61 214s Consumption_6 8.35 16.60 214s Consumption_8 52.33 106.81 214s Consumption_9 46.80 98.74 214s Consumption_11 -35.64 -70.78 214s Consumption_12 -27.07 -68.81 214s Consumption_14 5.83 27.78 214s Consumption_15 -11.88 -39.61 214s Consumption_16 -10.89 -35.54 214s Consumption_17 53.21 158.79 214s Consumption_18 -8.84 -23.92 214s Consumption_19 -51.90 -147.70 214s Consumption_20 30.78 97.67 214s Consumption_21 14.17 39.83 214s Consumption_22 -20.20 -58.19 214s Investment_2 0.00 0.00 214s Investment_3 0.00 0.00 214s Investment_4 0.00 0.00 214s Investment_5 0.00 0.00 214s Investment_6 0.00 0.00 214s Investment_8 0.00 0.00 214s Investment_9 0.00 0.00 214s Investment_10 0.00 0.00 214s Investment_11 0.00 0.00 214s Investment_12 0.00 0.00 214s Investment_14 0.00 0.00 214s Investment_15 0.00 0.00 214s Investment_17 0.00 0.00 214s Investment_18 0.00 0.00 214s Investment_19 0.00 0.00 214s Investment_20 0.00 0.00 214s Investment_21 0.00 0.00 214s Investment_22 0.00 0.00 214s PrivateWages_2 0.00 0.00 214s PrivateWages_3 0.00 0.00 214s PrivateWages_4 0.00 0.00 214s PrivateWages_5 0.00 0.00 214s PrivateWages_6 0.00 0.00 214s PrivateWages_8 0.00 0.00 214s PrivateWages_9 0.00 0.00 214s PrivateWages_10 0.00 0.00 214s PrivateWages_11 0.00 0.00 214s PrivateWages_12 0.00 0.00 214s PrivateWages_13 0.00 0.00 214s PrivateWages_14 0.00 0.00 214s PrivateWages_15 0.00 0.00 214s PrivateWages_16 0.00 0.00 214s PrivateWages_17 0.00 0.00 214s PrivateWages_18 0.00 0.00 214s PrivateWages_19 0.00 0.00 214s PrivateWages_20 0.00 0.00 214s PrivateWages_21 0.00 0.00 214s PrivateWages_22 0.00 0.00 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 0.000 0.00 214s Consumption_3 0.000 0.00 214s Consumption_4 0.000 0.00 214s Consumption_5 0.000 0.00 214s Consumption_6 0.000 0.00 214s Consumption_8 0.000 0.00 214s Consumption_9 0.000 0.00 214s Consumption_11 0.000 0.00 214s Consumption_12 0.000 0.00 214s Consumption_14 0.000 0.00 214s Consumption_15 0.000 0.00 214s Consumption_16 0.000 0.00 214s Consumption_17 0.000 0.00 214s Consumption_18 0.000 0.00 214s Consumption_19 0.000 0.00 214s Consumption_20 0.000 0.00 214s Consumption_21 0.000 0.00 214s Consumption_22 0.000 0.00 214s Investment_2 -1.375 -18.47 214s Investment_3 0.361 6.02 214s Investment_4 1.027 19.33 214s Investment_5 -1.558 -32.12 214s Investment_6 0.610 11.77 214s Investment_8 1.420 24.90 214s Investment_9 0.404 7.88 214s Investment_10 2.082 42.13 214s Investment_11 -1.150 -19.79 214s Investment_12 -1.339 -18.06 214s Investment_14 1.019 10.28 214s Investment_15 -0.475 -6.17 214s Investment_17 2.105 31.39 214s Investment_18 -0.465 -9.06 214s Investment_19 -3.871 -74.65 214s Investment_20 0.469 8.23 214s Investment_21 0.132 2.65 214s Investment_22 0.603 13.74 214s PrivateWages_2 0.000 0.00 214s PrivateWages_3 0.000 0.00 214s PrivateWages_4 0.000 0.00 214s PrivateWages_5 0.000 0.00 214s PrivateWages_6 0.000 0.00 214s PrivateWages_8 0.000 0.00 214s PrivateWages_9 0.000 0.00 214s PrivateWages_10 0.000 0.00 214s PrivateWages_11 0.000 0.00 214s PrivateWages_12 0.000 0.00 214s PrivateWages_13 0.000 0.00 214s PrivateWages_14 0.000 0.00 214s PrivateWages_15 0.000 0.00 214s PrivateWages_16 0.000 0.00 214s PrivateWages_17 0.000 0.00 214s PrivateWages_18 0.000 0.00 214s PrivateWages_19 0.000 0.00 214s PrivateWages_20 0.000 0.00 214s PrivateWages_21 0.000 0.00 214s PrivateWages_22 0.000 0.00 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 0.00 0.0 214s Consumption_3 0.00 0.0 214s Consumption_4 0.00 0.0 214s Consumption_5 0.00 0.0 214s Consumption_6 0.00 0.0 214s Consumption_8 0.00 0.0 214s Consumption_9 0.00 0.0 214s Consumption_11 0.00 0.0 214s Consumption_12 0.00 0.0 214s Consumption_14 0.00 0.0 214s Consumption_15 0.00 0.0 214s Consumption_16 0.00 0.0 214s Consumption_17 0.00 0.0 214s Consumption_18 0.00 0.0 214s Consumption_19 0.00 0.0 214s Consumption_20 0.00 0.0 214s Consumption_21 0.00 0.0 214s Consumption_22 0.00 0.0 214s Investment_2 -17.46 -251.4 214s Investment_3 4.48 65.9 214s Investment_4 17.35 189.4 214s Investment_5 -28.67 -295.5 214s Investment_6 11.83 117.5 214s Investment_8 27.83 288.8 214s Investment_9 8.00 83.9 214s Investment_10 43.93 438.5 214s Investment_11 -24.96 -248.1 214s Investment_12 -20.88 -290.1 214s Investment_14 7.14 211.1 214s Investment_15 -5.32 -95.9 214s Investment_17 29.48 416.3 214s Investment_18 -8.18 -92.9 214s Investment_19 -66.97 -781.2 214s Investment_20 7.18 93.8 214s Investment_21 2.50 26.5 214s Investment_22 12.73 123.4 214s PrivateWages_2 0.00 0.0 214s PrivateWages_3 0.00 0.0 214s PrivateWages_4 0.00 0.0 214s PrivateWages_5 0.00 0.0 214s PrivateWages_6 0.00 0.0 214s PrivateWages_8 0.00 0.0 214s PrivateWages_9 0.00 0.0 214s PrivateWages_10 0.00 0.0 214s PrivateWages_11 0.00 0.0 214s PrivateWages_12 0.00 0.0 214s PrivateWages_13 0.00 0.0 214s PrivateWages_14 0.00 0.0 214s PrivateWages_15 0.00 0.0 214s PrivateWages_16 0.00 0.0 214s PrivateWages_17 0.00 0.0 214s PrivateWages_18 0.00 0.0 214s PrivateWages_19 0.00 0.0 214s PrivateWages_20 0.00 0.0 214s PrivateWages_21 0.00 0.0 214s PrivateWages_22 0.00 0.0 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 0.0000 0.00 0.00 214s Consumption_3 0.0000 0.00 0.00 214s Consumption_4 0.0000 0.00 0.00 214s Consumption_5 0.0000 0.00 0.00 214s Consumption_6 0.0000 0.00 0.00 214s Consumption_8 0.0000 0.00 0.00 214s Consumption_9 0.0000 0.00 0.00 214s Consumption_11 0.0000 0.00 0.00 214s Consumption_12 0.0000 0.00 0.00 214s Consumption_14 0.0000 0.00 0.00 214s Consumption_15 0.0000 0.00 0.00 214s Consumption_16 0.0000 0.00 0.00 214s Consumption_17 0.0000 0.00 0.00 214s Consumption_18 0.0000 0.00 0.00 214s Consumption_19 0.0000 0.00 0.00 214s Consumption_20 0.0000 0.00 0.00 214s Consumption_21 0.0000 0.00 0.00 214s Consumption_22 0.0000 0.00 0.00 214s Investment_2 0.0000 0.00 0.00 214s Investment_3 0.0000 0.00 0.00 214s Investment_4 0.0000 0.00 0.00 214s Investment_5 0.0000 0.00 0.00 214s Investment_6 0.0000 0.00 0.00 214s Investment_8 0.0000 0.00 0.00 214s Investment_9 0.0000 0.00 0.00 214s Investment_10 0.0000 0.00 0.00 214s Investment_11 0.0000 0.00 0.00 214s Investment_12 0.0000 0.00 0.00 214s Investment_14 0.0000 0.00 0.00 214s Investment_15 0.0000 0.00 0.00 214s Investment_17 0.0000 0.00 0.00 214s Investment_18 0.0000 0.00 0.00 214s Investment_19 0.0000 0.00 0.00 214s Investment_20 0.0000 0.00 0.00 214s Investment_21 0.0000 0.00 0.00 214s Investment_22 0.0000 0.00 0.00 214s PrivateWages_2 -1.9924 -93.78 -89.46 214s PrivateWages_3 0.4683 23.22 21.35 214s PrivateWages_4 1.4034 79.35 70.31 214s PrivateWages_5 -1.7870 -108.45 -102.22 214s PrivateWages_6 -0.3627 -21.98 -20.71 214s PrivateWages_8 1.1629 69.77 74.43 214s PrivateWages_9 1.2735 79.30 82.01 214s PrivateWages_10 2.2141 142.96 142.81 214s PrivateWages_11 -1.2912 -82.26 -86.51 214s PrivateWages_12 -0.0350 -1.92 -2.14 214s PrivateWages_13 -1.0438 -49.04 -55.74 214s PrivateWages_14 1.8016 75.90 79.81 214s PrivateWages_15 -0.3714 -19.02 -16.75 214s PrivateWages_16 -0.3904 -21.61 -19.40 214s PrivateWages_17 1.4934 85.71 81.24 214s PrivateWages_18 0.0279 1.88 1.75 214s PrivateWages_19 -3.8229 -261.91 -248.49 214s PrivateWages_20 0.7870 52.61 47.93 214s PrivateWages_21 -0.7415 -55.52 -51.54 214s PrivateWages_22 1.2062 104.79 91.31 214s PrivateWages_trend 214s Consumption_2 0.000 214s Consumption_3 0.000 214s Consumption_4 0.000 214s Consumption_5 0.000 214s Consumption_6 0.000 214s Consumption_8 0.000 214s Consumption_9 0.000 214s Consumption_11 0.000 214s Consumption_12 0.000 214s Consumption_14 0.000 214s Consumption_15 0.000 214s Consumption_16 0.000 214s Consumption_17 0.000 214s Consumption_18 0.000 214s Consumption_19 0.000 214s Consumption_20 0.000 214s Consumption_21 0.000 214s Consumption_22 0.000 214s Investment_2 0.000 214s Investment_3 0.000 214s Investment_4 0.000 214s Investment_5 0.000 214s Investment_6 0.000 214s Investment_8 0.000 214s Investment_9 0.000 214s Investment_10 0.000 214s Investment_11 0.000 214s Investment_12 0.000 214s Investment_14 0.000 214s Investment_15 0.000 214s Investment_17 0.000 214s Investment_18 0.000 214s Investment_19 0.000 214s Investment_20 0.000 214s Investment_21 0.000 214s Investment_22 0.000 214s PrivateWages_2 19.924 214s PrivateWages_3 -4.214 214s PrivateWages_4 -11.227 214s PrivateWages_5 12.509 214s PrivateWages_6 2.176 214s PrivateWages_8 -4.652 214s PrivateWages_9 -3.820 214s PrivateWages_10 -4.428 214s PrivateWages_11 1.291 214s PrivateWages_12 0.000 214s PrivateWages_13 -1.044 214s PrivateWages_14 3.603 214s PrivateWages_15 -1.114 214s PrivateWages_16 -1.562 214s PrivateWages_17 7.467 214s PrivateWages_18 0.168 214s PrivateWages_19 -26.760 214s PrivateWages_20 6.296 214s PrivateWages_21 -6.674 214s PrivateWages_22 12.062 214s [1] TRUE 214s > Bread 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_(Intercept) 116.13 -4.139 214s Consumption_corpProf -4.14 1.213 214s Consumption_corpProfLag 1.01 -0.677 214s Consumption_wages -1.41 -0.133 214s Investment_(Intercept) 0.00 0.000 214s Investment_corpProf 0.00 0.000 214s Investment_corpProfLag 0.00 0.000 214s Investment_capitalLag 0.00 0.000 214s PrivateWages_(Intercept) 0.00 0.000 214s PrivateWages_gnp 0.00 0.000 214s PrivateWages_gnpLag 0.00 0.000 214s PrivateWages_trend 0.00 0.000 214s Consumption_corpProfLag Consumption_wages 214s Consumption_(Intercept) 1.0117 -1.4132 214s Consumption_corpProf -0.6770 -0.1333 214s Consumption_corpProfLag 0.6979 -0.0188 214s Consumption_wages -0.0188 0.0955 214s Investment_(Intercept) 0.0000 0.0000 214s Investment_corpProf 0.0000 0.0000 214s Investment_corpProfLag 0.0000 0.0000 214s Investment_capitalLag 0.0000 0.0000 214s PrivateWages_(Intercept) 0.0000 0.0000 214s PrivateWages_gnp 0.0000 0.0000 214s PrivateWages_gnpLag 0.0000 0.0000 214s PrivateWages_trend 0.0000 0.0000 214s Investment_(Intercept) Investment_corpProf 214s Consumption_(Intercept) 0.0 0.000 214s Consumption_corpProf 0.0 0.000 214s Consumption_corpProfLag 0.0 0.000 214s Consumption_wages 0.0 0.000 214s Investment_(Intercept) 2271.1 -40.229 214s Investment_corpProf -40.2 1.601 214s Investment_corpProfLag 32.3 -1.240 214s Investment_capitalLag -10.5 0.165 214s PrivateWages_(Intercept) 0.0 0.000 214s PrivateWages_gnp 0.0 0.000 214s PrivateWages_gnpLag 0.0 0.000 214s PrivateWages_trend 0.0 0.000 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_(Intercept) 0.000 0.0000 214s Consumption_corpProf 0.000 0.0000 214s Consumption_corpProfLag 0.000 0.0000 214s Consumption_wages 0.000 0.0000 214s Investment_(Intercept) 32.280 -10.5200 214s Investment_corpProf -1.240 0.1648 214s Investment_corpProfLag 1.187 -0.1522 214s Investment_capitalLag -0.152 0.0509 214s PrivateWages_(Intercept) 0.000 0.0000 214s PrivateWages_gnp 0.000 0.0000 214s PrivateWages_gnpLag 0.000 0.0000 214s PrivateWages_trend 0.000 0.0000 214s PrivateWages_(Intercept) PrivateWages_gnp 214s Consumption_(Intercept) 0.000 0.0000 214s Consumption_corpProf 0.000 0.0000 214s Consumption_corpProfLag 0.000 0.0000 214s Consumption_wages 0.000 0.0000 214s Investment_(Intercept) 0.000 0.0000 214s Investment_corpProf 0.000 0.0000 214s Investment_corpProfLag 0.000 0.0000 214s Investment_capitalLag 0.000 0.0000 214s PrivateWages_(Intercept) 159.333 -0.8670 214s PrivateWages_gnp -0.867 0.1475 214s PrivateWages_gnpLag -1.818 -0.1375 214s PrivateWages_trend 2.020 -0.0396 214s PrivateWages_gnpLag PrivateWages_trend 214s Consumption_(Intercept) 0.0000 0.0000 214s Consumption_corpProf 0.0000 0.0000 214s Consumption_corpProfLag 0.0000 0.0000 214s Consumption_wages 0.0000 0.0000 214s Investment_(Intercept) 0.0000 0.0000 214s Investment_corpProf 0.0000 0.0000 214s Investment_corpProfLag 0.0000 0.0000 214s Investment_capitalLag 0.0000 0.0000 214s PrivateWages_(Intercept) -1.8179 2.0198 214s PrivateWages_gnp -0.1375 -0.0396 214s PrivateWages_gnpLag 0.1737 0.0056 214s PrivateWages_trend 0.0056 0.1075 214s > 214s > # SUR 214s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 214s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 214s > summary 214s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 214s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 214s 214s systemfit results 214s method: SUR 214s 214s N DF SSR detRCov OLS-R2 McElroy-R2 214s system 58 46 45.1 0.199 0.975 0.993 214s 214s N DF SSR MSE RMSE R2 Adj R2 214s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 214s Investment 19 15 17.3 1.155 1.075 0.906 0.887 214s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 214s 214s The covariance matrix of the residuals used for estimation 214s Consumption Investment PrivateWages 214s Consumption 0.9830 0.0466 -0.391 214s Investment 0.0466 0.8101 0.115 214s PrivateWages -0.3906 0.1155 0.496 214s 214s The covariance matrix of the residuals 214s Consumption Investment PrivateWages 214s Consumption 0.979 0.080 -0.452 214s Investment 0.080 0.810 0.181 214s PrivateWages -0.452 0.181 0.521 214s 214s The correlations of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.0000 0.0907 -0.636 214s Investment 0.0907 1.0000 0.267 214s PrivateWages -0.6362 0.2671 1.000 214s 214s 214s SUR estimates for 'Consumption' (equation 1) 214s Model Formula: consump ~ corpProf + corpProfLag + wages 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 16.2670 1.3148 12.37 2.8e-09 *** 214s corpProf 0.1942 0.0954 2.04 0.06 . 214s corpProfLag 0.0747 0.0842 0.89 0.39 214s wages 0.8011 0.0383 20.93 1.6e-12 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.08 on 15 degrees of freedom 214s Number of observations: 19 Degrees of Freedom: 15 214s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 214s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 214s 214s 214s SUR estimates for 'Investment' (equation 2) 214s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 12.6390 4.7856 2.64 0.01852 * 214s corpProf 0.4708 0.0943 4.99 0.00016 *** 214s corpProfLag 0.3533 0.0907 3.89 0.00144 ** 214s capitalLag -0.1254 0.0236 -5.32 8.6e-05 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.075 on 15 degrees of freedom 214s Number of observations: 19 Degrees of Freedom: 15 214s SSR: 17.321 MSE: 1.155 Root MSE: 1.075 214s Multiple R-Squared: 0.906 Adjusted R-Squared: 0.887 214s 214s 214s SUR estimates for 'PrivateWages' (equation 3) 214s Model Formula: privWage ~ gnp + gnpLag + trend 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 1.3264 1.1240 1.18 0.2552 214s gnp 0.4184 0.0268 15.63 4.1e-11 *** 214s gnpLag 0.1714 0.0315 5.43 5.5e-05 *** 214s trend 0.1456 0.0284 5.13 0.0001 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 0.801 on 16 degrees of freedom 214s Number of observations: 20 Degrees of Freedom: 16 214s SSR: 10.266 MSE: 0.642 Root MSE: 0.801 214s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 214s 214s > residuals 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 -0.3143 -0.2326 -1.1434 214s 3 -1.2700 -0.1705 0.5084 214s 4 -1.5426 1.0718 1.4211 214s 5 -0.4489 -1.4767 -0.0992 214s 6 0.0588 0.3167 -0.3594 214s 7 0.9213 1.4446 NA 214s 8 1.3789 0.8296 -0.7554 214s 9 1.0900 -0.5263 0.2887 214s 10 NA 1.2083 1.1800 214s 11 0.3569 0.4082 -0.3673 214s 12 -0.2288 0.2663 0.3445 214s 13 NA NA -0.1571 214s 14 0.2181 0.4946 0.4220 214s 15 -0.1120 -0.0470 0.3147 214s 16 -0.0872 NA 0.0145 214s 17 1.5615 1.0289 -0.8091 214s 18 -0.4530 0.0617 0.8608 214s 19 0.1997 -2.5397 -0.7635 214s 20 0.9268 -0.6136 -0.4046 214s 21 0.7588 -0.7465 -1.2179 214s 22 -2.2137 -0.6044 0.5606 214s > fitted 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 42.2 0.0326 26.6 214s 3 46.3 2.0705 28.8 214s 4 50.7 4.1282 32.7 214s 5 51.0 4.4767 34.0 214s 6 52.5 4.7833 35.8 214s 7 54.2 4.1554 NA 214s 8 54.8 3.3704 38.7 214s 9 56.2 3.5263 38.9 214s 10 NA 3.8917 40.1 214s 11 54.6 0.5918 38.3 214s 12 51.1 -3.6663 34.2 214s 13 NA NA 29.2 214s 14 46.3 -5.5946 28.1 214s 15 48.8 -2.9530 30.3 214s 16 51.4 NA 33.2 214s 17 56.1 1.0711 37.6 214s 18 59.2 1.9383 40.1 214s 19 57.3 0.6397 39.0 214s 20 60.7 1.9136 42.0 214s 21 64.2 4.0465 46.2 214s 22 71.9 5.5044 52.7 214s > predict 214s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 214s 1 NA NA NA NA 214s 2 42.2 0.460 41.3 43.1 214s 3 46.3 0.489 45.3 47.3 214s 4 50.7 0.328 50.1 51.4 214s 5 51.0 0.384 50.3 51.8 214s 6 52.5 0.389 51.8 53.3 214s 7 54.2 0.347 53.5 54.9 214s 8 54.8 0.319 54.2 55.5 214s 9 56.2 0.353 55.5 56.9 214s 10 NA NA NA NA 214s 11 54.6 0.583 53.5 55.8 214s 12 51.1 0.524 50.1 52.2 214s 13 NA NA NA NA 214s 14 46.3 0.589 45.1 47.5 214s 15 48.8 0.393 48.0 49.6 214s 16 51.4 0.337 50.7 52.1 214s 17 56.1 0.345 55.4 56.8 214s 18 59.2 0.318 58.5 59.8 214s 19 57.3 0.381 56.5 58.1 214s 20 60.7 0.413 59.8 61.5 214s 21 64.2 0.417 63.4 65.1 214s 22 71.9 0.651 70.6 73.2 214s Investment.pred Investment.se.fit Investment.lwr Investment.upr 214s 1 NA NA NA NA 214s 2 0.0326 0.556 -1.0866 1.15 214s 3 2.0705 0.454 1.1575 2.98 214s 4 4.1282 0.399 3.3256 4.93 214s 5 4.4767 0.331 3.8101 5.14 214s 6 4.7833 0.314 4.1520 5.41 214s 7 4.1554 0.291 3.5687 4.74 214s 8 3.3704 0.260 2.8469 3.89 214s 9 3.5263 0.347 2.8278 4.22 214s 10 3.8917 0.397 3.0924 4.69 214s 11 0.5918 0.578 -0.5711 1.75 214s 12 -3.6663 0.551 -4.7762 -2.56 214s 13 NA NA NA NA 214s 14 -5.5946 0.661 -6.9261 -4.26 214s 15 -2.9530 0.392 -3.7430 -2.16 214s 16 NA NA NA NA 214s 17 1.0711 0.318 0.4315 1.71 214s 18 1.9383 0.225 1.4863 2.39 214s 19 0.6397 0.310 0.0165 1.26 214s 20 1.9136 0.333 1.2436 2.58 214s 21 4.0465 0.304 3.4345 4.66 214s 22 5.5044 0.429 4.6400 6.37 214s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 214s 1 NA NA NA NA 214s 2 26.6 0.321 26.0 27.3 214s 3 28.8 0.321 28.1 29.4 214s 4 32.7 0.316 32.0 33.3 214s 5 34.0 0.244 33.5 34.5 214s 6 35.8 0.242 35.3 36.2 214s 7 NA NA NA NA 214s 8 38.7 0.246 38.2 39.2 214s 9 38.9 0.234 38.4 39.4 214s 10 40.1 0.225 39.7 40.6 214s 11 38.3 0.301 37.7 38.9 214s 12 34.2 0.298 33.6 34.8 214s 13 29.2 0.353 28.4 29.9 214s 14 28.1 0.330 27.4 28.7 214s 15 30.3 0.328 29.6 30.9 214s 16 33.2 0.275 32.6 33.7 214s 17 37.6 0.270 37.1 38.2 214s 18 40.1 0.213 39.7 40.6 214s 19 39.0 0.301 38.4 39.6 214s 20 42.0 0.287 41.4 42.6 214s 21 46.2 0.304 45.6 46.8 214s 22 52.7 0.448 51.8 53.6 214s > model.frame 214s [1] TRUE 214s > model.matrix 214s [1] TRUE 214s > nobs 214s [1] 58 214s > linearHypothesis 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 47 214s 2 46 1 0.4 0.53 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 47 214s 2 46 1 0.49 0.49 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 47 214s 2 46 1 0.49 0.48 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 48 214s 2 46 2 0.31 0.74 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 48 214s 2 46 2 0.37 0.69 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 48 214s 2 46 2 0.75 0.69 214s > logLik 214s 'log Lik.' -66.4 (df=18) 214s 'log Lik.' -74.1 (df=18) 214s Estimating function 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 -0.4828 -5.986 214s Consumption_3 -1.9510 -32.972 214s Consumption_4 -2.3698 -43.605 214s Consumption_5 -0.6896 -13.377 214s Consumption_6 0.0903 1.814 214s Consumption_7 1.4152 27.739 214s Consumption_8 2.1183 41.942 214s Consumption_9 1.6745 35.332 214s Consumption_11 0.5483 8.553 214s Consumption_12 -0.3515 -4.008 214s Consumption_14 0.3350 3.752 214s Consumption_15 -0.1720 -2.116 214s Consumption_16 -0.1339 -1.875 214s Consumption_17 2.3987 42.218 214s Consumption_18 -0.6959 -12.040 214s Consumption_19 0.3068 4.694 214s Consumption_20 1.4238 27.052 214s Consumption_21 1.1656 24.594 214s Consumption_22 -3.4008 -79.918 214s Investment_2 0.0628 0.779 214s Investment_3 0.0460 0.778 214s Investment_4 -0.2893 -5.322 214s Investment_5 0.3986 7.732 214s Investment_6 -0.0855 -1.718 214s Investment_7 -0.3899 -7.642 214s Investment_8 -0.2239 -4.433 214s Investment_9 0.1420 2.997 214s Investment_10 0.0000 0.000 214s Investment_11 -0.1102 -1.719 214s Investment_12 -0.0719 -0.819 214s Investment_14 -0.1335 -1.495 214s Investment_15 0.0127 0.156 214s Investment_17 -0.2777 -4.887 214s Investment_18 -0.0167 -0.288 214s Investment_19 0.6855 10.488 214s Investment_20 0.1656 3.146 214s Investment_21 0.2015 4.251 214s Investment_22 0.1631 3.834 214s PrivateWages_2 -1.4560 -18.055 214s PrivateWages_3 0.6473 10.940 214s PrivateWages_4 1.8097 33.298 214s PrivateWages_5 -0.1264 -2.452 214s PrivateWages_6 -0.4576 -9.199 214s PrivateWages_8 -0.9619 -19.046 214s PrivateWages_9 0.3676 7.757 214s PrivateWages_10 0.0000 0.000 214s PrivateWages_11 -0.4677 -7.296 214s PrivateWages_12 0.4387 5.001 214s PrivateWages_13 0.0000 0.000 214s PrivateWages_14 0.5373 6.018 214s PrivateWages_15 0.4008 4.929 214s PrivateWages_16 0.0184 0.258 214s PrivateWages_17 -1.0303 -18.134 214s PrivateWages_18 1.0961 18.963 214s PrivateWages_19 -0.9722 -14.875 214s PrivateWages_20 -0.5153 -9.790 214s PrivateWages_21 -1.5509 -32.724 214s PrivateWages_22 0.7139 16.776 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 -6.131 -13.614 214s Consumption_3 -24.192 -62.822 214s Consumption_4 -40.050 -87.684 214s Consumption_5 -12.688 -25.514 214s Consumption_6 1.751 3.484 214s Consumption_7 28.447 57.601 214s Consumption_8 41.518 87.909 214s Consumption_9 33.155 71.835 214s Consumption_11 11.898 23.083 214s Consumption_12 -5.484 -13.816 214s Consumption_14 2.345 11.425 214s Consumption_15 -1.926 -6.295 214s Consumption_16 -1.647 -5.263 214s Consumption_17 33.582 106.024 214s Consumption_18 -12.249 -33.196 214s Consumption_19 5.307 14.081 214s Consumption_20 21.784 70.336 214s Consumption_21 22.146 61.777 214s Consumption_22 -71.756 -210.167 214s Investment_2 0.797 1.770 214s Investment_3 0.571 1.482 214s Investment_4 -4.889 -10.703 214s Investment_5 7.333 14.747 214s Investment_6 -1.658 -3.300 214s Investment_7 -7.837 -15.869 214s Investment_8 -4.389 -9.292 214s Investment_9 2.812 6.093 214s Investment_10 0.000 0.000 214s Investment_11 -2.391 -4.638 214s Investment_12 -1.121 -2.825 214s Investment_14 -0.934 -4.552 214s Investment_15 0.142 0.464 214s Investment_17 -3.888 -12.274 214s Investment_18 -0.293 -0.794 214s Investment_19 11.859 31.463 214s Investment_20 2.534 8.181 214s Investment_21 3.828 10.678 214s Investment_22 3.442 10.082 214s PrivateWages_2 -18.491 -41.059 214s PrivateWages_3 8.027 20.845 214s PrivateWages_4 30.584 66.958 214s PrivateWages_5 -2.325 -4.676 214s PrivateWages_6 -8.878 -17.665 214s PrivateWages_8 -18.854 -39.920 214s PrivateWages_9 7.279 15.770 214s PrivateWages_10 0.000 0.000 214s PrivateWages_11 -10.149 -19.690 214s PrivateWages_12 6.843 17.240 214s PrivateWages_13 0.000 0.000 214s PrivateWages_14 3.761 18.323 214s PrivateWages_15 4.489 14.668 214s PrivateWages_16 0.227 0.725 214s PrivateWages_17 -14.424 -45.540 214s PrivateWages_18 19.292 52.286 214s PrivateWages_19 -16.820 -44.626 214s PrivateWages_20 -7.884 -25.455 214s PrivateWages_21 -29.467 -82.197 214s PrivateWages_22 15.062 44.116 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 0.0848 1.052 214s Consumption_3 0.3428 5.793 214s Consumption_4 0.4164 7.661 214s Consumption_5 0.1211 2.350 214s Consumption_6 -0.0159 -0.319 214s Consumption_7 -0.2486 -4.873 214s Consumption_8 -0.3722 -7.369 214s Consumption_9 -0.2942 -6.207 214s Consumption_11 -0.0963 -1.503 214s Consumption_12 0.0618 0.704 214s Consumption_14 -0.0589 -0.659 214s Consumption_15 0.0302 0.372 214s Consumption_16 0.0000 0.000 214s Consumption_17 -0.4214 -7.417 214s Consumption_18 0.1223 2.115 214s Consumption_19 -0.0539 -0.825 214s Consumption_20 -0.2501 -4.753 214s Consumption_21 -0.2048 -4.321 214s Consumption_22 0.5975 14.041 214s Investment_2 -0.3080 -3.820 214s Investment_3 -0.2258 -3.815 214s Investment_4 1.4192 26.112 214s Investment_5 -1.9554 -37.935 214s Investment_6 0.4194 8.430 214s Investment_7 1.9129 37.493 214s Investment_8 1.0985 21.751 214s Investment_9 -0.6968 -14.703 214s Investment_10 1.6000 34.719 214s Investment_11 0.5405 8.432 214s Investment_12 0.3526 4.020 214s Investment_14 0.6549 7.335 214s Investment_15 -0.0622 -0.766 214s Investment_17 1.3624 23.978 214s Investment_18 0.0817 1.413 214s Investment_19 -3.3630 -51.454 214s Investment_20 -0.8125 -15.437 214s Investment_21 -0.9884 -20.856 214s Investment_22 -0.8004 -18.809 214s PrivateWages_2 0.5958 7.388 214s PrivateWages_3 -0.2649 -4.477 214s PrivateWages_4 -0.7405 -13.626 214s PrivateWages_5 0.0517 1.003 214s PrivateWages_6 0.1873 3.764 214s PrivateWages_8 0.3936 7.794 214s PrivateWages_9 -0.1504 -3.174 214s PrivateWages_10 -0.6149 -13.343 214s PrivateWages_11 0.1914 2.986 214s PrivateWages_12 -0.1795 -2.046 214s PrivateWages_13 0.0000 0.000 214s PrivateWages_14 -0.2199 -2.463 214s PrivateWages_15 -0.1640 -2.017 214s PrivateWages_16 0.0000 0.000 214s PrivateWages_17 0.4216 7.420 214s PrivateWages_18 -0.4485 -7.760 214s PrivateWages_19 0.3978 6.087 214s PrivateWages_20 0.2109 4.006 214s PrivateWages_21 0.6346 13.391 214s PrivateWages_22 -0.2921 -6.865 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 1.077 15.50 214s Consumption_3 4.250 62.59 214s Consumption_4 7.036 76.82 214s Consumption_5 2.229 22.98 214s Consumption_6 -0.308 -3.06 214s Consumption_7 -4.998 -49.18 214s Consumption_8 -7.294 -75.70 214s Consumption_9 -5.825 -61.07 214s Consumption_11 -2.090 -20.78 214s Consumption_12 0.963 13.38 214s Consumption_14 -0.412 -12.19 214s Consumption_15 0.338 6.10 214s Consumption_16 0.000 0.00 214s Consumption_17 -5.900 -83.32 214s Consumption_18 2.152 24.43 214s Consumption_19 -0.932 -10.88 214s Consumption_20 -3.827 -50.00 214s Consumption_21 -3.891 -41.20 214s Consumption_22 12.607 122.18 214s Investment_2 -3.912 -56.31 214s Investment_3 -2.799 -41.22 214s Investment_4 23.984 261.83 214s Investment_5 -35.979 -370.94 214s Investment_6 8.137 80.82 214s Investment_7 38.449 378.37 214s Investment_8 21.531 223.44 214s Investment_9 -13.797 -144.66 214s Investment_10 33.759 336.95 214s Investment_11 11.729 116.59 214s Investment_12 5.501 76.41 214s Investment_14 4.584 135.62 214s Investment_15 -0.697 -12.57 214s Investment_17 19.074 269.35 214s Investment_18 1.438 16.32 214s Investment_19 -58.180 -678.65 214s Investment_20 -12.431 -162.42 214s Investment_21 -18.780 -198.88 214s Investment_22 -16.888 -163.68 214s PrivateWages_2 7.567 108.91 214s PrivateWages_3 -3.285 -48.37 214s PrivateWages_4 -12.515 -136.63 214s PrivateWages_5 0.951 9.81 214s PrivateWages_6 3.633 36.09 214s PrivateWages_8 7.715 80.06 214s PrivateWages_9 -2.978 -31.23 214s PrivateWages_10 -12.974 -129.50 214s PrivateWages_11 4.153 41.28 214s PrivateWages_12 -2.800 -38.90 214s PrivateWages_13 0.000 0.00 214s PrivateWages_14 -1.539 -45.54 214s PrivateWages_15 -1.837 -33.13 214s PrivateWages_16 0.000 0.00 214s PrivateWages_17 5.903 83.35 214s PrivateWages_18 -7.894 -89.62 214s PrivateWages_19 6.883 80.29 214s PrivateWages_20 3.226 42.15 214s PrivateWages_21 12.058 127.69 214s PrivateWages_22 -6.164 -59.74 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 -0.4002 -18.25 -17.97 214s Consumption_3 -1.6172 -81.02 -73.75 214s Consumption_4 -1.9644 -112.37 -98.42 214s Consumption_5 -0.5716 -32.64 -32.70 214s Consumption_6 0.0748 4.56 4.27 214s Consumption_7 0.0000 0.00 0.00 214s Consumption_8 1.7559 113.08 112.38 214s Consumption_9 1.3880 89.53 89.39 214s Consumption_11 0.4545 27.81 30.45 214s Consumption_12 -0.2914 -15.56 -17.83 214s Consumption_14 0.2777 12.53 12.30 214s Consumption_15 -0.1426 -7.09 -6.43 214s Consumption_16 -0.1110 -6.04 -5.52 214s Consumption_17 1.9884 124.67 108.17 214s Consumption_18 -0.5769 -37.50 -36.17 214s Consumption_19 0.2543 15.49 16.53 214s Consumption_20 1.1803 82.03 71.88 214s Consumption_21 0.9662 73.14 67.15 214s Consumption_22 -2.8190 -249.20 -213.40 214s Investment_2 0.1212 5.53 5.44 214s Investment_3 0.0888 4.45 4.05 214s Investment_4 -0.5585 -31.95 -27.98 214s Investment_5 0.7695 43.94 44.02 214s Investment_6 -0.1651 -10.07 -9.42 214s Investment_7 0.0000 0.00 0.00 214s Investment_8 -0.4323 -27.84 -27.67 214s Investment_9 0.2742 17.69 17.66 214s Investment_10 -0.6296 -42.19 -40.61 214s Investment_11 -0.2127 -13.02 -14.25 214s Investment_12 -0.1388 -7.41 -8.49 214s Investment_14 -0.2577 -11.62 -11.42 214s Investment_15 0.0245 1.22 1.10 214s Investment_17 -0.5361 -33.62 -29.17 214s Investment_18 -0.0322 -2.09 -2.02 214s Investment_19 1.3234 80.60 86.02 214s Investment_20 0.3197 22.22 19.47 214s Investment_21 0.3890 29.45 27.03 214s Investment_22 0.3150 27.84 23.84 214s PrivateWages_2 -3.5926 -163.82 -161.31 214s PrivateWages_3 1.5973 80.02 72.84 214s PrivateWages_4 4.4653 255.42 223.71 214s PrivateWages_5 -0.3118 -17.80 -17.84 214s PrivateWages_6 -1.1292 -68.88 -64.48 214s PrivateWages_8 -2.3735 -152.85 -151.90 214s PrivateWages_9 0.9071 58.50 58.41 214s PrivateWages_10 3.7077 248.42 239.15 214s PrivateWages_11 -1.1540 -70.63 -77.32 214s PrivateWages_12 1.0824 57.80 66.24 214s PrivateWages_13 -0.4937 -21.87 -26.36 214s PrivateWages_14 1.3258 59.79 58.73 214s PrivateWages_15 0.9889 49.15 44.60 214s PrivateWages_16 0.0455 2.48 2.26 214s PrivateWages_17 -2.5423 -159.40 -138.30 214s PrivateWages_18 2.7047 175.80 169.58 214s PrivateWages_19 -2.3990 -146.10 -155.93 214s PrivateWages_20 -1.2714 -88.36 -77.43 214s PrivateWages_21 -3.8267 -289.68 -265.96 214s PrivateWages_22 1.7614 155.71 133.34 214s PrivateWages_trend 214s Consumption_2 4.0019 214s Consumption_3 14.5552 214s Consumption_4 15.7155 214s Consumption_5 4.0012 214s Consumption_6 -0.4490 214s Consumption_7 0.0000 214s Consumption_8 -7.0237 214s Consumption_9 -4.1641 214s Consumption_11 -0.4545 214s Consumption_12 0.0000 214s Consumption_14 0.5555 214s Consumption_15 -0.4277 214s Consumption_16 -0.4440 214s Consumption_17 9.9420 214s Consumption_18 -3.4614 214s Consumption_19 1.7801 214s Consumption_20 9.4420 214s Consumption_21 8.6959 214s Consumption_22 -28.1902 214s Investment_2 -1.2122 214s Investment_3 -0.7996 214s Investment_4 4.4678 214s Investment_5 -5.3865 214s Investment_6 0.9903 214s Investment_7 0.0000 214s Investment_8 1.7292 214s Investment_9 -0.8227 214s Investment_10 1.2593 214s Investment_11 0.2127 214s Investment_12 0.0000 214s Investment_14 -0.5154 214s Investment_15 0.0735 214s Investment_17 -2.6807 214s Investment_18 -0.1929 214s Investment_19 9.2640 214s Investment_20 2.5579 214s Investment_21 3.5008 214s Investment_22 3.1497 214s PrivateWages_2 35.9264 214s PrivateWages_3 -14.3757 214s PrivateWages_4 -35.7225 214s PrivateWages_5 2.1827 214s PrivateWages_6 6.7753 214s PrivateWages_8 9.4940 214s PrivateWages_9 -2.7212 214s PrivateWages_10 -7.4154 214s PrivateWages_11 1.1540 214s PrivateWages_12 0.0000 214s PrivateWages_13 -0.4937 214s PrivateWages_14 2.6517 214s PrivateWages_15 2.9666 214s PrivateWages_16 0.1820 214s PrivateWages_17 -12.7113 214s PrivateWages_18 16.2281 214s PrivateWages_19 -16.7928 214s PrivateWages_20 -10.1714 214s PrivateWages_21 -34.4407 214s PrivateWages_22 17.6141 214s [1] TRUE 214s > Bread 214s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 214s [1,] 1.00e+02 -1.05144 -0.70595 214s [2,] -1.05e+00 0.52767 -0.28007 214s [3,] -7.06e-01 -0.28007 0.41162 214s [4,] -1.63e+00 -0.08132 -0.03081 214s [5,] 5.03e+00 -0.06375 0.80965 214s [6,] -2.73e-01 0.05286 -0.04323 214s [7,] 4.77e-03 -0.03564 0.04677 214s [8,] -4.66e-04 -0.00135 -0.00415 214s [9,] -3.50e+01 0.07154 1.64913 214s [10,] 3.09e-01 -0.05491 0.03767 214s [11,] 2.66e-01 0.05541 -0.06699 214s [12,] 1.98e-01 0.03217 0.02582 214s Consumption_wages Investment_(Intercept) Investment_corpProf 214s [1,] -1.63020 5.0343 -0.27333 214s [2,] -0.08132 -0.0638 0.05286 214s [3,] -0.03081 0.8097 -0.04323 214s [4,] 0.08501 -0.3863 0.00122 214s [5,] -0.38629 1328.3034 -12.58281 214s [6,] 0.00122 -12.5828 0.51550 214s [7,] -0.00347 10.1576 -0.39286 214s [8,] 0.00211 -6.3831 0.05078 214s [9,] 0.13121 19.8408 -0.15336 214s [10,] -0.00022 0.2731 0.01339 214s [11,] -0.00213 -0.6257 -0.01103 214s [12,] -0.02827 -0.5788 0.00418 214s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 214s [1,] 0.00477 -0.000466 -34.9530 214s [2,] -0.03564 -0.001347 0.0715 214s [3,] 0.04677 -0.004153 1.6491 214s [4,] -0.00347 0.002105 0.1312 214s [5,] 10.15755 -6.383136 19.8408 214s [6,] -0.39286 0.050784 -0.1534 214s [7,] 0.47726 -0.056526 -0.3957 214s [8,] -0.05653 0.032233 -0.0526 214s [9,] -0.39566 -0.052599 73.2779 214s [10,] -0.00743 -0.001878 -0.2209 214s [11,] 0.01439 0.002876 -1.0159 214s [12,] -0.01026 0.003357 0.8108 214s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 214s [1,] 0.30855 0.26619 0.19754 214s [2,] -0.05491 0.05541 0.03217 214s [3,] 0.03767 -0.06699 0.02582 214s [4,] -0.00022 -0.00213 -0.02827 214s [5,] 0.27312 -0.62569 -0.57877 214s [6,] 0.01339 -0.01103 0.00418 214s [7,] -0.00743 0.01439 -0.01026 214s [8,] -0.00188 0.00288 0.00336 214s [9,] -0.22091 -1.01587 0.81082 214s [10,] 0.04154 -0.03895 -0.00995 214s [11,] -0.03895 0.05766 -0.00383 214s [12,] -0.00995 -0.00383 0.04664 214s > 214s > # 3SLS 214s > summary 214s 214s systemfit results 214s method: 3SLS 214s 214s N DF SSR detRCov OLS-R2 McElroy-R2 214s system 56 44 67.5 0.436 0.963 0.993 214s 214s N DF SSR MSE RMSE R2 Adj R2 214s Consumption 18 14 22.4 1.598 1.264 0.974 0.968 214s Investment 18 14 35.0 2.503 1.582 0.793 0.749 214s PrivateWages 20 16 10.1 0.629 0.793 0.987 0.985 214s 214s The covariance matrix of the residuals used for estimation 214s Consumption Investment PrivateWages 214s Consumption 1.307 0.540 -0.431 214s Investment 0.540 1.319 0.119 214s PrivateWages -0.431 0.119 0.496 214s 214s The covariance matrix of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.309 0.638 -0.440 214s Investment 0.638 1.749 0.233 214s PrivateWages -0.440 0.233 0.519 214s 214s The correlations of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.000 0.422 -0.532 214s Investment 0.422 1.000 0.247 214s PrivateWages -0.532 0.247 1.000 214s 214s 214s 3SLS estimates for 'Consumption' (equation 1) 214s Model Formula: consump ~ corpProf + corpProfLag + wages 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 18.0338 1.5648 11.52 1.6e-08 *** 214s corpProf -0.0632 0.1500 -0.42 0.68 214s corpProfLag 0.1784 0.1154 1.55 0.14 214s wages 0.8224 0.0444 18.54 3.0e-11 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.264 on 14 degrees of freedom 214s Number of observations: 18 Degrees of Freedom: 14 214s SSR: 22.377 MSE: 1.598 Root MSE: 1.264 214s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 214s 214s 214s 3SLS estimates for 'Investment' (equation 2) 214s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 24.6766 6.7008 3.68 0.00246 ** 214s corpProf 0.0472 0.1843 0.26 0.80149 214s corpProfLag 0.6874 0.1577 4.36 0.00065 *** 214s capitalLag -0.1776 0.0318 -5.59 6.7e-05 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.582 on 14 degrees of freedom 214s Number of observations: 18 Degrees of Freedom: 14 214s SSR: 35.037 MSE: 2.503 Root MSE: 1.582 214s Multiple R-Squared: 0.793 Adjusted R-Squared: 0.749 214s 214s 214s 3SLS estimates for 'PrivateWages' (equation 3) 214s Model Formula: privWage ~ gnp + gnpLag + trend 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 0.7823 1.1254 0.70 0.49695 214s gnp 0.4257 0.0308 13.80 2.6e-10 *** 214s gnpLag 0.1728 0.0341 5.07 0.00011 *** 214s trend 0.1252 0.0291 4.30 0.00055 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 0.793 on 16 degrees of freedom 214s Number of observations: 20 Degrees of Freedom: 16 214s SSR: 10.057 MSE: 0.629 Root MSE: 0.793 214s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 214s 214s > residuals 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 -0.8058 -1.721 -1.20135 214s 3 -0.6573 0.337 0.43696 214s 4 -1.1124 0.810 1.31177 214s 5 0.0833 -1.544 -0.19794 214s 6 0.6334 0.368 -0.46596 214s 7 NA NA NA 214s 8 1.7939 1.245 -0.85614 214s 9 1.7891 0.593 0.20698 214s 10 NA 2.303 1.10034 214s 11 -0.5397 -1.015 -0.38801 214s 12 -1.5147 -0.846 0.40949 214s 13 NA NA 0.00602 214s 14 -0.1171 1.670 0.61306 214s 15 -0.6526 -0.075 0.49152 214s 16 -0.3617 NA 0.17066 214s 17 1.9331 2.086 -0.69991 214s 18 -0.6063 -0.101 0.96136 214s 19 -0.3990 -3.345 -0.61606 214s 20 1.4134 0.717 -0.29343 214s 21 1.3257 0.306 -1.14412 214s 22 -1.4340 0.935 0.55310 214s > fitted 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 42.7 1.5213 26.7 214s 3 45.7 1.5632 28.9 214s 4 50.3 4.3898 32.8 214s 5 50.5 4.5444 34.1 214s 6 52.0 4.7320 35.9 214s 7 NA NA NA 214s 8 54.4 2.9547 38.8 214s 9 55.5 2.4075 39.0 214s 10 NA 2.7965 40.2 214s 11 55.5 2.0150 38.3 214s 12 52.4 -2.5541 34.1 214s 13 NA NA 29.0 214s 14 46.6 -6.7699 27.9 214s 15 49.4 -2.9250 30.1 214s 16 51.7 NA 33.0 214s 17 55.8 0.0139 37.5 214s 18 59.3 2.1013 40.0 214s 19 57.9 1.4453 38.8 214s 20 60.2 0.5828 41.9 214s 21 63.7 2.9944 46.1 214s 22 71.1 3.9651 52.7 214s > predict 214s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 214s 1 NA NA NA NA 214s 2 42.7 0.555 39.7 45.7 214s 3 45.7 0.628 42.6 48.7 214s 4 50.3 0.418 47.5 53.2 214s 5 50.5 0.492 47.6 53.4 214s 6 52.0 0.501 49.0 54.9 214s 7 NA NA NA NA 214s 8 54.4 0.405 51.6 57.3 214s 9 55.5 0.477 52.6 58.4 214s 10 NA NA NA NA 214s 11 55.5 0.832 52.3 58.8 214s 12 52.4 0.792 49.2 55.6 214s 13 NA NA NA NA 214s 14 46.6 0.676 43.5 49.7 214s 15 49.4 0.470 46.5 52.2 214s 16 51.7 0.386 48.8 54.5 214s 17 55.8 0.433 52.9 58.6 214s 18 59.3 0.368 56.5 62.1 214s 19 57.9 0.504 55.0 60.8 214s 20 60.2 0.513 57.3 63.1 214s 21 63.7 0.505 60.8 66.6 214s 22 71.1 0.771 68.0 74.3 214s Investment.pred Investment.se.fit Investment.lwr Investment.upr 214s 1 NA NA NA NA 214s 2 1.5213 0.857 -2.337 5.380 214s 3 1.5632 0.589 -2.058 5.184 214s 4 4.3898 0.519 0.819 7.961 214s 5 4.5444 0.436 1.025 8.064 214s 6 4.7320 0.415 1.224 8.240 214s 7 NA NA NA NA 214s 8 2.9547 0.342 -0.517 6.426 214s 9 2.4075 0.511 -1.158 5.973 214s 10 2.7965 0.556 -0.800 6.393 214s 11 2.0150 0.955 -1.948 5.978 214s 12 -2.5541 0.874 -6.431 1.323 214s 13 NA NA NA NA 214s 14 -6.7699 0.865 -10.637 -2.903 214s 15 -2.9250 0.503 -6.485 0.635 214s 16 NA NA NA NA 214s 17 0.0139 0.483 -3.534 3.561 214s 18 2.1013 0.320 -1.361 5.563 214s 19 1.4453 0.532 -2.134 5.025 214s 20 0.5828 0.550 -3.010 4.175 214s 21 2.9944 0.476 -0.549 6.538 214s 22 3.9651 0.692 0.261 7.669 214s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 214s 1 NA NA NA NA 214s 2 26.7 0.324 24.9 28.5 214s 3 28.9 0.331 27.0 30.7 214s 4 32.8 0.339 31.0 34.6 214s 5 34.1 0.248 32.3 35.9 214s 6 35.9 0.256 34.1 37.6 214s 7 NA NA NA NA 214s 8 38.8 0.251 37.0 40.5 214s 9 39.0 0.238 37.2 40.7 214s 10 40.2 0.232 38.4 42.0 214s 11 38.3 0.314 36.5 40.1 214s 12 34.1 0.327 32.3 35.9 214s 13 29.0 0.393 27.1 30.9 214s 14 27.9 0.329 26.1 29.7 214s 15 30.1 0.324 28.3 31.9 214s 16 33.0 0.271 31.3 34.8 214s 17 37.5 0.277 35.7 39.3 214s 18 40.0 0.213 38.3 41.8 214s 19 38.8 0.320 37.0 40.6 214s 20 41.9 0.295 40.1 43.7 214s 21 46.1 0.309 44.3 47.9 214s 22 52.7 0.476 50.8 54.7 214s > model.frame 214s [1] TRUE 214s > model.matrix 214s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 214s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 214s [3] "Numeric: lengths (696, 672) differ" 214s > nobs 214s [1] 56 214s > linearHypothesis 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 45 214s 2 44 1 1.91 0.17 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 45 214s 2 44 1 2.6 0.11 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 45 214s 2 44 1 2.6 0.11 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 44 2 1.62 0.21 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 44 2 2.2 0.12 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 46 214s 2 44 2 4.41 0.11 214s > logLik 214s 'log Lik.' -70.1 (df=18) 214s 'log Lik.' -80.6 (df=18) 214s Estimating function 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 -3.3369 -46.76 214s Consumption_3 -0.6260 -10.43 214s Consumption_4 0.5431 10.07 214s Consumption_5 -1.9287 -39.09 214s Consumption_6 0.9979 18.98 214s Consumption_8 4.7224 83.33 214s Consumption_9 4.2195 79.93 214s Consumption_11 -2.1144 -35.40 214s Consumption_12 -2.7531 -36.83 214s Consumption_14 0.7280 7.30 214s Consumption_15 -2.0340 -25.43 214s Consumption_16 -1.6770 -24.29 214s Consumption_17 6.1486 91.69 214s Consumption_18 -0.6466 -12.56 214s Consumption_19 -4.7474 -90.72 214s Consumption_20 3.3112 58.48 214s Consumption_21 1.5335 31.28 214s Consumption_22 -1.0772 -24.43 214s Investment_2 1.4470 20.28 214s Investment_3 -0.2844 -4.74 214s Investment_4 -0.6458 -11.98 214s Investment_5 1.3096 26.54 214s Investment_6 -0.3315 -6.31 214s Investment_8 -1.1056 -19.51 214s Investment_9 -0.5457 -10.34 214s Investment_10 0.0000 0.00 214s Investment_11 0.8919 14.93 214s Investment_12 0.7723 10.33 214s Investment_14 -1.4083 -14.12 214s Investment_15 0.0885 1.11 214s Investment_17 -1.8093 -26.98 214s Investment_18 0.1676 3.25 214s Investment_19 2.8888 55.20 214s Investment_20 -0.6425 -11.35 214s Investment_21 -0.2855 -5.82 214s Investment_22 -0.7925 -17.97 214s PrivateWages_2 -2.9611 -41.49 214s PrivateWages_3 1.0665 17.77 214s PrivateWages_4 2.5794 47.83 214s PrivateWages_5 -2.7951 -56.65 214s PrivateWages_6 -0.4865 -9.25 214s PrivateWages_8 1.6497 29.11 214s PrivateWages_9 1.8751 35.52Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 214s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 214s 214s PrivateWages_10 0.0000 0.00 214s PrivateWages_11 -2.3618 -39.54 214s PrivateWages_12 -0.3246 -4.34 214s PrivateWages_13 0.0000 0.00 214s PrivateWages_14 3.0441 30.51 214s PrivateWages_15 -0.2496 -3.12 214s PrivateWages_16 -0.3710 -5.37 214s PrivateWages_17 2.5263 37.67 214s PrivateWages_18 0.0583 1.13 214s PrivateWages_19 -6.2503 -119.43 214s PrivateWages_20 1.3565 23.96 214s PrivateWages_21 -1.2791 -26.09 214s PrivateWages_22 1.9457 44.12 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 -42.379 -99.51 214s Consumption_3 -7.762 -19.94 214s Consumption_4 9.179 19.15 214s Consumption_5 -35.489 -74.45 214s Consumption_6 19.359 38.46 214s Consumption_8 92.559 188.94 214s Consumption_9 83.547 176.28 214s Consumption_11 -45.883 -91.13 214s Consumption_12 -42.949 -109.17 214s Consumption_14 5.096 24.26 214s Consumption_15 -22.780 -75.93 214s Consumption_16 -20.627 -67.32 214s Consumption_17 86.080 256.88 214s Consumption_18 -11.379 -30.78 214s Consumption_19 -82.131 -233.73 214s Consumption_20 50.662 160.78 214s Consumption_21 29.137 81.92 214s Consumption_22 -22.729 -65.49 214s Investment_2 18.377 43.15 214s Investment_3 -3.526 -9.06 214s Investment_4 -10.914 -22.77 214s Investment_5 24.097 50.55 214s Investment_6 -6.431 -12.78 214s Investment_8 -21.669 -44.23 214s Investment_9 -10.805 -22.80 214s Investment_10 0.000 0.00 214s Investment_11 19.355 38.44 214s Investment_12 12.047 30.62 214s Investment_14 -9.858 -46.93 214s Investment_15 0.992 3.31 214s Investment_17 -25.331 -75.59 214s Investment_18 2.950 7.98 214s Investment_19 49.976 142.22 214s Investment_20 -9.831 -31.20 214s Investment_21 -5.425 -15.25 214s Investment_22 -16.723 -48.18 214s PrivateWages_2 -37.606 -88.31 214s PrivateWages_3 13.225 33.97 214s PrivateWages_4 43.593 90.94 214s PrivateWages_5 -51.429 -107.89 214s PrivateWages_6 -9.438 -18.75 214s PrivateWages_8 32.333 66.00 214s PrivateWages_9 37.126 78.33 214s PrivateWages_10 0.000 0.00 214s PrivateWages_11 -51.251 -101.80 214s PrivateWages_12 -5.063 -12.87 214s PrivateWages_13 0.000 0.00 214s PrivateWages_14 21.309 101.45 214s PrivateWages_15 -2.796 -9.32 214s PrivateWages_16 -4.563 -14.89 214s PrivateWages_17 35.368 105.55 214s PrivateWages_18 1.025 2.77 214s PrivateWages_19 -108.130 -307.72 214s PrivateWages_20 20.754 65.87 214s PrivateWages_21 -24.303 -68.33 214s PrivateWages_22 41.055 118.29 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 1.6657 22.369 214s Consumption_3 0.3125 5.208 214s Consumption_4 -0.2711 -5.105 214s Consumption_5 0.9628 19.850 214s Consumption_6 -0.4981 -9.617 214s Consumption_8 -2.3573 -41.335 214s Consumption_9 -2.1063 -41.098 214s Consumption_11 1.0555 18.165 214s Consumption_12 1.3743 18.540 214s Consumption_14 -0.3634 -3.664 214s Consumption_15 1.0153 13.204 214s Consumption_16 0.0000 0.000 214s Consumption_17 -3.0693 -45.765 214s Consumption_18 0.3228 6.293 214s Consumption_19 2.3698 45.702 214s Consumption_20 -1.6529 -29.000 214s Consumption_21 -0.7655 -15.445 214s Consumption_22 0.5377 12.243 214s Investment_2 -2.0943 -28.124 214s Investment_3 0.4116 6.860 214s Investment_4 0.9347 17.600 214s Investment_5 -1.8955 -39.080 214s Investment_6 0.4798 9.263 214s Investment_8 1.6002 28.058 214s Investment_9 0.7899 15.412 214s Investment_10 2.8075 56.810 214s Investment_11 -1.2910 -22.218 214s Investment_12 -1.1178 -15.079 214s Investment_14 2.0383 20.552 214s Investment_15 -0.1282 -1.667 214s Investment_17 2.6188 39.047 214s Investment_18 -0.2426 -4.730 214s Investment_19 -4.1811 -80.631 214s Investment_20 0.9300 16.316 214s Investment_21 0.4133 8.338 214s Investment_22 1.1471 26.118 214s PrivateWages_2 1.8190 24.427 214s PrivateWages_3 -0.6551 -10.919 214s PrivateWages_4 -1.5845 -29.835 214s PrivateWages_5 1.7170 35.400 214s PrivateWages_6 0.2989 5.770 214s PrivateWages_8 -1.0134 -17.769 214s PrivateWages_9 -1.1518 -22.474 214s PrivateWages_10 -2.1257 -43.013 214s PrivateWages_11 1.4508 24.969 214s PrivateWages_12 0.1994 2.690 214s PrivateWages_13 0.0000 0.000 214s PrivateWages_14 -1.8700 -18.855 214s PrivateWages_15 0.1533 1.994 214s PrivateWages_16 0.0000 0.000 214s PrivateWages_17 -1.5519 -23.140 214s PrivateWages_18 -0.0358 -0.698 214s PrivateWages_19 3.8395 74.045 214s PrivateWages_20 -0.8333 -14.620 214s PrivateWages_21 0.7858 15.853 214s PrivateWages_22 -1.1953 -27.215 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 21.15 304.50 214s Consumption_3 3.87 57.06 214s Consumption_4 -4.58 -50.02 214s Consumption_5 17.72 182.64 214s Consumption_6 -9.66 -95.99 214s Consumption_8 -46.20 -479.48 214s Consumption_9 -41.70 -437.27 214s Consumption_11 22.90 227.67 214s Consumption_12 21.44 297.81 214s Consumption_14 -2.54 -75.26 214s Consumption_15 11.37 205.09 214s Consumption_16 0.00 0.00 214s Consumption_17 -42.97 -606.79 214s Consumption_18 5.68 64.49 214s Consumption_19 41.00 478.23 214s Consumption_20 -25.29 -330.42 214s Consumption_21 -14.54 -154.02 214s Consumption_22 11.35 109.96 214s Investment_2 -26.60 -382.84 214s Investment_3 5.10 75.16 214s Investment_4 15.80 172.46 214s Investment_5 -34.88 -359.58 214s Investment_6 9.31 92.46 214s Investment_8 31.36 325.47 214s Investment_9 15.64 163.98 214s Investment_10 59.24 591.25 214s Investment_11 -28.01 -278.46 214s Investment_12 -17.44 -242.22 214s Investment_14 14.27 422.14 214s Investment_15 -1.44 -25.89 214s Investment_17 36.66 517.73 214s Investment_18 -4.27 -48.47 214s Investment_19 -72.33 -843.75 214s Investment_20 14.23 185.90 214s Investment_21 7.85 83.15 214s Investment_22 24.20 234.58 214s PrivateWages_2 23.10 332.51 214s PrivateWages_3 -8.12 -119.63 214s PrivateWages_4 -26.78 -292.35 214s PrivateWages_5 31.59 325.71 214s PrivateWages_6 5.80 57.59 214s PrivateWages_8 -19.86 -206.12 214s PrivateWages_9 -22.81 -239.12 214s PrivateWages_10 -44.85 -447.66 214s PrivateWages_11 31.48 312.95 214s PrivateWages_12 3.11 43.21 214s PrivateWages_13 0.00 0.00 214s PrivateWages_14 -13.09 -387.28 214s PrivateWages_15 1.72 30.97 214s PrivateWages_16 0.00 0.00 214s PrivateWages_17 -21.73 -306.81 214s PrivateWages_18 -0.63 -7.15 214s PrivateWages_19 66.42 774.82 214s PrivateWages_20 -12.75 -166.57 214s PrivateWages_21 14.93 158.09 214s PrivateWages_22 -25.22 -244.43 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 -3.302 -155.43 -148.27 214s Consumption_3 -0.619 -30.71 -28.25 214s Consumption_4 0.537 30.39 26.93 214s Consumption_5 -1.909 -115.83 -109.18 214s Consumption_6 0.987 59.85 56.39 214s Consumption_8 4.673 280.38 299.09 214s Consumption_9 4.176 260.01 268.91 214s Consumption_11 -2.092 -133.31 -140.19 214s Consumption_12 -2.724 -149.39 -166.74 214s Consumption_14 0.720 30.35 31.91 214s Consumption_15 -2.013 -103.09 -90.78 214s Consumption_16 -1.660 -91.84 -82.48 214s Consumption_17 6.085 349.22 331.00 214s Consumption_18 -0.640 -42.98 -40.12 214s Consumption_19 -4.698 -321.88 -305.37 214s Consumption_20 3.277 219.03 199.56 214s Consumption_21 1.518 113.62 105.47 214s Consumption_22 -1.066 -92.61 -80.70 214s Investment_2 1.762 82.94 79.12 214s Investment_3 -0.346 -17.17 -15.79 214s Investment_4 -0.786 -44.47 -39.40 214s Investment_5 1.595 96.79 91.23 214s Investment_6 -0.404 -24.47 -23.05 214s Investment_8 -1.346 -80.78 -86.17 214s Investment_9 -0.665 -41.38 -42.80 214s Investment_10 -2.362 -152.52 -152.36 214s Investment_11 1.086 69.20 72.78 214s Investment_12 0.940 51.57 57.56 214s Investment_14 -1.715 -72.25 -75.98 214s Investment_15 0.108 5.52 4.86 214s Investment_17 -2.203 -126.46 -119.87 214s Investment_18 0.204 13.71 12.80 214s Investment_19 3.518 241.02 228.67 214s Investment_20 -0.782 -52.30 -47.65 214s Investment_21 -0.348 -26.03 -24.17 214s Investment_22 -0.965 -83.85 -73.06 214s PrivateWages_2 -6.697 -315.21 -300.67 214s PrivateWages_3 2.412 119.58 109.98 214s PrivateWages_4 5.833 329.84 292.25 214s PrivateWages_5 -6.321 -383.60 -361.56 214s PrivateWages_6 -1.100 -66.69 -62.82 214s PrivateWages_8 3.731 223.83 238.77 214s PrivateWages_9 4.240 264.05 273.09 214s PrivateWages_10 7.826 505.29 504.75 214s PrivateWages_11 -5.341 -340.30 -357.86 214s PrivateWages_12 -0.734 -40.25 -44.92 214s PrivateWages_13 -4.155 -195.19 -221.87 214s PrivateWages_14 6.884 290.02 304.97 214s PrivateWages_15 -0.565 -28.91 -25.46 214s PrivateWages_16 -0.839 -46.43 -41.70 214s PrivateWages_17 5.713 327.90 310.80 214s PrivateWages_18 0.132 8.85 8.26 214s PrivateWages_19 -14.135 -968.43 -918.78 214s PrivateWages_20 3.068 205.06 186.82 214s PrivateWages_21 -2.893 -216.57 -201.04 214s PrivateWages_22 4.400 382.29 333.10 214s PrivateWages_trend 214s Consumption_2 33.022 214s Consumption_3 5.575 214s Consumption_4 -4.300 214s Consumption_5 13.361 214s Consumption_6 -5.925 214s Consumption_8 -18.693 214s Consumption_9 -12.527 214s Consumption_11 2.092 214s Consumption_12 0.000 214s Consumption_14 1.441 214s Consumption_15 -6.038 214s Consumption_16 -6.638 214s Consumption_17 30.423 214s Consumption_18 -3.839 214s Consumption_19 -32.886 214s Consumption_20 26.214 214s Consumption_21 13.658 214s Consumption_22 -10.660 214s Investment_2 -17.621 214s Investment_3 3.117 214s Investment_4 6.292 214s Investment_5 -11.164 214s Investment_6 2.422 214s Investment_8 5.385 214s Investment_9 1.994 214s Investment_10 4.724 214s Investment_11 -1.086 214s Investment_12 0.000 214s Investment_14 -3.430 214s Investment_15 0.323 214s Investment_17 -11.017 214s Investment_18 1.225 214s Investment_19 24.626 214s Investment_20 -6.260 214s Investment_21 -3.129 214s Investment_22 -9.652 214s PrivateWages_2 66.965 214s PrivateWages_3 -21.707 214s PrivateWages_4 -46.667 214s PrivateWages_5 44.247 214s PrivateWages_6 6.602 214s PrivateWages_8 -14.923 214s PrivateWages_9 -12.721 214s PrivateWages_10 -15.651 214s PrivateWages_11 5.341 214s PrivateWages_12 0.000 214s PrivateWages_13 -4.155 214s PrivateWages_14 13.769 214s PrivateWages_15 -1.694 214s PrivateWages_16 -3.356 214s PrivateWages_17 28.566 214s PrivateWages_18 0.791 214s PrivateWages_19 -98.946 214s PrivateWages_20 24.542 214s PrivateWages_21 -26.035 214s PrivateWages_22 44.003 214s [1] TRUE 214s > Bread 214s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 214s [1,] 137.1267 -4.2997 0.8463 214s [2,] -4.2997 1.2597 -0.6942 214s [3,] 0.8463 -0.6942 0.7454 214s [4,] -1.7733 -0.1394 -0.0281 214s [5,] 105.0265 3.4241 3.4807 214s [6,] -4.4721 0.5244 -0.4530 214s [7,] 1.6442 -0.3454 0.4268 214s [8,] -0.2644 -0.0340 -0.0134 214s [9,] -38.0151 0.3680 1.7655 214s [10,] 0.5379 -0.0825 0.0502 214s [11,] 0.0809 0.0782 -0.0821 214s [12,] 0.1895 0.0505 0.0265 214s Consumption_wages Investment_(Intercept) Investment_corpProf 214s [1,] -1.773256 105.03 -4.47211 214s [2,] -0.139424 3.42 0.52437 214s [3,] -0.028067 3.48 -0.45300 214s [4,] 0.110155 -5.14 0.06784 214s [5,] -5.138461 2514.46 -43.59967 214s [6,] 0.067843 -43.60 1.90216 214s [7,] -0.064178 34.75 -1.45456 214s [8,] 0.025084 -11.63 0.17310 214s [9,] 0.044238 27.92 -0.25822 214s [10,] 0.000203 1.31 0.00136 214s [11,] -0.000811 -1.85 0.00316 214s [12,] -0.035488 -0.85 0.01679 214s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 214s [1,] 1.64420 -0.26436 -38.0151 214s [2,] -0.34536 -0.03402 0.3680 214s [3,] 0.42680 -0.01343 1.7655 214s [4,] -0.06418 0.02508 0.0442 214s [5,] 34.75055 -11.63252 27.9186 214s [6,] -1.45456 0.17310 -0.2582 214s [7,] 1.39257 -0.16270 -0.3518 214s [8,] -0.16270 0.05655 -0.0905 214s [9,] -0.35175 -0.09046 70.9283 214s [10,] 0.00769 -0.00730 -0.3444 214s [11,] -0.00156 0.00915 -0.8533 214s [12,] -0.02239 0.00456 0.8163 214s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 214s [1,] 0.537909 0.080946 0.189459 214s [2,] -0.082456 0.078164 0.050460 214s [3,] 0.050248 -0.082092 0.026511 214s [4,] 0.000203 -0.000811 -0.035488 214s [5,] 1.312267 -1.847095 -0.850461 214s [6,] 0.001362 0.003160 0.016792 214s [7,] 0.007689 -0.001565 -0.022388 214s [8,] -0.007301 0.009148 0.004555 214s [9,] -0.344428 -0.853347 0.816265 214s [10,] 0.053258 -0.048785 -0.014522 214s [11,] -0.048785 0.064956 0.000648 214s [12,] -0.014522 0.000648 0.047452 214s > 214s > # I3SLS 214s > summary 214s 214s systemfit results 214s method: iterated 3SLS 214s 214s convergence achieved after 10 iterations 214s 214s N DF SSR detRCov OLS-R2 McElroy-R2 214s system 56 44 79.4 0.55 0.956 0.994 214s 214s N DF SSR MSE RMSE R2 Adj R2 214s Consumption 18 14 22.3 1.595 1.263 0.974 0.968 214s Investment 18 14 46.8 3.346 1.829 0.724 0.664 214s PrivateWages 20 16 10.2 0.639 0.799 0.987 0.985 214s 214s The covariance matrix of the residuals used for estimation 214s Consumption Investment PrivateWages 214s Consumption 1.307 0.750 -0.452 214s Investment 0.750 2.318 0.272 214s PrivateWages -0.452 0.272 0.530 214s 214s The covariance matrix of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.307 0.750 -0.452 214s Investment 0.750 2.318 0.272 214s PrivateWages -0.452 0.272 0.530 214s 214s The correlations of the residuals 214s Consumption Investment PrivateWages 214s Consumption 1.000 0.424 -0.542 214s Investment 0.424 1.000 0.254 214s PrivateWages -0.542 0.254 1.000 214s 214s 214s 3SLS estimates for 'Consumption' (equation 1) 214s Model Formula: consump ~ corpProf + corpProfLag + wages 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 18.3252 1.5452 11.86 1.1e-08 *** 214s corpProf -0.0436 0.1470 -0.30 0.77 214s corpProfLag 0.1614 0.1127 1.43 0.17 214s wages 0.8127 0.0436 18.65 2.8e-11 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.263 on 14 degrees of freedom 214s Number of observations: 18 Degrees of Freedom: 14 214s SSR: 22.337 MSE: 1.595 Root MSE: 1.263 214s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 214s 214s 214s 3SLS estimates for 'Investment' (equation 2) 214s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 30.2418 8.3674 3.61 0.00282 ** 214s corpProf -0.0437 0.2341 -0.19 0.85457 214s corpProfLag 0.7856 0.1993 3.94 0.00147 ** 214s capitalLag -0.2065 0.0397 -5.20 0.00014 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 1.829 on 14 degrees of freedom 214s Number of observations: 18 Degrees of Freedom: 14 214s SSR: 46.838 MSE: 3.346 Root MSE: 1.829 214s Multiple R-Squared: 0.724 Adjusted R-Squared: 0.664 214s 214s 214s 3SLS estimates for 'PrivateWages' (equation 3) 214s Model Formula: privWage ~ gnp + gnpLag + trend 214s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 214s gnpLag 214s 214s Estimate Std. Error t value Pr(>|t|) 214s (Intercept) 0.4741 1.1280 0.42 0.67983 214s gnp 0.4268 0.0296 14.44 1.4e-10 *** 214s gnpLag 0.1767 0.0330 5.35 6.5e-05 *** 214s trend 0.1201 0.0290 4.14 0.00076 *** 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s 214s Residual standard error: 0.799 on 16 degrees of freedom 214s Number of observations: 20 Degrees of Freedom: 16 214s SSR: 10.218 MSE: 0.639 Root MSE: 0.799 214s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 214s 214s > residuals 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 -0.8546 -2.1226 -1.1687 214s 3 -0.7611 0.3684 0.4670 214s 4 -1.1233 0.5912 1.3216 214s 5 0.0781 -1.6694 -0.2108 214s 6 0.6467 0.2952 -0.4776 214s 7 NA NA NA 214s 8 1.8444 1.4348 -0.8884 214s 9 1.8309 1.0020 0.1781 214s 10 NA 2.7265 1.0734 214s 11 -0.3652 -1.0581 -0.4134 214s 12 -1.3877 -0.6431 0.4203 214s 13 NA NA 0.0623 214s 14 -0.1818 2.4214 0.7091 214s 15 -0.6438 0.2168 0.5845 214s 16 -0.3417 NA 0.2455 214s 17 1.9583 2.4607 -0.6474 214s 18 -0.4806 -0.0468 0.9840 214s 19 -0.2563 -3.3855 -0.5930 214s 20 1.4832 1.1550 -0.2586 214s 21 1.4514 0.6086 -1.1446 214s 22 -1.2351 1.3453 0.5196 214s > fitted 214s Consumption Investment PrivateWages 214s 1 NA NA NA 214s 2 42.8 1.923 26.7 214s 3 45.8 1.532 28.8 214s 4 50.3 4.609 32.8 214s 5 50.5 4.669 34.1 214s 6 52.0 4.805 35.9 214s 7 NA NA NA 214s 8 54.4 2.765 38.8 214s 9 55.5 1.998 39.0 214s 10 NA 2.373 40.2 214s 11 55.4 2.058 38.3 214s 12 52.3 -2.757 34.1 214s 13 NA NA 28.9 214s 14 46.7 -7.521 27.8 214s 15 49.3 -3.217 30.0 214s 16 51.6 NA 33.0 214s 17 55.7 -0.361 37.4 214s 18 59.2 2.047 40.0 214s 19 57.8 1.485 38.8 214s 20 60.1 0.145 41.9 214s 21 63.5 2.691 46.1 214s 22 70.9 3.555 52.8 214s > predict 214s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 214s 1 NA NA NA NA 214s 2 42.8 0.548 41.7 43.9 214s 3 45.8 0.618 44.5 47.0 214s 4 50.3 0.411 49.5 51.2 214s 5 50.5 0.481 49.6 51.5 214s 6 52.0 0.490 51.0 52.9 214s 7 NA NA NA NA 214s 8 54.4 0.396 53.6 55.2 214s 9 55.5 0.467 54.5 56.4 214s 10 NA NA NA NA 214s 11 55.4 0.811 53.7 57.0 214s 12 52.3 0.775 50.7 53.8 214s 13 NA NA NA NA 214s 14 46.7 0.665 45.3 48.0 214s 15 49.3 0.463 48.4 50.3 214s 16 51.6 0.381 50.9 52.4 214s 17 55.7 0.428 54.9 56.6 214s 18 59.2 0.360 58.5 59.9 214s 19 57.8 0.492 56.8 58.7 214s 20 60.1 0.508 59.1 61.1 214s 21 63.5 0.499 62.5 64.6 214s 22 70.9 0.761 69.4 72.5 214s Investment.pred Investment.se.fit Investment.lwr Investment.upr 214s 1 NA NA NA NA 214s 2 1.923 1.079 -0.2526 4.098 214s 3 1.532 0.766 -0.0119 3.075 214s 4 4.609 0.668 3.2632 5.954 214s 5 4.669 0.566 3.5280 5.811 214s 6 4.805 0.543 3.7104 5.899 214s 7 NA NA NA NA 214s 8 2.765 0.447 1.8648 3.665 214s 9 1.998 0.651 0.6860 3.310 214s 10 2.373 0.710 0.9434 3.804 214s 11 2.058 1.237 -0.4350 4.551 214s 12 -2.757 1.139 -5.0532 -0.461 214s 13 NA NA NA NA 214s 14 -7.521 1.094 -9.7261 -5.317 214s 15 -3.217 0.648 -4.5217 -1.912 214s 16 NA NA NA NA 214s 17 -0.361 0.615 -1.6007 0.879 214s 18 2.047 0.417 1.2060 2.888 214s 19 1.485 0.684 0.1062 2.865 214s 20 0.145 0.699 -1.2632 1.553 214s 21 2.691 0.614 1.4548 3.928 214s 22 3.555 0.887 1.7674 5.342 214s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 214s 1 NA NA NA NA 214s 2 26.7 0.330 26.0 27.3 214s 3 28.8 0.336 28.2 29.5 214s 4 32.8 0.340 32.1 33.5 214s 5 34.1 0.251 33.6 34.6 214s 6 35.9 0.259 35.4 36.4 214s 7 NA NA NA NA 214s 8 38.8 0.253 38.3 39.3 214s 9 39.0 0.240 38.5 39.5 214s 10 40.2 0.236 39.8 40.7 214s 11 38.3 0.307 37.7 38.9 214s 12 34.1 0.313 33.4 34.7 214s 13 28.9 0.376 28.2 29.7 214s 14 27.8 0.327 27.1 28.4 214s 15 30.0 0.322 29.4 30.7 214s 16 33.0 0.270 32.4 33.5 214s 17 37.4 0.275 36.9 38.0 214s 18 40.0 0.216 39.6 40.5 214s 19 38.8 0.314 38.2 39.4 214s 20 41.9 0.296 41.3 42.5 214s 21 46.1 0.317 45.5 46.8 214s 22 52.8 0.480 51.8 53.7 214s > model.frame 214s [1] TRUE 214s > model.matrix 214s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 214s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 214s [3] "Numeric: lengths (696, 672) differ" 214s > nobs 214s [1] 56 214s > linearHypothesis 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 45 214s 2 44 1 2.29 0.14 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 45 214s 2 44 1 2.89 0.096 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 45 214s 2 44 1 2.89 0.089 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s Linear hypothesis test (Theil's F test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 44 2 2.3 0.11 214s Linear hypothesis test (F statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df F Pr(>F) 214s 1 46 214s 2 44 2 2.9 0.066 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s Linear hypothesis test (Chi^2 statistic of a Wald test) 214s 214s Hypothesis: 214s Consumption_corpProf + Investment_capitalLag = 0 214s Consumption_corpProfLag - PrivateWages_trend = 0 214s 214s Model 1: restricted model 214s Model 2: kleinModel 214s 214s Res.Df Df Chisq Pr(>Chisq) 214s 1 46 214s 2 44 2 5.79 0.055 . 214s --- 214s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 214s > logLik 214s 'log Lik.' -72.2 (df=18) 214s 'log Lik.' -83.4 (df=18) 214s Estimating function 214s Consumption_(Intercept) Consumption_corpProf 214s Consumption_2 -4.4102 -61.801 214s Consumption_3 -1.0169 -16.947 214s Consumption_4 0.6316 11.712 214s Consumption_5 -2.4849 -50.366 214s Consumption_6 1.3496 25.671 214s Consumption_8 6.2136 109.641 214s Consumption_9 5.5588 105.303 214s Consumption_11 -2.3690 -39.659 214s Consumption_12 -3.3344 -44.601 214s Consumption_14 0.8298 8.317 214s Consumption_15 -2.5803 -32.264 214s Consumption_16 -2.1088 -30.539 214s Consumption_17 7.9903 119.154 214s Consumption_18 -0.6538 -12.697 214s Consumption_19 -5.8714 -112.192 214s Consumption_20 4.4259 78.161 214s Consumption_21 2.2655 46.209 214s Consumption_22 -0.9489 -21.517 214s Investment_2 1.9674 27.570 214s Investment_3 -0.3392 -5.652 214s Investment_4 -0.5776 -10.712 214s Investment_5 1.5305 31.021 214s Investment_6 -0.2467 -4.692 214s Investment_8 -1.2650 -22.320 214s Investment_9 -0.8831 -16.728 214s Investment_10 0.0000 0.000 214s Investment_11 0.9353 15.658 214s Investment_12 0.5224 6.988 214s Investment_14 -2.2467 -22.520 214s Investment_15 -0.2344 -2.931 214s Investment_17 -2.2188 -33.088 214s Investment_18 -0.0466 -0.905 214s Investment_19 3.0409 58.107 214s Investment_20 -1.0335 -18.251 214s Investment_21 -0.5381 -10.975 214s Investment_22 -1.2437 -28.202 214s PrivateWages_2 -4.0943 -57.374 214s PrivateWages_3 1.5700 26.162 214s PrivateWages_4 3.6522 67.727 214s PrivateWages_5 -3.9696 -80.460 214s PrivateWages_6 -0.7099 -13.503 214s PrivateWages_8 2.2578 39.840 214s PrivateWages_9 2.5772 48.821 214s PrivateWages_10 0.0000 0.000 214s PrivateWages_11 -3.3861 -56.686 214s PrivateWages_12 -0.4354 -5.824 214s PrivateWages_13 0.0000 0.000 214s PrivateWages_14 4.5081 45.187 214s PrivateWages_15 -0.1430 -1.788 214s PrivateWages_16 -0.3534 -5.118 214s PrivateWages_17 3.6864 54.972 214s PrivateWages_18 0.1281 2.488 214s PrivateWages_19 -8.7578 -167.347 214s PrivateWages_20 1.9940 35.215 214s PrivateWages_21 -1.7982 -36.678 214s PrivateWages_22 2.6643 60.414 214s Consumption_corpProfLag Consumption_wages 214s Consumption_2 -56.01 -131.52 214s Consumption_3 -12.61 -32.39 214s Consumption_4 10.67 22.27 214s Consumption_5 -45.72 -95.92 214s Consumption_6 26.18 52.02 214s Consumption_8 121.79 248.60 214s Consumption_9 110.06 232.23 214s Consumption_11 -51.41 -102.11 214s Consumption_12 -52.02 -132.22 214s Consumption_14 5.81 27.65 214s Consumption_15 -28.90 -96.33 214s Consumption_16 -25.94 -84.65 214s Consumption_17 111.86 333.82 214s Consumption_18 -11.51 -31.13 214s Consumption_19 -101.57 -289.06 214s Consumption_20 67.72 214.91 214s Consumption_21 43.05 121.02 214s Consumption_22 -20.02 -57.69 214s Investment_2 24.99 58.67 214s Investment_3 -4.21 -10.80 214s Investment_4 -9.76 -20.36 214s Investment_5 28.16 59.08 214s Investment_6 -4.79 -9.51 214s Investment_8 -24.79 -50.61 214s Investment_9 -17.48 -36.89 214s Investment_10 0.00 0.00 214s Investment_11 20.30 40.31 214s Investment_12 8.15 20.72 214s Investment_14 -15.73 -74.88 214s Investment_15 -2.63 -8.75 214s Investment_17 -31.06 -92.70 214s Investment_18 -0.82 -2.22 214s Investment_19 52.61 149.71 214s Investment_20 -15.81 -50.18 214s Investment_21 -10.22 -28.74 214s Investment_22 -26.24 -75.61 214s PrivateWages_2 -52.00 -122.10 214s PrivateWages_3 19.47 50.00 214s PrivateWages_4 61.72 128.76 214s PrivateWages_5 -73.04 -153.23 214s PrivateWages_6 -13.77 -27.36 214s PrivateWages_8 44.25 90.33 214s PrivateWages_9 51.03 107.67 214s PrivateWages_10 0.00 0.00 214s PrivateWages_11 -73.48 -145.95 214s PrivateWages_12 -6.79 -17.27 214s PrivateWages_13 0.00 0.00 214s PrivateWages_14 31.56 150.24 214s PrivateWages_15 -1.60 -5.34 214s PrivateWages_16 -4.35 -14.19 214s PrivateWages_17 51.61 154.01 214s PrivateWages_18 2.25 6.10 214s PrivateWages_19 -151.51 -431.17 214s PrivateWages_20 30.51 96.82 214s PrivateWages_21 -34.17 -96.06 214s PrivateWages_22 56.22 161.97 214s Investment_(Intercept) Investment_corpProf 214s Consumption_2 1.9908 26.734 214s Consumption_3 0.4591 7.651 214s Consumption_4 -0.2851 -5.368 214s Consumption_5 1.1217 23.127 214s Consumption_6 -0.6092 -11.762 214s Consumption_8 -2.8049 -49.183 214s Consumption_9 -2.5093 -48.961 214s Consumption_11 1.0694 18.405 214s Consumption_12 1.5052 20.306 214s Consumption_14 -0.3746 -3.777 214s Consumption_15 1.1648 15.147 214s Consumption_16 0.0000 0.000 214s Consumption_17 -3.6069 -53.782 214s Consumption_18 0.2951 5.754 214s Consumption_19 2.6504 51.112 214s Consumption_20 -1.9979 -35.052 214s Consumption_21 -1.0227 -20.634 214s Consumption_22 0.4283 9.753 214s Investment_2 -1.8422 -24.739 214s Investment_3 0.3176 5.293 214s Investment_4 0.5409 10.184 214s Investment_5 -1.4331 -29.546 214s Investment_6 0.2310 4.459 214s Investment_8 1.1844 20.769 214s Investment_9 0.8269 16.134 214s Investment_10 2.3608 47.771 214s Investment_11 -0.8758 -15.072 214s Investment_12 -0.4892 -6.600 214s Investment_14 2.1037 21.212 214s Investment_15 0.2195 2.854 214s Investment_17 2.0776 30.979 214s Investment_18 0.0436 0.851 214s Investment_19 -2.8474 -54.911 214s Investment_20 0.9677 16.978 214s Investment_21 0.5038 10.165 214s Investment_22 1.1646 26.516 214s PrivateWages_2 2.2726 30.518 214s PrivateWages_3 -0.8714 -14.524 214s PrivateWages_4 -2.0272 -38.170 214s PrivateWages_5 2.2034 45.428 214s PrivateWages_6 0.3940 7.607 214s PrivateWages_8 -1.2532 -21.975 214s PrivateWages_9 -1.4305 -27.911 214s PrivateWages_10 -2.6709 -54.046 214s PrivateWages_11 1.8795 32.347 214s PrivateWages_12 0.2417 3.260 214s PrivateWages_13 0.0000 0.000 214s PrivateWages_14 -2.5023 -25.230 214s PrivateWages_15 0.0794 1.032 214s PrivateWages_16 0.0000 0.000 214s PrivateWages_17 -2.0461 -30.509 214s PrivateWages_18 -0.0711 -1.386 214s PrivateWages_19 4.8611 93.745 214s PrivateWages_20 -1.1068 -19.419 214s PrivateWages_21 0.9981 20.138 214s PrivateWages_22 -1.4788 -33.672 214s Investment_corpProfLag Investment_capitalLag 214s Consumption_2 25.283 363.92 214s Consumption_3 5.692 83.82 214s Consumption_4 -4.818 -52.60 214s Consumption_5 20.639 212.79 214s Consumption_6 -11.819 -117.39 214s Consumption_8 -54.976 -570.52 214s Consumption_9 -49.684 -520.93 214s Consumption_11 23.206 230.67 214s Consumption_12 23.481 326.17 214s Consumption_14 -2.622 -77.57 214s Consumption_15 13.045 235.28 214s Consumption_16 0.000 0.00 214s Consumption_17 -50.497 -713.09 214s Consumption_18 5.194 58.97 214s Consumption_19 45.852 534.85 214s Consumption_20 -30.568 -399.38 214s Consumption_21 -19.431 -205.77 214s Consumption_22 9.038 87.60 214s Investment_2 -23.396 -336.76 214s Investment_3 3.938 57.99 214s Investment_4 9.141 99.79 214s Investment_5 -26.369 -271.86 214s Investment_6 4.481 44.51 214s Investment_8 23.215 240.92 214s Investment_9 16.372 171.66 214s Investment_10 49.812 497.18 214s Investment_11 -19.004 -188.91 214s Investment_12 -7.631 -106.01 214s Investment_14 14.726 435.68 214s Investment_15 2.458 44.34 214s Investment_17 29.086 410.74 214s Investment_18 0.768 8.72 214s Investment_19 -49.260 -574.60 214s Investment_20 14.806 193.44 214s Investment_21 9.573 101.37 214s Investment_22 24.572 238.15 214s PrivateWages_2 28.862 415.43 214s PrivateWages_3 -10.806 -159.12 214s PrivateWages_4 -34.259 -374.01 214s PrivateWages_5 40.542 417.98 214s PrivateWages_6 7.644 75.93 214s PrivateWages_8 -24.563 -254.91 214s PrivateWages_9 -28.324 -296.97 214s PrivateWages_10 -56.356 -562.49 214s PrivateWages_11 40.785 405.41 214s PrivateWages_12 3.770 52.37 214s PrivateWages_13 0.000 0.00 214s PrivateWages_14 -17.516 -518.22 214s PrivateWages_15 0.889 16.03 214s PrivateWages_16 0.000 0.00 214s PrivateWages_17 -28.646 -404.52 214s PrivateWages_18 -1.251 -14.21 214s PrivateWages_19 84.097 980.97 214s PrivateWages_20 -16.934 -221.25 214s PrivateWages_21 18.964 200.82 214s PrivateWages_22 -31.204 -302.42 214s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 214s Consumption_2 -4.7927 -225.59 -215.2 214s Consumption_3 -1.1051 -54.79 -50.4 214s Consumption_4 0.6863 38.81 34.4 214s Consumption_5 -2.7004 -163.88 -154.5 214s Consumption_6 1.4666 88.89 83.7 214s Consumption_8 6.7526 405.14 432.2 214s Consumption_9 6.0409 376.16 389.0 214s Consumption_11 -2.5745 -164.03 -172.5 214s Consumption_12 -3.6236 -198.69 -221.8 214s Consumption_14 0.9017 37.99 39.9 214s Consumption_15 -2.8041 -143.62 -126.5 214s Consumption_16 -2.2917 -126.82 -113.9 214s Consumption_17 8.6833 498.37 472.4 214s Consumption_18 -0.7105 -47.73 -44.5 214s Consumption_19 -6.3806 -437.15 -414.7 214s Consumption_20 4.8097 321.50 292.9 214s Consumption_21 2.4620 184.32 171.1 214s Consumption_22 -1.0312 -89.59 -78.1 214s Investment_2 2.6290 123.75 118.0 214s Investment_3 -0.4532 -22.47 -20.7 214s Investment_4 -0.7719 -43.64 -38.7 214s Investment_5 2.0451 124.11 117.0 214s Investment_6 -0.3296 -19.98 -18.8 214s Investment_8 -1.6903 -101.41 -108.2 214s Investment_9 -1.1800 -73.48 -76.0 214s Investment_10 -3.3690 -217.54 -217.3 214s Investment_11 1.2498 79.63 83.7 214s Investment_12 0.6981 38.28 42.7 214s Investment_14 -3.0022 -126.47 -133.0 214s Investment_15 -0.3132 -16.04 -14.1 214s Investment_17 -2.9649 -170.17 -161.3 214s Investment_18 -0.0623 -4.18 -3.9 214s Investment_19 4.0635 278.40 264.1 214s Investment_20 -1.3810 -92.31 -84.1 214s Investment_21 -0.7190 -53.83 -50.0 214s Investment_22 -1.6619 -144.39 -125.8 214s PrivateWages_2 -8.0595 -379.36 -361.9 214s PrivateWages_3 3.0904 153.23 140.9 214s PrivateWages_4 7.1892 406.50 360.2 214s PrivateWages_5 -7.8142 -474.21 -447.0 214s PrivateWages_6 -1.3974 -84.70 -79.8 214s PrivateWages_8 4.4445 266.66 284.4 214s PrivateWages_9 5.0731 315.90 326.7 214s PrivateWages_10 9.4721 611.61 611.0 214s PrivateWages_11 -6.6655 -424.67 -446.6 214s PrivateWages_12 -0.8571 -46.99 -52.5 214s PrivateWages_13 -4.8476 -227.73 -258.9 214s PrivateWages_14 8.8741 373.85 393.1 214s PrivateWages_15 -0.2815 -14.42 -12.7 214s PrivateWages_16 -0.6957 -38.50 -34.6 214s PrivateWages_17 7.2565 416.48 394.8 214s PrivateWages_18 0.2522 16.94 15.8 214s PrivateWages_19 -17.2396 -1181.13 -1120.6 214s PrivateWages_20 3.9252 262.38 239.0 214s PrivateWages_21 -3.5398 -265.01 -246.0 214s PrivateWages_22 5.2446 455.65 397.0 214s PrivateWages_trend 214s Consumption_2 47.927 214s Consumption_3 9.946 214s Consumption_4 -5.491 214s Consumption_5 18.903 214s Consumption_6 -8.800 214s Consumption_8 -27.010 214s Consumption_9 -18.123 214s Consumption_11 2.574 214s Consumption_12 0.000 214s Consumption_14 1.803 214s Consumption_15 -8.412 214s Consumption_16 -9.167 214s Consumption_17 43.417 214s Consumption_18 -4.263 214s Consumption_19 -44.664 214s Consumption_20 38.478 214s Consumption_21 22.158 214s Consumption_22 -10.312 214s Investment_2 -26.290 214s Investment_3 4.079 214s Investment_4 6.175 214s Investment_5 -14.316 214s Investment_6 1.978 214s Investment_8 6.761 214s Investment_9 3.540 214s Investment_10 6.738 214s Investment_11 -1.250 214s Investment_12 0.000 214s Investment_14 -6.004 214s Investment_15 -0.940 214s Investment_17 -14.825 214s Investment_18 -0.374 214s Investment_19 28.444 214s Investment_20 -11.048 214s Investment_21 -6.471 214s Investment_22 -16.619 214s PrivateWages_2 80.595 214s PrivateWages_3 -27.814 214s PrivateWages_4 -57.514 214s PrivateWages_5 54.699 214s PrivateWages_6 8.384 214s PrivateWages_8 -17.778 214s PrivateWages_9 -15.219 214s PrivateWages_10 -18.944 214s PrivateWages_11 6.666 214s PrivateWages_12 0.000 214s PrivateWages_13 -4.848 214s PrivateWages_14 17.748 214s PrivateWages_15 -0.844 214s PrivateWages_16 -2.783 214s PrivateWages_17 36.283 214s PrivateWages_18 1.513 214s PrivateWages_19 -120.677 214s PrivateWages_20 31.402 214s PrivateWages_21 -31.858 214s PrivateWages_22 52.446 214s [1] TRUE 214s > Bread 214s Consumption_(Intercept) Consumption_corpProf Consumption_corpProfLag 214s [1,] 133.708 -4.1980 0.8576 214s [2,] -4.198 1.2100 -0.6653 214s [3,] 0.858 -0.6653 0.7119 214s [4,] -1.738 -0.1324 -0.0277 214s [5,] 125.235 3.6584 5.4171 214s [6,] -6.184 0.8150 -0.6677 214s [7,] 2.270 -0.5431 0.6187 214s [8,] -0.265 -0.0441 -0.0204 214s [9,] -39.027 0.3871 1.7425 214s [10,] 0.490 -0.0701 0.0456 214s [11,] 0.147 0.0648 -0.0766 214s [12,] 0.260 0.0523 0.0256 214s Consumption_wages Investment_(Intercept) Investment_corpProf 214s [1,] -1.73822 125.23 -6.18369 214s [2,] -0.13241 3.66 0.81500 214s [3,] -0.02768 5.42 -0.66769 214s [4,] 0.10634 -6.40 0.07260 214s [5,] -6.40260 3920.72 -66.16832 214s [6,] 0.07260 -66.17 3.06783 214s [7,] -0.07286 52.35 -2.32206 214s [8,] 0.03170 -18.13 0.25629 214s [9,] 0.06731 57.07 -0.51824 214s [10,] -0.00202 2.27 0.00785 214s [11,] 0.00109 -3.34 0.00101 214s [12,] -0.03773 -1.63 0.03241 214s Investment_corpProfLag Investment_capitalLag PrivateWages_(Intercept) 214s [1,] 2.27003 -0.26469 -39.0267 214s [2,] -0.54312 -0.04408 0.3871 214s [3,] 0.61867 -0.02038 1.7425 214s [4,] -0.07286 0.03170 0.0673 214s [5,] 52.35486 -18.13066 57.0659 214s [6,] -2.32206 0.25629 -0.5182 214s [7,] 2.22379 -0.24386 -0.7311 214s [8,] -0.24386 0.08845 -0.1851 214s [9,] -0.73109 -0.18506 71.2482 214s [10,] 0.01103 -0.01288 -0.3220 214s [11,] 0.00202 0.01653 -0.8851 214s [12,] -0.04341 0.00871 0.7698 214s PrivateWages_gnp PrivateWages_gnpLag PrivateWages_trend 214s [1,] 0.49031 0.147339 0.260437 214s [2,] -0.07008 0.064790 0.052347 214s [3,] 0.04558 -0.076595 0.025629 214s [4,] -0.00202 0.001086 -0.037728 214s [5,] 2.27149 -3.339873 -1.627913 214s [6,] 0.00785 0.001013 0.032414 214s [7,] 0.01103 0.002018 -0.043407 214s [8,] -0.01288 0.016530 0.008714 214s [9,] -0.32199 -0.885080 0.769761 214s [10,] 0.04892 -0.044549 -0.013616 214s [11,] -0.04455 0.061046 0.000449 214s [12,] -0.01362 0.000449 0.047057 214s > 214s BEGIN TEST KleinI_noMat.R 214s 214s R version 4.3.2 (2023-10-31) -- "Eye Holes" 214s Copyright (C) 2023 The R Foundation for Statistical Computing 214s Platform: aarch64-unknown-linux-gnu (64-bit) 214s 214s R is free software and comes with ABSOLUTELY NO WARRANTY. 214s You are welcome to redistribute it under certain conditions. 214s Type 'license()' or 'licence()' for distribution details. 214s 214s R is a collaborative project with many contributors. 214s Type 'contributors()' for more information and 214s 'citation()' on how to cite R or R packages in publications. 214s 214s Type 'demo()' for some demos, 'help()' for on-line help, or 214s 'help.start()' for an HTML browser interface to help. 214s Type 'q()' to quit R. 214s 215s > library( "systemfit" ) 215s Loading required package: Matrix 215s Loading required package: car 215s Loading required package: carData 215s Loading required package: lmtest 215s Loading required package: zoo 215s 215s Attaching package: ‘zoo’ 215s 215s The following objects are masked from ‘package:base’: 215s 215s as.Date, as.Date.numeric 215s 215s 215s Please cite the 'systemfit' package as: 215s 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/. 215s 215s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 215s https://r-forge.r-project.org/projects/systemfit/ 215s > options( warn = 1 ) 215s > options( digits = 3 ) 215s > 215s > data( "KleinI" ) 216s > eqConsump <- consump ~ corpProf + corpProfLag + wages 216s > eqInvest <- invest ~ corpProf + corpProfLag + capitalLag 216s > eqPrivWage <- privWage ~ gnp + gnpLag + trend 216s > inst <- ~ govExp + taxes + govWage + trend + capitalLag + corpProfLag + gnpLag 216s > system <- list( Consumption = eqConsump, Investment = eqInvest, 216s + PrivateWages = eqPrivWage ) 216s > restrict <- c( "Consumption_corpProf + Investment_capitalLag = 0" ) 216s > restrict2 <- c( restrict, "Consumption_corpProfLag - PrivateWages_trend = 0" ) 216s > 216s > for( dataNo in 1:5 ) { 216s + # set some values of some variables to NA 216s + if( dataNo == 2 ) { 216s + KleinI$gnpLag[ 7 ] <- NA 216s + } else if( dataNo == 3 ) { 216s + KleinI$wages[ 10 ] <- NA 216s + } else if( dataNo == 4 ) { 216s + KleinI$corpProf[ 13 ] <- NA 216s + } else if( dataNo == 5 ) { 216s + KleinI$invest[ 16 ] <- NA 216s + } 216s + 216s + # single-equation OLS 216s + lmConsump <- lm( eqConsump, data = KleinI ) 216s + lmInvest <- lm( eqInvest, data = KleinI ) 216s + lmPrivWage <- lm( eqPrivWage, data = KleinI ) 216s + 216s + for( methodNo in 1:5 ) { 216s + method <- c( "OLS", "2SLS", "SUR", "3SLS", "3SLS" )[ methodNo ] 216s + maxit <- ifelse( methodNo == 5, 500, 1 ) 216s + 216s + cat( "> \n> # ", ifelse( maxit == 1, "", "I" ), method, "\n", sep = "" ) 216s + if( method %in% c( "OLS", "WLS", "SUR" ) ) { 216s + kleinModel <- systemfit( system, method = method, data = KleinI, 216s + methodResidCov = ifelse( method == "OLS", "geomean", "noDfCor" ), 216s + maxit = maxit, useMatrix = FALSE ) 216s + } else { 216s + kleinModel <- systemfit( system, method = method, data = KleinI, 216s + inst = inst, methodResidCov = "noDfCor", maxit = maxit, 216s + useMatrix = FALSE ) 216s + } 216s + cat( "> summary\n" ) 216s + print( summary( kleinModel ) ) 216s + if( method == "OLS" ) { 216s + cat( "compare coef with single-equation OLS\n" ) 216s + print( all.equal( coef( kleinModel ), 216s + c( coef( lmConsump ), coef( lmInvest ), coef( lmPrivWage ) ), 216s + check.attributes = FALSE ) ) 216s + } 216s + cat( "> residuals\n" ) 216s + print( residuals( kleinModel ) ) 216s + cat( "> fitted\n" ) 216s + print( fitted( kleinModel ) ) 216s + cat( "> predict\n" ) 216s + print( predict( kleinModel, se.fit = TRUE, 216s + interval = ifelse( methodNo %in% c( 1, 4 ), "prediction", "confidence" ), 216s + useDfSys = methodNo %in% c( 1, 3, 5 ) ) ) 216s + cat( "> model.frame\n" ) 216s + if( methodNo == 1 ) { 216s + mfOls <- model.frame( kleinModel ) 216s + print( mfOls ) 216s + } else if( methodNo == 2 ) { 216s + mf2sls <- model.frame( kleinModel ) 216s + print( mf2sls ) 216s + } else if( methodNo == 3 ) { 216s + print( all.equal( mfOls, model.frame( kleinModel ) ) ) 216s + } else { 216s + print( all.equal( mf2sls, model.frame( kleinModel ) ) ) 216s + } 216s + cat( "> model.matrix\n" ) 216s + if( methodNo == 1 ) { 216s + mmOls <- model.matrix( kleinModel ) 216s + print( mmOls ) 216s + } else { 216s + print( all.equal( mmOls, model.matrix( kleinModel ) ) ) 216s + } 216s + cat( "> nobs\n" ) 216s + print( nobs( kleinModel ) ) 216s + cat( "> linearHypothesis\n" ) 216s + print( linearHypothesis( kleinModel, restrict ) ) 216s + print( linearHypothesis( kleinModel, restrict, test = "F" ) ) 216s + print( linearHypothesis( kleinModel, restrict, test = "Chisq" ) ) 216s + print( linearHypothesis( kleinModel, restrict2 ) ) 216s + print( linearHypothesis( kleinModel, restrict2, test = "F" ) ) 216s + print( linearHypothesis( kleinModel, restrict2, test = "Chisq" ) ) 216s + cat( "> logLik\n" ) 216s + print( logLik( kleinModel ) ) 216s + print( logLik( kleinModel, residCovDiag = TRUE ) ) 216s + if( method == "OLS" ) { 216s + cat( "compare log likelihood value with single-equation OLS\n" ) 216s + print( all.equal( logLik( kleinModel, residCovDiag = TRUE ), 216s + logLik( lmConsump ) + logLik( lmInvest ) + logLik( lmPrivWage ), 216s + check.attributes = FALSE ) ) 216s + } 216s + } 216s + } 216s > 216s > # OLS 216s > summary 216s 216s systemfit results 216s method: OLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 63 51 45.2 0.371 0.977 0.991 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 21 17 17.9 1.052 1.026 0.981 0.978 216s Investment 21 17 17.3 1.019 1.009 0.931 0.919 216s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.0517 0.0611 -0.470 216s Investment 0.0611 1.0190 0.150 216s PrivateWages -0.4704 0.1497 0.589 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.0000 0.0591 -0.598 216s Investment 0.0591 1.0000 0.193 216s PrivateWages -0.5979 0.1933 1.000 216s 216s 216s OLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.2366 1.3027 12.46 5.6e-10 *** 216s corpProf 0.1929 0.0912 2.12 0.049 * 216s corpProfLag 0.0899 0.0906 0.99 0.335 216s wages 0.7962 0.0399 19.93 3.2e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.026 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 216s 216s 216s OLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 10.1258 5.4655 1.85 0.08137 . 216s corpProf 0.4796 0.0971 4.94 0.00012 *** 216s corpProfLag 0.3330 0.1009 3.30 0.00421 ** 216s capitalLag -0.1118 0.0267 -4.18 0.00062 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.009 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 216s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 216s 216s 216s OLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.4970 1.2700 1.18 0.25474 216s gnp 0.4395 0.0324 13.56 1.5e-10 *** 216s gnpLag 0.1461 0.0374 3.90 0.00114 ** 216s trend 0.1302 0.0319 4.08 0.00078 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.767 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 216s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 216s 216s compare coef with single-equation OLS 216s [1] TRUE 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.32389 -0.0668 -1.2942 216s 3 -1.25001 -0.0476 0.2957 216s 4 -1.56574 1.2467 1.1877 216s 5 -0.49350 -1.3512 -0.1358 216s 6 0.00761 0.4154 -0.4654 216s 7 0.86910 1.4923 -0.4838 216s 8 1.33848 0.7889 -0.7281 216s 9 1.05498 -0.6317 0.3392 216s 10 -0.58856 1.0830 1.1957 216s 11 0.28231 0.2791 -0.1508 216s 12 -0.22965 0.0369 0.5942 216s 13 -0.32213 0.3659 0.1027 216s 14 0.32228 0.2237 0.4503 216s 15 -0.05801 -0.1728 0.2816 216s 16 -0.03466 0.0101 0.0138 216s 17 1.61650 0.9719 -0.8508 216s 18 -0.43597 0.0516 0.9956 216s 19 0.21005 -2.5656 -0.4688 216s 20 0.98920 -0.6866 -0.3795 216s 21 0.78508 -0.7807 -1.0909 216s 22 -2.17345 -0.6623 0.5917 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.2 -0.133 26.8 216s 3 46.3 1.948 29.0 216s 4 50.8 3.953 32.9 216s 5 51.1 4.351 34.0 216s 6 52.6 4.685 35.9 216s 7 54.2 4.108 37.9 216s 8 54.9 3.411 38.6 216s 9 56.2 3.632 38.9 216s 10 58.4 4.017 40.1 216s 11 54.7 0.721 38.1 216s 12 51.1 -3.437 33.9 216s 13 45.9 -6.566 28.9 216s 14 46.2 -5.324 28.0 216s 15 48.8 -2.827 30.3 216s 16 51.3 -1.310 33.2 216s 17 56.1 1.128 37.7 216s 18 59.1 1.948 40.0 216s 19 57.3 0.666 38.7 216s 20 60.6 1.987 42.0 216s 21 64.2 4.081 46.1 216s 22 71.9 5.562 52.7 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.2 0.462 40.0 44.5 216s 3 46.3 0.518 43.9 48.6 216s 4 50.8 0.341 48.6 52.9 216s 5 51.1 0.396 48.9 53.3 216s 6 52.6 0.397 50.4 54.8 216s 7 54.2 0.359 52.0 56.4 216s 8 54.9 0.327 52.7 57.0 216s 9 56.2 0.350 54.1 58.4 216s 10 58.4 0.370 56.2 60.6 216s 11 54.7 0.606 52.3 57.1 216s 12 51.1 0.484 48.9 53.4 216s 13 45.9 0.629 43.5 48.3 216s 14 46.2 0.602 43.8 48.6 216s 15 48.8 0.374 46.6 50.9 216s 16 51.3 0.333 49.2 53.5 216s 17 56.1 0.366 53.9 58.3 216s 18 59.1 0.321 57.0 61.3 216s 19 57.3 0.371 55.1 59.5 216s 20 60.6 0.434 58.4 62.8 216s 21 64.2 0.425 62.0 66.4 216s 22 71.9 0.666 69.4 74.3 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 -0.133 0.607 -2.498 2.231 216s 3 1.948 0.499 -0.313 4.208 216s 4 3.953 0.449 1.735 6.171 216s 5 4.351 0.371 2.192 6.510 216s 6 4.685 0.349 2.540 6.829 216s 7 4.108 0.329 1.976 6.239 216s 8 3.411 0.292 1.301 5.521 216s 9 3.632 0.389 1.460 5.804 216s 10 4.017 0.447 1.801 6.233 216s 11 0.721 0.601 -1.638 3.080 216s 12 -3.437 0.507 -5.704 -1.169 216s 13 -6.566 0.616 -8.940 -4.192 216s 14 -5.324 0.694 -7.783 -2.865 216s 15 -2.827 0.373 -4.988 -0.667 216s 16 -1.310 0.320 -3.436 0.816 216s 17 1.128 0.347 -1.015 3.271 216s 18 1.948 0.243 -0.136 4.033 216s 19 0.666 0.312 -1.456 2.787 216s 20 1.987 0.366 -0.169 4.143 216s 21 4.081 0.332 1.948 6.214 216s 22 5.562 0.461 3.334 7.790 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.354 25.1 28.5 216s 3 29.0 0.355 27.3 30.7 216s 4 32.9 0.354 31.2 34.6 216s 5 34.0 0.269 32.4 35.7 216s 6 35.9 0.266 34.2 37.5 216s 7 37.9 0.266 36.3 39.5 216s 8 38.6 0.273 37.0 40.3 216s 9 38.9 0.261 37.2 40.5 216s 10 40.1 0.247 38.5 41.7 216s 11 38.1 0.354 36.4 39.7 216s 12 33.9 0.363 32.2 35.6 216s 13 28.9 0.429 27.1 30.7 216s 14 28.0 0.376 26.3 29.8 216s 15 30.3 0.371 28.6 32.0 216s 16 33.2 0.310 31.5 34.8 216s 17 37.7 0.305 36.0 39.3 216s 18 40.0 0.238 38.4 41.6 216s 19 38.7 0.357 37.0 40.4 216s 20 42.0 0.321 40.3 43.6 216s 21 46.1 0.335 44.4 47.8 216s 22 52.7 0.502 50.9 54.5 216s > model.frame 216s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 216s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 216s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 216s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 216s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 216s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 216s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 216s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 216s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 216s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 216s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 216s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 216s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 216s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 216s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 216s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 216s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 216s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 216s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 216s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 216s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 216s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 216s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 216s trend 216s 1 -11 216s 2 -10 216s 3 -9 216s 4 -8 216s 5 -7 216s 6 -6 216s 7 -5 216s 8 -4 216s 9 -3 216s 10 -2 216s 11 -1 216s 12 0 216s 13 1 216s 14 2 216s 15 3 216s 16 4 216s 17 5 216s 18 6 216s 19 7 216s 20 8 216s 21 9 216s 22 10 216s > model.matrix 216s Consumption_(Intercept) Consumption_corpProf 216s Consumption_2 1 12.4 216s Consumption_3 1 16.9 216s Consumption_4 1 18.4 216s Consumption_5 1 19.4 216s Consumption_6 1 20.1 216s Consumption_7 1 19.6 216s Consumption_8 1 19.8 216s Consumption_9 1 21.1 216s Consumption_10 1 21.7 216s Consumption_11 1 15.6 216s Consumption_12 1 11.4 216s Consumption_13 1 7.0 216s Consumption_14 1 11.2 216s Consumption_15 1 12.3 216s Consumption_16 1 14.0 216s Consumption_17 1 17.6 216s Consumption_18 1 17.3 216s Consumption_19 1 15.3 216s Consumption_20 1 19.0 216s Consumption_21 1 21.1 216s Consumption_22 1 23.5 216s Investment_2 0 0.0 216s Investment_3 0 0.0 216s Investment_4 0 0.0 216s Investment_5 0 0.0 216s Investment_6 0 0.0 216s Investment_7 0 0.0 216s Investment_8 0 0.0 216s Investment_9 0 0.0 216s Investment_10 0 0.0 216s Investment_11 0 0.0 216s Investment_12 0 0.0 216s Investment_13 0 0.0 216s Investment_14 0 0.0 216s Investment_15 0 0.0 216s Investment_16 0 0.0 216s Investment_17 0 0.0 216s Investment_18 0 0.0 216s Investment_19 0 0.0 216s Investment_20 0 0.0 216s Investment_21 0 0.0 216s Investment_22 0 0.0 216s PrivateWages_2 0 0.0 216s PrivateWages_3 0 0.0 216s PrivateWages_4 0 0.0 216s PrivateWages_5 0 0.0 216s PrivateWages_6 0 0.0 216s PrivateWages_7 0 0.0 216s PrivateWages_8 0 0.0 216s PrivateWages_9 0 0.0 216s PrivateWages_10 0 0.0 216s PrivateWages_11 0 0.0 216s PrivateWages_12 0 0.0 216s PrivateWages_13 0 0.0 216s PrivateWages_14 0 0.0 216s PrivateWages_15 0 0.0 216s PrivateWages_16 0 0.0 216s PrivateWages_17 0 0.0 216s PrivateWages_18 0 0.0 216s PrivateWages_19 0 0.0 216s PrivateWages_20 0 0.0 216s PrivateWages_21 0 0.0 216s PrivateWages_22 0 0.0 216s Consumption_corpProfLag Consumption_wages 216s Consumption_2 12.7 28.2 216s Consumption_3 12.4 32.2 216s Consumption_4 16.9 37.0 216s Consumption_5 18.4 37.0 216s Consumption_6 19.4 38.6 216s Consumption_7 20.1 40.7 216s Consumption_8 19.6 41.5 216s Consumption_9 19.8 42.9 216s Consumption_10 21.1 45.3 216s Consumption_11 21.7 42.1 216s Consumption_12 15.6 39.3 216s Consumption_13 11.4 34.3 216s Consumption_14 7.0 34.1 216s Consumption_15 11.2 36.6 216s Consumption_16 12.3 39.3 216s Consumption_17 14.0 44.2 216s Consumption_18 17.6 47.7 216s Consumption_19 17.3 45.9 216s Consumption_20 15.3 49.4 216s Consumption_21 19.0 53.0 216s Consumption_22 21.1 61.8 216s Investment_2 0.0 0.0 216s Investment_3 0.0 0.0 216s Investment_4 0.0 0.0 216s Investment_5 0.0 0.0 216s Investment_6 0.0 0.0 216s Investment_7 0.0 0.0 216s Investment_8 0.0 0.0 216s Investment_9 0.0 0.0 216s Investment_10 0.0 0.0 216s Investment_11 0.0 0.0 216s Investment_12 0.0 0.0 216s Investment_13 0.0 0.0 216s Investment_14 0.0 0.0 216s Investment_15 0.0 0.0 216s Investment_16 0.0 0.0 216s Investment_17 0.0 0.0 216s Investment_18 0.0 0.0 216s Investment_19 0.0 0.0 216s Investment_20 0.0 0.0 216s Investment_21 0.0 0.0 216s Investment_22 0.0 0.0 216s PrivateWages_2 0.0 0.0 216s PrivateWages_3 0.0 0.0 216s PrivateWages_4 0.0 0.0 216s PrivateWages_5 0.0 0.0 216s PrivateWages_6 0.0 0.0 216s PrivateWages_7 0.0 0.0 216s PrivateWages_8 0.0 0.0 216s PrivateWages_9 0.0 0.0 216s PrivateWages_10 0.0 0.0 216s PrivateWages_11 0.0 0.0 216s PrivateWages_12 0.0 0.0 216s PrivateWages_13 0.0 0.0 216s PrivateWages_14 0.0 0.0 216s PrivateWages_15 0.0 0.0 216s PrivateWages_16 0.0 0.0 216s PrivateWages_17 0.0 0.0 216s PrivateWages_18 0.0 0.0 216s PrivateWages_19 0.0 0.0 216s PrivateWages_20 0.0 0.0 216s PrivateWages_21 0.0 0.0 216s PrivateWages_22 0.0 0.0 216s Investment_(Intercept) Investment_corpProf 216s Consumption_2 0 0.0 216s Consumption_3 0 0.0 216s Consumption_4 0 0.0 216s Consumption_5 0 0.0 216s Consumption_6 0 0.0 216s Consumption_7 0 0.0 216s Consumption_8 0 0.0 216s Consumption_9 0 0.0 216s Consumption_10 0 0.0 216s Consumption_11 0 0.0 216s Consumption_12 0 0.0 216s Consumption_13 0 0.0 216s Consumption_14 0 0.0 216s Consumption_15 0 0.0 216s Consumption_16 0 0.0 216s Consumption_17 0 0.0 216s Consumption_18 0 0.0 216s Consumption_19 0 0.0 216s Consumption_20 0 0.0 216s Consumption_21 0 0.0 216s Consumption_22 0 0.0 216s Investment_2 1 12.4 216s Investment_3 1 16.9 216s Investment_4 1 18.4 216s Investment_5 1 19.4 216s Investment_6 1 20.1 216s Investment_7 1 19.6 216s Investment_8 1 19.8 216s Investment_9 1 21.1 216s Investment_10 1 21.7 216s Investment_11 1 15.6 216s Investment_12 1 11.4 216s Investment_13 1 7.0 216s Investment_14 1 11.2 216s Investment_15 1 12.3 216s Investment_16 1 14.0 216s Investment_17 1 17.6 216s Investment_18 1 17.3 216s Investment_19 1 15.3 216s Investment_20 1 19.0 216s Investment_21 1 21.1 216s Investment_22 1 23.5 216s PrivateWages_2 0 0.0 216s PrivateWages_3 0 0.0 216s PrivateWages_4 0 0.0 216s PrivateWages_5 0 0.0 216s PrivateWages_6 0 0.0 216s PrivateWages_7 0 0.0 216s PrivateWages_8 0 0.0 216s PrivateWages_9 0 0.0 216s PrivateWages_10 0 0.0 216s PrivateWages_11 0 0.0 216s PrivateWages_12 0 0.0 216s PrivateWages_13 0 0.0 216s PrivateWages_14 0 0.0 216s PrivateWages_15 0 0.0 216s PrivateWages_16 0 0.0 216s PrivateWages_17 0 0.0 216s PrivateWages_18 0 0.0 216s PrivateWages_19 0 0.0 216s PrivateWages_20 0 0.0 216s PrivateWages_21 0 0.0 216s PrivateWages_22 0 0.0 216s Investment_corpProfLag Investment_capitalLag 216s Consumption_2 0.0 0 216s Consumption_3 0.0 0 216s Consumption_4 0.0 0 216s Consumption_5 0.0 0 216s Consumption_6 0.0 0 216s Consumption_7 0.0 0 216s Consumption_8 0.0 0 216s Consumption_9 0.0 0 216s Consumption_10 0.0 0 216s Consumption_11 0.0 0 216s Consumption_12 0.0 0 216s Consumption_13 0.0 0 216s Consumption_14 0.0 0 216s Consumption_15 0.0 0 216s Consumption_16 0.0 0 216s Consumption_17 0.0 0 216s Consumption_18 0.0 0 216s Consumption_19 0.0 0 216s Consumption_20 0.0 0 216s Consumption_21 0.0 0 216s Consumption_22 0.0 0 216s Investment_2 12.7 183 216s Investment_3 12.4 183 216s Investment_4 16.9 184 216s Investment_5 18.4 190 216s Investment_6 19.4 193 216s Investment_7 20.1 198 216s Investment_8 19.6 203 216s Investment_9 19.8 208 216s Investment_10 21.1 211 216s Investment_11 21.7 216 216s Investment_12 15.6 217 216s Investment_13 11.4 213 216s Investment_14 7.0 207 216s Investment_15 11.2 202 216s Investment_16 12.3 199 216s Investment_17 14.0 198 216s Investment_18 17.6 200 216s Investment_19 17.3 202 216s Investment_20 15.3 200 216s Investment_21 19.0 201 216s Investment_22 21.1 204 216s PrivateWages_2 0.0 0 216s PrivateWages_3 0.0 0 216s PrivateWages_4 0.0 0 216s PrivateWages_5 0.0 0 216s PrivateWages_6 0.0 0 216s PrivateWages_7 0.0 0 216s PrivateWages_8 0.0 0 216s PrivateWages_9 0.0 0 216s PrivateWages_10 0.0 0 216s PrivateWages_11 0.0 0 216s PrivateWages_12 0.0 0 216s PrivateWages_13 0.0 0 216s PrivateWages_14 0.0 0 216s PrivateWages_15 0.0 0 216s PrivateWages_16 0.0 0 216s PrivateWages_17 0.0 0 216s PrivateWages_18 0.0 0 216s PrivateWages_19 0.0 0 216s PrivateWages_20 0.0 0 216s PrivateWages_21 0.0 0 216s PrivateWages_22 0.0 0 216s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 216s Consumption_2 0 0.0 0.0 216s Consumption_3 0 0.0 0.0 216s Consumption_4 0 0.0 0.0 216s Consumption_5 0 0.0 0.0 216s Consumption_6 0 0.0 0.0 216s Consumption_7 0 0.0 0.0 216s Consumption_8 0 0.0 0.0 216s Consumption_9 0 0.0 0.0 216s Consumption_10 0 0.0 0.0 216s Consumption_11 0 0.0 0.0 216s Consumption_12 0 0.0 0.0 216s Consumption_13 0 0.0 0.0 216s Consumption_14 0 0.0 0.0 216s Consumption_15 0 0.0 0.0 216s Consumption_16 0 0.0 0.0 216s Consumption_17 0 0.0 0.0 216s Consumption_18 0 0.0 0.0 216s Consumption_19 0 0.0 0.0 216s Consumption_20 0 0.0 0.0 216s Consumption_21 0 0.0 0.0 216s Consumption_22 0 0.0 0.0 216s Investment_2 0 0.0 0.0 216s Investment_3 0 0.0 0.0 216s Investment_4 0 0.0 0.0 216s Investment_5 0 0.0 0.0 216s Investment_6 0 0.0 0.0 216s Investment_7 0 0.0 0.0 216s Investment_8 0 0.0 0.0 216s Investment_9 0 0.0 0.0 216s Investment_10 0 0.0 0.0 216s Investment_11 0 0.0 0.0 216s Investment_12 0 0.0 0.0 216s Investment_13 0 0.0 0.0 216s Investment_14 0 0.0 0.0 216s Investment_15 0 0.0 0.0 216s Investment_16 0 0.0 0.0 216s Investment_17 0 0.0 0.0 216s Investment_18 0 0.0 0.0 216s Investment_19 0 0.0 0.0 216s Investment_20 0 0.0 0.0 216s Investment_21 0 0.0 0.0 216s Investment_22 0 0.0 0.0 216s PrivateWages_2 1 45.6 44.9 216s PrivateWages_3 1 50.1 45.6 216s PrivateWages_4 1 57.2 50.1 216s PrivateWages_5 1 57.1 57.2 216s PrivateWages_6 1 61.0 57.1 216s PrivateWages_7 1 64.0 61.0 216s PrivateWages_8 1 64.4 64.0 216s PrivateWages_9 1 64.5 64.4 216s PrivateWages_10 1 67.0 64.5 216s PrivateWages_11 1 61.2 67.0 216s PrivateWages_12 1 53.4 61.2 216s PrivateWages_13 1 44.3 53.4 216s PrivateWages_14 1 45.1 44.3 216s PrivateWages_15 1 49.7 45.1 216s PrivateWages_16 1 54.4 49.7 216s PrivateWages_17 1 62.7 54.4 216s PrivateWages_18 1 65.0 62.7 216s PrivateWages_19 1 60.9 65.0 216s PrivateWages_20 1 69.5 60.9 216s PrivateWages_21 1 75.7 69.5 216s PrivateWages_22 1 88.4 75.7 216s PrivateWages_trend 216s Consumption_2 0 216s Consumption_3 0 216s Consumption_4 0 216s Consumption_5 0 216s Consumption_6 0 216s Consumption_7 0 216s Consumption_8 0 216s Consumption_9 0 216s Consumption_10 0 216s Consumption_11 0 216s Consumption_12 0 216s Consumption_13 0 216s Consumption_14 0 216s Consumption_15 0 216s Consumption_16 0 216s Consumption_17 0 216s Consumption_18 0 216s Consumption_19 0 216s Consumption_20 0 216s Consumption_21 0 216s Consumption_22 0 216s Investment_2 0 216s Investment_3 0 216s Investment_4 0 216s Investment_5 0 216s Investment_6 0 216s Investment_7 0 216s Investment_8 0 216s Investment_9 0 216s Investment_10 0 216s Investment_11 0 216s Investment_12 0 216s Investment_13 0 216s Investment_14 0 216s Investment_15 0 216s Investment_16 0 216s Investment_17 0 216s Investment_18 0 216s Investment_19 0 216s Investment_20 0 216s Investment_21 0 216s Investment_22 0 216s PrivateWages_2 -10 216s PrivateWages_3 -9 216s PrivateWages_4 -8 216s PrivateWages_5 -7 216s PrivateWages_6 -6 216s PrivateWages_7 -5 216s PrivateWages_8 -4 216s PrivateWages_9 -3 216s PrivateWages_10 -2 216s PrivateWages_11 -1 216s PrivateWages_12 0 216s PrivateWages_13 1 216s PrivateWages_14 2 216s PrivateWages_15 3 216s PrivateWages_16 4 216s PrivateWages_17 5 216s PrivateWages_18 6 216s PrivateWages_19 7 216s PrivateWages_20 8 216s PrivateWages_21 9 216s PrivateWages_22 10 216s > nobs 216s [1] 63 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 0.82 0.37 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 0.73 0.4 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 52 216s 2 51 1 0.73 0.39 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.42 0.66 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.37 0.69 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 53 216s 2 51 2 0.74 0.69 216s > logLik 216s 'log Lik.' -72.3 (df=13) 216s 'log Lik.' -77.9 (df=13) 216s compare log likelihood value with single-equation OLS 216s [1] TRUE 216s > 216s > # 2SLS 216s > summary 216s 216s systemfit results 216s method: 2SLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 63 51 61 0.288 0.969 0.992 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 21 17 21.9 1.290 1.136 0.977 0.973 216s Investment 21 17 29.0 1.709 1.307 0.885 0.865 216s PrivateWages 21 17 10.0 0.589 0.767 0.987 0.985 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.044 0.438 -0.385 216s Investment 0.438 1.383 0.193 216s PrivateWages -0.385 0.193 0.476 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.364 -0.546 216s Investment 0.364 1.000 0.237 216s PrivateWages -0.546 0.237 1.000 216s 216s 216s 2SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.5548 1.3208 12.53 5.2e-10 *** 216s corpProf 0.0173 0.1180 0.15 0.89 216s corpProfLag 0.2162 0.1073 2.02 0.06 . 216s wages 0.8102 0.0402 20.13 2.7e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.136 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 21.925 MSE: 1.29 Root MSE: 1.136 216s Multiple R-Squared: 0.977 Adjusted R-Squared: 0.973 216s 216s 216s 2SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 20.2782 7.5427 2.69 0.01555 * 216s corpProf 0.1502 0.1732 0.87 0.39792 216s corpProfLag 0.6159 0.1628 3.78 0.00148 ** 216s capitalLag -0.1578 0.0361 -4.37 0.00042 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.307 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 29.047 MSE: 1.709 Root MSE: 1.307 216s Multiple R-Squared: 0.885 Adjusted R-Squared: 0.865 216s 216s 216s 2SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.5003 1.1478 1.31 0.20857 216s gnp 0.4389 0.0356 12.32 6.8e-10 *** 216s gnpLag 0.1467 0.0388 3.78 0.00150 ** 216s trend 0.1304 0.0291 4.47 0.00033 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.767 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 10.005 MSE: 0.589 Root MSE: 0.767 216s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.46263 -1.320 -1.2940 216s 3 -0.61635 0.257 0.2981 216s 4 -1.30423 0.860 1.1918 216s 5 -0.24588 -1.594 -0.1361 216s 6 0.22948 0.259 -0.4634 216s 7 0.88538 1.207 -0.4824 216s 8 1.44189 0.969 -0.7284 216s 9 1.34190 0.113 0.3387 216s 10 -0.39403 1.796 1.1965 216s 11 -0.62564 -0.953 -0.1552 216s 12 -1.06543 -0.807 0.5882 216s 13 -1.33021 -0.895 0.0955 216s 14 0.61059 1.306 0.4487 216s 15 -0.14208 -0.151 0.2822 216s 16 0.00315 0.142 0.0145 216s 17 2.00337 1.749 -0.8478 216s 18 -0.60552 -0.192 0.9950 216s 19 -0.24771 -3.291 -0.4734 216s 20 1.38510 0.285 -0.3766 216s 21 1.03204 -0.104 -1.0893 216s 22 -1.89319 0.363 0.5974 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.4 1.120 26.8 216s 3 45.6 1.643 29.0 216s 4 50.5 4.340 32.9 216s 5 50.8 4.594 34.0 216s 6 52.4 4.841 35.9 216s 7 54.2 4.393 37.9 216s 8 54.8 3.231 38.6 216s 9 56.0 2.887 38.9 216s 10 58.2 3.304 40.1 216s 11 55.6 1.953 38.1 216s 12 52.0 -2.593 33.9 216s 13 46.9 -5.305 28.9 216s 14 45.9 -6.406 28.1 216s 15 48.8 -2.849 30.3 216s 16 51.3 -1.442 33.2 216s 17 55.7 0.351 37.6 216s 18 59.3 2.192 40.0 216s 19 57.7 1.391 38.7 216s 20 60.2 1.015 42.0 216s 21 64.0 3.404 46.1 216s 22 71.6 4.537 52.7 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.4 0.471 41.4 43.4 216s 3 45.6 0.577 44.4 46.8 216s 4 50.5 0.354 49.8 51.3 216s 5 50.8 0.405 50.0 51.7 216s 6 52.4 0.404 51.5 53.2 216s 7 54.2 0.359 53.5 55.0 216s 8 54.8 0.328 54.1 55.4 216s 9 56.0 0.368 55.2 56.7 216s 10 58.2 0.377 57.4 59.0 216s 11 55.6 0.728 54.1 57.2 216s 12 52.0 0.604 50.7 53.2 216s 13 46.9 0.765 45.3 48.5 216s 14 45.9 0.615 44.6 47.2 216s 15 48.8 0.374 48.1 49.6 216s 16 51.3 0.333 50.6 52.0 216s 17 55.7 0.409 54.8 56.6 216s 18 59.3 0.326 58.6 60.0 216s 19 57.7 0.414 56.9 58.6 216s 20 60.2 0.478 59.2 61.2 216s 21 64.0 0.446 63.0 64.9 216s 22 71.6 0.689 70.1 73.0 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 1.120 0.865 -0.706 2.946 216s 3 1.643 0.594 0.390 2.895 216s 4 4.340 0.545 3.190 5.490 216s 5 4.594 0.443 3.660 5.527 216s 6 4.841 0.411 3.973 5.709 216s 7 4.393 0.399 3.550 5.235 216s 8 3.231 0.348 2.497 3.965 216s 9 2.887 0.542 1.744 4.030 216s 10 3.304 0.593 2.054 4.555 216s 11 1.953 0.855 0.148 3.757 216s 12 -2.593 0.679 -4.026 -1.160 216s 13 -5.305 0.876 -7.152 -3.457 216s 14 -6.406 0.916 -8.338 -4.473 216s 15 -2.849 0.435 -3.765 -1.932 216s 16 -1.442 0.376 -2.236 -0.649 216s 17 0.351 0.510 -0.724 1.426 216s 18 2.192 0.299 1.560 2.823 216s 19 1.391 0.464 0.411 2.371 216s 20 1.015 0.576 -0.201 2.230 216s 21 3.404 0.471 2.410 4.398 216s 22 4.537 0.675 3.114 5.961 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.318 26.1 27.5 216s 3 29.0 0.330 28.3 29.7 216s 4 32.9 0.346 32.2 33.6 216s 5 34.0 0.242 33.5 34.5 216s 6 35.9 0.248 35.3 36.4 216s 7 37.9 0.244 37.4 38.4 216s 8 38.6 0.246 38.1 39.1 216s 9 38.9 0.235 38.4 39.4 216s 10 40.1 0.224 39.6 40.6 216s 11 38.1 0.350 37.3 38.8 216s 12 33.9 0.382 33.1 34.7 216s 13 28.9 0.454 27.9 29.9 216s 14 28.1 0.342 27.3 28.8 216s 15 30.3 0.335 29.6 31.0 216s 16 33.2 0.280 32.6 33.8 216s 17 37.6 0.291 37.0 38.3 216s 18 40.0 0.215 39.6 40.5 216s 19 38.7 0.356 37.9 39.4 216s 20 42.0 0.304 41.3 42.6 216s 21 46.1 0.306 45.4 46.7 216s 22 52.7 0.489 51.7 53.7 216s > model.frame 216s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 216s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 216s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 216s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 216s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 216s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 216s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 216s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 61.0 216s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 216s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 216s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 216s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 216s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 216s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 216s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 216s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 216s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 216s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 216s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 216s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 216s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 216s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 216s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 216s trend 216s 1 -11 216s 2 -10 216s 3 -9 216s 4 -8 216s 5 -7 216s 6 -6 216s 7 -5 216s 8 -4 216s 9 -3 216s 10 -2 216s 11 -1 216s 12 0 216s 13 1 216s 14 2 216s 15 3 216s 16 4 216s 17 5 216s 18 6 216s 19 7 216s 20 8 216s 21 9 216s 22 10 216s > model.matrix 216s [1] TRUE 216s > nobs 216s [1] 63 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 1.08 0.3 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 1.29 0.26 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 52 216s 2 51 1 1.29 0.26 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.54 0.58 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.65 0.53 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 53 216s 2 51 2 1.3 0.52 216s > logLik 216s 'log Lik.' -76.3 (df=13) 216s 'log Lik.' -85.5 (df=13) 216s > 216s > # SUR 216s > summary 216s 216s systemfit results 216s method: SUR 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 63 51 46.5 0.158 0.977 0.993 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 21 17 18.1 1.065 1.032 0.981 0.977 216s Investment 21 17 17.6 1.036 1.018 0.930 0.918 216s PrivateWages 21 17 10.8 0.633 0.796 0.986 0.984 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 0.8514 0.0495 -0.381 216s Investment 0.0495 0.8249 0.121 216s PrivateWages -0.3808 0.1212 0.476 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.8618 0.0766 -0.437 216s Investment 0.0766 0.8384 0.203 216s PrivateWages -0.4368 0.2027 0.513 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.0000 0.0901 -0.657 216s Investment 0.0901 1.0000 0.309 216s PrivateWages -0.6572 0.3092 1.000 216s 216s 216s SUR estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 15.9805 1.1687 13.67 1.3e-10 *** 216s corpProf 0.2302 0.0767 3.00 0.008 ** 216s corpProfLag 0.0673 0.0769 0.87 0.394 216s wages 0.7962 0.0353 22.58 4.1e-14 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.032 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 18.098 MSE: 1.065 Root MSE: 1.032 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 216s 216s 216s SUR estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 12.9293 4.8014 2.69 0.01540 * 216s corpProf 0.4429 0.0861 5.15 8.1e-05 *** 216s corpProfLag 0.3655 0.0894 4.09 0.00077 *** 216s capitalLag -0.1253 0.0235 -5.34 5.4e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.018 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.606 MSE: 1.036 Root MSE: 1.018 216s Multiple R-Squared: 0.93 Adjusted R-Squared: 0.918 216s 216s 216s SUR estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.6347 1.1173 1.46 0.16 216s gnp 0.4098 0.0273 15.04 3.0e-11 *** 216s gnpLag 0.1744 0.0312 5.59 3.2e-05 *** 216s trend 0.1558 0.0276 5.65 2.9e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.796 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 10.763 MSE: 0.633 Root MSE: 0.796 216s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.24064 -0.3522 -1.0960 216s 3 -1.34080 -0.1605 0.5818 216s 4 -1.61038 1.0687 1.5313 216s 5 -0.54147 -1.4707 -0.0220 216s 6 -0.04372 0.3299 -0.2587 216s 7 0.85234 1.4346 -0.3243 216s 8 1.30302 0.8306 -0.6674 216s 9 0.97574 -0.4918 0.3660 216s 10 -0.66060 1.2434 1.2682 216s 11 0.45069 0.2647 -0.3467 216s 12 -0.04295 0.0795 0.3057 216s 13 -0.06686 0.3369 -0.2602 216s 14 0.32177 0.4080 0.3434 216s 15 -0.00441 -0.1533 0.2628 216s 16 -0.01931 0.0158 -0.0216 216s 17 1.53656 1.0372 -0.7988 216s 18 -0.42317 0.0176 0.8550 216s 19 0.29041 -2.6364 -0.8217 216s 20 0.88685 -0.5822 -0.3869 216s 21 0.68839 -0.7015 -1.1838 216s 22 -2.31147 -0.5183 0.6742 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.1 0.152 26.6 216s 3 46.3 2.060 28.7 216s 4 50.8 4.131 32.6 216s 5 51.1 4.471 33.9 216s 6 52.6 4.770 35.7 216s 7 54.2 4.165 37.7 216s 8 54.9 3.369 38.6 216s 9 56.3 3.492 38.8 216s 10 58.5 3.857 40.0 216s 11 54.5 0.735 38.2 216s 12 50.9 -3.479 34.2 216s 13 45.7 -6.537 29.3 216s 14 46.2 -5.508 28.2 216s 15 48.7 -2.847 30.3 216s 16 51.3 -1.316 33.2 216s 17 56.2 1.063 37.6 216s 18 59.1 1.982 40.1 216s 19 57.2 0.736 39.0 216s 20 60.7 1.882 42.0 216s 21 64.3 4.002 46.2 216s 22 72.0 5.418 52.6 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.1 0.415 41.3 43.0 216s 3 46.3 0.449 45.4 47.2 216s 4 50.8 0.300 50.2 51.4 216s 5 51.1 0.348 50.4 51.8 216s 6 52.6 0.350 51.9 53.3 216s 7 54.2 0.317 53.6 54.9 216s 8 54.9 0.289 54.3 55.5 216s 9 56.3 0.309 55.7 56.9 216s 10 58.5 0.328 57.8 59.1 216s 11 54.5 0.516 53.5 55.6 216s 12 50.9 0.414 50.1 51.8 216s 13 45.7 0.544 44.6 46.8 216s 14 46.2 0.527 45.1 47.2 216s 15 48.7 0.332 48.0 49.4 216s 16 51.3 0.295 50.7 51.9 216s 17 56.2 0.319 55.5 56.8 216s 18 59.1 0.286 58.5 59.7 216s 19 57.2 0.323 56.6 57.9 216s 20 60.7 0.381 59.9 61.5 216s 21 64.3 0.381 63.5 65.1 216s 22 72.0 0.597 70.8 73.2 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 0.152 0.536 -0.924 1.229 216s 3 2.060 0.446 1.166 2.955 216s 4 4.131 0.397 3.334 4.929 216s 5 4.471 0.329 3.809 5.132 216s 6 4.770 0.311 4.145 5.395 216s 7 4.165 0.294 3.575 4.756 216s 8 3.369 0.263 2.842 3.897 216s 9 3.492 0.347 2.796 4.188 216s 10 3.857 0.398 3.058 4.656 216s 11 0.735 0.539 -0.346 1.816 216s 12 -3.479 0.454 -4.390 -2.569 216s 13 -6.537 0.552 -7.646 -5.428 216s 14 -5.508 0.617 -6.747 -4.269 216s 15 -2.847 0.335 -3.519 -2.175 216s 16 -1.316 0.287 -1.892 -0.739 216s 17 1.063 0.311 0.439 1.686 216s 18 1.982 0.218 1.545 2.420 216s 19 0.736 0.279 0.176 1.296 216s 20 1.882 0.327 1.227 2.538 216s 21 4.002 0.297 3.405 4.598 216s 22 5.418 0.412 4.591 6.245 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.6 0.313 26.0 27.2 216s 3 28.7 0.310 28.1 29.3 216s 4 32.6 0.305 32.0 33.2 216s 5 33.9 0.236 33.4 34.4 216s 6 35.7 0.233 35.2 36.1 216s 7 37.7 0.234 37.3 38.2 216s 8 38.6 0.239 38.1 39.0 216s 9 38.8 0.229 38.4 39.3 216s 10 40.0 0.219 39.6 40.5 216s 11 38.2 0.301 37.6 38.9 216s 12 34.2 0.308 33.6 34.8 216s 13 29.3 0.370 28.5 30.0 216s 14 28.2 0.332 27.5 28.8 216s 15 30.3 0.324 29.7 31.0 216s 16 33.2 0.271 32.7 33.8 216s 17 37.6 0.263 37.1 38.1 216s 18 40.1 0.211 39.7 40.6 216s 19 39.0 0.306 38.4 39.6 216s 20 42.0 0.280 41.4 42.5 216s 21 46.2 0.298 45.6 46.8 216s 22 52.6 0.445 51.7 53.5 216s > model.frame 216s [1] TRUE 216s > model.matrix 216s [1] TRUE 216s > nobs 216s [1] 63 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 1.44 0.24 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 1.69 0.2 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 52 216s 2 51 1 1.69 0.19 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.77 0.47 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.91 0.41 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 53 216s 2 51 2 1.83 0.4 216s > logLik 216s 'log Lik.' -70 (df=18) 216s 'log Lik.' -79 (df=18) 216s > 216s > # 3SLS 216s > summary 216s 216s systemfit results 216s method: 3SLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 63 51 73.6 0.283 0.963 0.995 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 21 17 18.7 1.102 1.050 0.980 0.977 216s Investment 21 17 44.0 2.586 1.608 0.826 0.795 216s PrivateWages 21 17 10.9 0.642 0.801 0.986 0.984 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 1.044 0.438 -0.385 216s Investment 0.438 1.383 0.193 216s PrivateWages -0.385 0.193 0.476 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.892 0.411 -0.394 216s Investment 0.411 2.093 0.403 216s PrivateWages -0.394 0.403 0.520 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.301 -0.578 216s Investment 0.301 1.000 0.386 216s PrivateWages -0.578 0.386 1.000 216s 216s 216s 3SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.4408 1.3045 12.60 4.7e-10 *** 216s corpProf 0.1249 0.1081 1.16 0.26 216s corpProfLag 0.1631 0.1004 1.62 0.12 216s wages 0.7901 0.0379 20.83 1.5e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.05 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 18.727 MSE: 1.102 Root MSE: 1.05 216s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 216s 216s 216s 3SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 28.1778 6.7938 4.15 0.00067 *** 216s corpProf -0.0131 0.1619 -0.08 0.93655 216s corpProfLag 0.7557 0.1529 4.94 0.00012 *** 216s capitalLag -0.1948 0.0325 -5.99 1.5e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.608 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 43.954 MSE: 2.586 Root MSE: 1.608 216s Multiple R-Squared: 0.826 Adjusted R-Squared: 0.795 216s 216s 216s 3SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.7972 1.1159 1.61 0.13 216s gnp 0.4005 0.0318 12.59 4.8e-10 *** 216s gnpLag 0.1813 0.0342 5.31 5.8e-05 *** 216s trend 0.1497 0.0279 5.36 5.2e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.801 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 10.921 MSE: 0.642 Root MSE: 0.801 216s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.984 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.4416 -2.1951 -1.20287 216s 3 -1.0150 0.1515 0.51834 216s 4 -1.5289 0.4406 1.50936 216s 5 -0.4985 -1.8667 -0.08743 216s 6 -0.0132 0.0713 -0.28089 216s 7 0.7759 1.0294 -0.33908 216s 8 1.3004 1.1011 -0.69282 216s 9 1.0993 0.5853 0.34494 216s 10 -0.5839 2.2952 1.27590 216s 11 -0.1917 -1.3443 -0.40414 216s 12 -0.5598 -0.9944 0.22151 216s 13 -0.6746 -1.3404 -0.36962 216s 14 0.5767 1.9316 0.31006 216s 15 -0.0211 -0.1217 0.27309 216s 16 0.0539 0.1847 0.00716 216s 17 1.8555 2.0937 -0.71866 216s 18 -0.4596 -0.3216 0.90582 216s 19 0.0613 -3.6314 -0.81881 216s 20 1.2602 0.7582 -0.26942 216s 21 0.9500 0.2428 -1.06125 216s 22 -1.9451 0.9302 0.87883 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.3 1.99510 26.7 216s 3 46.0 1.74850 28.8 216s 4 50.7 4.75942 32.6 216s 5 51.1 4.86672 34.0 216s 6 52.6 5.02874 35.7 216s 7 54.3 4.57056 37.7 216s 8 54.9 3.09893 38.6 216s 9 56.2 2.41471 38.9 216s 10 58.4 2.80476 40.0 216s 11 55.2 2.34425 38.3 216s 12 51.5 -2.40558 34.3 216s 13 46.3 -4.85959 29.4 216s 14 45.9 -7.03164 28.2 216s 15 48.7 -2.87827 30.3 216s 16 51.2 -1.48466 33.2 216s 17 55.8 0.00629 37.5 216s 18 59.2 2.32164 40.1 216s 19 57.4 1.73138 39.0 216s 20 60.3 0.54175 41.9 216s 21 64.1 3.05716 46.1 216s 22 71.6 3.96979 52.4 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.3 0.464 39.9 44.8 216s 3 46.0 0.541 43.5 48.5 216s 4 50.7 0.337 48.4 53.1 216s 5 51.1 0.385 48.7 53.5 216s 6 52.6 0.386 50.3 55.0 216s 7 54.3 0.349 52.0 56.7 216s 8 54.9 0.320 52.6 57.2 216s 9 56.2 0.355 53.9 58.5 216s 10 58.4 0.370 56.0 60.7 216s 11 55.2 0.682 52.6 57.8 216s 12 51.5 0.563 48.9 54.0 216s 13 46.3 0.719 43.6 49.0 216s 14 45.9 0.597 43.4 48.5 216s 15 48.7 0.370 46.4 51.1 216s 16 51.2 0.327 48.9 53.6 216s 17 55.8 0.391 53.5 58.2 216s 18 59.2 0.316 56.8 61.5 216s 19 57.4 0.389 55.1 59.8 216s 20 60.3 0.459 57.9 62.8 216s 21 64.1 0.438 61.7 66.4 216s 22 71.6 0.674 69.0 74.3 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 1.99510 0.792 -1.787 5.777 216s 3 1.74850 0.585 -1.861 5.358 216s 4 4.75942 0.510 1.200 8.319 216s 5 4.86672 0.423 1.359 8.375 216s 6 5.02874 0.400 1.533 8.525 216s 7 4.57056 0.391 1.079 8.062 216s 8 3.09893 0.345 -0.371 6.568 216s 9 2.41471 0.511 -1.145 5.974 216s 10 2.80476 0.560 -0.788 6.397 216s 11 2.34425 0.839 -1.482 6.170 216s 12 -2.40558 0.673 -6.083 1.272 216s 13 -4.85959 0.862 -8.708 -1.011 216s 14 -7.03164 0.874 -10.893 -3.171 216s 15 -2.87827 0.433 -6.392 0.635 216s 16 -1.48466 0.375 -4.968 1.999 216s 17 0.00629 0.491 -3.541 3.554 216s 18 2.32164 0.294 -1.127 5.771 216s 19 1.73138 0.446 -1.789 5.252 216s 20 0.54175 0.547 -3.042 4.125 216s 21 3.05716 0.454 -0.468 6.582 216s 22 3.96979 0.642 0.317 7.623 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.7 0.314 24.9 28.5 216s 3 28.8 0.318 27.0 30.6 216s 4 32.6 0.325 30.8 34.4 216s 5 34.0 0.235 32.2 35.7 216s 6 35.7 0.241 33.9 37.4 216s 7 37.7 0.238 36.0 39.5 216s 8 38.6 0.237 36.8 40.4 216s 9 38.9 0.227 37.1 40.6 216s 10 40.0 0.219 38.3 41.8 216s 11 38.3 0.317 36.5 40.1 216s 12 34.3 0.344 32.4 36.1 216s 13 29.4 0.419 27.5 31.3 216s 14 28.2 0.334 26.4 30.0 216s 15 30.3 0.320 28.5 32.1 216s 16 33.2 0.268 31.4 35.0 216s 17 37.5 0.269 35.7 39.3 216s 18 40.1 0.212 38.3 41.8 216s 19 39.0 0.331 37.2 40.8 216s 20 41.9 0.287 40.1 43.7 216s 21 46.1 0.301 44.3 47.9 216s 22 52.4 0.471 50.5 54.4 216s > model.frame 216s [1] TRUE 216s > model.matrix 216s [1] TRUE 216s > nobs 216s [1] 63 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 0.29 0.59 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 0.39 0.54 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 52 216s 2 51 1 0.39 0.53 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.3 0.74 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.4 0.67 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 53 216s 2 51 2 0.8 0.67 216s > logLik 216s 'log Lik.' -76.1 (df=18) 216s 'log Lik.' -89.1 (df=18) 216s > 216s > # I3SLS 216s > summary 216s 216s systemfit results 216s method: iterated 3SLS 216s 216s convergence achieved after 20 iterations 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 63 51 128 0.509 0.936 0.996 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 21 17 19.2 1.130 1.063 0.980 0.976 216s Investment 21 17 95.7 5.627 2.372 0.621 0.554 216s PrivateWages 21 17 12.7 0.748 0.865 0.984 0.981 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 0.915 0.642 -0.435 216s Investment 0.642 4.555 0.734 216s PrivateWages -0.435 0.734 0.606 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.915 0.642 -0.435 216s Investment 0.642 4.555 0.734 216s PrivateWages -0.435 0.734 0.606 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.314 -0.584 216s Investment 0.314 1.000 0.442 216s PrivateWages -0.584 0.442 1.000 216s 216s 216s 3SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.5590 1.2244 13.52 1.6e-10 *** 216s corpProf 0.1645 0.0962 1.71 0.105 216s corpProfLag 0.1766 0.0901 1.96 0.067 . 216s wages 0.7658 0.0348 22.03 6.1e-14 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.063 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 19.213 MSE: 1.13 Root MSE: 1.063 216s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 216s 216s 216s 3SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 42.8959 10.5937 4.05 0.00083 *** 216s corpProf -0.3565 0.2602 -1.37 0.18838 216s corpProfLag 1.0113 0.2488 4.07 0.00081 *** 216s capitalLag -0.2602 0.0509 -5.12 8.6e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 2.372 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 95.661 MSE: 5.627 Root MSE: 2.372 216s Multiple R-Squared: 0.621 Adjusted R-Squared: 0.554 216s 216s 216s 3SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 2.6247 1.1956 2.20 0.042 * 216s gnp 0.3748 0.0311 12.05 9.4e-10 *** 216s gnpLag 0.1937 0.0324 5.98 1.5e-05 *** 216s trend 0.1679 0.0289 5.80 2.1e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.865 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 12.719 MSE: 0.748 Root MSE: 0.865 216s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.981 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.537 -3.95419 -1.2303 216s 3 -1.187 0.00151 0.5797 216s 4 -1.705 -0.22015 1.6794 216s 5 -0.734 -2.22753 -0.0260 216s 6 -0.251 -0.10866 -0.1362 216s 7 0.600 0.83218 -0.1837 216s 8 1.142 1.46624 -0.5825 216s 9 0.921 1.62030 0.4347 216s 10 -0.745 3.40013 1.4104 216s 11 -0.197 -2.15443 -0.4679 216s 12 -0.385 -1.62274 0.0106 216s 13 -0.390 -2.62869 -0.7363 216s 14 0.749 2.80517 0.0581 216s 15 0.112 -0.27710 0.1113 216s 16 0.170 0.13598 -0.1089 216s 17 1.925 2.76200 -0.6976 216s 18 -0.341 -0.53919 0.8651 216s 19 0.219 -4.32845 -1.0116 216s 20 1.383 1.71889 -0.2087 216s 21 1.028 1.06406 -0.9656 216s 22 -1.777 2.25466 1.2061 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.4 3.754 26.7 216s 3 46.2 1.898 28.7 216s 4 50.9 5.420 32.4 216s 5 51.3 5.228 33.9 216s 6 52.9 5.209 35.5 216s 7 54.5 4.768 37.6 216s 8 55.1 2.734 38.5 216s 9 56.4 1.380 38.8 216s 10 58.5 1.700 39.9 216s 11 55.2 3.154 38.4 216s 12 51.3 -1.777 34.5 216s 13 46.0 -3.571 29.7 216s 14 45.8 -7.905 28.4 216s 15 48.6 -2.723 30.5 216s 16 51.1 -1.436 33.3 216s 17 55.8 -0.662 37.5 216s 18 59.0 2.539 40.1 216s 19 57.3 2.428 39.2 216s 20 60.2 -0.419 41.8 216s 21 64.0 2.236 46.0 216s 22 71.5 2.645 52.1 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.4 0.434 41.6 43.3 216s 3 46.2 0.491 45.2 47.2 216s 4 50.9 0.309 50.3 51.5 216s 5 51.3 0.351 50.6 52.0 216s 6 52.9 0.352 52.1 53.6 216s 7 54.5 0.320 53.9 55.1 216s 8 55.1 0.293 54.5 55.6 216s 9 56.4 0.324 55.7 57.0 216s 10 58.5 0.340 57.9 59.2 216s 11 55.2 0.613 54.0 56.4 216s 12 51.3 0.506 50.3 52.3 216s 13 46.0 0.649 44.7 47.3 216s 14 45.8 0.546 44.7 46.8 216s 15 48.6 0.341 47.9 49.3 216s 16 51.1 0.301 50.5 51.7 216s 17 55.8 0.357 55.1 56.5 216s 18 59.0 0.293 58.5 59.6 216s 19 57.3 0.353 56.6 58.0 216s 20 60.2 0.421 59.4 61.1 216s 21 64.0 0.409 63.2 64.8 216s 22 71.5 0.630 70.2 72.7 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 3.754 1.263 1.218 6.2906 216s 3 1.898 1.022 -0.153 3.9503 216s 4 5.420 0.853 3.709 7.1317 216s 5 5.228 0.727 3.767 6.6877 216s 6 5.209 0.703 3.797 6.6200 216s 7 4.768 0.688 3.387 6.1487 216s 8 2.734 0.615 1.499 3.9683 216s 9 1.380 0.852 -0.330 3.0893 216s 10 1.700 0.938 -0.184 3.5836 216s 11 3.154 1.437 0.269 6.0398 216s 12 -1.777 1.173 -4.133 0.5780 216s 13 -3.571 1.494 -6.570 -0.5725 216s 14 -7.905 1.479 -10.875 -4.9350 216s 15 -2.723 0.778 -4.285 -1.1613 216s 16 -1.436 0.672 -2.784 -0.0875 216s 17 -0.662 0.832 -2.333 1.0088 216s 18 2.539 0.522 1.491 3.5875 216s 19 2.428 0.753 0.918 3.9392 216s 20 -0.419 0.907 -2.240 1.4019 216s 21 2.236 0.775 0.679 3.7928 216s 22 2.645 1.076 0.486 4.8047 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.7 0.340 26.0 27.4 216s 3 28.7 0.339 28.0 29.4 216s 4 32.4 0.340 31.7 33.1 216s 5 33.9 0.250 33.4 34.4 216s 6 35.5 0.258 35.0 36.1 216s 7 37.6 0.256 37.1 38.1 216s 8 38.5 0.252 38.0 39.0 216s 9 38.8 0.241 38.3 39.2 216s 10 39.9 0.239 39.4 40.4 216s 11 38.4 0.314 37.7 39.0 216s 12 34.5 0.342 33.8 35.2 216s 13 29.7 0.430 28.9 30.6 216s 14 28.4 0.361 27.7 29.2 216s 15 30.5 0.336 29.8 31.2 216s 16 33.3 0.281 32.7 33.9 216s 17 37.5 0.270 37.0 38.0 216s 18 40.1 0.231 39.7 40.6 216s 19 39.2 0.343 38.5 39.9 216s 20 41.8 0.294 41.2 42.4 216s 21 46.0 0.326 45.3 46.6 216s 22 52.1 0.501 51.1 53.1 216s > model.frame 216s [1] TRUE 216s > model.matrix 216s [1] TRUE 216s > nobs 216s [1] 63 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 0.59 0.45 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 51 1 0.73 0.4 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 52 216s 2 51 1 0.73 0.39 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.72 0.49 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 53 216s 2 51 2 0.88 0.42 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 53 216s 2 51 2 1.77 0.41 216s > logLik 216s 'log Lik.' -82.3 (df=18) 216s 'log Lik.' -99.1 (df=18) 216s > 216s > # OLS 216s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 216s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 216s > summary 216s 216s systemfit results 216s method: OLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 62 50 44.9 0.372 0.977 0.991 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 21 17 17.88 1.052 1.03 0.981 0.978 216s Investment 21 17 17.32 1.019 1.01 0.931 0.919 216s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.0703 -0.0161 -0.463 216s Investment -0.0161 0.9435 0.199 216s PrivateWages -0.4633 0.1993 0.609 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.0000 -0.0201 -0.575 216s Investment -0.0201 1.0000 0.264 216s PrivateWages -0.5747 0.2639 1.000 216s 216s 216s OLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.2366 1.3141 12.36 6.4e-10 *** 216s corpProf 0.1929 0.0920 2.10 0.051 . 216s corpProfLag 0.0899 0.0914 0.98 0.339 216s wages 0.7962 0.0403 19.76 3.6e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.026 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.879 MSE: 1.052 Root MSE: 1.026 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 216s 216s 216s OLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 10.1258 5.2592 1.93 0.07108 . 216s corpProf 0.4796 0.0934 5.13 8.3e-05 *** 216s corpProfLag 0.3330 0.0971 3.43 0.00318 ** 216s capitalLag -0.1118 0.0257 -4.35 0.00044 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.009 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 216s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 216s 216s 216s OLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.3550 1.3093 1.03 0.3161 216s gnp 0.4417 0.0331 13.33 4.4e-10 *** 216s gnpLag 0.1466 0.0381 3.85 0.0014 ** 216s trend 0.1244 0.0336 3.70 0.0020 ** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.78 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 216s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 216s 216s compare coef with single-equation OLS 216s [1] TRUE 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.32389 -0.0668 -1.3389 216s 3 -1.25001 -0.0476 0.2462 216s 4 -1.56574 1.2467 1.1255 216s 5 -0.49350 -1.3512 -0.1959 216s 6 0.00761 0.4154 -0.5284 216s 7 0.86910 1.4923 NA 216s 8 1.33848 0.7889 -0.7909 216s 9 1.05498 -0.6317 0.2819 216s 10 -0.58856 1.0830 1.1384 216s 11 0.28231 0.2791 -0.1904 216s 12 -0.22965 0.0369 0.5813 216s 13 -0.32213 0.3659 0.1206 216s 14 0.32228 0.2237 0.4773 216s 15 -0.05801 -0.1728 0.3035 216s 16 -0.03466 0.0101 0.0284 216s 17 1.61650 0.9719 -0.8517 216s 18 -0.43597 0.0516 0.9908 216s 19 0.21005 -2.5656 -0.4597 216s 20 0.98920 -0.6866 -0.3819 216s 21 0.78508 -0.7807 -1.1062 216s 22 -2.17345 -0.6623 0.5501 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.2 -0.133 26.8 216s 3 46.3 1.948 29.1 216s 4 50.8 3.953 33.0 216s 5 51.1 4.351 34.1 216s 6 52.6 4.685 35.9 216s 7 54.2 4.108 NA 216s 8 54.9 3.411 38.7 216s 9 56.2 3.632 38.9 216s 10 58.4 4.017 40.2 216s 11 54.7 0.721 38.1 216s 12 51.1 -3.437 33.9 216s 13 45.9 -6.566 28.9 216s 14 46.2 -5.324 28.0 216s 15 48.8 -2.827 30.3 216s 16 51.3 -1.310 33.2 216s 17 56.1 1.128 37.7 216s 18 59.1 1.948 40.0 216s 19 57.3 0.666 38.7 216s 20 60.6 1.987 42.0 216s 21 64.2 4.081 46.1 216s 22 71.9 5.562 52.7 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.2 0.466 40.0 44.5 216s 3 46.3 0.523 43.9 48.6 216s 4 50.8 0.344 48.6 52.9 216s 5 51.1 0.399 48.9 53.3 216s 6 52.6 0.401 50.4 54.8 216s 7 54.2 0.363 52.0 56.4 216s 8 54.9 0.330 52.7 57.0 216s 9 56.2 0.354 54.1 58.4 216s 10 58.4 0.373 56.2 60.6 216s 11 54.7 0.612 52.3 57.1 216s 12 51.1 0.489 48.8 53.4 216s 13 45.9 0.634 43.5 48.3 216s 14 46.2 0.608 43.8 48.6 216s 15 48.8 0.378 46.6 51.0 216s 16 51.3 0.336 49.2 53.5 216s 17 56.1 0.369 53.9 58.3 216s 18 59.1 0.324 57.0 61.3 216s 19 57.3 0.375 55.1 59.5 216s 20 60.6 0.437 58.4 62.9 216s 21 64.2 0.429 62.0 66.4 216s 22 71.9 0.672 69.4 74.3 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 -0.133 0.584 -2.476 2.209 216s 3 1.948 0.480 -0.297 4.193 216s 4 3.953 0.432 1.748 6.159 216s 5 4.351 0.357 2.201 6.502 216s 6 4.685 0.336 2.548 6.821 216s 7 4.108 0.316 1.983 6.232 216s 8 3.411 0.281 1.306 5.516 216s 9 3.632 0.374 1.469 5.794 216s 10 4.017 0.430 1.813 6.221 216s 11 0.721 0.579 -1.616 3.058 216s 12 -3.437 0.488 -5.688 -1.185 216s 13 -6.566 0.592 -8.917 -4.215 216s 14 -5.324 0.667 -7.754 -2.893 216s 15 -2.827 0.359 -4.979 -0.675 216s 16 -1.310 0.308 -3.430 0.810 216s 17 1.128 0.334 -1.008 3.264 216s 18 1.948 0.234 -0.133 4.030 216s 19 0.666 0.300 -1.450 2.781 216s 20 1.987 0.353 -0.161 4.134 216s 21 4.081 0.319 1.954 6.207 216s 22 5.562 0.444 3.348 7.777 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.366 25.1 28.6 216s 3 29.1 0.369 27.3 30.8 216s 4 33.0 0.372 31.2 34.7 216s 5 34.1 0.288 32.4 35.8 216s 6 35.9 0.287 34.3 37.6 216s 7 NA NA NA NA 216s 8 38.7 0.293 37.0 40.4 216s 9 38.9 0.279 37.3 40.6 216s 10 40.2 0.266 38.5 41.8 216s 11 38.1 0.365 36.4 39.8 216s 12 33.9 0.369 32.2 35.7 216s 13 28.9 0.438 27.1 30.7 216s 14 28.0 0.385 26.3 29.8 216s 15 30.3 0.379 28.6 32.0 216s 16 33.2 0.316 31.5 34.9 216s 17 37.7 0.310 36.0 39.3 216s 18 40.0 0.243 38.4 41.7 216s 19 38.7 0.363 36.9 40.4 216s 20 42.0 0.326 40.3 43.7 216s 21 46.1 0.341 44.4 47.8 216s 22 52.7 0.514 50.9 54.6 216s > model.frame 216s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 216s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 216s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 216s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 216s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 216s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 216s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 216s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 216s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 216s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 216s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 216s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 216s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 216s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 216s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 216s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 216s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 216s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 216s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 216s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 216s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 216s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 216s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 216s trend 216s 1 -11 216s 2 -10 216s 3 -9 216s 4 -8 216s 5 -7 216s 6 -6 216s 7 -5 216s 8 -4 216s 9 -3 216s 10 -2 216s 11 -1 216s 12 0 216s 13 1 216s 14 2 216s 15 3 216s 16 4 216s 17 5 216s 18 6 216s 19 7 216s 20 8 216s 21 9 216s 22 10 216s > model.matrix 216s Consumption_(Intercept) Consumption_corpProf 216s Consumption_2 1 12.4 216s Consumption_3 1 16.9 216s Consumption_4 1 18.4 216s Consumption_5 1 19.4 216s Consumption_6 1 20.1 216s Consumption_7 1 19.6 216s Consumption_8 1 19.8 216s Consumption_9 1 21.1 216s Consumption_10 1 21.7 216s Consumption_11 1 15.6 216s Consumption_12 1 11.4 216s Consumption_13 1 7.0 216s Consumption_14 1 11.2 216s Consumption_15 1 12.3 216s Consumption_16 1 14.0 216s Consumption_17 1 17.6 216s Consumption_18 1 17.3 216s Consumption_19 1 15.3 216s Consumption_20 1 19.0 216s Consumption_21 1 21.1 216s Consumption_22 1 23.5 216s Investment_2 0 0.0 216s Investment_3 0 0.0 216s Investment_4 0 0.0 216s Investment_5 0 0.0 216s Investment_6 0 0.0 216s Investment_7 0 0.0 216s Investment_8 0 0.0 216s Investment_9 0 0.0 216s Investment_10 0 0.0 216s Investment_11 0 0.0 216s Investment_12 0 0.0 216s Investment_13 0 0.0 216s Investment_14 0 0.0 216s Investment_15 0 0.0 216s Investment_16 0 0.0 216s Investment_17 0 0.0 216s Investment_18 0 0.0 216s Investment_19 0 0.0 216s Investment_20 0 0.0 216s Investment_21 0 0.0 216s Investment_22 0 0.0 216s PrivateWages_2 0 0.0 216s PrivateWages_3 0 0.0 216s PrivateWages_4 0 0.0 216s PrivateWages_5 0 0.0 216s PrivateWages_6 0 0.0 216s PrivateWages_8 0 0.0 216s PrivateWages_9 0 0.0 216s PrivateWages_10 0 0.0 216s PrivateWages_11 0 0.0 216s PrivateWages_12 0 0.0 216s PrivateWages_13 0 0.0 216s PrivateWages_14 0 0.0 216s PrivateWages_15 0 0.0 216s PrivateWages_16 0 0.0 216s PrivateWages_17 0 0.0 216s PrivateWages_18 0 0.0 216s PrivateWages_19 0 0.0 216s PrivateWages_20 0 0.0 216s PrivateWages_21 0 0.0 216s PrivateWages_22 0 0.0 216s Consumption_corpProfLag Consumption_wages 216s Consumption_2 12.7 28.2 216s Consumption_3 12.4 32.2 216s Consumption_4 16.9 37.0 216s Consumption_5 18.4 37.0 216s Consumption_6 19.4 38.6 216s Consumption_7 20.1 40.7 216s Consumption_8 19.6 41.5 216s Consumption_9 19.8 42.9 216s Consumption_10 21.1 45.3 216s Consumption_11 21.7 42.1 216s Consumption_12 15.6 39.3 216s Consumption_13 11.4 34.3 216s Consumption_14 7.0 34.1 216s Consumption_15 11.2 36.6 216s Consumption_16 12.3 39.3 216s Consumption_17 14.0 44.2 216s Consumption_18 17.6 47.7 216s Consumption_19 17.3 45.9 216s Consumption_20 15.3 49.4 216s Consumption_21 19.0 53.0 216s Consumption_22 21.1 61.8 216s Investment_2 0.0 0.0 216s Investment_3 0.0 0.0 216s Investment_4 0.0 0.0 216s Investment_5 0.0 0.0 216s Investment_6 0.0 0.0 216s Investment_7 0.0 0.0 216s Investment_8 0.0 0.0 216s Investment_9 0.0 0.0 216s Investment_10 0.0 0.0 216s Investment_11 0.0 0.0 216s Investment_12 0.0 0.0 216s Investment_13 0.0 0.0 216s Investment_14 0.0 0.0 216s Investment_15 0.0 0.0 216s Investment_16 0.0 0.0 216s Investment_17 0.0 0.0 216s Investment_18 0.0 0.0 216s Investment_19 0.0 0.0 216s Investment_20 0.0 0.0 216s Investment_21 0.0 0.0 216s Investment_22 0.0 0.0 216s PrivateWages_2 0.0 0.0 216s PrivateWages_3 0.0 0.0 216s PrivateWages_4 0.0 0.0 216s PrivateWages_5 0.0 0.0 216s PrivateWages_6 0.0 0.0 216s PrivateWages_8 0.0 0.0 216s PrivateWages_9 0.0 0.0 216s PrivateWages_10 0.0 0.0 216s PrivateWages_11 0.0 0.0 216s PrivateWages_12 0.0 0.0 216s PrivateWages_13 0.0 0.0 216s PrivateWages_14 0.0 0.0 216s PrivateWages_15 0.0 0.0 216s PrivateWages_16 0.0 0.0 216s PrivateWages_17 0.0 0.0 216s PrivateWages_18 0.0 0.0 216s PrivateWages_19 0.0 0.0 216s PrivateWages_20 0.0 0.0 216s PrivateWages_21 0.0 0.0 216s PrivateWages_22 0.0 0.0 216s Investment_(Intercept) Investment_corpProf 216s Consumption_2 0 0.0 216s Consumption_3 0 0.0 216s Consumption_4 0 0.0 216s Consumption_5 0 0.0 216s Consumption_6 0 0.0 216s Consumption_7 0 0.0 216s Consumption_8 0 0.0 216s Consumption_9 0 0.0 216s Consumption_10 0 0.0 216s Consumption_11 0 0.0 216s Consumption_12 0 0.0 216s Consumption_13 0 0.0 216s Consumption_14 0 0.0 216s Consumption_15 0 0.0 216s Consumption_16 0 0.0 216s Consumption_17 0 0.0 216s Consumption_18 0 0.0 216s Consumption_19 0 0.0 216s Consumption_20 0 0.0 216s Consumption_21 0 0.0 216s Consumption_22 0 0.0 216s Investment_2 1 12.4 216s Investment_3 1 16.9 216s Investment_4 1 18.4 216s Investment_5 1 19.4 216s Investment_6 1 20.1 216s Investment_7 1 19.6 216s Investment_8 1 19.8 216s Investment_9 1 21.1 216s Investment_10 1 21.7 216s Investment_11 1 15.6 216s Investment_12 1 11.4 216s Investment_13 1 7.0 216s Investment_14 1 11.2 216s Investment_15 1 12.3 216s Investment_16 1 14.0 216s Investment_17 1 17.6 216s Investment_18 1 17.3 216s Investment_19 1 15.3 216s Investment_20 1 19.0 216s Investment_21 1 21.1 216s Investment_22 1 23.5 216s PrivateWages_2 0 0.0 216s PrivateWages_3 0 0.0 216s PrivateWages_4 0 0.0 216s PrivateWages_5 0 0.0 216s PrivateWages_6 0 0.0 216s PrivateWages_8 0 0.0 216s PrivateWages_9 0 0.0 216s PrivateWages_10 0 0.0 216s PrivateWages_11 0 0.0 216s PrivateWages_12 0 0.0 216s PrivateWages_13 0 0.0 216s PrivateWages_14 0 0.0 216s PrivateWages_15 0 0.0 216s PrivateWages_16 0 0.0 216s PrivateWages_17 0 0.0 216s PrivateWages_18 0 0.0 216s PrivateWages_19 0 0.0 216s PrivateWages_20 0 0.0 216s PrivateWages_21 0 0.0 216s PrivateWages_22 0 0.0 216s Investment_corpProfLag Investment_capitalLag 216s Consumption_2 0.0 0 216s Consumption_3 0.0 0 216s Consumption_4 0.0 0 216s Consumption_5 0.0 0 216s Consumption_6 0.0 0 216s Consumption_7 0.0 0 216s Consumption_8 0.0 0 216s Consumption_9 0.0 0 216s Consumption_10 0.0 0 216s Consumption_11 0.0 0 216s Consumption_12 0.0 0 216s Consumption_13 0.0 0 216s Consumption_14 0.0 0 216s Consumption_15 0.0 0 216s Consumption_16 0.0 0 216s Consumption_17 0.0 0 216s Consumption_18 0.0 0 216s Consumption_19 0.0 0 216s Consumption_20 0.0 0 216s Consumption_21 0.0 0 216s Consumption_22 0.0 0 216s Investment_2 12.7 183 216s Investment_3 12.4 183 216s Investment_4 16.9 184 216s Investment_5 18.4 190 216s Investment_6 19.4 193 216s Investment_7 20.1 198 216s Investment_8 19.6 203 216s Investment_9 19.8 208 216s Investment_10 21.1 211 216s Investment_11 21.7 216 216s Investment_12 15.6 217 216s Investment_13 11.4 213 216s Investment_14 7.0 207 216s Investment_15 11.2 202 216s Investment_16 12.3 199 216s Investment_17 14.0 198 216s Investment_18 17.6 200 216s Investment_19 17.3 202 216s Investment_20 15.3 200 216s Investment_21 19.0 201 216s Investment_22 21.1 204 216s PrivateWages_2 0.0 0 216s PrivateWages_3 0.0 0 216s PrivateWages_4 0.0 0 216s PrivateWages_5 0.0 0 216s PrivateWages_6 0.0 0 216s PrivateWages_8 0.0 0 216s PrivateWages_9 0.0 0 216s PrivateWages_10 0.0 0 216s PrivateWages_11 0.0 0 216s PrivateWages_12 0.0 0 216s PrivateWages_13 0.0 0 216s PrivateWages_14 0.0 0 216s PrivateWages_15 0.0 0 216s PrivateWages_16 0.0 0 216s PrivateWages_17 0.0 0 216s PrivateWages_18 0.0 0 216s PrivateWages_19 0.0 0 216s PrivateWages_20 0.0 0 216s PrivateWages_21 0.0 0 216s PrivateWages_22 0.0 0 216s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 216s Consumption_2 0 0.0 0.0 216s Consumption_3 0 0.0 0.0 216s Consumption_4 0 0.0 0.0 216s Consumption_5 0 0.0 0.0 216s Consumption_6 0 0.0 0.0 216s Consumption_7 0 0.0 0.0 216s Consumption_8 0 0.0 0.0 216s Consumption_9 0 0.0 0.0 216s Consumption_10 0 0.0 0.0 216s Consumption_11 0 0.0 0.0 216s Consumption_12 0 0.0 0.0 216s Consumption_13 0 0.0 0.0 216s Consumption_14 0 0.0 0.0 216s Consumption_15 0 0.0 0.0 216s Consumption_16 0 0.0 0.0 216s Consumption_17 0 0.0 0.0 216s Consumption_18 0 0.0 0.0 216s Consumption_19 0 0.0 0.0 216s Consumption_20 0 0.0 0.0 216s Consumption_21 0 0.0 0.0 216s Consumption_22 0 0.0 0.0 216s Investment_2 0 0.0 0.0 216s Investment_3 0 0.0 0.0 216s Investment_4 0 0.0 0.0 216s Investment_5 0 0.0 0.0 216s Investment_6 0 0.0 0.0 216s Investment_7 0 0.0 0.0 216s Investment_8 0 0.0 0.0 216s Investment_9 0 0.0 0.0 216s Investment_10 0 0.0 0.0 216s Investment_11 0 0.0 0.0 216s Investment_12 0 0.0 0.0 216s Investment_13 0 0.0 0.0 216s Investment_14 0 0.0 0.0 216s Investment_15 0 0.0 0.0 216s Investment_16 0 0.0 0.0 216s Investment_17 0 0.0 0.0 216s Investment_18 0 0.0 0.0 216s Investment_19 0 0.0 0.0 216s Investment_20 0 0.0 0.0 216s Investment_21 0 0.0 0.0 216s Investment_22 0 0.0 0.0 216s PrivateWages_2 1 45.6 44.9 216s PrivateWages_3 1 50.1 45.6 216s PrivateWages_4 1 57.2 50.1 216s PrivateWages_5 1 57.1 57.2 216s PrivateWages_6 1 61.0 57.1 216s PrivateWages_8 1 64.4 64.0 216s PrivateWages_9 1 64.5 64.4 216s PrivateWages_10 1 67.0 64.5 216s PrivateWages_11 1 61.2 67.0 216s PrivateWages_12 1 53.4 61.2 216s PrivateWages_13 1 44.3 53.4 216s PrivateWages_14 1 45.1 44.3 216s PrivateWages_15 1 49.7 45.1 216s PrivateWages_16 1 54.4 49.7 216s PrivateWages_17 1 62.7 54.4 216s PrivateWages_18 1 65.0 62.7 216s PrivateWages_19 1 60.9 65.0 216s PrivateWages_20 1 69.5 60.9 216s PrivateWages_21 1 75.7 69.5 216s PrivateWages_22 1 88.4 75.7 216s PrivateWages_trend 216s Consumption_2 0 216s Consumption_3 0 216s Consumption_4 0 216s Consumption_5 0 216s Consumption_6 0 216s Consumption_7 0 216s Consumption_8 0 216s Consumption_9 0 216s Consumption_10 0 216s Consumption_11 0 216s Consumption_12 0 216s Consumption_13 0 216s Consumption_14 0 216s Consumption_15 0 216s Consumption_16 0 216s Consumption_17 0 216s Consumption_18 0 216s Consumption_19 0 216s Consumption_20 0 216s Consumption_21 0 216s Consumption_22 0 216s Investment_2 0 216s Investment_3 0 216s Investment_4 0 216s Investment_5 0 216s Investment_6 0 216s Investment_7 0 216s Investment_8 0 216s Investment_9 0 216s Investment_10 0 216s Investment_11 0 216s Investment_12 0 216s Investment_13 0 216s Investment_14 0 216s Investment_15 0 216s Investment_16 0 216s Investment_17 0 216s Investment_18 0 216s Investment_19 0 216s Investment_20 0 216s Investment_21 0 216s Investment_22 0 216s PrivateWages_2 -10 216s PrivateWages_3 -9 216s PrivateWages_4 -8 216s PrivateWages_5 -7 216s PrivateWages_6 -6 216s PrivateWages_8 -4 216s PrivateWages_9 -3 216s PrivateWages_10 -2 216s PrivateWages_11 -1 216s PrivateWages_12 0 216s PrivateWages_13 1 216s PrivateWages_14 2 216s PrivateWages_15 3 216s PrivateWages_16 4 216s PrivateWages_17 5 216s PrivateWages_18 6 216s PrivateWages_19 7 216s PrivateWages_20 8 216s PrivateWages_21 9 216s PrivateWages_22 10 216s > nobs 216s [1] 62 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 50 1 0.8 0.37 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 50 1 0.72 0.4 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 51 216s 2 50 1 0.72 0.4 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 50 2 0.42 0.66 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 50 2 0.37 0.69 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 52 216s 2 50 2 0.75 0.69 216s > logLik 216s 'log Lik.' -71.9 (df=13) 216s 'log Lik.' -77.1 (df=13) 216s compare log likelihood value with single-equation OLS 216s [1] "Mean relative difference: 0.000555" 216s > 216s > # 2SLS 216s > summary 216s 216s systemfit results 216s method: 2SLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 60 48 53.4 0.274 0.973 0.992 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 20 16 20.67 1.292 1.14 0.978 0.974 216s Investment 20 16 23.02 1.438 1.20 0.901 0.883 216s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.034 0.309 -0.383 216s Investment 0.309 1.151 0.202 216s PrivateWages -0.383 0.202 0.487 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.284 -0.540 216s Investment 0.284 1.000 0.269 216s PrivateWages -0.540 0.269 1.000 216s 216s 216s 2SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.5093 1.3121 12.58 1.0e-09 *** 216s corpProf 0.0219 0.1159 0.19 0.85 216s corpProfLag 0.1931 0.1071 1.80 0.09 . 216s wages 0.8174 0.0408 20.05 9.2e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.137 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 20.671 MSE: 1.292 Root MSE: 1.137 216s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.974 216s 216s 216s 2SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 17.843 6.850 2.60 0.01915 * 216s corpProf 0.217 0.155 1.40 0.18106 216s corpProfLag 0.542 0.148 3.65 0.00216 ** 216s capitalLag -0.145 0.033 -4.41 0.00044 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.199 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 216s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 216s 216s 216s 2SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.3431 1.1772 1.14 0.27070 216s gnp 0.4438 0.0358 12.39 1.3e-09 *** 216s gnpLag 0.1447 0.0389 3.72 0.00185 ** 216s trend 0.1238 0.0306 4.05 0.00093 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.78 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 216s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.383 -1.0104 -1.3401 216s 3 -0.593 0.2478 0.2378 216s 4 -1.219 1.0621 1.1117 216s 5 -0.130 -1.4104 -0.1954 216s 6 0.354 0.4328 -0.5355 216s 7 NA NA NA 216s 8 1.551 1.0463 -0.7908 216s 9 1.440 0.0674 0.2831 216s 10 -0.286 1.7698 1.1353 216s 11 -0.453 -0.5912 -0.1765 216s 12 -0.994 -0.6318 0.6007 216s 13 -1.300 -0.6983 0.1443 216s 14 0.521 0.9724 0.4826 216s 15 -0.157 -0.1827 0.3016 216s 16 -0.014 0.1167 0.0261 216s 17 1.974 1.6266 -0.8614 216s 18 -0.576 -0.0525 0.9927 216s 19 -0.203 -3.0656 -0.4446 216s 20 1.342 0.1393 -0.3914 216s 21 1.039 -0.1305 -1.1115 216s 22 -1.912 0.2922 0.5312 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.3 0.810 26.8 216s 3 45.6 1.652 29.1 216s 4 50.4 4.138 33.0 216s 5 50.7 4.410 34.1 216s 6 52.2 4.667 35.9 216s 7 NA NA NA 216s 8 54.6 3.154 38.7 216s 9 55.9 2.933 38.9 216s 10 58.1 3.330 40.2 216s 11 55.5 1.591 38.1 216s 12 51.9 -2.768 33.9 216s 13 46.9 -5.502 28.9 216s 14 46.0 -6.072 28.0 216s 15 48.9 -2.817 30.3 216s 16 51.3 -1.417 33.2 216s 17 55.7 0.473 37.7 216s 18 59.3 2.053 40.0 216s 19 57.7 1.166 38.6 216s 20 60.3 1.161 42.0 216s 21 64.0 3.431 46.1 216s 22 71.6 4.608 52.8 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.3 0.473 41.3 43.3 216s 3 45.6 0.573 44.4 46.8 216s 4 50.4 0.366 49.6 51.2 216s 5 50.7 0.423 49.8 51.6 216s 6 52.2 0.426 51.3 53.1 216s 7 NA NA NA NA 216s 8 54.6 0.347 53.9 55.4 216s 9 55.9 0.384 55.0 56.7 216s 10 58.1 0.395 57.2 58.9 216s 11 55.5 0.729 53.9 57.0 216s 12 51.9 0.594 50.6 53.2 216s 13 46.9 0.752 45.3 48.5 216s 14 46.0 0.616 44.7 47.3 216s 15 48.9 0.373 48.1 49.6 216s 16 51.3 0.331 50.6 52.0 216s 17 55.7 0.403 54.9 56.6 216s 18 59.3 0.326 58.6 60.0 216s 19 57.7 0.411 56.8 58.6 216s 20 60.3 0.472 59.3 61.3 216s 21 64.0 0.443 63.0 64.9 216s 22 71.6 0.683 70.2 73.1 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 0.810 0.786 -0.8569 2.48 216s 3 1.652 0.541 0.5056 2.80 216s 4 4.138 0.511 3.0552 5.22 216s 5 4.410 0.421 3.5172 5.30 216s 6 4.667 0.395 3.8294 5.51 216s 7 NA NA NA NA 216s 8 3.154 0.327 2.4602 3.85 216s 9 2.933 0.489 1.8967 3.97 216s 10 3.330 0.537 2.1915 4.47 216s 11 1.591 0.786 -0.0748 3.26 216s 12 -2.768 0.615 -4.0716 -1.46 216s 13 -5.502 0.787 -7.1696 -3.83 216s 14 -6.072 0.842 -7.8568 -4.29 216s 15 -2.817 0.397 -3.6591 -1.98 216s 16 -1.417 0.343 -2.1436 -0.69 216s 17 0.473 0.457 -0.4954 1.44 216s 18 2.053 0.286 1.4471 2.66 216s 19 1.166 0.430 0.2549 2.08 216s 20 1.161 0.515 0.0698 2.25 216s 21 3.431 0.426 2.5282 4.33 216s 22 4.608 0.606 3.3223 5.89 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.328 26.1 27.5 216s 3 29.1 0.340 28.3 29.8 216s 4 33.0 0.360 32.2 33.8 216s 5 34.1 0.258 33.5 34.6 216s 6 35.9 0.266 35.4 36.5 216s 7 NA NA NA NA 216s 8 38.7 0.262 38.1 39.2 216s 9 38.9 0.250 38.4 39.4 216s 10 40.2 0.240 39.7 40.7 216s 11 38.1 0.355 37.3 38.8 216s 12 33.9 0.382 33.1 34.7 216s 13 28.9 0.456 27.9 29.8 216s 14 28.0 0.348 27.3 28.8 216s 15 30.3 0.339 29.6 31.0 216s 16 33.2 0.284 32.6 33.8 216s 17 37.7 0.293 37.0 38.3 216s 18 40.0 0.218 39.5 40.5 216s 19 38.6 0.358 37.9 39.4 216s 20 42.0 0.307 41.3 42.6 216s 21 46.1 0.310 45.5 46.8 216s 22 52.8 0.496 51.7 53.8 216s > model.frame 216s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 216s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 216s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 216s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 216s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 216s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 216s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 216s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 216s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 216s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 216s 10 57.8 21.7 21.1 45.3 5.1 211 41.3 67.0 64.5 216s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 216s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 216s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 216s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 216s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 216s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 216s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 216s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 216s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 216s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 216s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 216s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 216s trend 216s 1 -11 216s 2 -10 216s 3 -9 216s 4 -8 216s 5 -7 216s 6 -6 216s 7 -5 216s 8 -4 216s 9 -3 216s 10 -2 216s 11 -1 216s 12 0 216s 13 1 216s 14 2 216s 15 3 216s 16 4 216s 17 5 216s 18 6 216s 19 7 216s 20 8 216s 21 9 216s 22 10 216s > model.matrix 216s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 216s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 216s [3] "Numeric: lengths (744, 720) differ" 216s > nobs 216s [1] 60 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 48 1 0.95 0.34 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 48 1 1.05 0.31 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 49 216s 2 48 1 1.05 0.3 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 48 2 0.48 0.62 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 48 2 0.53 0.59 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 50 216s 2 48 2 1.06 0.59 216s > logLik 216s 'log Lik.' -72.2 (df=13) 216s 'log Lik.' -79.7 (df=13) 216s > 216s > # SUR 216s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 216s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 216s > summary 216s 216s systemfit results 216s method: SUR 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 62 50 46.2 0.154 0.977 0.993 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 21 17 18.1 1.062 1.031 0.981 0.977 216s Investment 21 17 17.5 1.030 1.015 0.931 0.918 216s PrivateWages 20 16 10.6 0.663 0.814 0.987 0.984 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 0.8562 -0.0129 -0.371 216s Investment -0.0129 0.7548 0.159 216s PrivateWages -0.3706 0.1594 0.487 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.8684 0.0078 -0.442 216s Investment 0.0078 0.7702 0.237 216s PrivateWages -0.4416 0.2366 0.531 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.00000 0.00562 -0.651 216s Investment 0.00562 1.00000 0.372 216s PrivateWages -0.65109 0.37198 1.000 216s 216s 216s SUR estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.0647 1.1729 13.70 1.3e-10 *** 216s corpProf 0.2283 0.0775 2.94 0.0091 ** 216s corpProfLag 0.0723 0.0771 0.94 0.3615 216s wages 0.7930 0.0352 22.51 4.3e-14 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.031 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 18.06 MSE: 1.062 Root MSE: 1.031 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 216s 216s 216s SUR estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 12.3516 4.5762 2.70 0.01520 * 216s corpProf 0.4461 0.0818 5.45 4.3e-05 *** 216s corpProfLag 0.3609 0.0849 4.25 0.00054 *** 216s capitalLag -0.1224 0.0223 -5.47 4.1e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.015 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.514 MSE: 1.03 Root MSE: 1.015 216s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 216s 216s 216s SUR estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.5433 1.1371 1.36 0.19 216s gnp 0.4117 0.0279 14.77 9.6e-11 *** 216s gnpLag 0.1743 0.0317 5.50 4.8e-05 *** 216s trend 0.1550 0.0283 5.49 5.0e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.814 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 10.611 MSE: 0.663 Root MSE: 0.814 216s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.27628 -0.3003 -1.0910 216s 3 -1.35400 -0.1239 0.5795 216s 4 -1.62816 1.1154 1.5172 216s 5 -0.56494 -1.4358 -0.0341 216s 6 -0.06584 0.3581 -0.2772 216s 7 0.83245 1.4526 NA 216s 8 1.28855 0.8290 -0.6896 216s 9 0.96709 -0.5092 0.3445 216s 10 -0.66705 1.2210 1.2429 216s 11 0.41992 0.2497 -0.3602 216s 12 -0.05971 0.0470 0.3068 216s 13 -0.08649 0.3096 -0.2426 216s 14 0.33124 0.3652 0.3591 216s 15 -0.00604 -0.1652 0.2710 216s 16 -0.01478 0.0124 -0.0207 216s 17 1.55472 1.0339 -0.8117 216s 18 -0.41250 0.0255 0.8398 216s 19 0.29322 -2.6293 -0.8283 216s 20 0.91756 -0.5906 -0.4091 216s 21 0.71583 -0.7036 -1.2154 216s 22 -2.26223 -0.5283 0.6207 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.2 0.100 26.6 216s 3 46.4 2.024 28.7 216s 4 50.8 4.085 32.6 216s 5 51.2 4.436 33.9 216s 6 52.7 4.742 35.7 216s 7 54.3 4.147 NA 216s 8 54.9 3.371 38.6 216s 9 56.3 3.509 38.9 216s 10 58.5 3.879 40.1 216s 11 54.6 0.750 38.3 216s 12 51.0 -3.447 34.2 216s 13 45.7 -6.510 29.2 216s 14 46.2 -5.465 28.1 216s 15 48.7 -2.835 30.3 216s 16 51.3 -1.312 33.2 216s 17 56.1 1.066 37.6 216s 18 59.1 1.974 40.2 216s 19 57.2 0.729 39.0 216s 20 60.7 1.891 42.0 216s 21 64.3 4.004 46.2 216s 22 72.0 5.428 52.7 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.2 0.414 41.3 43.0 216s 3 46.4 0.451 45.4 47.3 216s 4 50.8 0.296 50.2 51.4 216s 5 51.2 0.342 50.5 51.9 216s 6 52.7 0.342 52.0 53.4 216s 7 54.3 0.309 53.6 54.9 216s 8 54.9 0.282 54.3 55.5 216s 9 56.3 0.303 55.7 56.9 216s 10 58.5 0.321 57.8 59.1 216s 11 54.6 0.515 53.5 55.6 216s 12 51.0 0.418 50.1 51.8 216s 13 45.7 0.548 44.6 46.8 216s 14 46.2 0.528 45.1 47.2 216s 15 48.7 0.333 48.0 49.4 216s 16 51.3 0.296 50.7 51.9 216s 17 56.1 0.321 55.5 56.8 216s 18 59.1 0.287 58.5 59.7 216s 19 57.2 0.325 56.6 57.9 216s 20 60.7 0.383 59.9 61.5 216s 21 64.3 0.382 63.5 65.1 216s 22 72.0 0.599 70.8 73.2 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 0.100 0.511 -0.926 1.127 216s 3 2.024 0.425 1.170 2.878 216s 4 4.085 0.378 3.325 4.845 216s 5 4.436 0.313 3.806 5.065 216s 6 4.742 0.296 4.147 5.336 216s 7 4.147 0.279 3.586 4.709 216s 8 3.371 0.250 2.868 3.874 216s 9 3.509 0.331 2.845 4.174 216s 10 3.879 0.380 3.116 4.642 216s 11 0.750 0.512 -0.279 1.779 216s 12 -3.447 0.433 -4.316 -2.578 216s 13 -6.510 0.527 -7.568 -5.451 216s 14 -5.465 0.587 -6.645 -4.285 216s 15 -2.835 0.320 -3.477 -2.193 216s 16 -1.312 0.274 -1.863 -0.761 216s 17 1.066 0.296 0.472 1.661 216s 18 1.974 0.208 1.558 2.391 216s 19 0.729 0.265 0.197 1.262 216s 20 1.891 0.311 1.266 2.515 216s 21 4.004 0.283 3.435 4.572 216s 22 5.428 0.393 4.640 6.217 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.6 0.318 26.0 27.2 216s 3 28.7 0.317 28.1 29.4 216s 4 32.6 0.315 32.0 33.2 216s 5 33.9 0.243 33.4 34.4 216s 6 35.7 0.242 35.2 36.2 216s 7 NA NA NA NA 216s 8 38.6 0.247 38.1 39.1 216s 9 38.9 0.236 38.4 39.3 216s 10 40.1 0.227 39.6 40.5 216s 11 38.3 0.306 37.6 38.9 216s 12 34.2 0.312 33.6 34.8 216s 13 29.2 0.376 28.5 30.0 216s 14 28.1 0.337 27.5 28.8 216s 15 30.3 0.328 29.7 31.0 216s 16 33.2 0.274 32.7 33.8 216s 17 37.6 0.266 37.1 38.1 216s 18 40.2 0.213 39.7 40.6 216s 19 39.0 0.310 38.4 39.7 216s 20 42.0 0.282 41.4 42.6 216s 21 46.2 0.300 45.6 46.8 216s 22 52.7 0.451 51.8 53.6 216s > model.frame 216s [1] TRUE 216s > model.matrix 216s [1] TRUE 216s > nobs 216s [1] 62 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 50 1 1.39 0.24 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 50 1 1.7 0.2 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 51 216s 2 50 1 1.7 0.19 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 50 2 0.72 0.49 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 52 216s 2 50 2 0.87 0.42 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 52 216s 2 50 2 1.75 0.42 216s > logLik 216s 'log Lik.' -69.4 (df=18) 216s 'log Lik.' -78.2 (df=18) 216s > 216s > # 3SLS 216s > summary 216s 216s systemfit results 216s method: 3SLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 60 48 62.6 0.265 0.968 0.994 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 20 16 17.8 1.114 1.06 0.981 0.977 216s Investment 20 16 34.3 2.143 1.46 0.853 0.825 216s PrivateWages 20 16 10.5 0.656 0.81 0.987 0.984 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 1.034 0.309 -0.383 216s Investment 0.309 1.151 0.202 216s PrivateWages -0.383 0.202 0.487 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.891 0.304 -0.391 216s Investment 0.304 1.715 0.388 216s PrivateWages -0.391 0.388 0.525 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.246 -0.571 216s Investment 0.246 1.000 0.409 216s PrivateWages -0.571 0.409 1.000 216s 216s 216s 3SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.3668 1.3024 12.57 1.1e-09 *** 216s corpProf 0.1186 0.1073 1.10 0.29 216s corpProfLag 0.1448 0.1008 1.44 0.17 216s wages 0.8006 0.0391 20.47 6.7e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.056 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 17.825 MSE: 1.114 Root MSE: 1.056 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 216s 216s 216s 3SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 24.8872 6.2956 3.95 0.00114 ** 216s corpProf 0.0702 0.1458 0.48 0.63648 216s corpProfLag 0.6688 0.1402 4.77 0.00021 *** 216s capitalLag -0.1786 0.0303 -5.90 2.3e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.464 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 34.295 MSE: 2.143 Root MSE: 1.464 216s Multiple R-Squared: 0.853 Adjusted R-Squared: 0.825 216s 216s 216s 3SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.6387 1.1457 1.43 0.17188 216s gnp 0.4062 0.0324 12.52 1.1e-09 *** 216s gnpLag 0.1784 0.0347 5.14 1.0e-04 *** 216s trend 0.1435 0.0292 4.91 0.00016 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.81 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 10.497 MSE: 0.656 Root MSE: 0.81 216s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.984 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.3538 -1.795 -1.2388 216s 3 -0.9465 0.154 0.4649 216s 4 -1.4189 0.678 1.4344 216s 5 -0.3546 -1.666 -0.1354 216s 6 0.1366 0.251 -0.3452 216s 7 NA NA NA 216s 8 1.4213 1.150 -0.7445 216s 9 1.2173 0.476 0.3001 216s 10 -0.4636 2.200 1.2232 216s 11 -0.0650 -0.962 -0.4104 216s 12 -0.5422 -0.808 0.2495 216s 13 -0.7092 -1.098 -0.3057 216s 14 0.4898 1.542 0.3497 216s 15 -0.0502 -0.155 0.2949 216s 16 0.0272 0.154 0.0214 216s 17 1.8311 1.932 -0.7322 216s 18 -0.4567 -0.180 0.9090 216s 19 0.0650 -3.381 -0.7795 216s 20 1.2135 0.557 -0.2847 216s 21 0.9466 0.167 -1.0812 216s 22 -1.9877 0.784 0.8102 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.3 1.595 26.7 216s 3 45.9 1.746 28.8 216s 4 50.6 4.522 32.7 216s 5 51.0 4.666 34.0 216s 6 52.5 4.849 35.7 216s 7 NA NA NA 216s 8 54.8 3.050 38.6 216s 9 56.1 2.524 38.9 216s 10 58.3 2.900 40.1 216s 11 55.1 1.962 38.3 216s 12 51.4 -2.592 34.3 216s 13 46.3 -5.102 29.3 216s 14 46.0 -6.642 28.2 216s 15 48.8 -2.845 30.3 216s 16 51.3 -1.454 33.2 216s 17 55.9 0.168 37.5 216s 18 59.2 2.180 40.1 216s 19 57.4 1.481 39.0 216s 20 60.4 0.743 41.9 216s 21 64.1 3.133 46.1 216s 22 71.7 4.116 52.5 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.3 0.468 39.8 44.7 216s 3 45.9 0.543 43.4 48.5 216s 4 50.6 0.352 48.3 53.0 216s 5 51.0 0.407 48.6 53.4 216s 6 52.5 0.411 50.1 54.9 216s 7 NA NA NA NA 216s 8 54.8 0.340 52.4 57.1 216s 9 56.1 0.372 53.7 58.5 216s 10 58.3 0.387 55.9 60.6 216s 11 55.1 0.687 52.4 57.7 216s 12 51.4 0.558 48.9 54.0 216s 13 46.3 0.713 43.6 49.0 216s 14 46.0 0.599 43.4 48.6 216s 15 48.8 0.368 46.4 51.1 216s 16 51.3 0.326 48.9 53.6 216s 17 55.9 0.388 53.5 58.3 216s 18 59.2 0.319 56.8 61.5 216s 19 57.4 0.391 55.0 59.8 216s 20 60.4 0.457 57.9 62.8 216s 21 64.1 0.437 61.6 66.5 216s 22 71.7 0.674 69.0 74.3 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 1.595 0.731 -1.8742 5.065 216s 3 1.746 0.533 -1.5566 5.050 216s 4 4.522 0.484 1.2530 7.791 216s 5 4.666 0.406 1.4458 7.887 216s 6 4.849 0.386 1.6390 8.058 216s 7 NA NA NA NA 216s 8 3.050 0.325 -0.1296 6.229 216s 9 2.524 0.467 -0.7334 5.782 216s 10 2.900 0.515 -0.3900 6.190 216s 11 1.962 0.769 -1.5438 5.467 216s 12 -2.592 0.608 -5.9519 0.769 216s 13 -5.102 0.774 -8.6129 -1.592 216s 14 -6.642 0.807 -10.1867 -3.098 216s 15 -2.845 0.395 -6.0599 0.370 216s 16 -1.454 0.341 -4.6409 1.733 216s 17 0.168 0.442 -3.0739 3.410 216s 18 2.180 0.281 -0.9807 5.340 216s 19 1.481 0.414 -1.7440 4.706 216s 20 0.743 0.492 -2.5310 4.017 216s 21 3.133 0.414 -0.0924 6.358 216s 22 4.116 0.583 0.7756 7.457 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.7 0.322 24.9 28.6 216s 3 28.8 0.328 27.0 30.7 216s 4 32.7 0.340 30.8 34.5 216s 5 34.0 0.250 32.2 35.8 216s 6 35.7 0.257 33.9 37.5 216s 7 NA NA NA NA 216s 8 38.6 0.254 36.8 40.4 216s 9 38.9 0.241 37.1 40.7 216s 10 40.1 0.235 38.3 41.9 216s 11 38.3 0.325 36.5 40.2 216s 12 34.3 0.349 32.4 36.1 216s 13 29.3 0.425 27.4 31.2 216s 14 28.2 0.340 26.3 30.0 216s 15 30.3 0.326 28.5 32.2 216s 16 33.2 0.272 31.4 35.0 216s 17 37.5 0.273 35.7 39.3 216s 18 40.1 0.214 38.3 41.9 216s 19 39.0 0.336 37.1 40.8 216s 20 41.9 0.290 40.1 43.7 216s 21 46.1 0.305 44.2 47.9 216s 22 52.5 0.479 50.5 54.5 216s > model.frame 216s [1] TRUE 216s > model.matrix 216s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 216s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 216s [3] "Numeric: lengths (744, 720) differ" 216s > nobs 216s [1] 60 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 48 1 0.22 0.64 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 48 1 0.29 0.59 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 49 216s 2 48 1 0.29 0.59 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 48 2 0.29 0.75 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 48 2 0.38 0.68 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 50 216s 2 48 2 0.77 0.68 216s > logLik 216s 'log Lik.' -71.9 (df=18) 216s 'log Lik.' -82.9 (df=18) 216s > 216s > # I3SLS 216s > summary 216s 216s systemfit results 216s method: iterated 3SLS 216s 216s convergence achieved after 22 iterations 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 60 48 107 0.47 0.946 0.996 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 20 16 18.1 1.13 1.063 0.981 0.977 216s Investment 20 16 76.4 4.77 2.185 0.672 0.610 216s PrivateWages 20 16 12.3 0.77 0.877 0.984 0.982 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 0.905 0.509 -0.437 216s Investment 0.509 3.819 0.709 216s PrivateWages -0.437 0.709 0.616 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.905 0.509 -0.437 216s Investment 0.509 3.819 0.709 216s PrivateWages -0.437 0.709 0.616 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.274 -0.585 216s Investment 0.274 1.000 0.462 216s PrivateWages -0.585 0.462 1.000 216s 216s 216s 3SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.4728 1.2187 13.52 3.6e-10 *** 216s corpProf 0.1642 0.0952 1.73 0.10 216s corpProfLag 0.1552 0.0903 1.72 0.11 216s wages 0.7756 0.0356 21.82 2.5e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.063 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 18.095 MSE: 1.131 Root MSE: 1.063 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 216s 216s 216s 3SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 38.7938 9.7249 3.99 0.00106 ** 216s corpProf -0.2501 0.2337 -1.07 0.30036 216s corpProfLag 0.9129 0.2271 4.02 0.00099 *** 216s capitalLag -0.2409 0.0469 -5.14 9.9e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 2.185 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 76.371 MSE: 4.773 Root MSE: 2.185 216s Multiple R-Squared: 0.672 Adjusted R-Squared: 0.61 216s 216s 216s 3SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 2.4620 1.2228 2.01 0.061 . 216s gnp 0.3776 0.0318 11.88 2.4e-09 *** 216s gnpLag 0.1937 0.0331 5.85 2.5e-05 *** 216s trend 0.1619 0.0300 5.40 5.9e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.877 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 12.318 MSE: 0.77 Root MSE: 0.877 216s Multiple R-Squared: 0.984 Adjusted R-Squared: 0.982 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.4522 -3.4485 -1.2596 216s 3 -1.1470 0.0027 0.5437 216s 4 -1.6147 0.0274 1.6290 216s 5 -0.6117 -2.0392 -0.0707 216s 6 -0.1229 0.0457 -0.1859 216s 7 NA NA NA 216s 8 1.2461 1.4658 -0.6304 216s 9 1.0158 1.4202 0.3924 216s 10 -0.6460 3.2062 1.3671 216s 11 -0.0554 -1.7386 -0.4891 216s 12 -0.3472 -1.3793 0.0179 216s 13 -0.3947 -2.2646 -0.6968 216s 14 0.6536 2.4092 0.1021 216s 15 0.0821 -0.2787 0.1482 216s 16 0.1381 0.1196 -0.0796 216s 17 1.8826 2.5548 -0.6862 216s 18 -0.3415 -0.4009 0.8755 216s 19 0.2296 -4.0454 -0.9839 216s 20 1.3178 1.4481 -0.1989 216s 21 1.0065 0.9087 -0.9681 216s 22 -1.8388 1.9868 1.1734 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.4 3.249 26.8 216s 3 46.1 1.897 28.8 216s 4 50.8 5.173 32.5 216s 5 51.2 5.039 34.0 216s 6 52.7 5.054 35.6 216s 7 NA NA NA 216s 8 55.0 2.734 38.5 216s 9 56.3 1.580 38.8 216s 10 58.4 1.894 39.9 216s 11 55.1 2.739 38.4 216s 12 51.2 -2.021 34.5 216s 13 46.0 -3.935 29.7 216s 14 45.8 -7.509 28.4 216s 15 48.6 -2.721 30.5 216s 16 51.2 -1.420 33.3 216s 17 55.8 -0.455 37.5 216s 18 59.0 2.401 40.1 216s 19 57.3 2.145 39.2 216s 20 60.3 -0.148 41.8 216s 21 64.0 2.391 46.0 216s 22 71.5 2.913 52.1 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.4 0.437 41.5 43.2 216s 3 46.1 0.492 45.2 47.1 216s 4 50.8 0.321 50.2 51.5 216s 5 51.2 0.369 50.5 52.0 216s 6 52.7 0.372 52.0 53.5 216s 7 NA NA NA NA 216s 8 55.0 0.310 54.3 55.6 216s 9 56.3 0.338 55.6 57.0 216s 10 58.4 0.355 57.7 59.2 216s 11 55.1 0.618 53.8 56.3 216s 12 51.2 0.501 50.2 52.3 216s 13 46.0 0.642 44.7 47.3 216s 14 45.8 0.547 44.7 46.9 216s 15 48.6 0.340 47.9 49.3 216s 16 51.2 0.300 50.6 51.8 216s 17 55.8 0.354 55.1 56.5 216s 18 59.0 0.294 58.4 59.6 216s 19 57.3 0.354 56.6 58.0 216s 20 60.3 0.418 59.4 61.1 216s 21 64.0 0.407 63.2 64.8 216s 22 71.5 0.628 70.3 72.8 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 3.249 1.160 0.91672 5.580 216s 3 1.897 0.934 0.02009 3.775 216s 4 5.173 0.803 3.55865 6.787 216s 5 5.039 0.693 3.64486 6.433 216s 6 5.054 0.674 3.69840 6.410 216s 7 NA NA NA NA 216s 8 2.734 0.584 1.56002 3.908 216s 9 1.580 0.783 0.00466 3.155 216s 10 1.894 0.868 0.14846 3.639 216s 11 2.739 1.321 0.08241 5.395 216s 12 -2.021 1.064 -4.16036 0.119 216s 13 -3.935 1.349 -6.64712 -1.224 216s 14 -7.509 1.360 -10.24349 -4.775 216s 15 -2.721 0.712 -4.15288 -1.290 216s 16 -1.420 0.614 -2.65412 -0.185 216s 17 -0.455 0.751 -1.96433 1.055 216s 18 2.401 0.498 1.39939 3.402 216s 19 2.145 0.698 0.74152 3.549 216s 20 -0.148 0.816 -1.78957 1.493 216s 21 2.391 0.713 0.95855 3.824 216s 22 2.913 0.984 0.93419 4.892 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.347 26.1 27.5 216s 3 28.8 0.348 28.1 29.5 216s 4 32.5 0.354 31.8 33.2 216s 5 34.0 0.263 33.4 34.5 216s 6 35.6 0.274 35.0 36.1 216s 7 NA NA NA NA 216s 8 38.5 0.268 38.0 39.1 216s 9 38.8 0.256 38.3 39.3 216s 10 39.9 0.254 39.4 40.4 216s 11 38.4 0.323 37.7 39.0 216s 12 34.5 0.347 33.8 35.2 216s 13 29.7 0.435 28.8 30.6 216s 14 28.4 0.366 27.7 29.1 216s 15 30.5 0.341 29.8 31.1 216s 16 33.3 0.285 32.7 33.9 216s 17 37.5 0.275 36.9 38.0 216s 18 40.1 0.233 39.7 40.6 216s 19 39.2 0.346 38.5 39.9 216s 20 41.8 0.298 41.2 42.4 216s 21 46.0 0.329 45.3 46.6 216s 22 52.1 0.510 51.1 53.2 216s > model.frame 216s [1] TRUE 216s > model.matrix 216s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0323 >" 216s [2] "Attributes: < Component “dimnames”: Component 1: 55 string mismatches >" 216s [3] "Numeric: lengths (744, 720) differ" 216s > nobs 216s [1] 60 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 48 1 0.4 0.53 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 48 1 0.5 0.49 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 49 216s 2 48 1 0.5 0.48 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 48 2 0.66 0.52 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 48 2 0.83 0.44 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 50 216s 2 48 2 1.66 0.44 216s > logLik 216s 'log Lik.' -77.6 (df=18) 216s 'log Lik.' -92.7 (df=18) 216s > 216s > # OLS 216s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == :> summary 216s 216s systemfit results 216s method: OLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 61 49 44.5 0.382 0.977 0.99 216s 216s N DF SSR MSE RMSE R2 216s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 216s Adj R2 216s Consumption 20 16 17.48 1.093 1.04 0.981 0.978 216s Investment 21 17 17.32 1.019 1.01 0.931 0.919 216s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.124 0.034 -0.442 216s Investment 0.034 0.928 0.130 216s PrivateWages -0.442 0.130 0.563 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.0000 0.0266 -0.563 216s Investment 0.0266 1.0000 0.169 216s PrivateWages -0.5630 0.1689 1.000 216s 216s 216s OLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.1357 1.3571 11.89 2.4e-09 *** 216s corpProf 0.1994 0.0949 2.10 0.052 . 216s corpProfLag 0.0969 0.0944 1.03 0.320 216s wages 0.7940 0.0415 19.16 1.9e-12 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.045 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 17.481 MSE: 1.093 Root MSE: 1.045 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.978 216s 216s 216s OLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 10.1258 5.2164 1.94 0.06901 . 216s corpProf 0.4796 0.0927 5.17 7.6e-05 *** 216s corpProfLag 0.3330 0.0963 3.46 0.00299 ** 216s capitalLag -0.1118 0.0255 -4.38 0.00041 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.009 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.323 MSE: 1.019 Root MSE: 1.009 216s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.919 216s 216s 216s OLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.3550 1.2591 1.08 0.2978 216s gnp 0.4417 0.0319 13.86 2.5e-10 *** 216s gnpLag 0.1466 0.0366 4.01 0.0010 ** 216s trend 0.1244 0.0323 3.85 0.0014 ** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.78 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 216s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 216s 216s compare coef with single-equation OLS 216s [1] TRUE 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.3304 -0.0668 -1.3389 216s 3 -1.2748 -0.0476 0.2462 216s 4 -1.6213 1.2467 1.1255 216s 5 -0.5661 -1.3512 -0.1959 216s 6 -0.0730 0.4154 -0.5284 216s 7 0.7915 1.4923 NA 216s 8 1.2648 0.7889 -0.7909 216s 9 0.9746 -0.6317 0.2819 216s 10 NA 1.0830 1.1384 216s 11 0.2225 0.2791 -0.1904 216s 12 -0.2256 0.0369 0.5813 216s 13 -0.2711 0.3659 0.1206 216s 14 0.3765 0.2237 0.4773 216s 15 -0.0349 -0.1728 0.3035 216s 16 -0.0243 0.0101 0.0284 216s 17 1.6023 0.9719 -0.8517 216s 18 -0.4658 0.0516 0.9908 216s 19 0.1914 -2.5656 -0.4597 216s 20 0.9683 -0.6866 -0.3819 216s 21 0.7325 -0.7807 -1.1062 216s 22 -2.2370 -0.6623 0.5501 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.2 -0.133 26.8 216s 3 46.3 1.948 29.1 216s 4 50.8 3.953 33.0 216s 5 51.2 4.351 34.1 216s 6 52.7 4.685 35.9 216s 7 54.3 4.108 NA 216s 8 54.9 3.411 38.7 216s 9 56.3 3.632 38.9 216s 10 NA 4.017 40.2 216s 11 54.8 0.721 38.1 216s 12 51.1 -3.437 33.9 216s 13 45.9 -6.566 28.9 216s 14 46.1 -5.324 28.0 216s 15 48.7 -2.827 30.3 216s 16 51.3 -1.310 33.2 216s 17 56.1 1.128 37.7 216s 18 59.2 1.948 40.0 216s 19 57.3 0.666 38.7 216s 20 60.6 1.987 42.0 216s 21 64.3 4.081 46.1 216s 22 71.9 5.562 52.7 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.2 0.478 39.9 44.5 216s 3 46.3 0.537 43.9 48.6 216s 4 50.8 0.364 48.6 53.0 216s 5 51.2 0.427 48.9 53.4 216s 6 52.7 0.433 50.4 54.9 216s 7 54.3 0.394 52.1 56.6 216s 8 54.9 0.360 52.7 57.2 216s 9 56.3 0.387 54.1 58.6 216s 10 NA NA NA NA 216s 11 54.8 0.635 52.3 57.2 216s 12 51.1 0.501 48.8 53.5 216s 13 45.9 0.656 43.4 48.4 216s 14 46.1 0.629 43.7 48.6 216s 15 48.7 0.389 46.5 51.0 216s 16 51.3 0.345 49.1 53.5 216s 17 56.1 0.379 53.9 58.3 216s 18 59.2 0.336 57.0 61.4 216s 19 57.3 0.385 55.1 59.5 216s 20 60.6 0.450 58.3 62.9 216s 21 64.3 0.448 62.0 66.6 216s 22 71.9 0.697 69.4 74.5 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 -0.133 0.579 -2.472 2.206 216s 3 1.948 0.476 -0.295 4.190 216s 4 3.953 0.428 1.750 6.157 216s 5 4.351 0.354 2.202 6.501 216s 6 4.685 0.333 2.548 6.821 216s 7 4.108 0.314 1.983 6.232 216s 8 3.411 0.279 1.306 5.516 216s 9 3.632 0.371 1.470 5.793 216s 10 4.017 0.426 1.815 6.219 216s 11 0.721 0.574 -1.613 3.054 216s 12 -3.437 0.484 -5.686 -1.188 216s 13 -6.566 0.588 -8.913 -4.219 216s 14 -5.324 0.662 -7.750 -2.898 216s 15 -2.827 0.356 -4.978 -0.676 216s 16 -1.310 0.305 -3.429 0.809 216s 17 1.128 0.332 -1.007 3.263 216s 18 1.948 0.232 -0.133 4.030 216s 19 0.666 0.298 -1.449 2.781 216s 20 1.987 0.350 -0.160 4.133 216s 21 4.081 0.317 1.955 6.207 216s 22 5.562 0.440 3.349 7.775 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.352 25.1 28.6 216s 3 29.1 0.355 27.3 30.8 216s 4 33.0 0.358 31.2 34.7 216s 5 34.1 0.277 32.4 35.8 216s 6 35.9 0.276 34.3 37.6 216s 7 NA NA NA NA 216s 8 38.7 0.282 37.0 40.4 216s 9 38.9 0.268 37.3 40.6 216s 10 40.2 0.255 38.5 41.8 216s 11 38.1 0.351 36.4 39.8 216s 12 33.9 0.355 32.2 35.6 216s 13 28.9 0.421 27.1 30.7 216s 14 28.0 0.370 26.3 29.8 216s 15 30.3 0.364 28.6 32.0 216s 16 33.2 0.304 31.5 34.9 216s 17 37.7 0.298 36.0 39.3 216s 18 40.0 0.233 38.4 41.6 216s 19 38.7 0.349 36.9 40.4 216s 20 42.0 0.314 40.3 43.7 216s 21 46.1 0.328 44.4 47.8 216s 22 52.7 0.494 50.9 54.6 216s > model.frame 216s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 216s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 216s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 216s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 216s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 216s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 216s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 216s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 216s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 216s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 216s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 216s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 216s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 216s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 216s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 216s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 216s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 216s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 216s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 216s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 216s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 216s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 216s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 216s trend 216s 1 -11 216s 2 -10 216s 3 -9 216s 4 -8 216s 5 -7 216s 6 -6 216s 7 -5 216s 8 -4 216s 9 -3 216s 10 -2 216s 11 -1 216s 12 0 216s 13 1 216s 14 2 216s 15 3 216s 16 4 216s 17 5 216s 18 6 216s 19 7 216s 20 8 216s 21 9 216s 22 10 216s > model.matrix 216s Consumption_(Intercept) Consumption_corpProf 216s Consumption_2 1 12.4 216s Consumption_3 1 16.9 216s Consumption_4 1 18.4 216s Consumption_5 1 19.4 216s Consumption_6 1 20.1 216s Consumption_7 1 19.6 216s Consumption_8 1 19.8 216s Consumption_9 1 21.1 216s Consumption_11 1 15.6 216s Consumption_12 1 11.4 216s Consumption_13 1 7.0 216s Consumption_14 1 11.2 216s Consumption_15 1 12.3 216s Consumption_16 1 14.0 216s Consumption_17 1 17.6 216s Consumption_18 1 17.3 216s Consumption_19 1 15.3 216s Consumption_20 1 19.0 216s Consumption_21 1 21.1 216s Consumption_22 1 23.5 216s Investment_2 0 0.0 216s Investment_3 0 0.0 216s Investment_4 0 0.0 216s Investment_5 0 0.0 216s Investment_6 0 0.0 216s Investment_7 0 0.0 216s Investment_8 0 0.0 216s Investment_9 0 0.0 216s Investment_10 0 0.0 216s Investment_11 0 0.0 216s Investment_12 0 0.0 216s Investment_13 0 0.0 216s Investment_14 0 0.0 216s Investment_15 0 0.0 216s Investment_16 0 0.0 216s Investment_17 0 0.0 216s Investment_18 0 0.0 216s Investment_19 0 0.0 216s Investment_20 0 0.0 216s Investment_21 0 0.0 216s Investment_22 0 0.0 216s PrivateWages_2 0 0.0 216s PrivateWages_3 0 0.0 216s PrivateWages_4 0 0.0 216s PrivateWages_5 0 0.0 216s PrivateWages_6 0 0.0 216s PrivateWages_8 0 0.0 216s PrivateWages_9 0 0.0 216s PrivateWages_10 0 0.0 216s PrivateWages_11 0 0.0 216s PrivateWages_12 0 0.0 216s PrivateWages_13 0 0.0 216s PrivateWages_14 0 0.0 216s PrivateWages_15 0 0.0 216s PrivateWages_16 0 0.0 216s PrivateWages_17 0 0.0 216s PrivateWages_18 0 0.0 216s PrivateWages_19 0 0.0 216s PrivateWages_20 0 0.0 216s PrivateWages_21 0 0.0 216s PrivateWages_22 0 0.0 216s Consumption_corpProfLag Consumption_wages 216s Consumption_2 12.7 28.2 216s Consumption_3 12.4 32.2 216s Consumption_4 16.9 37.0 216s Consumption_5 18.4 37.0 216s Consumption_6 19.4 38.6 216s Consumption_7 20.1 40.7 216s Consumption_8 19.6 41.5 216s Consumption_9 19.8 42.9 216s Consumption_11 21.7 42.1 216s Consumption_12 15.6 39.3 216s Consumption_13 11.4 34.3 216s Consumption_14 7.0 34.1 216s Consumption_15 11.2 36.6 216s Consumption_16 12.3 39.3 216s Consumption_17 14.0 44.2 216s Consumption_18 17.6 47.7 216s Consumption_19 17.3 45.9 216s Consumption_20 15.3 49.4 216s Consumption_21 19.0 53.0 216s Consumption_22 21.1 61.8 216s Investment_2 0.0 0.0 216s Investment_3 0.0 0.0 216s Investment_4 0.0 0.0 216s Investment_5 0.0 0.0 216s Investment_6 0.0 0.0 216s Investment_7 0.0 0.0 216s Investment_8 0.0 0.0 216s Investment_9 0.0 0.0 216s Investment_10 0.0 0.0 216s Investment_11 0.0 0.0 216s Investment_12 0.0 0.0 216s Investment_13 0.0 0.0 216s Investment_14 0.0 0.0 216s Investment_15 0.0 0.0 216s Investment_16 0.0 0.0 216s Investment_17 0.0 0.0 216s Investment_18 0.0 0.0 216s Investment_19 0.0 0.0 216s Investment_20 0.0 0.0 216s Investment_21 0.0 0.0 216s Investment_22 0.0 0.0 216s PrivateWages_2 0.0 0.0 216s PrivateWages_3 0.0 0.0 216s PrivateWages_4 0.0 0.0 216s PrivateWages_5 0.0 0.0 216s PrivateWages_6 0.0 0.0 216s PrivateWages_8 0.0 0.0 216s PrivateWages_9 0.0 0.0 216s PrivateWages_10 0.0 0.0 216s PrivateWages_11 0.0 0.0 216s PrivateWages_12 0.0 0.0 216s PrivateWages_13 0.0 0.0 216s PrivateWages_14 0.0 0.0 216s PrivateWages_15 0.0 0.0 216s PrivateWages_16 0.0 0.0 216s PrivateWages_17 0.0 0.0 216s PrivateWages_18 0.0 0.0 216s PrivateWages_19 0.0 0.0 216s PrivateWages_20 0.0 0.0 216s PrivateWages_21 0.0 0.0 216s PrivateWages_22 0.0 0.0 216s Investment_(Intercept) Investment_corpProf 216s Consumption_2 0 0.0 216s Consumption_3 0 0.0 216s Consumption_4 0 0.0 216s Consumption_5 0 0.0 216s Consumption_6 0 0.0 216s Consumption_7 0 0.0 216s Consumption_8 0 0.0 216s Consumption_9 0 0.0 216s Consumption_11 0 0.0 216s Consumption_12 0 0.0 216s Consumption_13 0 0.0 216s Consumption_14 0 0.0 216s Consumption_15 0 0.0 216s Consumption_16 0 0.0 216s Consumption_17 0 0.0 216s Consumption_18 0 0.0 216s Consumption_19 0 0.0 216s Consumption_20 0 0.0 216s Consumption_21 0 0.0 216s Consumption_22 0 0.0 216s Investment_2 1 12.4 216s Investment_3 1 16.9 216s Investment_4 1 18.4 216s Investment_5 1 19.4 216s Investment_6 1 20.1 216s Investment_7 1 19.6 216s Investment_8 1 19.8 216s Investment_9 1 21.1 216s Investment_10 1 21.7 216s Investment_11 1 15.6 216s Investment_12 1 11.4 216s Investment_13 1 7.0 216s Investment_14 1 11.2 216s Investment_15 1 12.3 216s Investment_16 1 14.0 216s Investment_17 1 17.6 216s Investment_18 1 17.3 216s Investment_19 1 15.3 216s Investment_20 1 19.0 216s Investment_21 1 21.1 216s Investment_22 1 23.5 216s PrivateWages_2 0 0.0 216s PrivateWages_3 0 0.0 216s PrivateWages_4 0 0.0 216s PrivateWages_5 0 0.0 216s PrivateWages_6 0 0.0 216s PrivateWages_8 0 0.0 216s PrivateWages_9 0 0.0 216s PrivateWages_10 0 0.0 216s PrivateWages_11 0 0.0 216s PrivateWages_12 0 0.0 216s PrivateWages_13 0 0.0 216s PrivateWages_14 0 0.0 216s PrivateWages_15 0 0.0 216s PrivateWages_16 0 0.0 216s PrivateWages_17 0 0.0 216s PrivateWages_18 0 0.0 216s PrivateWages_19 0 0.0 216s PrivateWages_20 0 0.0 216s PrivateWages_21 0 0.0 216s PrivateWages_22 0 0.0 216s Investment_corpProfLag Investment_capitalLag 216s Consumption_2 0.0 0 216s Consumption_3 0.0 0 216s Consumption_4 0.0 0 216s Consumption_5 0.0 0 216s Consumption_6 0.0 0 216s Consumption_7 0.0 0 216s Consumption_8 0.0 0 216s Consumption_9 0.0 0 216s Consumption_11 0.0 0 216s Consumption_12 0.0 0 216s Consumption_13 0.0 0 216s Consumption_14 0.0 0 216s Consumption_15 0.0 0 216s Consumption_16 0.0 0 216s Consumption_17 0.0 0 216s Consumption_18 0.0 0 216s Consumption_19 0.0 0 216s Consumption_20 0.0 0 216s Consumption_21 0.0 0 216s Consumption_22 0.0 0 216s Investment_2 12.7 183 216s Investment_3 12.4 183 216s Investment_4 16.9 184 216s Investment_5 18.4 190 216s Investment_6 19.4 193 216s Investment_7 20.1 198 216s Investment_8 19.6 203 216s Investment_9 19.8 208 216s Investment_10 21.1 211 216s Investment_11 21.7 216 216s Investment_12 15.6 217 216s Investment_13 11.4 213 216s Investment_14 7.0 207 216s Investment_15 11.2 202 216s Investment_16 12.3 199 216s Investment_17 14.0 198 216s Investment_18 17.6 200 216s Investment_19 17.3 202 216s Investment_20 15.3 200 216s Investment_21 19.0 201 216s Investment_22 21.1 204 216s PrivateWages_2 0.0 0 216s PrivateWages_3 0.0 0 216s PrivateWages_4 0.0 0 216s PrivateWages_5 0.0 0 216s PrivateWages_6 0.0 0 216s PrivateWages_8 0.0 0 216s PrivateWages_9 0.0 0 216s PrivateWages_10 0.0 0 216s PrivateWages_11 0.0 0 216s PrivateWages_12 0.0 0 216s PrivateWages_13 0.0 0 216s PrivateWages_14 0.0 0 216s PrivateWages_15 0.0 0 216s PrivateWages_16 0.0 0 216s PrivateWages_17 0.0 0 216s PrivateWages_18 0.0 0 216s PrivateWages_19 0.0 0 216s PrivateWages_20 0.0 0 216s PrivateWages_21 0.0 0 216s PrivateWages_22 0.0 0 216s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 216s Consumption_2 0 0.0 0.0 216s Consumption_3 0 0.0 0.0 216s Consumption_4 0 0.0 0.0 216s Consumption_5 0 0.0 0.0 216s Consumption_6 0 0.0 0.0 216s Consumption_7 0 0.0 0.0 216s Consumption_8 0 0.0 0.0 216s Consumption_9 0 0.0 0.0 216s Consumption_11 0 0.0 0.0 216s Consumption_12 0 0.0 0.0 216s Consumption_13 0 0.0 0.0 216s Consumption_14 0 0.0 0.0 216s Consumption_15 0 0.0 0.0 216s Consumption_16 0 0.0 0.0 216s Consumption_17 0 0.0 0.0 216s Consumption_18 0 0.0 0.0 216s Consumption_19 0 0.0 0.0 216s Consumption_20 0 0.0 0.0 216s Consumption_21 0 0.0 0.0 216s Consumption_22 0 0.0 0.0 216s Investment_2 0 0.0 0.0 216s Investment_3 0 0.0 0.0 216s Investment_4 0 0.0 0.0 216s Investment_5 0 0.0 0.0 216s Investment_6 0 0.0 0.0 216s Investment_7 0 0.0 0.0 216s Investment_8 0 0.0 0.0 216s Investment_9 0 0.0 0.0 216s Investment_10 0 0.0 0.0 216s Investment_11 0 0.0 0.0 216s Investment_12 0 0.0 0.0 216s Investment_13 0 0.0 0.0 216s Investment_14 0 0.0 0.0 216s Investment_15 0 0.0 0.0 216s Investment_16 0 0.0 0.0 216s Investment_17 0 0.0 0.0 216s Investment_18 0 0.0 0.0 216s Investment_19 0 0.0 0.0 216s Investment_20 0 0.0 0.0 216s Investment_21 0 0.0 0.0 216s Investment_22 0 0.0 0.0 216s PrivateWages_2 1 45.6 44.9 216s PrivateWages_3 1 50.1 45.6 216s PrivateWages_4 1 57.2 50.1 216s PrivateWages_5 1 57.1 57.2 216s PrivateWages_6 1 61.0 57.1 216s PrivateWages_8 1 64.4 64.0 216s PrivateWages_9 1 64.5 64.4 216s PrivateWages_10 1 67.0 64.5 216s PrivateWages_11 1 61.2 67.0 216s PrivateWages_12 1 53.4 61.2 216s PrivateWages_13 1 44.3 53.4 216s PrivateWages_14 1 45.1 44.3 216s PrivateWages_15 1 49.7 45.1 216s PrivateWages_16 1 54.4 49.7 216s PrivateWages_17 1 62.7 54.4 216s PrivateWages_18 1 65.0 62.7 216s PrivateWages_19 1 60.9 65.0 216s PrivateWages_20 1 69.5 60.9 216s PrivateWages_21 1 75.7 69.5 216s PrivateWages_22 1 88.4 75.7 216s PrivateWages_trend 216s Consumption_2 0 216s Consumption_3 0 216s Consumption_4 0 216s Consumption_5 0 216s Consumption_6 0 216s Consumption_7 0 216s Consumption_8 0 216s Consumption_9 0 216s Consumption_11 0 216s Consumption_12 0 216s Consumption_13 0 216s Consumption_14 0 216s Consumption_15 0 216s Consumption_16 0 216s Consumption_17 0 216s Consumption_18 0 216s Consumption_19 0 216s Consumption_20 0 216s Consumption_21 0 216s Consumption_22 0 216s Investment_2 0 216s Investment_3 0 216s Investment_4 0 216s Investment_5 0 216s Investment_6 0 216s Investment_7 0 216s Investment_8 0 216s Investment_9 0 216s Investment_10 0 216s Investment_11 0 216s Investment_12 0 216s Investment_13 0 216s Investment_14 0 216s Investment_15 0 216s Investment_16 0 216s Investment_17 0 216s Investment_18 0 216s Investment_19 0 216s Investment_20 0 216s Investment_21 0 216s Investment_22 0 216s PrivateWages_2 -10 216s PrivateWages_3 -9 216s PrivateWages_4 -8 216s PrivateWages_5 -7 216s PrivateWages_6 -6 216s PrivateWages_8 -4 216s PrivateWages_9 -3 216s PrivateWages_10 -2 216s PrivateWages_11 -1 216s PrivateWages_12 0 216s PrivateWages_13 1 216s PrivateWages_14 2 216s PrivateWages_15 3 216s PrivateWages_16 4 216s PrivateWages_17 5 216s PrivateWages_18 6 216s PrivateWages_19 7 216s PrivateWages_20 8 216s PrivateWages_21 9 216s PrivateWages_22 10 216s > nobs 216s [1] 61 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 49 1 0.87 0.35 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 49 1 0.8 0.38 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 50 216s 2 49 1 0.8 0.37 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 49 2 0.48 0.62 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 49 2 0.43 0.65 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 51 216s 2 49 2 0.87 0.65 216s > logLik 216s 'log Lik.' -71.7 (df=13) 216s 'log Lik.' -76.1 (df=13) 216s compare log likelihood value with single-equation OLS 216s [1] "Mean relative difference: 0.00159" 216s > 216s > # 2SLS 216s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 216s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 216s > summary 216s 216s systemfit results 216s method: 2SLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 59 47 53.2 0.251 0.973 0.991 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 19 15 20.49 1.366 1.17 0.978 0.973 216s Investment 20 16 23.02 1.438 1.20 0.901 0.883 216s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.079 0.354 -0.383 216s Investment 0.354 1.047 0.107 216s PrivateWages -0.383 0.107 0.445 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.335 -0.556 216s Investment 0.335 1.000 0.149 216s PrivateWages -0.556 0.149 1.000 216s 216s 216s 2SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.4657 1.3505 12.19 3.5e-09 *** 216s corpProf 0.0243 0.1180 0.21 0.839 216s corpProfLag 0.1981 0.1087 1.82 0.088 . 216s wages 0.8159 0.0420 19.45 4.7e-12 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.169 on 15 degrees of freedom 216s Number of observations: 19 Degrees of Freedom: 15 216s SSR: 20.493 MSE: 1.366 Root MSE: 1.169 216s Multiple R-Squared: 0.978 Adjusted R-Squared: 0.973 216s 216s 216s 2SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 17.8425 6.5319 2.73 0.01478 * 216s corpProf 0.2167 0.1478 1.47 0.16189 216s corpProfLag 0.5416 0.1415 3.83 0.00149 ** 216s capitalLag -0.1455 0.0314 -4.63 0.00028 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.199 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 23.016 MSE: 1.438 Root MSE: 1.199 216s Multiple R-Squared: 0.901 Adjusted R-Squared: 0.883 216s 216s 216s 2SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.3431 1.1250 1.19 0.24995 216s gnp 0.4438 0.0342 12.97 6.6e-10 *** 216s gnpLag 0.1447 0.0371 3.90 0.00128 ** 216s trend 0.1238 0.0292 4.24 0.00063 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.78 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 216s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.39161 -1.0104 -1.3401 216s 3 -0.60524 0.2478 0.2378 216s 4 -1.24952 1.0621 1.1117 216s 5 -0.17101 -1.4104 -0.1954 216s 6 0.30841 0.4328 -0.5355 216s 7 NA NA NA 216s 8 1.50999 1.0463 -0.7908 216s 9 1.39649 0.0674 0.2831 216s 10 NA 1.7698 1.1353 216s 11 -0.49339 -0.5912 -0.1765 216s 12 -0.99824 -0.6318 0.6007 216s 13 -1.27965 -0.6983 0.1443 216s 14 0.55302 0.9724 0.4826 216s 15 -0.14553 -0.1827 0.3016 216s 16 -0.00773 0.1167 0.0261 216s 17 1.97001 1.6266 -0.8614 216s 18 -0.59152 -0.0525 0.9927 216s 19 -0.21481 -3.0656 -0.4446 216s 20 1.33575 0.1393 -0.3914 216s 21 1.01443 -0.1305 -1.1115 216s 22 -1.93986 0.2922 0.5312 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.3 0.810 26.8 216s 3 45.6 1.652 29.1 216s 4 50.4 4.138 33.0 216s 5 50.8 4.410 34.1 216s 6 52.3 4.667 35.9 216s 7 NA NA NA 216s 8 54.7 3.154 38.7 216s 9 55.9 2.933 38.9 216s 10 NA 3.330 40.2 216s 11 55.5 1.591 38.1 216s 12 51.9 -2.768 33.9 216s 13 46.9 -5.502 28.9 216s 14 45.9 -6.072 28.0 216s 15 48.8 -2.817 30.3 216s 16 51.3 -1.417 33.2 216s 17 55.7 0.473 37.7 216s 18 59.3 2.053 40.0 216s 19 57.7 1.166 38.6 216s 20 60.3 1.161 42.0 216s 21 64.0 3.431 46.1 216s 22 71.6 4.608 52.8 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.3 0.483 41.3 43.3 216s 3 45.6 0.586 44.4 46.9 216s 4 50.4 0.390 49.6 51.3 216s 5 50.8 0.456 49.8 51.7 216s 6 52.3 0.463 51.3 53.3 216s 7 NA NA NA NA 216s 8 54.7 0.382 53.9 55.5 216s 9 55.9 0.422 55.0 56.8 216s 10 NA NA NA NA 216s 11 55.5 0.742 53.9 57.1 216s 12 51.9 0.600 50.6 53.2 216s 13 46.9 0.770 45.2 48.5 216s 14 45.9 0.635 44.6 47.3 216s 15 48.8 0.383 48.0 49.7 216s 16 51.3 0.339 50.6 52.0 216s 17 55.7 0.410 54.9 56.6 216s 18 59.3 0.336 58.6 60.0 216s 19 57.7 0.418 56.8 58.6 216s 20 60.3 0.481 59.2 61.3 216s 21 64.0 0.462 63.0 65.0 216s 22 71.6 0.706 70.1 73.1 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 0.810 0.750 -0.77956 2.400 216s 3 1.652 0.516 0.55883 2.746 216s 4 4.138 0.487 3.10541 5.170 216s 5 4.410 0.402 3.55860 5.262 216s 6 4.667 0.377 3.86830 5.466 216s 7 NA NA NA NA 216s 8 3.154 0.312 2.49238 3.815 216s 9 2.933 0.466 1.94478 3.920 216s 10 3.330 0.512 2.24435 4.416 216s 11 1.591 0.749 0.00249 3.180 216s 12 -2.768 0.586 -4.01111 -1.525 216s 13 -5.502 0.750 -7.09222 -3.911 216s 14 -6.072 0.803 -7.77404 -4.371 216s 15 -2.817 0.379 -3.62002 -2.015 216s 16 -1.417 0.327 -2.10985 -0.723 216s 17 0.473 0.436 -0.45046 1.397 216s 18 2.053 0.272 1.47523 2.630 216s 19 1.166 0.410 0.29710 2.034 216s 20 1.161 0.491 0.12044 2.201 216s 21 3.431 0.406 2.57004 4.291 216s 22 4.608 0.578 3.38197 5.834 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.313 26.2 27.5 216s 3 29.1 0.325 28.4 29.8 216s 4 33.0 0.344 32.3 33.7 216s 5 34.1 0.246 33.6 34.6 216s 6 35.9 0.254 35.4 36.5 216s 7 NA NA NA NA 216s 8 38.7 0.251 38.2 39.2 216s 9 38.9 0.239 38.4 39.4 216s 10 40.2 0.229 39.7 40.7 216s 11 38.1 0.339 37.4 38.8 216s 12 33.9 0.365 33.1 34.7 216s 13 28.9 0.436 27.9 29.8 216s 14 28.0 0.333 27.3 28.7 216s 15 30.3 0.324 29.6 31.0 216s 16 33.2 0.271 32.6 33.7 216s 17 37.7 0.280 37.1 38.3 216s 18 40.0 0.208 39.6 40.4 216s 19 38.6 0.342 37.9 39.4 216s 20 42.0 0.293 41.4 42.6 216s 21 46.1 0.296 45.5 46.7 216s 22 52.8 0.474 51.8 53.8 216s > model.frame 216s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 216s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 216s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 216s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 216s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 216s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 216s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 216s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 216s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 216s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 216s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 216s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 216s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 216s 13 45.6 7.0 11.4 34.3 -6.2 213 29.0 44.3 53.4 216s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 216s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 216s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 216s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 216s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 216s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 216s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 216s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 216s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 216s trend 216s 1 -11 216s 2 -10 216s 3 -9 216s 4 -8 216s 5 -7 216s 6 -6 216s 7 -5 216s 8 -4 216s 9 -3 216s 10 -2 216s 11 -1 216s 12 0 216s 13 1 216s 14 2 216s 15 3 216s 16 4 216s 17 5 216s 18 6 216s 19 7 216s 20 8 216s 21 9 216s 22 10 216s > model.matrix 216s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 216s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 216s [3] "Numeric: lengths (732, 708) differ" 216s > nobs 216s [1] 59 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 48 216s 2 47 1 0.87 0.36 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 48 216s 2 47 1 0.98 0.33 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 48 216s 2 47 1 0.98 0.32 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 47 2 0.43 0.65 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 49 216s 2 47 2 0.49 0.61 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 49 216s 2 47 2 0.98 0.61 216s > logLik 216s 'log Lik.' -71.5 (df=13) 216s 'log Lik.' -78.7 (df=13) 216s > 216s > # SUR 216s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 216s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 216s > summary 216s 216s systemfit results 216s method: SUR 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 61 49 45.4 0.151 0.977 0.992 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 20 16 17.6 1.102 1.050 0.981 0.977 216s Investment 21 17 17.5 1.029 1.015 0.931 0.918 216s PrivateWages 20 16 10.3 0.643 0.802 0.987 0.985 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 0.8871 0.0268 -0.349 216s Investment 0.0268 0.7328 0.103 216s PrivateWages -0.3492 0.1029 0.444 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.8852 0.0508 -0.406 216s Investment 0.0508 0.7313 0.161 216s PrivateWages -0.4063 0.1609 0.467 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.065 -0.635 216s Investment 0.065 1.000 0.262 216s PrivateWages -0.635 0.262 1.000 216s 216s 216s SUR estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.0876 1.2010 13.39 4.1e-10 *** 216s corpProf 0.2173 0.0799 2.72 0.015 * 216s corpProfLag 0.0694 0.0793 0.88 0.394 216s wages 0.7975 0.0360 22.15 2.0e-13 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.05 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 17.63 MSE: 1.102 Root MSE: 1.05 216s Multiple R-Squared: 0.981 Adjusted R-Squared: 0.977 216s 216s 216s SUR estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 12.3518 4.5615 2.71 0.01493 * 216s corpProf 0.4511 0.0814 5.54 3.6e-05 *** 216s corpProfLag 0.3570 0.0846 4.22 0.00058 *** 216s capitalLag -0.1225 0.0223 -5.49 4.0e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.015 on 17 degrees of freedom 216s Number of observations: 21 Degrees of Freedom: 17 216s SSR: 17.5 MSE: 1.029 Root MSE: 1.015 216s Multiple R-Squared: 0.931 Adjusted R-Squared: 0.918 216s 216s 216s SUR estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.3964 1.0825 1.29 0.22 216s gnp 0.4177 0.0269 15.55 4.4e-11 *** 216s gnpLag 0.1709 0.0306 5.59 4.0e-05 *** 216s trend 0.1467 0.0272 5.40 5.9e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.802 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 10.284 MSE: 0.643 Root MSE: 0.802 216s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.2529 -0.2920 -1.15193 216s 3 -1.2998 -0.1392 0.50193 216s 4 -1.5662 1.1106 1.42026 216s 5 -0.4876 -1.4391 -0.09801 216s 6 0.0149 0.3556 -0.35678 216s 7 0.9002 1.4558 NA 216s 8 1.3535 0.8299 -0.74964 216s 9 1.0406 -0.5136 0.29355 216s 10 NA 1.2191 1.18544 216s 11 0.4417 0.2810 -0.36558 216s 12 -0.0892 0.0754 0.33733 216s 13 -0.1541 0.3429 -0.17490 216s 14 0.2984 0.3597 0.39941 216s 15 -0.0260 -0.1602 0.29441 216s 16 -0.0250 0.0130 -0.00177 216s 17 1.5671 1.0231 -0.81891 216s 18 -0.4089 0.0306 0.85516 216s 19 0.2819 -2.6153 -0.77184 216s 20 0.9257 -0.6030 -0.41040 216s 21 0.7415 -0.7118 -1.21679 216s 22 -2.2437 -0.5398 0.57166 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.2 0.092 26.7 216s 3 46.3 2.039 28.8 216s 4 50.8 4.089 32.7 216s 5 51.1 4.439 34.0 216s 6 52.6 4.744 35.8 216s 7 54.2 4.144 NA 216s 8 54.8 3.370 38.6 216s 9 56.3 3.514 38.9 216s 10 NA 3.881 40.1 216s 11 54.6 0.719 38.3 216s 12 51.0 -3.475 34.2 216s 13 45.8 -6.543 29.2 216s 14 46.2 -5.460 28.1 216s 15 48.7 -2.840 30.3 216s 16 51.3 -1.313 33.2 216s 17 56.1 1.077 37.6 216s 18 59.1 1.969 40.1 216s 19 57.2 0.715 39.0 216s 20 60.7 1.903 42.0 216s 21 64.3 4.012 46.2 216s 22 71.9 5.440 52.7 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.2 0.422 41.3 43.0 216s 3 46.3 0.462 45.4 47.2 216s 4 50.8 0.309 50.1 51.4 216s 5 51.1 0.359 50.4 51.8 216s 6 52.6 0.362 51.9 53.3 216s 7 54.2 0.328 53.5 54.9 216s 8 54.8 0.300 54.2 55.4 216s 9 56.3 0.323 55.6 56.9 216s 10 NA NA NA NA 216s 11 54.6 0.531 53.5 55.6 216s 12 51.0 0.427 50.1 51.8 216s 13 45.8 0.564 44.6 46.9 216s 14 46.2 0.543 45.1 47.3 216s 15 48.7 0.341 48.0 49.4 216s 16 51.3 0.302 50.7 51.9 216s 17 56.1 0.328 55.5 56.8 216s 18 59.1 0.294 58.5 59.7 216s 19 57.2 0.332 56.6 57.9 216s 20 60.7 0.392 59.9 61.5 216s 21 64.3 0.394 63.5 65.0 216s 22 71.9 0.615 70.7 73.2 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 0.092 0.508 -0.929 1.113 216s 3 2.039 0.421 1.193 2.885 216s 4 4.089 0.376 3.333 4.846 216s 5 4.439 0.311 3.813 5.065 216s 6 4.744 0.294 4.154 5.335 216s 7 4.144 0.277 3.587 4.701 216s 8 3.370 0.247 2.873 3.867 216s 9 3.514 0.328 2.855 4.172 216s 10 3.881 0.376 3.126 4.636 216s 11 0.719 0.508 -0.301 1.739 216s 12 -3.475 0.428 -4.336 -2.615 216s 13 -6.543 0.521 -7.590 -5.496 216s 14 -5.460 0.583 -6.632 -4.288 216s 15 -2.840 0.316 -3.474 -2.205 216s 16 -1.313 0.271 -1.857 -0.769 216s 17 1.077 0.293 0.488 1.666 216s 18 1.969 0.205 1.557 2.382 216s 19 0.715 0.263 0.187 1.244 216s 20 1.903 0.309 1.283 2.523 216s 21 4.012 0.280 3.449 4.574 216s 22 5.440 0.389 4.659 6.221 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.7 0.306 26.0 27.3 216s 3 28.8 0.305 28.2 29.4 216s 4 32.7 0.302 32.1 33.3 216s 5 34.0 0.231 33.5 34.5 216s 6 35.8 0.230 35.3 36.2 216s 7 NA NA NA NA 216s 8 38.6 0.233 38.2 39.1 216s 9 38.9 0.222 38.5 39.4 216s 10 40.1 0.213 39.7 40.5 216s 11 38.3 0.292 37.7 38.9 216s 12 34.2 0.300 33.6 34.8 216s 13 29.2 0.361 28.4 29.9 216s 14 28.1 0.322 27.5 28.7 216s 15 30.3 0.314 29.7 30.9 216s 16 33.2 0.263 32.7 33.7 216s 17 37.6 0.256 37.1 38.1 216s 18 40.1 0.204 39.7 40.6 216s 19 39.0 0.298 38.4 39.6 216s 20 42.0 0.272 41.5 42.6 216s 21 46.2 0.288 45.6 46.8 216s 22 52.7 0.431 51.9 53.6 216s > model.frame 216s [1] TRUE 216s > model.matrix 216s [1] TRUE 216s > nobs 216s [1] 61 216s > linearHypothesis 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 49 1 1.01 0.32 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 50 216s 2 49 1 1.3 0.26 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 50 216s 2 49 1 1.3 0.25 216s Linear hypothesis test (Theil's F test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 49 2 0.53 0.59 216s Linear hypothesis test (F statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df F Pr(>F) 216s 1 51 216s 2 49 2 0.69 0.51 216s Linear hypothesis test (Chi^2 statistic of a Wald test) 216s 216s Hypothesis: 216s Consumption_corpProf + Investment_capitalLag = 0 216s Consumption_corpProfLag - PrivateWages_trend = 0 216s 216s Model 1: restricted model 216s Model 2: kleinModel 216s 216s Res.Df Df Chisq Pr(>Chisq) 216s 1 51 216s 2 49 2 1.38 0.5 216s > logLik 216s 'log Lik.' -69.6 (df=18) 216s 'log Lik.' -76.9 (df=18) 216s > 216s > # 3SLS 216s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 216s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 216s > summary 216s 216s systemfit results 216s method: 3SLS 216s 216s N DF SSR detRCov OLS-R2 McElroy-R2 216s system 59 47 59.5 0.241 0.97 0.994 216s 216s N DF SSR MSE RMSE R2 Adj R2 216s Consumption 19 15 18.1 1.203 1.097 0.980 0.977 216s Investment 20 16 31.1 1.945 1.395 0.866 0.841 216s PrivateWages 20 16 10.3 0.645 0.803 0.987 0.985 216s 216s The covariance matrix of the residuals used for estimation 216s Consumption Investment PrivateWages 216s Consumption 1.079 0.354 -0.383 216s Investment 0.354 1.047 0.107 216s PrivateWages -0.383 0.107 0.445 216s 216s The covariance matrix of the residuals 216s Consumption Investment PrivateWages 216s Consumption 0.950 0.324 -0.395 216s Investment 0.324 1.385 0.242 216s PrivateWages -0.395 0.242 0.475 216s 216s The correlations of the residuals 216s Consumption Investment PrivateWages 216s Consumption 1.000 0.293 -0.582 216s Investment 0.293 1.000 0.292 216s PrivateWages -0.582 0.292 1.000 216s 216s 216s 3SLS estimates for 'Consumption' (equation 1) 216s Model Formula: consump ~ corpProf + corpProfLag + wages 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 16.5606 1.3295 12.46 2.6e-09 *** 216s corpProf 0.1100 0.1098 1.00 0.33 216s corpProfLag 0.1155 0.1007 1.15 0.27 216s wages 0.8086 0.0401 20.18 2.8e-12 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.097 on 15 degrees of freedom 216s Number of observations: 19 Degrees of Freedom: 15 216s SSR: 18.051 MSE: 1.203 Root MSE: 1.097 216s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.977 216s 216s 216s 3SLS estimates for 'Investment' (equation 2) 216s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 23.6871 6.1159 3.87 0.00135 ** 216s corpProf 0.1072 0.1414 0.76 0.45918 216s corpProfLag 0.6278 0.1361 4.61 0.00029 *** 216s capitalLag -0.1726 0.0295 -5.85 2.5e-05 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 1.395 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 31.126 MSE: 1.945 Root MSE: 1.395 216s Multiple R-Squared: 0.866 Adjusted R-Squared: 0.841 216s 216s 216s 3SLS estimates for 'PrivateWages' (equation 3) 216s Model Formula: privWage ~ gnp + gnpLag + trend 216s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 216s gnpLag 216s 216s Estimate Std. Error t value Pr(>|t|) 216s (Intercept) 1.3603 1.0927 1.24 0.23109 216s gnp 0.4117 0.0315 13.06 6.0e-10 *** 216s gnpLag 0.1782 0.0336 5.31 7.1e-05 *** 216s trend 0.1370 0.0280 4.89 0.00016 *** 216s --- 216s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 216s 216s Residual standard error: 0.803 on 16 degrees of freedom 216s Number of observations: 20 Degrees of Freedom: 16 216s SSR: 10.318 MSE: 0.645 Root MSE: 0.803 216s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 216s 216s > residuals 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 -0.29542 -1.636 -1.2658 216s 3 -0.89033 0.135 0.4198 216s 4 -1.25669 0.777 1.3578 216s 5 -0.14000 -1.574 -0.2036 216s 6 0.37365 0.341 -0.4283 216s 7 NA NA NA 216s 8 1.63850 1.194 -0.8319 216s 9 1.44030 0.454 0.2186 216s 10 NA 2.192 1.1346 216s 11 0.17274 -0.750 -0.4603 216s 12 -0.49629 -0.698 0.2476 216s 13 -0.78384 -0.976 -0.2528 216s 14 0.32420 1.365 0.4028 216s 15 -0.10364 -0.170 0.3295 216s 16 -0.00105 0.140 0.0377 216s 17 1.84421 1.862 -0.7540 216s 18 -0.36893 -0.103 0.8827 216s 19 0.14129 -3.255 -0.7764 216s 20 1.23511 0.475 -0.3230 216s 21 1.06553 0.152 -1.1453 216s 22 -1.85709 0.746 0.6843 216s > fitted 216s Consumption Investment PrivateWages 216s 1 NA NA NA 216s 2 42.2 1.436 26.8 216s 3 45.9 1.765 28.9 216s 4 50.5 4.423 32.7 216s 5 50.7 4.574 34.1 216s 6 52.2 4.759 35.8 216s 7 NA NA NA 216s 8 54.6 3.006 38.7 216s 9 55.9 2.546 39.0 216s 10 NA 2.908 40.2 216s 11 54.8 1.750 38.4 216s 12 51.4 -2.702 34.3 216s 13 46.4 -5.224 29.3 216s 14 46.2 -6.465 28.1 216s 15 48.8 -2.830 30.3 216s 16 51.3 -1.440 33.2 216s 17 55.9 0.238 37.6 216s 18 59.1 2.103 40.1 216s 19 57.4 1.355 39.0 216s 20 60.4 0.825 41.9 216s 21 63.9 3.148 46.1 216s 22 71.6 4.154 52.6 216s > predict 216s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 216s 1 NA NA NA NA 216s 2 42.2 0.475 39.6 44.7 216s 3 45.9 0.557 43.3 48.5 216s 4 50.5 0.372 48.0 52.9 216s 5 50.7 0.433 48.2 53.3 216s 6 52.2 0.438 49.7 54.7 216s 7 NA NA NA NA 216s 8 54.6 0.362 52.1 57.0 216s 9 55.9 0.401 53.4 58.3 216s 10 NA NA NA NA 216s 11 54.8 0.684 52.1 57.6 216s 12 51.4 0.563 48.8 54.0 216s 13 46.4 0.733 43.6 49.2 216s 14 46.2 0.612 43.5 48.9 216s 15 48.8 0.379 46.3 51.3 216s 16 51.3 0.334 48.9 53.7 216s 17 55.9 0.394 53.4 58.3 216s 18 59.1 0.322 56.6 61.5 216s 19 57.4 0.392 54.9 59.8 216s 20 60.4 0.462 57.8 62.9 216s 21 63.9 0.448 61.4 66.5 216s 22 71.6 0.686 68.8 74.3 216s Investment.pred Investment.se.fit Investment.lwr Investment.upr 216s 1 NA NA NA NA 216s 2 1.436 0.709 -1.8811 4.754 216s 3 1.765 0.512 -1.3848 4.915 216s 4 4.423 0.470 1.3027 7.543 216s 5 4.574 0.392 1.5029 7.645 216s 6 4.759 0.370 1.7000 7.818 216s 7 NA NA NA NA 216s 8 3.006 0.306 -0.0214 6.033 216s 9 2.546 0.444 -0.5575 5.649 216s 10 2.908 0.488 -0.2245 6.041 216s 11 1.750 0.738 -1.5953 5.096 216s 12 -2.702 0.583 -5.9068 0.503 216s 13 -5.224 0.743 -8.5738 -1.874 216s 14 -6.465 0.780 -9.8530 -3.077 216s 15 -2.830 0.378 -5.8936 0.233 216s 16 -1.440 0.326 -4.4762 1.597 216s 17 0.238 0.426 -2.8533 3.329 216s 18 2.103 0.268 -0.9077 5.114 216s 19 1.355 0.399 -1.7201 4.431 216s 20 0.825 0.474 -2.2981 3.947 216s 21 3.148 0.393 0.0761 6.220 216s 22 4.154 0.555 0.9719 7.336 216s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 216s 1 NA NA NA NA 216s 2 26.8 0.309 24.9 28.6 216s 3 28.9 0.315 27.1 30.7 216s 4 32.7 0.326 30.9 34.6 216s 5 34.1 0.236 32.3 35.9 216s 6 35.8 0.244 34.0 37.6 216s 7 NA NA NA NA 216s 8 38.7 0.237 37.0 40.5 216s 9 39.0 0.225 37.2 40.7 216s 10 40.2 0.219 38.4 41.9 216s 11 38.4 0.309 36.5 40.2 216s 12 34.3 0.336 32.4 36.1 216s 13 29.3 0.411 27.3 31.2 216s 14 28.1 0.326 26.3 29.9 216s 15 30.3 0.313 28.4 32.1 216s 16 33.2 0.262 31.4 35.0 216s 17 37.6 0.265 35.8 39.3 216s 18 40.1 0.205 38.4 41.9 216s 19 39.0 0.323 37.1 40.8 216s 20 41.9 0.282 40.1 43.7 216s 21 46.1 0.293 44.3 48.0 216s 22 52.6 0.463 50.7 54.6 216s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 217s [3] "Numeric: lengths (732, 708) differ" 217s > nobs 217s [1] 59 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.23 0.64 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.31 0.58 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 48 217s 2 47 1 0.31 0.58 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 0.5 0.61 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 0.68 0.51 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 49 217s 2 47 2 1.37 0.5 217s > logLik 217s 'log Lik.' -71 (df=18) 217s 'log Lik.' -81.1 (df=18) 217s > 217s > # I3SLS 217s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: iterated 3SLS 217s 217s convergence achieved after 15 iterations 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 59 47 81.3 0.349 0.958 0.995 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 19 15 18.1 1.209 1.100 0.980 0.976 217s Investment 20 16 52.0 3.250 1.803 0.776 0.735 217s PrivateWages 20 16 11.2 0.699 0.836 0.986 0.983 217s 217s The covariance matrix of the residuals used for estimation 217s Consumption Investment PrivateWages 217s Consumption 0.955 0.456 -0.421 217s Investment 0.456 2.294 0.375 217s PrivateWages -0.421 0.375 0.522 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 0.955 0.456 -0.421 217s Investment 0.456 2.294 0.375 217s PrivateWages -0.421 0.375 0.522 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.000 0.322 -0.582 217s Investment 0.322 1.000 0.341 217s PrivateWages -0.582 0.341 1.000 217s 217s 217s 3SLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 16.8311 1.2489 13.48 8.7e-10 *** 217s corpProf 0.1468 0.0991 1.48 0.16 217s corpProfLag 0.0924 0.0906 1.02 0.32 217s wages 0.7945 0.0371 21.43 1.2e-12 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.1 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 18.14 MSE: 1.209 Root MSE: 1.1 217s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 217s 217s 217s 3SLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 32.4128 8.2695 3.92 0.00122 ** 217s corpProf -0.0799 0.1934 -0.41 0.68498 217s corpProfLag 0.7607 0.1878 4.05 0.00093 *** 217s capitalLag -0.2114 0.0400 -5.29 7.4e-05 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.803 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 51.999 MSE: 3.25 Root MSE: 1.803 217s Multiple R-Squared: 0.776 Adjusted R-Squared: 0.735 217s 217s 217s 3SLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 1.5421 1.1496 1.34 0.19852 217s gnp 0.3936 0.0313 12.57 1.0e-09 *** 217s gnpLag 0.1945 0.0328 5.93 2.1e-05 *** 217s trend 0.1416 0.0286 4.95 0.00014 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.836 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 11.181 MSE: 0.699 Root MSE: 0.836 217s Multiple R-Squared: 0.986 Adjusted R-Squared: 0.983 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.3309 -2.6308 -1.3061 217s 3 -1.0419 0.0146 0.4450 217s 4 -1.2918 0.4128 1.4338 217s 5 -0.1772 -1.7488 -0.2494 217s 6 0.3563 0.2807 -0.4066 217s 7 NA NA NA 217s 8 1.6778 1.4671 -0.8700 217s 9 1.4561 1.1068 0.1712 217s 10 NA 2.9002 1.1262 217s 11 0.4237 -1.0652 -0.6189 217s 12 -0.2711 -0.9488 0.0375 217s 13 -0.5643 -1.6241 -0.5055 217s 14 0.2845 1.8477 0.3080 217s 15 -0.0514 -0.2379 0.3003 217s 16 0.0521 0.1268 0.0141 217s 17 1.8733 2.2462 -0.7083 217s 18 -0.1962 -0.1724 0.8305 217s 19 0.3553 -3.5810 -0.9448 217s 20 1.3161 1.0343 -0.2738 217s 21 1.2055 0.6622 -1.1283 217s 22 -1.6327 1.5541 0.8257 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.2 2.431 26.8 217s 3 46.0 1.885 28.9 217s 4 50.5 4.787 32.7 217s 5 50.8 4.749 34.1 217s 6 52.2 4.819 35.8 217s 7 NA NA NA 217s 8 54.5 2.733 38.8 217s 9 55.8 1.893 39.0 217s 10 NA 2.200 40.2 217s 11 54.6 2.065 38.5 217s 12 51.2 -2.451 34.5 217s 13 46.2 -4.576 29.5 217s 14 46.2 -6.948 28.2 217s 15 48.8 -2.762 30.3 217s 16 51.2 -1.427 33.2 217s 17 55.8 -0.146 37.5 217s 18 58.9 2.172 40.2 217s 19 57.1 1.681 39.1 217s 20 60.3 0.266 41.9 217s 21 63.8 2.638 46.1 217s 22 71.3 3.346 52.5 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.2 0.446 41.3 43.1 217s 3 46.0 0.511 45.0 47.1 217s 4 50.5 0.340 49.8 51.2 217s 5 50.8 0.393 50.0 51.6 217s 6 52.2 0.396 51.4 53.0 217s 7 NA NA NA NA 217s 8 54.5 0.326 53.9 55.2 217s 9 55.8 0.362 55.1 56.6 217s 10 NA NA NA NA 217s 11 54.6 0.612 53.3 55.8 217s 12 51.2 0.511 50.1 52.2 217s 13 46.2 0.671 44.8 47.5 217s 14 46.2 0.563 45.1 47.3 217s 15 48.8 0.354 48.0 49.5 217s 16 51.2 0.311 50.6 51.9 217s 17 55.8 0.362 55.1 56.6 217s 18 58.9 0.297 58.3 59.5 217s 19 57.1 0.357 56.4 57.9 217s 20 60.3 0.427 59.4 61.1 217s 21 63.8 0.416 63.0 64.6 217s 22 71.3 0.640 70.0 72.6 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 2.431 0.970 0.4798 4.382 217s 3 1.885 0.745 0.3859 3.385 217s 4 4.787 0.664 3.4506 6.124 217s 5 4.749 0.562 3.6174 5.880 217s 6 4.819 0.537 3.7391 5.900 217s 7 NA NA NA NA 217s 8 2.733 0.446 1.8351 3.631 217s 9 1.893 0.620 0.6455 3.141 217s 10 2.200 0.684 0.8232 3.576 217s 11 2.065 1.055 -0.0569 4.187 217s 12 -2.451 0.845 -4.1517 -0.751 217s 13 -4.576 1.070 -6.7293 -2.423 217s 14 -6.948 1.103 -9.1676 -4.728 217s 15 -2.762 0.556 -3.8806 -1.644 217s 16 -1.427 0.480 -2.3919 -0.462 217s 17 -0.146 0.603 -1.3588 1.066 217s 18 2.172 0.390 1.3869 2.958 217s 19 1.681 0.563 0.5476 2.815 217s 20 0.266 0.661 -1.0634 1.595 217s 21 2.638 0.558 1.5144 3.761 217s 22 3.346 0.778 1.7808 4.911 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.8 0.326 26.2 27.5 217s 3 28.9 0.328 28.2 29.5 217s 4 32.7 0.334 32.0 33.3 217s 5 34.1 0.242 33.7 34.6 217s 6 35.8 0.252 35.3 36.3 217s 7 NA NA NA NA 217s 8 38.8 0.244 38.3 39.3 217s 9 39.0 0.232 38.6 39.5 217s 10 40.2 0.230 39.7 40.6 217s 11 38.5 0.308 37.9 39.1 217s 12 34.5 0.336 33.8 35.1 217s 13 29.5 0.420 28.7 30.4 217s 14 28.2 0.345 27.5 28.9 217s 15 30.3 0.325 29.6 31.0 217s 16 33.2 0.271 32.6 33.7 217s 17 37.5 0.267 37.0 38.0 217s 18 40.2 0.218 39.7 40.6 217s 19 39.1 0.331 38.5 39.8 217s 20 41.9 0.289 41.3 42.5 217s 21 46.1 0.311 45.5 46.8 217s 22 52.5 0.485 51.5 53.5 217s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0328 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 54 string mismatches >" 217s [3] "Numeric: lengths (732, 708) differ" 217s > nobs 217s [1] 59 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.28 0.6 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.37 0.55 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 48 217s 2 47 1 0.37 0.54 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 1.25 0.3 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 1.64 0.21 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 49 217s 2 47 2 3.28 0.19 217s > logLik 217s 'log Lik.' -74.5 (df=18) 217s 'log Lik.' -87.1 (df=18) 217s > 217s > # OLS 217s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: OLS 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 59 47 44.2 0.453 0.976 0.99 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 217s Investment 20 16 17.11 1.069 1.03 0.912 0.895 217s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.1939 0.0559 -0.474 217s Investment 0.0559 0.9839 0.140 217s PrivateWages -0.4745 0.1403 0.602 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.0000 0.0447 -0.568 217s Investment 0.0447 1.0000 0.169 217s PrivateWages -0.5680 0.1689 1.000 217s 217s 217s OLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 16.2957 1.4879 10.95 1.5e-08 *** 217s corpProf 0.1796 0.1162 1.55 0.14 217s corpProfLag 0.1032 0.0994 1.04 0.32 217s wages 0.7962 0.0433 18.39 1.1e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.076 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 217s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 217s 217s 217s OLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 10.1813 5.3720 1.90 0.07627 . 217s corpProf 0.5003 0.1052 4.75 0.00022 *** 217s corpProfLag 0.3259 0.1003 3.25 0.00502 ** 217s capitalLag -0.1134 0.0265 -4.28 0.00057 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.034 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 17.109 MSE: 1.069 Root MSE: 1.034 217s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.895 217s 217s 217s OLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 1.3550 1.3021 1.04 0.3135 217s gnp 0.4417 0.0330 13.40 4.1e-10 *** 217s gnpLag 0.1466 0.0379 3.87 0.0013 ** 217s trend 0.1244 0.0335 3.72 0.0019 ** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.78 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 217s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 217s 217s compare coef with single-equation OLS 217s [1] TRUE 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.3863 -0.000301 -1.3389 217s 3 -1.2484 -0.076489 0.2462 217s 4 -1.6040 1.221792 1.1255 217s 5 -0.5384 -1.377872 -0.1959 217s 6 -0.0413 0.386104 -0.5284 217s 7 0.8043 1.486279 NA 217s 8 1.2830 0.784055 -0.7909 217s 9 1.0142 -0.655354 0.2819 217s 10 NA 1.060871 1.1384 217s 11 0.1429 0.395249 -0.1904 217s 12 -0.3439 0.198005 0.5813 217s 13 NA NA 0.1206 217s 14 0.3199 0.312725 0.4773 217s 15 -0.1016 -0.084685 0.3035 217s 16 -0.0702 0.066194 0.0284 217s 17 1.6064 0.963697 -0.8517 217s 18 -0.4980 0.078506 0.9908 217s 19 0.1253 -2.496401 -0.4597 217s 20 0.9805 -0.711004 -0.3819 217s 21 0.7551 -0.820172 -1.1062 217s 22 -2.1992 -0.731199 0.5501 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.3 -0.200 26.8 217s 3 46.2 1.976 29.1 217s 4 50.8 3.978 33.0 217s 5 51.1 4.378 34.1 217s 6 52.6 4.714 35.9 217s 7 54.3 4.114 NA 217s 8 54.9 3.416 38.7 217s 9 56.3 3.655 38.9 217s 10 NA 4.039 40.2 217s 11 54.9 0.605 38.1 217s 12 51.2 -3.598 33.9 217s 13 NA NA 28.9 217s 14 46.2 -5.413 28.0 217s 15 48.8 -2.915 30.3 217s 16 51.4 -1.366 33.2 217s 17 56.1 1.136 37.7 217s 18 59.2 1.921 40.0 217s 19 57.4 0.596 38.7 217s 20 60.6 2.011 42.0 217s 21 64.2 4.120 46.1 217s 22 71.9 5.631 52.7 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.3 0.523 39.9 44.7 217s 3 46.2 0.560 43.8 48.7 217s 4 50.8 0.379 48.5 53.1 217s 5 51.1 0.448 48.8 53.5 217s 6 52.6 0.457 50.3 55.0 217s 7 54.3 0.408 52.0 56.6 217s 8 54.9 0.375 52.6 57.2 217s 9 56.3 0.418 54.0 58.6 217s 10 NA NA NA NA 217s 11 54.9 0.701 52.3 57.4 217s 12 51.2 0.638 48.7 53.8 217s 13 NA NA NA NA 217s 14 46.2 0.673 43.6 48.7 217s 15 48.8 0.453 46.5 51.2 217s 16 51.4 0.384 49.1 53.7 217s 17 56.1 0.391 53.8 58.4 217s 18 59.2 0.361 56.9 61.5 217s 19 57.4 0.449 55.0 59.7 217s 20 60.6 0.465 58.3 63.0 217s 21 64.2 0.468 61.9 66.6 217s 22 71.9 0.728 69.3 74.5 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 -0.200 0.613 -2.618 2.219 217s 3 1.976 0.494 -0.329 4.282 217s 4 3.978 0.444 1.714 6.242 217s 5 4.378 0.369 2.169 6.587 217s 6 4.714 0.349 2.519 6.909 217s 7 4.114 0.323 1.934 6.293 217s 8 3.416 0.287 1.257 5.575 217s 9 3.655 0.386 1.435 5.876 217s 10 4.039 0.441 1.777 6.301 217s 11 0.605 0.641 -1.843 3.053 217s 12 -3.598 0.606 -6.010 -1.186 217s 13 NA NA NA NA 217s 14 -5.413 0.708 -7.934 -2.892 217s 15 -2.915 0.412 -5.155 -0.676 217s 16 -1.366 0.336 -3.554 0.821 217s 17 1.136 0.342 -1.055 3.327 217s 18 1.921 0.246 -0.217 4.060 217s 19 0.596 0.341 -1.594 2.787 217s 20 2.011 0.364 -0.194 4.216 217s 21 4.120 0.337 1.932 6.308 217s 22 5.631 0.477 3.341 7.922 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.8 0.364 25.1 28.6 217s 3 29.1 0.367 27.3 30.8 217s 4 33.0 0.370 31.2 34.7 217s 5 34.1 0.286 32.4 35.8 217s 6 35.9 0.285 34.3 37.6 217s 7 NA NA NA NA 217s 8 38.7 0.292 37.0 40.4 217s 9 38.9 0.277 37.3 40.6 217s 10 40.2 0.264 38.5 41.8 217s 11 38.1 0.363 36.4 39.8 217s 12 33.9 0.367 32.2 35.7 217s 13 28.9 0.435 27.1 30.7 217s 14 28.0 0.383 26.3 29.8 217s 15 30.3 0.377 28.6 32.0 217s 16 33.2 0.315 31.5 34.9 217s 17 37.7 0.308 36.0 39.3 217s 18 40.0 0.241 38.4 41.7 217s 19 38.7 0.361 36.9 40.4 217s 20 42.0 0.324 40.3 43.7 217s 21 46.1 0.339 44.4 47.8 217s 22 52.7 0.511 50.9 54.6 217s > model.frame 217s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 217s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 217s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 217s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 217s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 217s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 217s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 217s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 217s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 217s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 217s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 217s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 217s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 217s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 217s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 217s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 217s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 217s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 217s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 217s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 217s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 217s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 217s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 217s trend 217s 1 -11 217s 2 -10 217s 3 -9 217s 4 -8 217s 5 -7 217s 6 -6 217s 7 -5 217s 8 -4 217s 9 -3 217s 10 -2 217s 11 -1 217s 12 0 217s 13 1 217s 14 2 217s 15 3 217s 16 4 217s 17 5 217s 18 6 217s 19 7 217s 20 8 217s 21 9 217s 22 10 217s > model.matrix 217s Consumption_(Intercept) Consumption_corpProf 217s Consumption_2 1 12.4 217s Consumption_3 1 16.9 217s Consumption_4 1 18.4 217s Consumption_5 1 19.4 217s Consumption_6 1 20.1 217s Consumption_7 1 19.6 217s Consumption_8 1 19.8 217s Consumption_9 1 21.1 217s Consumption_11 1 15.6 217s Consumption_12 1 11.4 217s Consumption_14 1 11.2 217s Consumption_15 1 12.3 217s Consumption_16 1 14.0 217s Consumption_17 1 17.6 217s Consumption_18 1 17.3 217s Consumption_19 1 15.3 217s Consumption_20 1 19.0 217s Consumption_21 1 21.1 217s Consumption_22 1 23.5 217s Investment_2 0 0.0 217s Investment_3 0 0.0 217s Investment_4 0 0.0 217s Investment_5 0 0.0 217s Investment_6 0 0.0 217s Investment_7 0 0.0 217s Investment_8 0 0.0 217s Investment_9 0 0.0 217s Investment_10 0 0.0 217s Investment_11 0 0.0 217s Investment_12 0 0.0 217s Investment_14 0 0.0 217s Investment_15 0 0.0 217s Investment_16 0 0.0 217s Investment_17 0 0.0 217s Investment_18 0 0.0 217s Investment_19 0 0.0 217s Investment_20 0 0.0 217s Investment_21 0 0.0 217s Investment_22 0 0.0 217s PrivateWages_2 0 0.0 217s PrivateWages_3 0 0.0 217s PrivateWages_4 0 0.0 217s PrivateWages_5 0 0.0 217s PrivateWages_6 0 0.0 217s PrivateWages_8 0 0.0 217s PrivateWages_9 0 0.0 217s PrivateWages_10 0 0.0 217s PrivateWages_11 0 0.0 217s PrivateWages_12 0 0.0 217s PrivateWages_13 0 0.0 217s PrivateWages_14 0 0.0 217s PrivateWages_15 0 0.0 217s PrivateWages_16 0 0.0 217s PrivateWages_17 0 0.0 217s PrivateWages_18 0 0.0 217s PrivateWages_19 0 0.0 217s PrivateWages_20 0 0.0 217s PrivateWages_21 0 0.0 217s PrivateWages_22 0 0.0 217s Consumption_corpProfLag Consumption_wages 217s Consumption_2 12.7 28.2 217s Consumption_3 12.4 32.2 217s Consumption_4 16.9 37.0 217s Consumption_5 18.4 37.0 217s Consumption_6 19.4 38.6 217s Consumption_7 20.1 40.7 217s Consumption_8 19.6 41.5 217s Consumption_9 19.8 42.9 217s Consumption_11 21.7 42.1 217s Consumption_12 15.6 39.3 217s Consumption_14 7.0 34.1 217s Consumption_15 11.2 36.6 217s Consumption_16 12.3 39.3 217s Consumption_17 14.0 44.2 217s Consumption_18 17.6 47.7 217s Consumption_19 17.3 45.9 217s Consumption_20 15.3 49.4 217s Consumption_21 19.0 53.0 217s Consumption_22 21.1 61.8 217s Investment_2 0.0 0.0 217s Investment_3 0.0 0.0 217s Investment_4 0.0 0.0 217s Investment_5 0.0 0.0 217s Investment_6 0.0 0.0 217s Investment_7 0.0 0.0 217s Investment_8 0.0 0.0 217s Investment_9 0.0 0.0 217s Investment_10 0.0 0.0 217s Investment_11 0.0 0.0 217s Investment_12 0.0 0.0 217s Investment_14 0.0 0.0 217s Investment_15 0.0 0.0 217s Investment_16 0.0 0.0 217s Investment_17 0.0 0.0 217s Investment_18 0.0 0.0 217s Investment_19 0.0 0.0 217s Investment_20 0.0 0.0 217s Investment_21 0.0 0.0 217s Investment_22 0.0 0.0 217s PrivateWages_2 0.0 0.0 217s PrivateWages_3 0.0 0.0 217s PrivateWages_4 0.0 0.0 217s PrivateWages_5 0.0 0.0 217s PrivateWages_6 0.0 0.0 217s PrivateWages_8 0.0 0.0 217s PrivateWages_9 0.0 0.0 217s PrivateWages_10 0.0 0.0 217s PrivateWages_11 0.0 0.0 217s PrivateWages_12 0.0 0.0 217s PrivateWages_13 0.0 0.0 217s PrivateWages_14 0.0 0.0 217s PrivateWages_15 0.0 0.0 217s PrivateWages_16 0.0 0.0 217s PrivateWages_17 0.0 0.0 217s PrivateWages_18 0.0 0.0 217s PrivateWages_19 0.0 0.0 217s PrivateWages_20 0.0 0.0 217s PrivateWages_21 0.0 0.0 217s PrivateWages_22 0.0 0.0 217s Investment_(Intercept) Investment_corpProf 217s Consumption_2 0 0.0 217s Consumption_3 0 0.0 217s Consumption_4 0 0.0 217s Consumption_5 0 0.0 217s Consumption_6 0 0.0 217s Consumption_7 0 0.0 217s Consumption_8 0 0.0 217s Consumption_9 0 0.0 217s Consumption_11 0 0.0 217s Consumption_12 0 0.0 217s Consumption_14 0 0.0 217s Consumption_15 0 0.0 217s Consumption_16 0 0.0 217s Consumption_17 0 0.0 217s Consumption_18 0 0.0 217s Consumption_19 0 0.0 217s Consumption_20 0 0.0 217s Consumption_21 0 0.0 217s Consumption_22 0 0.0 217s Investment_2 1 12.4 217s Investment_3 1 16.9 217s Investment_4 1 18.4 217s Investment_5 1 19.4 217s Investment_6 1 20.1 217s Investment_7 1 19.6 217s Investment_8 1 19.8 217s Investment_9 1 21.1 217s Investment_10 1 21.7 217s Investment_11 1 15.6 217s Investment_12 1 11.4 217s Investment_14 1 11.2 217s Investment_15 1 12.3 217s Investment_16 1 14.0 217s Investment_17 1 17.6 217s Investment_18 1 17.3 217s Investment_19 1 15.3 217s Investment_20 1 19.0 217s Investment_21 1 21.1 217s Investment_22 1 23.5 217s PrivateWages_2 0 0.0 217s PrivateWages_3 0 0.0 217s PrivateWages_4 0 0.0 217s PrivateWages_5 0 0.0 217s PrivateWages_6 0 0.0 217s PrivateWages_8 0 0.0 217s PrivateWages_9 0 0.0 217s PrivateWages_10 0 0.0 217s PrivateWages_11 0 0.0 217s PrivateWages_12 0 0.0 217s PrivateWages_13 0 0.0 217s PrivateWages_14 0 0.0 217s PrivateWages_15 0 0.0 217s PrivateWages_16 0 0.0 217s PrivateWages_17 0 0.0 217s PrivateWages_18 0 0.0 217s PrivateWages_19 0 0.0 217s PrivateWages_20 0 0.0 217s PrivateWages_21 0 0.0 217s PrivateWages_22 0 0.0 217s Investment_corpProfLag Investment_capitalLag 217s Consumption_2 0.0 0 217s Consumption_3 0.0 0 217s Consumption_4 0.0 0 217s Consumption_5 0.0 0 217s Consumption_6 0.0 0 217s Consumption_7 0.0 0 217s Consumption_8 0.0 0 217s Consumption_9 0.0 0 217s Consumption_11 0.0 0 217s Consumption_12 0.0 0 217s Consumption_14 0.0 0 217s Consumption_15 0.0 0 217s Consumption_16 0.0 0 217s Consumption_17 0.0 0 217s Consumption_18 0.0 0 217s Consumption_19 0.0 0 217s Consumption_20 0.0 0 217s Consumption_21 0.0 0 217s Consumption_22 0.0 0 217s Investment_2 12.7 183 217s Investment_3 12.4 183 217s Investment_4 16.9 184 217s Investment_5 18.4 190 217s Investment_6 19.4 193 217s Investment_7 20.1 198 217s Investment_8 19.6 203 217s Investment_9 19.8 208 217s Investment_10 21.1 211 217s Investment_11 21.7 216 217s Investment_12 15.6 217 217s Investment_14 7.0 207 217s Investment_15 11.2 202 217s Investment_16 12.3 199 217s Investment_17 14.0 198 217s Investment_18 17.6 200 217s Investment_19 17.3 202 217s Investment_20 15.3 200 217s Investment_21 19.0 201 217s Investment_22 21.1 204 217s PrivateWages_2 0.0 0 217s PrivateWages_3 0.0 0 217s PrivateWages_4 0.0 0 217s PrivateWages_5 0.0 0 217s PrivateWages_6 0.0 0 217s PrivateWages_8 0.0 0 217s PrivateWages_9 0.0 0 217s PrivateWages_10 0.0 0 217s PrivateWages_11 0.0 0 217s PrivateWages_12 0.0 0 217s PrivateWages_13 0.0 0 217s PrivateWages_14 0.0 0 217s PrivateWages_15 0.0 0 217s PrivateWages_16 0.0 0 217s PrivateWages_17 0.0 0 217s PrivateWages_18 0.0 0 217s PrivateWages_19 0.0 0 217s PrivateWages_20 0.0 0 217s PrivateWages_21 0.0 0 217s PrivateWages_22 0.0 0 217s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 217s Consumption_2 0 0.0 0.0 217s Consumption_3 0 0.0 0.0 217s Consumption_4 0 0.0 0.0 217s Consumption_5 0 0.0 0.0 217s Consumption_6 0 0.0 0.0 217s Consumption_7 0 0.0 0.0 217s Consumption_8 0 0.0 0.0 217s Consumption_9 0 0.0 0.0 217s Consumption_11 0 0.0 0.0 217s Consumption_12 0 0.0 0.0 217s Consumption_14 0 0.0 0.0 217s Consumption_15 0 0.0 0.0 217s Consumption_16 0 0.0 0.0 217s Consumption_17 0 0.0 0.0 217s Consumption_18 0 0.0 0.0 217s Consumption_19 0 0.0 0.0 217s Consumption_20 0 0.0 0.0 217s Consumption_21 0 0.0 0.0 217s Consumption_22 0 0.0 0.0 217s Investment_2 0 0.0 0.0 217s Investment_3 0 0.0 0.0 217s Investment_4 0 0.0 0.0 217s Investment_5 0 0.0 0.0 217s Investment_6 0 0.0 0.0 217s Investment_7 0 0.0 0.0 217s Investment_8 0 0.0 0.0 217s Investment_9 0 0.0 0.0 217s Investment_10 0 0.0 0.0 217s Investment_11 0 0.0 0.0 217s Investment_12 0 0.0 0.0 217s Investment_14 0 0.0 0.0 217s Investment_15 0 0.0 0.0 217s Investment_16 0 0.0 0.0 217s Investment_17 0 0.0 0.0 217s Investment_18 0 0.0 0.0 217s Investment_19 0 0.0 0.0 217s Investment_20 0 0.0 0.0 217s Investment_21 0 0.0 0.0 217s Investment_22 0 0.0 0.0 217s PrivateWages_2 1 45.6 44.9 217s PrivateWages_3 1 50.1 45.6 217s PrivateWages_4 1 57.2 50.1 217s PrivateWages_5 1 57.1 57.2 217s PrivateWages_6 1 61.0 57.1 217s PrivateWages_8 1 64.4 64.0 217s PrivateWages_9 1 64.5 64.4 217s PrivateWages_10 1 67.0 64.5 217s PrivateWages_11 1 61.2 67.0 217s PrivateWages_12 1 53.4 61.2 217s PrivateWages_13 1 44.3 53.4 217s PrivateWages_14 1 45.1 44.3 217s PrivateWages_15 1 49.7 45.1 217s PrivateWages_16 1 54.4 49.7 217s PrivateWages_17 1 62.7 54.4 217s PrivateWages_18 1 65.0 62.7 217s PrivateWages_19 1 60.9 65.0 217s PrivateWages_20 1 69.5 60.9 217s PrivateWages_21 1 75.7 69.5 217s PrivateWages_22 1 88.4 75.7 217s PrivateWages_trend 217s Consumption_2 0 217s Consumption_3 0 217s Consumption_4 0 217s Consumption_5 0 217s Consumption_6 0 217s Consumption_7 0 217s Consumption_8 0 217s Consumption_9 0 217s Consumption_11 0 217s Consumption_12 0 217s Consumption_14 0 217s Consumption_15 0 217s Consumption_16 0 217s Consumption_17 0 217s Consumption_18 0 217s Consumption_19 0 217s Consumption_20 0 217s Consumption_21 0 217s Consumption_22 0 217s Investment_2 0 217s Investment_3 0 217s Investment_4 0 217s Investment_5 0 217s Investment_6 0 217s Investment_7 0 217s Investment_8 0 217s Investment_9 0 217s Investment_10 0 217s Investment_11 0 217s Investment_12 0 217s Investment_14 0 217s Investment_15 0 217s Investment_16 0 217s Investment_17 0 217s Investment_18 0 217s Investment_19 0 217s Investment_20 0 217s Investment_21 0 217s Investment_22 0 217s PrivateWages_2 -10 217s PrivateWages_3 -9 217s PrivateWages_4 -8 217s PrivateWages_5 -7 217s PrivateWages_6 -6 217s PrivateWages_8 -4 217s PrivateWages_9 -3 217s PrivateWages_10 -2 217s PrivateWages_11 -1 217s PrivateWages_12 0 217s PrivateWages_13 1 217s PrivateWages_14 2 217s PrivateWages_15 3 217s PrivateWages_16 4 217s PrivateWages_17 5 217s PrivateWages_18 6 217s PrivateWages_19 7 217s PrivateWages_20 8 217s PrivateWages_21 9 217s PrivateWages_22 10 217s > nobs 217s [1] 59 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.33 0.57 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.31 0.58 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 48 217s 2 47 1 0.31 0.58 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 0.17 0.84 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 0.16 0.85 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 49 217s 2 47 2 0.33 0.85 217s > logLik 217s 'log Lik.' -69.6 (df=13) 217s 'log Lik.' -74.2 (df=13) 217s compare log likelihood value with single-equation OLS 217s [1] "Mean relative difference: 0.00099" 217s > 217s > # 2SLS 217s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: 2SLS 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 57 45 58.2 0.333 0.968 0.991 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 217s Investment 19 15 26.21 1.748 1.32 0.852 0.823 217s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.237 0.518 -0.408 217s Investment 0.518 1.263 0.113 217s PrivateWages -0.408 0.113 0.468 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.000 0.416 -0.538 217s Investment 0.416 1.000 0.139 217s PrivateWages -0.538 0.139 1.000 217s 217s 217s 2SLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 17.2849 1.6018 10.79 3.6e-08 *** 217s corpProf -0.0770 0.1637 -0.47 0.645 217s corpProfLag 0.2327 0.1242 1.87 0.082 . 217s wages 0.8259 0.0459 17.98 4.5e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.261 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 217s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 217s 217s 217s 2SLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 18.4005 7.1627 2.57 0.02138 * 217s corpProf 0.1507 0.1905 0.79 0.44118 217s corpProfLag 0.5757 0.1634 3.52 0.00307 ** 217s capitalLag -0.1452 0.0339 -4.28 0.00065 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.322 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 26.213 MSE: 1.748 Root MSE: 1.322 217s Multiple R-Squared: 0.852 Adjusted R-Squared: 0.823 217s 217s 217s 2SLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 1.3431 1.1544 1.16 0.26172 217s gnp 0.4438 0.0351 12.64 9.7e-10 *** 217s gnpLag 0.1447 0.0381 3.80 0.00158 ** 217s trend 0.1238 0.0300 4.13 0.00078 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.78 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 217s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.6754 -1.23599 -1.3401 217s 3 -0.4627 0.32957 0.2378 217s 4 -1.1585 1.08894 1.1117 217s 5 -0.0305 -1.37017 -0.1954 217s 6 0.4693 0.48431 -0.5355 217s 7 NA NA NA 217s 8 1.6045 1.06811 -0.7908 217s 9 1.6018 0.16695 0.2831 217s 10 NA 1.86380 1.1353 217s 11 -0.9031 -0.92183 -0.1765 217s 12 -1.5948 -1.03217 0.6007 217s 13 NA NA 0.1443 217s 14 0.2854 0.85468 0.4826 217s 15 -0.4718 -0.36943 0.3016 217s 16 -0.2268 0.00554 0.0261 217s 17 2.0079 1.69566 -0.8614 217s 18 -0.7434 -0.12659 0.9927 217s 19 -0.5410 -3.26209 -0.4446 217s 20 1.4186 0.25579 -0.3914 217s 21 1.1462 -0.00185 -1.1115 217s 22 -1.7256 0.50679 0.5312 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.6 1.036 26.8 217s 3 45.5 1.570 29.1 217s 4 50.4 4.111 33.0 217s 5 50.6 4.370 34.1 217s 6 52.1 4.616 35.9 217s 7 NA NA NA 217s 8 54.6 3.132 38.7 217s 9 55.7 2.833 38.9 217s 10 NA 3.236 40.2 217s 11 55.9 1.922 38.1 217s 12 52.5 -2.368 33.9 217s 13 NA NA 28.9 217s 14 46.2 -5.955 28.0 217s 15 49.2 -2.631 30.3 217s 16 51.5 -1.306 33.2 217s 17 55.7 0.404 37.7 217s 18 59.4 2.127 40.0 217s 19 58.0 1.362 38.6 217s 20 60.2 1.044 42.0 217s 21 63.9 3.302 46.1 217s 22 71.4 4.393 52.8 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.6 0.571 41.4 43.8 217s 3 45.5 0.656 44.1 46.9 217s 4 50.4 0.431 49.4 51.3 217s 5 50.6 0.510 49.5 51.7 217s 6 52.1 0.521 51.0 53.2 217s 7 NA NA NA NA 217s 8 54.6 0.419 53.7 55.5 217s 9 55.7 0.496 54.6 56.8 217s 10 NA NA NA NA 217s 11 55.9 0.910 54.0 57.9 217s 12 52.5 0.869 50.6 54.4 217s 13 NA NA NA NA 217s 14 46.2 0.694 44.7 47.7 217s 15 49.2 0.487 48.1 50.2 217s 16 51.5 0.396 50.7 52.4 217s 17 55.7 0.445 54.7 56.6 217s 18 59.4 0.386 58.6 60.3 217s 19 58.0 0.548 56.9 59.2 217s 20 60.2 0.528 59.0 61.3 217s 21 63.9 0.515 62.8 65.0 217s 22 71.4 0.786 69.7 73.1 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 1.036 0.892 -0.865 2.937 217s 3 1.570 0.579 0.335 2.805 217s 4 4.111 0.531 2.979 5.243 217s 5 4.370 0.440 3.432 5.308 217s 6 4.616 0.416 3.729 5.502 217s 7 NA NA NA NA 217s 8 3.132 0.344 2.398 3.866 217s 9 2.833 0.533 1.696 3.970 217s 10 3.236 0.580 2.000 4.473 217s 11 1.922 0.959 -0.122 3.966 217s 12 -2.368 0.860 -4.201 -0.534 217s 13 NA NA NA NA 217s 14 -5.955 0.865 -7.799 -4.110 217s 15 -2.631 0.479 -3.652 -1.610 217s 16 -1.306 0.382 -2.120 -0.491 217s 17 0.404 0.487 -0.635 1.443 217s 18 2.127 0.319 1.447 2.806 217s 19 1.362 0.537 0.218 2.506 217s 20 1.044 0.566 -0.162 2.250 217s 21 3.302 0.486 2.265 4.339 217s 22 4.393 0.713 2.874 5.912 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.8 0.321 26.2 27.5 217s 3 29.1 0.334 28.4 29.8 217s 4 33.0 0.353 32.2 33.7 217s 5 34.1 0.253 33.6 34.6 217s 6 35.9 0.261 35.4 36.5 217s 7 NA NA NA NA 217s 8 38.7 0.257 38.1 39.2 217s 9 38.9 0.245 38.4 39.4 217s 10 40.2 0.235 39.7 40.7 217s 11 38.1 0.348 37.3 38.8 217s 12 33.9 0.374 33.1 34.7 217s 13 28.9 0.447 27.9 29.8 217s 14 28.0 0.341 27.3 28.7 217s 15 30.3 0.333 29.6 31.0 217s 16 33.2 0.278 32.6 33.8 217s 17 37.7 0.288 37.1 38.3 217s 18 40.0 0.214 39.6 40.5 217s 19 38.6 0.351 37.9 39.4 217s 20 42.0 0.301 41.4 42.6 217s 21 46.1 0.304 45.5 46.8 217s 22 52.8 0.486 51.7 53.8 217s > model.frame 217s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 217s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 217s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 217s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 217s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 217s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 217s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 217s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 217s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 217s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 217s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 217s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 217s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 217s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 217s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 217s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 217s 16 51.3 14.0 12.3 39.3 -1.3 199 33.2 54.4 49.7 217s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 217s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 217s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 217s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 217s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 217s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 217s trend 217s 1 -11 217s 2 -10 217s 3 -9 217s 4 -8 217s 5 -7 217s 6 -6 217s 7 -5 217s 8 -4 217s 9 -3 217s 10 -2 217s 11 -1 217s 12 0 217s 13 1 217s 14 2 217s 15 3 217s 16 4 217s 17 5 217s 18 6 217s 19 7 217s 20 8 217s 21 9 217s 22 10 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 217s [3] "Numeric: lengths (708, 684) differ" 217s > nobs 217s [1] 57 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 45 1 1.37 0.25 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 45 1 1.77 0.19 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 46 217s 2 45 1 1.77 0.18 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 45 2 0.69 0.51 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 45 2 0.89 0.42 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 47 217s 2 45 2 1.78 0.41 217s > logLik 217s 'log Lik.' -70.6 (df=13) 217s 'log Lik.' -78.7 (df=13) 217s > 217s > # SUR 217s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: SUR 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 59 47 45.1 0.168 0.976 0.992 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 217s Investment 20 16 17.3 1.083 1.041 0.911 0.894 217s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 217s 217s The covariance matrix of the residuals used for estimation 217s Consumption Investment PrivateWages 217s Consumption 0.9286 0.0435 -0.369 217s Investment 0.0435 0.7653 0.109 217s PrivateWages -0.3690 0.1091 0.468 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 0.9251 0.0748 -0.427 217s Investment 0.0748 0.7653 0.171 217s PrivateWages -0.4268 0.1706 0.492 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.0000 0.0888 -0.636 217s Investment 0.0888 1.0000 0.268 217s PrivateWages -0.6364 0.2678 1.000 217s 217s 217s SUR estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 16.2684 1.2781 12.73 1.9e-09 *** 217s corpProf 0.1942 0.0927 2.10 0.054 . 217s corpProfLag 0.0746 0.0819 0.91 0.377 217s wages 0.8011 0.0372 21.53 1.1e-12 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.08 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 217s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 217s 217s 217s SUR estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 12.6462 4.6500 2.72 0.01515 * 217s corpProf 0.4707 0.0916 5.14 9.9e-05 *** 217s corpProfLag 0.3519 0.0874 4.03 0.00097 *** 217s capitalLag -0.1253 0.0229 -5.47 5.1e-05 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.041 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 17.325 MSE: 1.083 Root MSE: 1.041 217s Multiple R-Squared: 0.911 Adjusted R-Squared: 0.894 217s 217s 217s SUR estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 1.3245 1.0946 1.21 0.24 217s gnp 0.4184 0.0260 16.08 2.7e-11 *** 217s gnpLag 0.1714 0.0307 5.59 4.1e-05 *** 217s trend 0.1455 0.0276 5.27 7.6e-05 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.801 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 10.265 MSE: 0.642 Root MSE: 0.801 217s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.3146 -0.2419 -1.1439 217s 3 -1.2707 -0.1795 0.5080 217s 4 -1.5428 1.0691 1.4208 217s 5 -0.4489 -1.4778 -0.1000 217s 6 0.0588 0.3168 -0.3599 217s 7 0.9215 1.4450 NA 217s 8 1.3791 0.8287 -0.7561 217s 9 1.0901 -0.5272 0.2880 217s 10 NA 1.2089 1.1795 217s 11 0.3577 0.4081 -0.3681 217s 12 -0.2286 0.2569 0.3439 217s 13 NA NA -0.1574 217s 14 0.2172 0.4743 0.4225 217s 15 -0.1124 -0.0607 0.3154 217s 16 -0.0876 0.0761 0.0151 217s 17 1.5611 1.0205 -0.8084 217s 18 -0.4529 0.0580 0.8611 217s 19 0.1999 -2.5444 -0.7635 217s 20 0.9266 -0.6202 -0.4039 217s 21 0.7589 -0.7478 -1.2175 217s 22 -2.2135 -0.6029 0.5611 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.2 0.0419 26.6 217s 3 46.3 2.0795 28.8 217s 4 50.7 4.1309 32.7 217s 5 51.0 4.4778 34.0 217s 6 52.5 4.7832 35.8 217s 7 54.2 4.1550 NA 217s 8 54.8 3.3713 38.7 217s 9 56.2 3.5272 38.9 217s 10 NA 3.8911 40.1 217s 11 54.6 0.5919 38.3 217s 12 51.1 -3.6569 34.2 217s 13 NA NA 29.2 217s 14 46.3 -5.5743 28.1 217s 15 48.8 -2.9393 30.3 217s 16 51.4 -1.3761 33.2 217s 17 56.1 1.0795 37.6 217s 18 59.2 1.9420 40.1 217s 19 57.3 0.6444 39.0 217s 20 60.7 1.9202 42.0 217s 21 64.2 4.0478 46.2 217s 22 71.9 5.5029 52.7 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.2 0.448 41.3 43.1 217s 3 46.3 0.476 45.3 47.2 217s 4 50.7 0.318 50.1 51.4 217s 5 51.0 0.373 50.3 51.8 217s 6 52.5 0.378 51.8 53.3 217s 7 54.2 0.337 53.5 54.9 217s 8 54.8 0.310 54.2 55.4 217s 9 56.2 0.343 55.5 56.9 217s 10 NA NA NA NA 217s 11 54.6 0.567 53.5 55.8 217s 12 51.1 0.509 50.1 52.2 217s 13 NA NA NA NA 217s 14 46.3 0.573 45.1 47.4 217s 15 48.8 0.382 48.0 49.6 217s 16 51.4 0.328 50.7 52.0 217s 17 56.1 0.336 55.5 56.8 217s 18 59.2 0.309 58.5 59.8 217s 19 57.3 0.370 56.6 58.0 217s 20 60.7 0.401 59.9 61.5 217s 21 64.2 0.405 63.4 65.1 217s 22 71.9 0.633 70.6 73.2 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 0.0419 0.533 -1.0309 1.115 217s 3 2.0795 0.433 1.2082 2.951 217s 4 4.1309 0.387 3.3532 4.909 217s 5 4.4778 0.322 3.8307 5.125 217s 6 4.7832 0.305 4.1700 5.396 217s 7 4.1550 0.283 3.5852 4.725 217s 8 3.3713 0.253 2.8630 3.880 217s 9 3.5272 0.337 2.8488 4.206 217s 10 3.8911 0.386 3.1149 4.667 217s 11 0.5919 0.561 -0.5376 1.722 217s 12 -3.6569 0.530 -4.7223 -2.591 217s 13 NA NA NA NA 217s 14 -5.5743 0.618 -6.8176 -4.331 217s 15 -2.9393 0.362 -3.6671 -2.212 217s 16 -1.3761 0.296 -1.9710 -0.781 217s 17 1.0795 0.300 0.4763 1.683 217s 18 1.9420 0.216 1.5081 2.376 217s 19 0.6444 0.298 0.0451 1.244 217s 20 1.9202 0.318 1.2798 2.561 217s 21 4.0478 0.295 3.4537 4.642 217s 22 5.5029 0.417 4.6638 6.342 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.6 0.312 26.0 27.3 217s 3 28.8 0.312 28.2 29.4 217s 4 32.7 0.307 32.1 33.3 217s 5 34.0 0.237 33.5 34.5 217s 6 35.8 0.235 35.3 36.2 217s 7 NA NA NA NA 217s 8 38.7 0.239 38.2 39.1 217s 9 38.9 0.228 38.5 39.4 217s 10 40.1 0.218 39.7 40.6 217s 11 38.3 0.293 37.7 38.9 217s 12 34.2 0.290 33.6 34.7 217s 13 29.2 0.343 28.5 29.8 217s 14 28.1 0.321 27.4 28.7 217s 15 30.3 0.320 29.6 30.9 217s 16 33.2 0.268 32.6 33.7 217s 17 37.6 0.263 37.1 38.1 217s 18 40.1 0.207 39.7 40.6 217s 19 39.0 0.293 38.4 39.6 217s 20 42.0 0.279 41.4 42.6 217s 21 46.2 0.295 45.6 46.8 217s 22 52.7 0.435 51.9 53.6 217s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] TRUE 217s > nobs 217s [1] 59 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.41 0.52 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 47 1 0.52 0.47 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 48 217s 2 47 1 0.52 0.47 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 0.31 0.73 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 49 217s 2 47 2 0.4 0.67 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 49 217s 2 47 2 0.79 0.67 217s > logLik 217s 'log Lik.' -67.3 (df=18) 217s 'log Lik.' -74.9 (df=18) 217s > 217s > # 3SLS 217s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: 3SLS 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 57 45 66.8 0.361 0.963 0.993 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 18 14 22.6 1.616 1.271 0.974 0.968 217s Investment 19 15 34.1 2.277 1.509 0.807 0.769 217s PrivateWages 20 16 10.1 0.628 0.793 0.987 0.985 217s 217s The covariance matrix of the residuals used for estimation 217s Consumption Investment PrivateWages 217s Consumption 1.237 0.518 -0.408 217s Investment 0.518 1.263 0.113 217s PrivateWages -0.408 0.113 0.468 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.257 0.601 -0.421 217s Investment 0.601 1.601 0.214 217s PrivateWages -0.421 0.214 0.491 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.000 0.425 -0.537 217s Investment 0.425 1.000 0.239 217s PrivateWages -0.537 0.239 1.000 217s 217s 217s 3SLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 18.2100 1.5273 11.92 1e-08 *** 217s corpProf -0.0639 0.1461 -0.44 0.67 217s corpProfLag 0.1687 0.1125 1.50 0.16 217s wages 0.8230 0.0431 19.07 2e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.271 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 22.626 MSE: 1.616 Root MSE: 1.271 217s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 217s 217s 217s 3SLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 24.7534 6.5548 3.78 0.00183 ** 217s corpProf 0.0524 0.1807 0.29 0.77600 217s corpProfLag 0.6584 0.1551 4.24 0.00071 *** 217s capitalLag -0.1756 0.0311 -5.64 4.7e-05 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.509 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 34.149 MSE: 2.277 Root MSE: 1.509 217s Multiple R-Squared: 0.807 Adjusted R-Squared: 0.769 217s 217s 217s 3SLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 0.8154 1.0961 0.74 0.46772 217s gnp 0.4250 0.0299 14.19 1.7e-10 *** 217s gnpLag 0.1731 0.0331 5.23 8.3e-05 *** 217s trend 0.1255 0.0283 4.43 0.00042 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.793 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 10.054 MSE: 0.628 Root MSE: 0.793 217s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.8680 -1.857 -1.21010 217s 3 -0.7217 0.170 0.43075 217s 4 -1.1353 0.762 1.30899 217s 5 0.0755 -1.565 -0.20270 217s 6 0.6348 0.367 -0.46842 217s 7 NA NA NA 217s 8 1.7953 1.230 -0.85853 217s 9 1.7924 0.568 0.20422 217s 10 NA 2.308 1.09889 217s 11 -0.5211 -0.972 -0.39427 217s 12 -1.5560 -0.960 0.39889 217s 13 NA NA -0.00934 217s 14 -0.2384 1.327 0.59990 217s 15 -0.7342 -0.292 0.48094 217s 16 -0.4331 0.068 0.16188 217s 17 1.8775 1.932 -0.70448 217s 18 -0.6294 -0.154 0.95616 217s 19 -0.4252 -3.400 -0.62489 217s 20 1.3682 0.589 -0.29589 217s 21 1.3155 0.271 -1.14466 217s 22 -1.4276 0.942 0.55941 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.8 1.657 26.7 217s 3 45.7 1.730 28.9 217s 4 50.3 4.438 32.8 217s 5 50.5 4.565 34.1 217s 6 52.0 4.733 35.9 217s 7 NA NA NA 217s 8 54.4 2.970 38.8 217s 9 55.5 2.432 39.0 217s 10 NA 2.792 40.2 217s 11 55.5 1.972 38.3 217s 12 52.5 -2.440 34.1 217s 13 NA NA 29.0 217s 14 46.7 -6.427 27.9 217s 15 49.4 -2.708 30.1 217s 16 51.7 -1.368 33.0 217s 17 55.8 0.168 37.5 217s 18 59.3 2.154 40.0 217s 19 57.9 1.500 38.8 217s 20 60.2 0.711 41.9 217s 21 63.7 3.029 46.1 217s 22 71.1 3.958 52.7 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.8 0.542 39.8 45.7 217s 3 45.7 0.612 42.7 48.7 217s 4 50.3 0.407 47.5 53.2 217s 5 50.5 0.478 47.6 53.4 217s 6 52.0 0.488 49.0 54.9 217s 7 NA NA NA NA 217s 8 54.4 0.394 51.5 57.3 217s 9 55.5 0.464 52.6 58.4 217s 10 NA NA NA NA 217s 11 55.5 0.811 52.3 58.8 217s 12 52.5 0.773 49.3 55.6 217s 13 NA NA NA NA 217s 14 46.7 0.666 43.7 49.8 217s 15 49.4 0.463 46.5 52.3 217s 16 51.7 0.381 48.9 54.6 217s 17 55.8 0.424 52.9 58.7 217s 18 59.3 0.359 56.5 62.2 217s 19 57.9 0.492 55.0 60.8 217s 20 60.2 0.501 57.3 63.2 217s 21 63.7 0.491 60.8 66.6 217s 22 71.1 0.749 68.0 74.3 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 1.657 0.831 -2.015 5.329 217s 3 1.730 0.574 -1.711 5.171 217s 4 4.438 0.507 1.045 7.831 217s 5 4.565 0.426 1.223 7.907 217s 6 4.733 0.406 1.402 8.064 217s 7 NA NA NA NA 217s 8 2.970 0.334 -0.324 6.263 217s 9 2.432 0.501 -0.957 5.820 217s 10 2.792 0.544 -0.627 6.211 217s 11 1.972 0.937 -1.814 5.757 217s 12 -2.440 0.849 -6.131 1.250 217s 13 NA NA NA NA 217s 14 -6.427 0.836 -10.104 -2.750 217s 15 -2.708 0.477 -6.081 0.665 217s 16 -1.368 0.381 -4.685 1.949 217s 17 0.168 0.473 -3.202 3.538 217s 18 2.154 0.311 -1.130 5.438 217s 19 1.500 0.518 -1.900 4.900 217s 20 0.711 0.541 -2.705 4.127 217s 21 3.029 0.467 -0.338 6.395 217s 22 3.958 0.677 0.432 7.483 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.7 0.315 24.9 28.5 217s 3 28.9 0.322 27.1 30.7 217s 4 32.8 0.330 31.0 34.6 217s 5 34.1 0.241 32.3 35.9 217s 6 35.9 0.249 34.1 37.6 217s 7 NA NA NA NA 217s 8 38.8 0.243 37.0 40.5 217s 9 39.0 0.231 37.2 40.7 217s 10 40.2 0.225 38.5 41.9 217s 11 38.3 0.305 36.5 40.1 217s 12 34.1 0.317 32.3 35.9 217s 13 29.0 0.382 27.1 30.9 217s 14 27.9 0.321 26.1 29.7 217s 15 30.1 0.316 28.3 31.9 217s 16 33.0 0.265 31.3 34.8 217s 17 37.5 0.270 35.7 39.3 217s 18 40.0 0.207 38.3 41.8 217s 19 38.8 0.311 37.0 40.6 217s 20 41.9 0.287 40.1 43.7 217s 21 46.1 0.300 44.3 47.9 217s 22 52.7 0.463 50.8 54.7 217s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 217s [3] "Numeric: lengths (708, 684) differ" 217s > nobs 217s [1] 57 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 45 1 1.95 0.17 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 45 1 2.71 0.11 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 46 217s 2 45 1 2.71 0.1 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 45 2 1.78 0.18 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 45 2 2.48 0.095 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 47 217s 2 45 2 4.95 0.084 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s > logLik 217s 'log Lik.' -71.2 (df=18) 217s 'log Lik.' -81.7 (df=18) 217s > 217s > # I3SLS 217s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: iterated 3SLS 217s 217s convergence achieved after 9 iterations 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 57 45 75 0.422 0.959 0.993 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 18 14 22.7 1.622 1.273 0.973 0.968 217s Investment 19 15 42.1 2.809 1.676 0.762 0.715 217s PrivateWages 20 16 10.2 0.638 0.799 0.987 0.985 217s 217s The covariance matrix of the residuals used for estimation 217s Consumption Investment PrivateWages 217s Consumption 1.261 0.675 -0.439 217s Investment 0.675 1.949 0.237 217s PrivateWages -0.439 0.237 0.503 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.261 0.675 -0.439 217s Investment 0.675 1.949 0.237 217s PrivateWages -0.439 0.237 0.503 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.000 0.431 -0.550 217s Investment 0.431 1.000 0.239 217s PrivateWages -0.550 0.239 1.000 217s 217s 217s 3SLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 18.5887 1.5250 12.19 7.6e-09 *** 217s corpProf -0.0438 0.1441 -0.30 0.77 217s corpProfLag 0.1456 0.1109 1.31 0.21 217s wages 0.8141 0.0428 19.01 2.1e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.273 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 22.704 MSE: 1.622 Root MSE: 1.273 217s Multiple R-Squared: 0.973 Adjusted R-Squared: 0.968 217s 217s 217s 3SLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 29.4725 7.6857 3.83 0.0016 ** 217s corpProf -0.0183 0.2154 -0.09 0.9333 217s corpProfLag 0.7195 0.1850 3.89 0.0015 ** 217s capitalLag -0.1985 0.0366 -5.43 6.9e-05 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.676 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 42.136 MSE: 2.809 Root MSE: 1.676 217s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.715 217s 217s 217s 3SLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 0.5385 1.1055 0.49 0.63277 217s gnp 0.4251 0.0287 14.80 9.3e-11 *** 217s gnpLag 0.1776 0.0322 5.51 4.7e-05 *** 217s trend 0.1211 0.0283 4.28 0.00057 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.799 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 10.204 MSE: 0.638 Root MSE: 0.799 217s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.9524 -2.2888 -1.1837 217s 3 -0.8681 0.0698 0.4581 217s 4 -1.1653 0.5368 1.3199 217s 5 0.0601 -1.6917 -0.2194 217s 6 0.6426 0.2972 -0.4805 217s 7 NA NA NA 217s 8 1.8394 1.3723 -0.8931 217s 9 1.8275 0.8861 0.1723 217s 10 NA 2.6574 1.0707 217s 11 -0.3387 -0.9736 -0.4288 217s 12 -1.4550 -0.8630 0.3956 217s 13 NA NA 0.0277 217s 14 -0.3782 1.7151 0.6823 217s 15 -0.7768 -0.1993 0.5638 217s 16 -0.4606 0.1448 0.2281 217s 17 1.8605 2.1295 -0.6557 217s 18 -0.5262 -0.1493 0.9718 217s 19 -0.3047 -3.4730 -0.6148 217s 20 1.3992 0.8566 -0.2636 217s 21 1.4216 0.4910 -1.1472 217s 22 -1.2431 1.2792 0.5323 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.9 2.0888 26.7 217s 3 45.9 1.8302 28.8 217s 4 50.4 4.6632 32.8 217s 5 50.5 4.6917 34.1 217s 6 52.0 4.8028 35.9 217s 7 NA NA NA 217s 8 54.4 2.8277 38.8 217s 9 55.5 2.1139 39.0 217s 10 NA 2.4426 40.2 217s 11 55.3 1.9736 38.3 217s 12 52.4 -2.5370 34.1 217s 13 NA NA 29.0 217s 14 46.9 -6.8151 27.8 217s 15 49.5 -2.8007 30.0 217s 16 51.8 -1.4448 33.0 217s 17 55.8 -0.0295 37.5 217s 18 59.2 2.1493 40.0 217s 19 57.8 1.5730 38.8 217s 20 60.2 0.4434 41.9 217s 21 63.6 2.8090 46.1 217s 22 70.9 3.6208 52.8 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.9 0.541 41.8 43.9 217s 3 45.9 0.608 44.6 47.1 217s 4 50.4 0.403 49.6 51.2 217s 5 50.5 0.472 49.6 51.5 217s 6 52.0 0.481 51.0 52.9 217s 7 NA NA NA NA 217s 8 54.4 0.388 53.6 55.1 217s 9 55.5 0.458 54.6 56.4 217s 10 NA NA NA NA 217s 11 55.3 0.795 53.7 56.9 217s 12 52.4 0.762 50.8 53.9 217s 13 NA NA NA NA 217s 14 46.9 0.663 45.5 48.2 217s 15 49.5 0.462 48.5 50.4 217s 16 51.8 0.381 51.0 52.5 217s 17 55.8 0.423 55.0 56.7 217s 18 59.2 0.355 58.5 59.9 217s 19 57.8 0.484 56.8 58.8 217s 20 60.2 0.500 59.2 61.2 217s 21 63.6 0.490 62.6 64.6 217s 22 70.9 0.747 69.4 72.4 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 2.0888 0.985 0.105 4.072 217s 3 1.8302 0.708 0.404 3.257 217s 4 4.6632 0.612 3.430 5.897 217s 5 4.6917 0.519 3.645 5.738 217s 6 4.8028 0.498 3.800 5.806 217s 7 NA NA NA NA 217s 8 2.8277 0.410 2.003 3.653 217s 9 2.1139 0.599 0.908 3.320 217s 10 2.4426 0.651 1.131 3.754 217s 11 1.9736 1.138 -0.320 4.267 217s 12 -2.5370 1.038 -4.627 -0.447 217s 13 NA NA NA NA 217s 14 -6.8151 1.011 -8.851 -4.779 217s 15 -2.8007 0.587 -3.984 -1.617 217s 16 -1.4448 0.470 -2.392 -0.498 217s 17 -0.0295 0.573 -1.183 1.124 217s 18 2.1493 0.380 1.384 2.915 217s 19 1.5730 0.624 0.315 2.831 217s 20 0.4434 0.649 -0.864 1.751 217s 21 2.8090 0.565 1.671 3.947 217s 22 3.6208 0.814 1.982 5.260 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.7 0.322 26.0 27.3 217s 3 28.8 0.328 28.2 29.5 217s 4 32.8 0.332 32.1 33.4 217s 5 34.1 0.244 33.6 34.6 217s 6 35.9 0.252 35.4 36.4 217s 7 NA NA NA NA 217s 8 38.8 0.246 38.3 39.3 217s 9 39.0 0.234 38.6 39.5 217s 10 40.2 0.230 39.8 40.7 217s 11 38.3 0.299 37.7 38.9 217s 12 34.1 0.304 33.5 34.7 217s 13 29.0 0.366 28.2 29.7 217s 14 27.8 0.321 27.2 28.5 217s 15 30.0 0.317 29.4 30.7 217s 16 33.0 0.266 32.4 33.5 217s 17 37.5 0.270 36.9 38.0 217s 18 40.0 0.211 39.6 40.5 217s 19 38.8 0.305 38.2 39.4 217s 20 41.9 0.290 41.3 42.4 217s 21 46.1 0.309 45.5 46.8 217s 22 52.8 0.468 51.8 53.7 217s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0339 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 52 string mismatches >" 217s [3] "Numeric: lengths (708, 684) differ" 217s > nobs 217s [1] 57 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 45 1 2.17 0.15 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 45 1 2.84 0.099 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 46 217s 2 45 1 2.84 0.092 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 45 2 2.45 0.098 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 45 2 3.2 0.05 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 47 217s 2 45 2 6.4 0.041 * 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s > logLik 217s 'log Lik.' -72.7 (df=18) 217s 'log Lik.' -83.9 (df=18) 217s > 217s > # OLS 217s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: OLS 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 58 46 44.2 0.565 0.976 0.991 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 19 15 17.36 1.157 1.08 0.980 0.976 217s Investment 19 15 17.11 1.140 1.07 0.907 0.889 217s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.285 0.061 -0.511 217s Investment 0.061 1.059 0.151 217s PrivateWages -0.511 0.151 0.648 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.0000 0.0457 -0.568 217s Investment 0.0457 1.0000 0.168 217s PrivateWages -0.5681 0.1676 1.000 217s 217s 217s OLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 16.2957 1.5438 10.56 2.4e-08 *** 217s corpProf 0.1796 0.1206 1.49 0.16 217s corpProfLag 0.1032 0.1031 1.00 0.33 217s wages 0.7962 0.0449 17.73 1.8e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.076 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 17.362 MSE: 1.157 Root MSE: 1.076 217s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.976 217s 217s 217s OLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 10.1724 5.5758 1.82 0.08808 . 217s corpProf 0.5004 0.1092 4.58 0.00036 *** 217s corpProfLag 0.3270 0.1052 3.11 0.00718 ** 217s capitalLag -0.1134 0.0275 -4.13 0.00090 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.068 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 17.105 MSE: 1.14 Root MSE: 1.068 217s Multiple R-Squared: 0.907 Adjusted R-Squared: 0.889 217s 217s 217s OLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 1.3550 1.3512 1.00 0.3309 217s gnp 0.4417 0.0342 12.92 7e-10 *** 217s gnpLag 0.1466 0.0393 3.73 0.0018 ** 217s trend 0.1244 0.0347 3.58 0.0025 ** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.78 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 9.739 MSE: 0.609 Root MSE: 0.78 217s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 217s 217s compare coef with single-equation OLS 217s [1] TRUE 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.3863 0.00693 -1.3389 217s 3 -1.2484 -0.06954 0.2462 217s 4 -1.6040 1.22401 1.1255 217s 5 -0.5384 -1.37697 -0.1959 217s 6 -0.0413 0.38610 -0.5284 217s 7 0.8043 1.48598 NA 217s 8 1.2830 0.78465 -0.7909 217s 9 1.0142 -0.65483 0.2819 217s 10 NA 1.06018 1.1384 217s 11 0.1429 0.39508 -0.1904 217s 12 -0.3439 0.20479 0.5813 217s 13 NA NA 0.1206 217s 14 0.3199 0.32778 0.4773 217s 15 -0.1016 -0.07450 0.3035 217s 16 -0.0702 NA 0.0284 217s 17 1.6064 0.96998 -0.8517 217s 18 -0.4980 0.08124 0.9908 217s 19 0.1253 -2.49295 -0.4597 217s 20 0.9805 -0.70609 -0.3819 217s 21 0.7551 -0.81928 -1.1062 217s 22 -2.1992 -0.73256 0.5501 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.3 -0.207 26.8 217s 3 46.2 1.970 29.1 217s 4 50.8 3.976 33.0 217s 5 51.1 4.377 34.1 217s 6 52.6 4.714 35.9 217s 7 54.3 4.114 NA 217s 8 54.9 3.415 38.7 217s 9 56.3 3.655 38.9 217s 10 NA 4.040 40.2 217s 11 54.9 0.605 38.1 217s 12 51.2 -3.605 33.9 217s 13 NA NA 28.9 217s 14 46.2 -5.428 28.0 217s 15 48.8 -2.926 30.3 217s 16 51.4 NA 33.2 217s 17 56.1 1.130 37.7 217s 18 59.2 1.919 40.0 217s 19 57.4 0.593 38.7 217s 20 60.6 2.006 42.0 217s 21 64.2 4.119 46.1 217s 22 71.9 5.633 52.7 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.3 0.543 39.9 44.7 217s 3 46.2 0.581 43.8 48.7 217s 4 50.8 0.394 48.5 53.1 217s 5 51.1 0.465 48.8 53.5 217s 6 52.6 0.474 50.3 55.0 217s 7 54.3 0.423 52.0 56.6 217s 8 54.9 0.389 52.6 57.2 217s 9 56.3 0.434 54.0 58.6 217s 10 NA NA NA NA 217s 11 54.9 0.727 52.2 57.5 217s 12 51.2 0.662 48.7 53.8 217s 13 NA NA NA NA 217s 14 46.2 0.698 43.6 48.8 217s 15 48.8 0.470 46.4 51.2 217s 16 51.4 0.398 49.1 53.7 217s 17 56.1 0.405 53.8 58.4 217s 18 59.2 0.375 56.9 61.5 217s 19 57.4 0.466 55.0 59.7 217s 20 60.6 0.482 58.2 63.0 217s 21 64.2 0.485 61.9 66.6 217s 22 71.9 0.755 69.3 74.5 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 -0.207 0.645 -2.718 2.30 217s 3 1.970 0.523 -0.423 4.36 217s 4 3.976 0.462 1.634 6.32 217s 5 4.377 0.383 2.094 6.66 217s 6 4.714 0.362 2.444 6.98 217s 7 4.114 0.336 1.861 6.37 217s 8 3.415 0.298 1.184 5.65 217s 9 3.655 0.400 1.359 5.95 217s 10 4.040 0.458 1.701 6.38 217s 11 0.605 0.666 -1.928 3.14 217s 12 -3.605 0.637 -6.108 -1.10 217s 13 NA NA NA NA 217s 14 -5.428 0.767 -8.074 -2.78 217s 15 -2.926 0.453 -5.261 -0.59 217s 16 NA NA NA NA 217s 17 1.130 0.366 -1.142 3.40 217s 18 1.919 0.258 -0.293 4.13 217s 19 0.593 0.357 -1.674 2.86 217s 20 2.006 0.384 -0.278 4.29 217s 21 4.119 0.350 1.858 6.38 217s 22 5.633 0.495 3.263 8.00 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.8 0.378 25.1 28.6 217s 3 29.1 0.381 27.3 30.8 217s 4 33.0 0.384 31.2 34.7 217s 5 34.1 0.297 32.4 35.8 217s 6 35.9 0.296 34.2 37.6 217s 7 NA NA NA NA 217s 8 38.7 0.303 37.0 40.4 217s 9 38.9 0.288 37.2 40.6 217s 10 40.2 0.274 38.5 41.8 217s 11 38.1 0.377 36.3 39.8 217s 12 33.9 0.381 32.2 35.7 217s 13 28.9 0.452 27.1 30.7 217s 14 28.0 0.397 26.3 29.8 217s 15 30.3 0.391 28.5 32.1 217s 16 33.2 0.327 31.5 34.9 217s 17 37.7 0.320 36.0 39.3 217s 18 40.0 0.250 38.4 41.7 217s 19 38.7 0.375 36.9 40.4 217s 20 42.0 0.337 40.3 43.7 217s 21 46.1 0.352 44.4 47.8 217s 22 52.7 0.530 50.9 54.6 217s > model.frame 217s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 217s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 217s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 217s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 217s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 217s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 217s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 217s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 217s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 217s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 217s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 217s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 217s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 217s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 217s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 217s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 217s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 217s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 217s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 217s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 217s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 217s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 217s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 217s trend 217s 1 -11 217s 2 -10 217s 3 -9 217s 4 -8 217s 5 -7 217s 6 -6 217s 7 -5 217s 8 -4 217s 9 -3 217s 10 -2 217s 11 -1 217s 12 0 217s 13 1 217s 14 2 217s 15 3 217s 16 4 217s 17 5 217s 18 6 217s 19 7 217s 20 8 217s 21 9 217s 22 10 217s > model.matrix 217s Consumption_(Intercept) Consumption_corpProf 217s Consumption_2 1 12.4 217s Consumption_3 1 16.9 217s Consumption_4 1 18.4 217s Consumption_5 1 19.4 217s Consumption_6 1 20.1 217s Consumption_7 1 19.6 217s Consumption_8 1 19.8 217s Consumption_9 1 21.1 217s Consumption_11 1 15.6 217s Consumption_12 1 11.4 217s Consumption_14 1 11.2 217s Consumption_15 1 12.3 217s Consumption_16 1 14.0 217s Consumption_17 1 17.6 217s Consumption_18 1 17.3 217s Consumption_19 1 15.3 217s Consumption_20 1 19.0 217s Consumption_21 1 21.1 217s Consumption_22 1 23.5 217s Investment_2 0 0.0 217s Investment_3 0 0.0 217s Investment_4 0 0.0 217s Investment_5 0 0.0 217s Investment_6 0 0.0 217s Investment_7 0 0.0 217s Investment_8 0 0.0 217s Investment_9 0 0.0 217s Investment_10 0 0.0 217s Investment_11 0 0.0 217s Investment_12 0 0.0 217s Investment_14 0 0.0 217s Investment_15 0 0.0 217s Investment_17 0 0.0 217s Investment_18 0 0.0 217s Investment_19 0 0.0 217s Investment_20 0 0.0 217s Investment_21 0 0.0 217s Investment_22 0 0.0 217s PrivateWages_2 0 0.0 217s PrivateWages_3 0 0.0 217s PrivateWages_4 0 0.0 217s PrivateWages_5 0 0.0 217s PrivateWages_6 0 0.0 217s PrivateWages_8 0 0.0 217s PrivateWages_9 0 0.0 217s PrivateWages_10 0 0.0 217s PrivateWages_11 0 0.0 217s PrivateWages_12 0 0.0 217s PrivateWages_13 0 0.0 217s PrivateWages_14 0 0.0 217s PrivateWages_15 0 0.0 217s PrivateWages_16 0 0.0 217s PrivateWages_17 0 0.0 217s PrivateWages_18 0 0.0 217s PrivateWages_19 0 0.0 217s PrivateWages_20 0 0.0 217s PrivateWages_21 0 0.0 217s PrivateWages_22 0 0.0 217s Consumption_corpProfLag Consumption_wages 217s Consumption_2 12.7 28.2 217s Consumption_3 12.4 32.2 217s Consumption_4 16.9 37.0 217s Consumption_5 18.4 37.0 217s Consumption_6 19.4 38.6 217s Consumption_7 20.1 40.7 217s Consumption_8 19.6 41.5 217s Consumption_9 19.8 42.9 217s Consumption_11 21.7 42.1 217s Consumption_12 15.6 39.3 217s Consumption_14 7.0 34.1 217s Consumption_15 11.2 36.6 217s Consumption_16 12.3 39.3 217s Consumption_17 14.0 44.2 217s Consumption_18 17.6 47.7 217s Consumption_19 17.3 45.9 217s Consumption_20 15.3 49.4 217s Consumption_21 19.0 53.0 217s Consumption_22 21.1 61.8 217s Investment_2 0.0 0.0 217s Investment_3 0.0 0.0 217s Investment_4 0.0 0.0 217s Investment_5 0.0 0.0 217s Investment_6 0.0 0.0 217s Investment_7 0.0 0.0 217s Investment_8 0.0 0.0 217s Investment_9 0.0 0.0 217s Investment_10 0.0 0.0 217s Investment_11 0.0 0.0 217s Investment_12 0.0 0.0 217s Investment_14 0.0 0.0 217s Investment_15 0.0 0.0 217s Investment_17 0.0 0.0 217s Investment_18 0.0 0.0 217s Investment_19 0.0 0.0 217s Investment_20 0.0 0.0 217s Investment_21 0.0 0.0 217s Investment_22 0.0 0.0 217s PrivateWages_2 0.0 0.0 217s PrivateWages_3 0.0 0.0 217s PrivateWages_4 0.0 0.0 217s PrivateWages_5 0.0 0.0 217s PrivateWages_6 0.0 0.0 217s PrivateWages_8 0.0 0.0 217s PrivateWages_9 0.0 0.0 217s PrivateWages_10 0.0 0.0 217s PrivateWages_11 0.0 0.0 217s PrivateWages_12 0.0 0.0 217s PrivateWages_13 0.0 0.0 217s PrivateWages_14 0.0 0.0 217s PrivateWages_15 0.0 0.0 217s PrivateWages_16 0.0 0.0 217s PrivateWages_17 0.0 0.0 217s PrivateWages_18 0.0 0.0 217s PrivateWages_19 0.0 0.0 217s PrivateWages_20 0.0 0.0 217s PrivateWages_21 0.0 0.0 217s PrivateWages_22 0.0 0.0 217s Investment_(Intercept) Investment_corpProf 217s Consumption_2 0 0.0 217s Consumption_3 0 0.0 217s Consumption_4 0 0.0 217s Consumption_5 0 0.0 217s Consumption_6 0 0.0 217s Consumption_7 0 0.0 217s Consumption_8 0 0.0 217s Consumption_9 0 0.0 217s Consumption_11 0 0.0 217s Consumption_12 0 0.0 217s Consumption_14 0 0.0 217s Consumption_15 0 0.0 217s Consumption_16 0 0.0 217s Consumption_17 0 0.0 217s Consumption_18 0 0.0 217s Consumption_19 0 0.0 217s Consumption_20 0 0.0 217s Consumption_21 0 0.0 217s Consumption_22 0 0.0 217s Investment_2 1 12.4 217s Investment_3 1 16.9 217s Investment_4 1 18.4 217s Investment_5 1 19.4 217s Investment_6 1 20.1 217s Investment_7 1 19.6 217s Investment_8 1 19.8 217s Investment_9 1 21.1 217s Investment_10 1 21.7 217s Investment_11 1 15.6 217s Investment_12 1 11.4 217s Investment_14 1 11.2 217s Investment_15 1 12.3 217s Investment_17 1 17.6 217s Investment_18 1 17.3 217s Investment_19 1 15.3 217s Investment_20 1 19.0 217s Investment_21 1 21.1 217s Investment_22 1 23.5 217s PrivateWages_2 0 0.0 217s PrivateWages_3 0 0.0 217s PrivateWages_4 0 0.0 217s PrivateWages_5 0 0.0 217s PrivateWages_6 0 0.0 217s PrivateWages_8 0 0.0 217s PrivateWages_9 0 0.0 217s PrivateWages_10 0 0.0 217s PrivateWages_11 0 0.0 217s PrivateWages_12 0 0.0 217s PrivateWages_13 0 0.0 217s PrivateWages_14 0 0.0 217s PrivateWages_15 0 0.0 217s PrivateWages_16 0 0.0 217s PrivateWages_17 0 0.0 217s PrivateWages_18 0 0.0 217s PrivateWages_19 0 0.0 217s PrivateWages_20 0 0.0 217s PrivateWages_21 0 0.0 217s PrivateWages_22 0 0.0 217s Investment_corpProfLag Investment_capitalLag 217s Consumption_2 0.0 0 217s Consumption_3 0.0 0 217s Consumption_4 0.0 0 217s Consumption_5 0.0 0 217s Consumption_6 0.0 0 217s Consumption_7 0.0 0 217s Consumption_8 0.0 0 217s Consumption_9 0.0 0 217s Consumption_11 0.0 0 217s Consumption_12 0.0 0 217s Consumption_14 0.0 0 217s Consumption_15 0.0 0 217s Consumption_16 0.0 0 217s Consumption_17 0.0 0 217s Consumption_18 0.0 0 217s Consumption_19 0.0 0 217s Consumption_20 0.0 0 217s Consumption_21 0.0 0 217s Consumption_22 0.0 0 217s Investment_2 12.7 183 217s Investment_3 12.4 183 217s Investment_4 16.9 184 217s Investment_5 18.4 190 217s Investment_6 19.4 193 217s Investment_7 20.1 198 217s Investment_8 19.6 203 217s Investment_9 19.8 208 217s Investment_10 21.1 211 217s Investment_11 21.7 216 217s Investment_12 15.6 217 217s Investment_14 7.0 207 217s Investment_15 11.2 202 217s Investment_17 14.0 198 217s Investment_18 17.6 200 217s Investment_19 17.3 202 217s Investment_20 15.3 200 217s Investment_21 19.0 201 217s Investment_22 21.1 204 217s PrivateWages_2 0.0 0 217s PrivateWages_3 0.0 0 217s PrivateWages_4 0.0 0 217s PrivateWages_5 0.0 0 217s PrivateWages_6 0.0 0 217s PrivateWages_8 0.0 0 217s PrivateWages_9 0.0 0 217s PrivateWages_10 0.0 0 217s PrivateWages_11 0.0 0 217s PrivateWages_12 0.0 0 217s PrivateWages_13 0.0 0 217s PrivateWages_14 0.0 0 217s PrivateWages_15 0.0 0 217s PrivateWages_16 0.0 0 217s PrivateWages_17 0.0 0 217s PrivateWages_18 0.0 0 217s PrivateWages_19 0.0 0 217s PrivateWages_20 0.0 0 217s PrivateWages_21 0.0 0 217s PrivateWages_22 0.0 0 217s PrivateWages_(Intercept) PrivateWages_gnp PrivateWages_gnpLag 217s Consumption_2 0 0.0 0.0 217s Consumption_3 0 0.0 0.0 217s Consumption_4 0 0.0 0.0 217s Consumption_5 0 0.0 0.0 217s Consumption_6 0 0.0 0.0 217s Consumption_7 0 0.0 0.0 217s Consumption_8 0 0.0 0.0 217s Consumption_9 0 0.0 0.0 217s Consumption_11 0 0.0 0.0 217s Consumption_12 0 0.0 0.0 217s Consumption_14 0 0.0 0.0 217s Consumption_15 0 0.0 0.0 217s Consumption_16 0 0.0 0.0 217s Consumption_17 0 0.0 0.0 217s Consumption_18 0 0.0 0.0 217s Consumption_19 0 0.0 0.0 217s Consumption_20 0 0.0 0.0 217s Consumption_21 0 0.0 0.0 217s Consumption_22 0 0.0 0.0 217s Investment_2 0 0.0 0.0 217s Investment_3 0 0.0 0.0 217s Investment_4 0 0.0 0.0 217s Investment_5 0 0.0 0.0 217s Investment_6 0 0.0 0.0 217s Investment_7 0 0.0 0.0 217s Investment_8 0 0.0 0.0 217s Investment_9 0 0.0 0.0 217s Investment_10 0 0.0 0.0 217s Investment_11 0 0.0 0.0 217s Investment_12 0 0.0 0.0 217s Investment_14 0 0.0 0.0 217s Investment_15 0 0.0 0.0 217s Investment_17 0 0.0 0.0 217s Investment_18 0 0.0 0.0 217s Investment_19 0 0.0 0.0 217s Investment_20 0 0.0 0.0 217s Investment_21 0 0.0 0.0 217s Investment_22 0 0.0 0.0 217s PrivateWages_2 1 45.6 44.9 217s PrivateWages_3 1 50.1 45.6 217s PrivateWages_4 1 57.2 50.1 217s PrivateWages_5 1 57.1 57.2 217s PrivateWages_6 1 61.0 57.1 217s PrivateWages_8 1 64.4 64.0 217s PrivateWages_9 1 64.5 64.4 217s PrivateWages_10 1 67.0 64.5 217s PrivateWages_11 1 61.2 67.0 217s PrivateWages_12 1 53.4 61.2 217s PrivateWages_13 1 44.3 53.4 217s PrivateWages_14 1 45.1 44.3 217s PrivateWages_15 1 49.7 45.1 217s PrivateWages_16 1 54.4 49.7 217s PrivateWages_17 1 62.7 54.4 217s PrivateWages_18 1 65.0 62.7 217s PrivateWages_19 1 60.9 65.0 217s PrivateWages_20 1 69.5 60.9 217s PrivateWages_21 1 75.7 69.5 217s PrivateWages_22 1 88.4 75.7 217s PrivateWages_trend 217s Consumption_2 0 217s Consumption_3 0 217s Consumption_4 0 217s Consumption_5 0 217s Consumption_6 0 217s Consumption_7 0 217s Consumption_8 0 217s Consumption_9 0 217s Consumption_11 0 217s Consumption_12 0 217s Consumption_14 0 217s Consumption_15 0 217s Consumption_16 0 217s Consumption_17 0 217s Consumption_18 0 217s Consumption_19 0 217s Consumption_20 0 217s Consumption_21 0 217s Consumption_22 0 217s Investment_2 0 217s Investment_3 0 217s Investment_4 0 217s Investment_5 0 217s Investment_6 0 217s Investment_7 0 217s Investment_8 0 217s Investment_9 0 217s Investment_10 0 217s Investment_11 0 217s Investment_12 0 217s Investment_14 0 217s Investment_15 0 217s Investment_17 0 217s Investment_18 0 217s Investment_19 0 217s Investment_20 0 217s Investment_21 0 217s Investment_22 0 217s PrivateWages_2 -10 217s PrivateWages_3 -9 217s PrivateWages_4 -8 217s PrivateWages_5 -7 217s PrivateWages_6 -6 217s PrivateWages_8 -4 217s PrivateWages_9 -3 217s PrivateWages_10 -2 217s PrivateWages_11 -1 217s PrivateWages_12 0 217s PrivateWages_13 1 217s PrivateWages_14 2 217s PrivateWages_15 3 217s PrivateWages_16 4 217s PrivateWages_17 5 217s PrivateWages_18 6 217s PrivateWages_19 7 217s PrivateWages_20 8 217s PrivateWages_21 9 217s PrivateWages_22 10 217s > nobs 217s [1] 58 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 46 1 0.3 0.59 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 46 1 0.29 0.6 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 47 217s 2 46 1 0.29 0.59 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 46 2 0.16 0.85 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 46 2 0.15 0.86 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 48 217s 2 46 2 0.3 0.86 217s > logLik 217s 'log Lik.' -68.8 (df=13) 217s 'log Lik.' -73.3 (df=13) 217s compare log likelihood value with single-equation OLS 217s [1] "Mean relative difference: 0.0011" 217s > 217s > # 2SLS 217s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: 2SLS 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 56 44 57.9 0.391 0.968 0.992 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 18 14 22.27 1.591 1.26 0.974 0.968 217s Investment 18 14 25.85 1.847 1.36 0.847 0.815 217s PrivateWages 20 16 9.74 0.609 0.78 0.988 0.985 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.307 0.540 -0.431 217s Investment 0.540 1.319 0.119 217s PrivateWages -0.431 0.119 0.496 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.000 0.414 -0.538 217s Investment 0.414 1.000 0.139 217s PrivateWages -0.538 0.139 1.000 217s 217s 217s 2SLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 17.2849 1.6463 10.50 5.1e-08 *** 217s corpProf -0.0770 0.1683 -0.46 0.65 217s corpProfLag 0.2327 0.1276 1.82 0.09 . 217s wages 0.8259 0.0472 17.49 6.6e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.261 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 22.269 MSE: 1.591 Root MSE: 1.261 217s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 217s 217s 217s 2SLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 18.2571 7.3132 2.50 0.02564 * 217s corpProf 0.1564 0.1942 0.81 0.43408 217s corpProfLag 0.5714 0.1672 3.42 0.00417 ** 217s capitalLag -0.1446 0.0346 -4.18 0.00093 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.359 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 25.852 MSE: 1.847 Root MSE: 1.359 217s Multiple R-Squared: 0.847 Adjusted R-Squared: 0.815 217s 217s 217s 2SLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 1.3431 1.1879 1.13 0.275 217s gnp 0.4438 0.0361 12.28 1.5e-09 *** 217s gnpLag 0.1447 0.0392 3.69 0.002 ** 217s trend 0.1238 0.0308 4.01 0.001 ** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.78 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 9.741 MSE: 0.609 Root MSE: 0.78 217s Multiple R-Squared: 0.988 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.6754 -1.214 -1.3401 217s 3 -0.4627 0.325 0.2378 217s 4 -1.1585 1.094 1.1117 217s 5 -0.0305 -1.368 -0.1954 217s 6 0.4693 0.486 -0.5355 217s 7 NA NA NA 217s 8 1.6045 1.066 -0.7908 217s 9 1.6018 0.156 0.2831 217s 10 NA 1.853 1.1353 217s 11 -0.9031 -0.898 -0.1765 217s 12 -1.5948 -1.012 0.6007 217s 13 NA NA 0.1443 217s 14 0.2854 0.845 0.4826 217s 15 -0.4718 -0.365 0.3016 217s 16 -0.2268 NA 0.0261 217s 17 2.0079 1.685 -0.8614 217s 18 -0.7434 -0.121 0.9927 217s 19 -0.5410 -3.248 -0.4446 217s 20 1.4186 0.241 -0.3914 217s 21 1.1462 -0.013 -1.1115 217s 22 -1.7256 0.489 0.5312 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.6 1.014 26.8 217s 3 45.5 1.575 29.1 217s 4 50.4 4.106 33.0 217s 5 50.6 4.368 34.1 217s 6 52.1 4.614 35.9 217s 7 NA NA NA 217s 8 54.6 3.134 38.7 217s 9 55.7 2.844 38.9 217s 10 NA 3.247 40.2 217s 11 55.9 1.898 38.1 217s 12 52.5 -2.388 33.9 217s 13 NA NA 28.9 217s 14 46.2 -5.945 28.0 217s 15 49.2 -2.635 30.3 217s 16 51.5 NA 33.2 217s 17 55.7 0.415 37.7 217s 18 59.4 2.121 40.0 217s 19 58.0 1.348 38.6 217s 20 60.2 1.059 42.0 217s 21 63.9 3.313 46.1 217s 22 71.4 4.411 52.8 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.6 0.586 41.3 43.8 217s 3 45.5 0.674 44.0 46.9 217s 4 50.4 0.443 49.4 51.3 217s 5 50.6 0.524 49.5 51.8 217s 6 52.1 0.535 51.0 53.3 217s 7 NA NA NA NA 217s 8 54.6 0.431 53.7 55.5 217s 9 55.7 0.510 54.6 56.8 217s 10 NA NA NA NA 217s 11 55.9 0.936 53.9 57.9 217s 12 52.5 0.893 50.6 54.4 217s 13 NA NA NA NA 217s 14 46.2 0.713 44.7 47.7 217s 15 49.2 0.501 48.1 50.2 217s 16 51.5 0.407 50.7 52.4 217s 17 55.7 0.457 54.7 56.7 217s 18 59.4 0.397 58.6 60.3 217s 19 58.0 0.564 56.8 59.2 217s 20 60.2 0.543 59.0 61.3 217s 21 63.9 0.529 62.7 65.0 217s 22 71.4 0.808 69.7 73.2 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 1.014 0.919 -0.957 2.985 217s 3 1.575 0.602 0.284 2.867 217s 4 4.106 0.544 2.940 5.272 217s 5 4.368 0.450 3.402 5.333 217s 6 4.614 0.425 3.703 5.526 217s 7 NA NA NA NA 217s 8 3.134 0.352 2.380 3.889 217s 9 2.844 0.544 1.677 4.012 217s 10 3.247 0.592 1.976 4.518 217s 11 1.898 0.978 -0.200 3.996 217s 12 -2.388 0.886 -4.289 -0.488 217s 13 NA NA NA NA 217s 14 -5.945 0.916 -7.909 -3.980 217s 15 -2.635 0.518 -3.745 -1.525 217s 16 NA NA NA NA 217s 17 0.415 0.507 -0.671 1.501 217s 18 2.121 0.329 1.416 2.826 217s 19 1.348 0.551 0.166 2.529 217s 20 1.059 0.582 -0.189 2.306 217s 21 3.313 0.496 2.248 4.377 217s 22 4.411 0.728 2.850 5.971 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.8 0.330 26.1 27.5 217s 3 29.1 0.344 28.3 29.8 217s 4 33.0 0.363 32.2 33.8 217s 5 34.1 0.260 33.5 34.6 217s 6 35.9 0.268 35.4 36.5 217s 7 NA NA NA NA 217s 8 38.7 0.265 38.1 39.3 217s 9 38.9 0.252 38.4 39.5 217s 10 40.2 0.242 39.7 40.7 217s 11 38.1 0.358 37.3 38.8 217s 12 33.9 0.385 33.1 34.7 217s 13 28.9 0.460 27.9 29.8 217s 14 28.0 0.351 27.3 28.8 217s 15 30.3 0.343 29.6 31.0 217s 16 33.2 0.287 32.6 33.8 217s 17 37.7 0.296 37.0 38.3 217s 18 40.0 0.220 39.5 40.5 217s 19 38.6 0.361 37.9 39.4 217s 20 42.0 0.309 41.3 42.6 217s 21 46.1 0.312 45.4 46.8 217s 22 52.8 0.501 51.7 53.8 217s > model.frame 217s consump corpProf corpProfLag wages invest capitalLag privWage gnp gnpLag 217s 1 39.8 12.7 NA 31.0 2.7 180 28.8 44.9 NA 217s 2 41.9 12.4 12.7 28.2 -0.2 183 25.5 45.6 44.9 217s 3 45.0 16.9 12.4 32.2 1.9 183 29.3 50.1 45.6 217s 4 49.2 18.4 16.9 37.0 5.2 184 34.1 57.2 50.1 217s 5 50.6 19.4 18.4 37.0 3.0 190 33.9 57.1 57.2 217s 6 52.6 20.1 19.4 38.6 5.1 193 35.4 61.0 57.1 217s 7 55.1 19.6 20.1 40.7 5.6 198 37.4 64.0 NA 217s 8 56.2 19.8 19.6 41.5 4.2 203 37.9 64.4 64.0 217s 9 57.3 21.1 19.8 42.9 3.0 208 39.2 64.5 64.4 217s 10 57.8 21.7 21.1 NA 5.1 211 41.3 67.0 64.5 217s 11 55.0 15.6 21.7 42.1 1.0 216 37.9 61.2 67.0 217s 12 50.9 11.4 15.6 39.3 -3.4 217 34.5 53.4 61.2 217s 13 45.6 NA 11.4 34.3 -6.2 213 29.0 44.3 53.4 217s 14 46.5 11.2 7.0 34.1 -5.1 207 28.5 45.1 44.3 217s 15 48.7 12.3 11.2 36.6 -3.0 202 30.6 49.7 45.1 217s 16 51.3 14.0 12.3 39.3 NA 199 33.2 54.4 49.7 217s 17 57.7 17.6 14.0 44.2 2.1 198 36.8 62.7 54.4 217s 18 58.7 17.3 17.6 47.7 2.0 200 41.0 65.0 62.7 217s 19 57.5 15.3 17.3 45.9 -1.9 202 38.2 60.9 65.0 217s 20 61.6 19.0 15.3 49.4 1.3 200 41.6 69.5 60.9 217s 21 65.0 21.1 19.0 53.0 3.3 201 45.0 75.7 69.5 217s 22 69.7 23.5 21.1 61.8 4.9 204 53.3 88.4 75.7 217s trend 217s 1 -11 217s 2 -10 217s 3 -9 217s 4 -8 217s 5 -7 217s 6 -6 217s 7 -5 217s 8 -4 217s 9 -3 217s 10 -2 217s 11 -1 217s 12 0 217s 13 1 217s 14 2 217s 15 3 217s 16 4 217s 17 5 217s 18 6 217s 19 7 217s 20 8 217s 21 9 217s 22 10 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 217s [3] "Numeric: lengths (696, 672) differ" 217s > nobs 217s [1] 56 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 45 217s 2 44 1 1.27 0.27 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 45 217s 2 44 1 1.66 0.2 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 45 217s 2 44 1 1.66 0.2 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 44 2 0.64 0.53 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 44 2 0.84 0.44 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 46 217s 2 44 2 1.68 0.43 217s > logLik 217s 'log Lik.' -69.5 (df=13) 217s 'log Lik.' -77.5 (df=13) 217s > 217s > # SUR 217s Warning in systemfit(system, method = method, data = KleinI, methodResidCov = ifelse(method == : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: SUR 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 58 46 45.1 0.199 0.975 0.993 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 19 15 17.5 1.167 1.080 0.980 0.975 217s Investment 19 15 17.3 1.155 1.075 0.906 0.887 217s PrivateWages 20 16 10.3 0.642 0.801 0.987 0.985 217s 217s The covariance matrix of the residuals used for estimation 217s Consumption Investment PrivateWages 217s Consumption 0.9830 0.0466 -0.391 217s Investment 0.0466 0.8101 0.115 217s PrivateWages -0.3906 0.1155 0.496 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 0.979 0.080 -0.452 217s Investment 0.080 0.810 0.181 217s PrivateWages -0.452 0.181 0.521 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.0000 0.0907 -0.636 217s Investment 0.0907 1.0000 0.267 217s PrivateWages -0.6362 0.2671 1.000 217s 217s 217s SUR estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 16.2670 1.3148 12.37 2.8e-09 *** 217s corpProf 0.1942 0.0954 2.04 0.06 . 217s corpProfLag 0.0747 0.0842 0.89 0.39 217s wages 0.8011 0.0383 20.93 1.6e-12 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.08 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 17.501 MSE: 1.167 Root MSE: 1.08 217s Multiple R-Squared: 0.98 Adjusted R-Squared: 0.975 217s 217s 217s SUR estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 12.6390 4.7856 2.64 0.01852 * 217s corpProf 0.4708 0.0943 4.99 0.00016 *** 217s corpProfLag 0.3533 0.0907 3.89 0.00144 ** 217s capitalLag -0.1254 0.0236 -5.32 8.6e-05 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.075 on 15 degrees of freedom 217s Number of observations: 19 Degrees of Freedom: 15 217s SSR: 17.321 MSE: 1.155 Root MSE: 1.075 217s Multiple R-Squared: 0.906 Adjusted R-Squared: 0.887 217s 217s 217s SUR estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 1.3264 1.1240 1.18 0.2552 217s gnp 0.4184 0.0268 15.63 4.1e-11 *** 217s gnpLag 0.1714 0.0315 5.43 5.5e-05 *** 217s trend 0.1456 0.0284 5.13 0.0001 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.801 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 10.266 MSE: 0.642 Root MSE: 0.801 217s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.3143 -0.2326 -1.1434 217s 3 -1.2700 -0.1705 0.5084 217s 4 -1.5426 1.0718 1.4211 217s 5 -0.4489 -1.4767 -0.0992 217s 6 0.0588 0.3167 -0.3594 217s 7 0.9213 1.4446 NA 217s 8 1.3789 0.8296 -0.7554 217s 9 1.0900 -0.5263 0.2887 217s 10 NA 1.2083 1.1800 217s 11 0.3569 0.4082 -0.3673 217s 12 -0.2288 0.2663 0.3445 217s 13 NA NA -0.1571 217s 14 0.2181 0.4946 0.4220 217s 15 -0.1120 -0.0470 0.3147 217s 16 -0.0872 NA 0.0145 217s 17 1.5615 1.0289 -0.8091 217s 18 -0.4530 0.0617 0.8608 217s 19 0.1997 -2.5397 -0.7635 217s 20 0.9268 -0.6136 -0.4046 217s 21 0.7588 -0.7465 -1.2179 217s 22 -2.2137 -0.6044 0.5606 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.2 0.0326 26.6 217s 3 46.3 2.0705 28.8 217s 4 50.7 4.1282 32.7 217s 5 51.0 4.4767 34.0 217s 6 52.5 4.7833 35.8 217s 7 54.2 4.1554 NA 217s 8 54.8 3.3704 38.7 217s 9 56.2 3.5263 38.9 217s 10 NA 3.8917 40.1 217s 11 54.6 0.5918 38.3 217s 12 51.1 -3.6663 34.2 217s 13 NA NA 29.2 217s 14 46.3 -5.5946 28.1 217s 15 48.8 -2.9530 30.3 217s 16 51.4 NA 33.2 217s 17 56.1 1.0711 37.6 217s 18 59.2 1.9383 40.1 217s 19 57.3 0.6397 39.0 217s 20 60.7 1.9136 42.0 217s 21 64.2 4.0465 46.2 217s 22 71.9 5.5044 52.7 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.2 0.460 41.3 43.1 217s 3 46.3 0.489 45.3 47.3 217s 4 50.7 0.328 50.1 51.4 217s 5 51.0 0.384 50.3 51.8 217s 6 52.5 0.389 51.8 53.3 217s 7 54.2 0.347 53.5 54.9 217s 8 54.8 0.319 54.2 55.5 217s 9 56.2 0.353 55.5 56.9 217s 10 NA NA NA NA 217s 11 54.6 0.583 53.5 55.8 217s 12 51.1 0.524 50.1 52.2 217s 13 NA NA NA NA 217s 14 46.3 0.589 45.1 47.5 217s 15 48.8 0.393 48.0 49.6 217s 16 51.4 0.337 50.7 52.1 217s 17 56.1 0.345 55.4 56.8 217s 18 59.2 0.318 58.5 59.8 217s 19 57.3 0.381 56.5 58.1 217s 20 60.7 0.413 59.8 61.5 217s 21 64.2 0.417 63.4 65.1 217s 22 71.9 0.651 70.6 73.2 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 0.0326 0.556 -1.0866 1.15 217s 3 2.0705 0.454 1.1575 2.98 217s 4 4.1282 0.399 3.3256 4.93 217s 5 4.4767 0.331 3.8101 5.14 217s 6 4.7833 0.314 4.1520 5.41 217s 7 4.1554 0.291 3.5687 4.74 217s 8 3.3704 0.260 2.8469 3.89 217s 9 3.5263 0.347 2.8278 4.22 217s 10 3.8917 0.397 3.0924 4.69 217s 11 0.5918 0.578 -0.5711 1.75 217s 12 -3.6663 0.551 -4.7762 -2.56 217s 13 NA NA NA NA 217s 14 -5.5946 0.661 -6.9261 -4.26 217s 15 -2.9530 0.392 -3.7430 -2.16 217s 16 NA NA NA NA 217s 17 1.0711 0.318 0.4315 1.71 217s 18 1.9383 0.225 1.4863 2.39 217s 19 0.6397 0.310 0.0165 1.26 217s 20 1.9136 0.333 1.2436 2.58 217s 21 4.0465 0.304 3.4345 4.66 217s 22 5.5044 0.429 4.6400 6.37 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.6 0.321 26.0 27.3 217s 3 28.8 0.321 28.1 29.4 217s 4 32.7 0.316 32.0 33.3 217s 5 34.0 0.244 33.5 34.5 217s 6 35.8 0.242 35.3 36.2 217s 7 NA NA NA NA 217s 8 38.7 0.246 38.2 39.2 217s 9 38.9 0.234 38.4 39.4 217s 10 40.1 0.225 39.7 40.6 217s 11 38.3 0.301 37.7 38.9 217s 12 34.2 0.298 33.6 34.8 217s 13 29.2 0.353 28.4 29.9 217s 14 28.1 0.330 27.4 28.7 217s 15 30.3 0.328 29.6 30.9 217s 16 33.2 0.275 32.6 33.7 217s 17 37.6 0.270 37.1 38.2 217s 18 40.1 0.213 39.7 40.6 217s 19 39.0 0.301 38.4 39.6 217s 20 42.0 0.287 41.4 42.6 217s 21 46.2 0.304 45.6 46.8 217s 22 52.7 0.448 51.8 53.6 217s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] TRUE 217s > nobs 217s [1] 58 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 46 1 0.4 0.53 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 47 217s 2 46 1 0.49 0.49 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 47 217s 2 46 1 0.49 0.48 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 46 2 0.31 0.74 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 48 217s 2 46 2 0.37 0.69 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 48 217s 2 46 2 0.75 0.69 217s > logLik 217s 'log Lik.' -66.4 (df=18) 217s 'log Lik.' -74.1 (df=18) 217s > 217s > # 3SLS 217s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: 3SLS 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 56 44 67.5 0.436 0.963 0.993 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 18 14 22.4 1.598 1.264 0.974 0.968 217s Investment 18 14 35.0 2.503 1.582 0.793 0.749 217s PrivateWages 20 16 10.1 0.629 0.793 0.987 0.985 217s 217s The covariance matrix of the residuals used for estimation 217s Consumption Investment PrivateWages 217s Consumption 1.307 0.540 -0.431 217s Investment 0.540 1.319 0.119 217s PrivateWages -0.431 0.119 0.496 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.309 0.638 -0.440 217s Investment 0.638 1.749 0.233 217s PrivateWages -0.440 0.233 0.519 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.000 0.422 -0.532 217s Investment 0.422 1.000 0.247 217s PrivateWages -0.532 0.247 1.000 217s 217s 217s 3SLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 18.0338 1.5648 11.52 1.6e-08 *** 217s corpProf -0.0632 0.1500 -0.42 0.68 217s corpProfLag 0.1784 0.1154 1.55 0.14 217s wages 0.8224 0.0444 18.54 3.0e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.264 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 22.377 MSE: 1.598 Root MSE: 1.264 217s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 217s 217s 217s 3SLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 24.6766 6.7008 3.68 0.00246 ** 217s corpProf 0.0472 0.1843 0.26 0.80149 217s corpProfLag 0.6874 0.1577 4.36 0.00065 *** 217s capitalLag -0.1776 0.0318 -5.59 6.7e-05 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.582 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 35.037 MSE: 2.503 Root MSE: 1.582 217s Multiple R-Squared: 0.793 Adjusted R-Squared: 0.749 217s 217s 217s 3SLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 0.7823 1.1254 0.70 0.49695 217s gnp 0.4257 0.0308 13.80 2.6e-10 *** 217s gnpLag 0.1728 0.0341 5.07 0.00011 *** 217s trend 0.1252 0.0291 4.30 0.00055 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.793 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 10.057 MSE: 0.629 Root MSE: 0.793 217s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.8058 -1.721 -1.20135 217s 3 -0.6573 0.337 0.43696 217s 4 -1.1124 0.810 1.31177 217s 5 0.0833 -1.544 -0.19794 217s 6 0.6334 0.368 -0.46596 217s 7 NA NA NA 217s 8 1.7939 1.245 -0.85614 217s 9 1.7891 0.593 0.20698 217s 10 NA 2.303 1.10034 217s 11 -0.5397 -1.015 -0.38801 217s 12 -1.5147 -0.846 0.40949 217s 13 NA NA 0.00602 217s 14 -0.1171 1.670 0.61306 217s 15 -0.6526 -0.075 0.49152 217s 16 -0.3617 NA 0.17066 217s 17 1.9331 2.086 -0.69991 217s 18 -0.6063 -0.101 0.96136 217s 19 -0.3990 -3.345 -0.61606 217s 20 1.4134 0.717 -0.29343 217s 21 1.3257 0.306 -1.14412 217s 22 -1.4340 0.935 0.55310 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.7 1.5213 26.7 217s 3 45.7 1.5632 28.9 217s 4 50.3 4.3898 32.8 217s 5 50.5 4.5444 34.1 217s 6 52.0 4.7320 35.9 217s 7 NA NA NA 217s 8 54.4 2.9547 38.8 217s 9 55.5 2.4075 39.0 217s 10 NA 2.7965 40.2 217s 11 55.5 2.0150 38.3 217s 12 52.4 -2.5541 34.1 217s 13 NA NA 29.0 217s 14 46.6 -6.7699 27.9 217s 15 49.4 -2.9250 30.1 217s 16 51.7 NA 33.0 217s 17 55.8 0.0139 37.5 217s 18 59.3 2.1013 40.0 217s 19 57.9 1.4453 38.8 217s 20 60.2 0.5828 41.9 217s 21 63.7 2.9944 46.1 217s 22 71.1 3.9651 52.7 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.7 0.555 39.7 45.7 217s 3 45.7 0.628 42.6 48.7 217s 4 50.3 0.418 47.5 53.2 217s 5 50.5 0.492 47.6 53.4 217s 6 52.0 0.501 49.0 54.9 217s 7 NA NA NA NA 217s 8 54.4 0.405 51.6 57.3 217s 9 55.5 0.477 52.6 58.4 217s 10 NA NA NA NA 217s 11 55.5 0.832 52.3 58.8 217s 12 52.4 0.792 49.2 55.6 217s 13 NA NA NA NA 217s 14 46.6 0.676 43.5 49.7 217s 15 49.4 0.470 46.5 52.2 217s 16 51.7 0.386 48.8 54.5 217s 17 55.8 0.433 52.9 58.6 217s 18 59.3 0.368 56.5 62.1 217s 19 57.9 0.504 55.0 60.8 217s 20 60.2 0.513 57.3 63.1 217s 21 63.7 0.505 60.8 66.6 217s 22 71.1 0.771 68.0 74.3 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 1.5213 0.857 -2.337 5.380 217s 3 1.5632 0.589 -2.058 5.184 217s 4 4.3898 0.519 0.819 7.961 217s 5 4.5444 0.436 1.025 8.064 217s 6 4.7320 0.415 1.224 8.240 217s 7 NA NA NA NA 217s 8 2.9547 0.342 -0.517 6.426 217s 9 2.4075 0.511 -1.158 5.973 217s 10 2.7965 0.556 -0.800 6.393 217s 11 2.0150 0.955 -1.948 5.978 217s 12 -2.5541 0.874 -6.431 1.323 217s 13 NA NA NA NA 217s 14 -6.7699 0.865 -10.637 -2.903 217s 15 -2.9250 0.503 -6.485 0.635 217s 16 NA NA NA NA 217s 17 0.0139 0.483 -3.534 3.561 217s 18 2.1013 0.320 -1.361 5.563 217s 19 1.4453 0.532 -2.134 5.025 217s 20 0.5828 0.550 -3.010 4.175 217s 21 2.9944 0.476 -0.549 6.538 217s 22 3.9651 0.692 0.261 7.669 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.7 0.324 24.9 28.5 217s 3 28.9 0.331 27.0 30.7 217s 4 32.8 0.339 31.0 34.6 217s 5 34.1 0.248 32.3 35.9 217s 6 35.9 0.256 34.1 37.6 217s 7 NA NA NA NA 217s 8 38.8 0.251 37.0 40.5 217s 9 39.0 0.238 37.2 40.7 217s 10 40.2 0.232 38.4 42.0 217s 11 38.3 0.314 36.5 40.1 217s 12 34.1 0.327 32.3 35.9 217s 13 29.0 0.393 27.1 30.9 217s 14 27.9 0.329 26.1 29.7 217s 15 30.1 0.324 28.3 31.9 217s 16 33.0 0.271 31.3 34.8 217s 17 37.5 0.277 35.7 39.3 217s 18 40.0 0.213 38.3 41.8 217s 19 38.8 0.320 37.0 40.6 217s 20 41.9 0.295 40.1 43.7 217s 21 46.1 0.309 44.3 47.9 217s 22 52.7 0.476 50.8 54.7 217s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 217s [3] "Numeric: lengths (696, 672) differ" 217s > nobs 217s [1] 56 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 45 217s 2 44 1 1.91 0.17 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 45 217s 2 44 1 2.6 0.11 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 45 217s 2 44 1 2.6 0.11 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 44 2 1.62 0.21 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 44 2 2.2 0.12 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 46 217s 2 44 2 4.41 0.11 217s > logLik 217s 'log Lik.' -70.1 (df=18) 217s 'log Lik.' -80.6 (df=18) 217s > 217s > # I3SLS 217s Warning in systemfit(system, method = method, data = KleinI, inst = inst, : 217s the estimation of systems of equations with unequal numbers of observations has not been thoroughly tested yet 217s > summary 217s 217s systemfit results 217s method: iterated 3SLS 217s 217s convergence achieved after 10 iterations 217s 217s N DF SSR detRCov OLS-R2 McElroy-R2 217s system 56 44 79.4 0.55 0.956 0.994 217s 217s N DF SSR MSE RMSE R2 Adj R2 217s Consumption 18 14 22.3 1.595 1.263 0.974 0.968 217s Investment 18 14 46.8 3.346 1.829 0.724 0.664 217s PrivateWages 20 16 10.2 0.639 0.799 0.987 0.985 217s 217s The covariance matrix of the residuals used for estimation 217s Consumption Investment PrivateWages 217s Consumption 1.307 0.750 -0.452 217s Investment 0.750 2.318 0.272 217s PrivateWages -0.452 0.272 0.530 217s 217s The covariance matrix of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.307 0.750 -0.452 217s Investment 0.750 2.318 0.272 217s PrivateWages -0.452 0.272 0.530 217s 217s The correlations of the residuals 217s Consumption Investment PrivateWages 217s Consumption 1.000 0.424 -0.542 217s Investment 0.424 1.000 0.254 217s PrivateWages -0.542 0.254 1.000 217s 217s 217s 3SLS estimates for 'Consumption' (equation 1) 217s Model Formula: consump ~ corpProf + corpProfLag + wages 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 18.3252 1.5452 11.86 1.1e-08 *** 217s corpProf -0.0436 0.1470 -0.30 0.77 217s corpProfLag 0.1614 0.1127 1.43 0.17 217s wages 0.8127 0.0436 18.65 2.8e-11 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.263 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 22.337 MSE: 1.595 Root MSE: 1.263 217s Multiple R-Squared: 0.974 Adjusted R-Squared: 0.968 217s 217s 217s 3SLS estimates for 'Investment' (equation 2) 217s Model Formula: invest ~ corpProf + corpProfLag + capitalLag 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 30.2418 8.3674 3.61 0.00282 ** 217s corpProf -0.0437 0.2341 -0.19 0.85457 217s corpProfLag 0.7856 0.1993 3.94 0.00147 ** 217s capitalLag -0.2065 0.0397 -5.20 0.00014 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 1.829 on 14 degrees of freedom 217s Number of observations: 18 Degrees of Freedom: 14 217s SSR: 46.838 MSE: 3.346 Root MSE: 1.829 217s Multiple R-Squared: 0.724 Adjusted R-Squared: 0.664 217s 217s 217s 3SLS estimates for 'PrivateWages' (equation 3) 217s Model Formula: privWage ~ gnp + gnpLag + trend 217s Instruments: ~govExp + taxes + govWage + trend + capitalLag + corpProfLag + 217s gnpLag 217s 217s Estimate Std. Error t value Pr(>|t|) 217s (Intercept) 0.4741 1.1280 0.42 0.67983 217s gnp 0.4268 0.0296 14.44 1.4e-10 *** 217s gnpLag 0.1767 0.0330 5.35 6.5e-05 *** 217s trend 0.1201 0.0290 4.14 0.00076 *** 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s 217s Residual standard error: 0.799 on 16 degrees of freedom 217s Number of observations: 20 Degrees of Freedom: 16 217s SSR: 10.218 MSE: 0.639 Root MSE: 0.799 217s Multiple R-Squared: 0.987 Adjusted R-Squared: 0.985 217s 217s > residuals 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 -0.8546 -2.1226 -1.1687 217s 3 -0.7611 0.3684 0.4670 217s 4 -1.1233 0.5912 1.3216 217s 5 0.0781 -1.6694 -0.2108 217s 6 0.6467 0.2952 -0.4776 217s 7 NA NA NA 217s 8 1.8444 1.4348 -0.8884 217s 9 1.8309 1.0020 0.1781 217s 10 NA 2.7265 1.0734 217s 11 -0.3652 -1.0581 -0.4134 217s 12 -1.3877 -0.6431 0.4203 217s 13 NA NA 0.0623 217s 14 -0.1818 2.4214 0.7091 217s 15 -0.6438 0.2168 0.5845 217s 16 -0.3417 NA 0.2455 217s 17 1.9583 2.4607 -0.6474 217s 18 -0.4806 -0.0468 0.9840 217s 19 -0.2563 -3.3855 -0.5930 217s 20 1.4832 1.1550 -0.2586 217s 21 1.4514 0.6086 -1.1446 217s 22 -1.2351 1.3453 0.5196 217s > fitted 217s Consumption Investment PrivateWages 217s 1 NA NA NA 217s 2 42.8 1.923 26.7 217s 3 45.8 1.532 28.8 217s 4 50.3 4.609 32.8 217s 5 50.5 4.669 34.1 217s 6 52.0 4.805 35.9 217s 7 NA NA NA 217s 8 54.4 2.765 38.8 217s 9 55.5 1.998 39.0 217s 10 NA 2.373 40.2 217s 11 55.4 2.058 38.3 217s 12 52.3 -2.757 34.1 217s 13 NA NA 28.9 217s 14 46.7 -7.521 27.8 217s 15 49.3 -3.217 30.0 217s 16 51.6 NA 33.0 217s 17 55.7 -0.361 37.4 217s 18 59.2 2.047 40.0 217s 19 57.8 1.485 38.8 217s 20 60.1 0.145 41.9 217s 21 63.5 2.691 46.1 217s 22 70.9 3.555 52.8 217s > predict 217s Consumption.pred Consumption.se.fit Consumption.lwr Consumption.upr 217s 1 NA NA NA NA 217s 2 42.8 0.548 41.7 43.9 217s 3 45.8 0.618 44.5 47.0 217s 4 50.3 0.411 49.5 51.2 217s 5 50.5 0.481 49.6 51.5 217s 6 52.0 0.490 51.0 52.9 217s 7 NA NA NA NA 217s 8 54.4 0.396 53.6 55.2 217s 9 55.5 0.467 54.5 56.4 217s 10 NA NA NA NA 217s 11 55.4 0.811 53.7 57.0 217s 12 52.3 0.775 50.7 53.8 217s 13 NA NA NA NA 217s 14 46.7 0.665 45.3 48.0 217s 15 49.3 0.463 48.4 50.3 217s 16 51.6 0.381 50.9 52.4 217s 17 55.7 0.428 54.9 56.6 217s 18 59.2 0.360 58.5 59.9 217s 19 57.8 0.492 56.8 58.7 217s 20 60.1 0.508 59.1 61.1 217s 21 63.5 0.499 62.5 64.6 217s 22 70.9 0.761 69.4 72.5 217s Investment.pred Investment.se.fit Investment.lwr Investment.upr 217s 1 NA NA NA NA 217s 2 1.923 1.079 -0.2526 4.098 217s 3 1.532 0.766 -0.0119 3.075 217s 4 4.609 0.668 3.2632 5.954 217s 5 4.669 0.566 3.5280 5.811 217s 6 4.805 0.543 3.7104 5.899 217s 7 NA NA NA NA 217s 8 2.765 0.447 1.8648 3.665 217s 9 1.998 0.651 0.6860 3.310 217s 10 2.373 0.710 0.9434 3.804 217s 11 2.058 1.237 -0.4350 4.551 217s 12 -2.757 1.139 -5.0532 -0.461 217s 13 NA NA NA NA 217s 14 -7.521 1.094 -9.7261 -5.317 217s 15 -3.217 0.648 -4.5217 -1.912 217s 16 NA NA NA NA 217s 17 -0.361 0.615 -1.6007 0.879 217s 18 2.047 0.417 1.2060 2.888 217s 19 1.485 0.684 0.1062 2.865 217s 20 0.145 0.699 -1.2632 1.553 217s 21 2.691 0.614 1.4548 3.928 217s 22 3.555 0.887 1.7674 5.342 217s PrivateWages.pred PrivateWages.se.fit PrivateWages.lwr PrivateWages.upr 217s 1 NA NA NA NA 217s 2 26.7 0.330 26.0 27.3 217s 3 28.8 0.336 28.2 29.5 217s 4 32.8 0.340 32.1 33.5 217s 5 34.1 0.251 33.6 34.6 217s 6 35.9 0.259 35.4 36.4 217s 7 NA NA NA NA 217s 8 38.8 0.253 38.3 39.3 217s 9 39.0 0.240 38.5 39.5 217s 10 40.2 0.236 39.8 40.7 217s 11 38.3 0.307 37.7 38.9 217s 12 34.1 0.313 33.4 34.7 217s 13 28.9 0.376 28.2 29.7 217s 14 27.8 0.327 27.1 28.4 217s 15 30.0 0.322 29.4 30.7 217s 16 33.0 0.270 32.4 33.5 217s 17 37.4 0.275 36.9 38.0 217s 18 40.0 0.216 39.6 40.5 217s 19 38.8 0.314 38.2 39.4 217s 20 41.9 0.296 41.3 42.5 217s 21 46.1 0.317 45.5 46.8 217s 22 52.8 0.480 51.8 53.7 217s > model.frame 217s [1] TRUE 217s > model.matrix 217s [1] "Attributes: < Component “dim”: Mean relative difference: 0.0345 >" 217s [2] "Attributes: < Component “dimnames”: Component 1: 51 string mismatches >" 217s [3] "Numeric: lengths (696, 672) differ" 217s > nobs 217s [1] 56 217s > linearHypothesis 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 45 217s 2 44 1 2.29 0.14 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 45 217s 2 44 1 2.89 0.096 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (Chi^2 statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df Chisq Pr(>Chisq) 217s 1 45 217s 2 44 1 2.89 0.089 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 217s Linear hypothesis test (Theil's F test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 44 2 2.3 0.11 217s Linear hypothesis test (F statistic of a Wald test) 217s 217s Hypothesis: 217s Consumption_corpProf + Investment_capitalLag = 0 217s Consumption_corpProfLag - PrivateWages_trend = 0 217s 217s Model 1: restricted model 217s Model 2: kleinModel 217s 217s Res.Df Df F Pr(>F) 217s 1 46 217s 2 44 2 2.9 0.066 . 217s --- 217s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 218s Linear hypothesis test (Chi^2 statistic of a Wald test) 218s 218s Hypothesis: 218s Consumption_corpProf + Investment_capitalLag = 0 218s Consumption_corpProfLag - PrivateWages_trend = 0 218s 218s Model 1: restricted model 218s Model 2: kleinModel 218s 218s Res.Df Df Chisq Pr(>Chisq) 218s 1 46 218s 2 44 2 5.79 0.055 . 218s --- 218s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 218s > logLik 218s 'log Lik.' -72.2 (df=18) 218s 'log Lik.' -83.4 (df=18) 218s > 218s BEGIN TEST test_2sls.R 218s 218s R version 4.3.2 (2023-10-31) -- "Eye Holes" 218s Copyright (C) 2023 The R Foundation for Statistical Computing 218s Platform: aarch64-unknown-linux-gnu (64-bit) 218s 218s R is free software and comes with ABSOLUTELY NO WARRANTY. 218s You are welcome to redistribute it under certain conditions. 218s Type 'license()' or 'licence()' for distribution details. 218s 218s R is a collaborative project with many contributors. 218s Type 'contributors()' for more information and 218s 'citation()' on how to cite R or R packages in publications. 218s 218s Type 'demo()' for some demos, 'help()' for on-line help, or 218s 'help.start()' for an HTML browser interface to help. 218s Type 'q()' to quit R. 218s 218s > library( systemfit ) 218s Loading required package: Matrix 219s Loading required package: car 219s Loading required package: carData 219s Loading required package: lmtest 219s Loading required package: zoo 219s 219s Attaching package: ‘zoo’ 219s 219s The following objects are masked from ‘package:base’: 219s 219s as.Date, as.Date.numeric 219s 219s 219s Please cite the 'systemfit' package as: 219s 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/. 219s 219s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 219s https://r-forge.r-project.org/projects/systemfit/ 219s > options( digits = 3 ) 219s > 219s > data( "Kmenta" ) 219s > useMatrix <- FALSE 219s > 219s > demand <- consump ~ price + income 219s > supply <- consump ~ price + farmPrice + trend 219s > inst <- ~ income + farmPrice + trend 219s > inst1 <- ~ income + farmPrice 219s > instlist <- list( inst1, inst ) 219s > system <- list( demand = demand, supply = supply ) 219s > restrm <- matrix(0,1,7) # restriction matrix "R" 219s > restrm[1,3] <- 1 219s > restrm[1,7] <- -1 219s > restrict <- "demand_income - supply_trend = 0" 219s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 219s > restr2m[1,3] <- 1 219s > restr2m[1,7] <- -1 219s > restr2m[2,2] <- -1 219s > restr2m[2,5] <- 1 219s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 219s > restrict2 <- c( "demand_income - supply_trend = 0", 219s + "- demand_price + supply_price = 0.5" ) 219s > tc <- matrix(0,7,6) 219s > tc[1,1] <- 1 219s > tc[2,2] <- 1 219s > tc[3,3] <- 1 219s > tc[4,4] <- 1 219s > tc[5,5] <- 1 219s > tc[6,6] <- 1 219s > tc[7,3] <- 1 219s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 219s > restr3m[1,2] <- -1 219s > restr3m[1,5] <- 1 219s > restr3q <- c( 0.5 ) # restriction vector "q" 2 219s > restrict3 <- "- C2 + C5 = 0.5" 219s > 219s > # It is not possible to estimate 2SLS with systemfit exactly 219s > # as EViews does, because EViews uses 219s > # methodResidCov == "geomean" for the coefficient covariance matrix and 219s > # methodResidCov == "noDfCor" for the residual covariance matrix. 219s > # systemfit uses always the same formulas for both calculations. 219s > 219s > ## *************** 2SLS estimation ************************ 219s > ## ************ 2SLS estimation (default)********************* 219s > fit2sls1 <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 219s + x = TRUE, useMatrix = useMatrix ) 219s > print( summary( fit2sls1 ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 33 162 4.36 0.697 0.548 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 65.7 3.87 1.97 0.755 0.726 219s supply 20 16 96.6 6.04 2.46 0.640 0.572 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.87 4.36 219s supply 4.36 6.04 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.902 219s supply 0.902 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 219s price -0.2436 0.0965 -2.52 0.022 * 219s income 0.3140 0.0469 6.69 3.8e-06 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.966 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 219s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 219s price 0.2401 0.0999 2.40 0.0288 * 219s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 219s trend 0.2529 0.0997 2.54 0.0219 * 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.458 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 219s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 219s 219s > nobs( fit2sls1 ) 219s [1] 40 219s > 219s > ## *************** 2SLS estimation (singleEqSigma=F)******************* 219s > fit2sls1s <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 219s + singleEqSigma = FALSE, useMatrix = useMatrix ) 219s > print( summary( fit2sls1s ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 33 162 4.36 0.697 0.548 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 65.7 3.87 1.97 0.755 0.726 219s supply 20 16 96.6 6.04 2.46 0.640 0.572 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.87 4.36 219s supply 4.36 6.04 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.902 219s supply 0.902 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.633 8.935 10.59 6.6e-09 *** 219s price -0.244 0.109 -2.24 0.039 * 219s income 0.314 0.053 5.93 1.6e-05 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.966 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 219s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 49.5324 10.8404 4.57 0.00032 *** 219s price 0.2401 0.0902 2.66 0.01706 * 219s farmPrice 0.2556 0.0426 5.99 1.9e-05 *** 219s trend 0.2529 0.0899 2.81 0.01253 * 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.458 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 219s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 219s 219s > nobs( fit2sls1s ) 219s [1] 40 219s > 219s > ## ********************* 2SLS (useDfSys = TRUE) ***************** 219s > print( summary( fit2sls1, useDfSys = TRUE ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 33 162 4.36 0.697 0.548 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 65.7 3.87 1.97 0.755 0.726 219s supply 20 16 96.6 6.04 2.46 0.640 0.572 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.87 4.36 219s supply 4.36 6.04 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.902 219s supply 0.902 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 219s price -0.2436 0.0965 -2.52 0.017 * 219s income 0.3140 0.0469 6.69 1.3e-07 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.966 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 219s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 219s price 0.2401 0.0999 2.40 0.02208 * 219s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 219s trend 0.2529 0.0997 2.54 0.01605 * 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.458 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 219s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 219s 219s > nobs( fit2sls1 ) 219s [1] 40 219s > 219s > ## ********************* 2SLS (methodResidCov = "noDfCor" ) ***************** 219s > fit2sls1r <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 219s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 219s > print( summary( fit2sls1r ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 33 162 2.97 0.697 0.525 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 65.7 3.87 1.97 0.755 0.726 219s supply 20 16 96.6 6.04 2.46 0.640 0.572 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.29 3.59 219s supply 3.59 4.83 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.902 219s supply 0.902 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 219s price -0.2436 0.0890 -2.74 0.014 * 219s income 0.3140 0.0433 7.25 1.3e-06 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.966 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 219s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 219s price 0.2401 0.0894 2.69 0.01623 * 219s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 219s trend 0.2529 0.0891 2.84 0.01188 * 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.458 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 219s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 219s 219s > nobs( fit2sls1r ) 219s [1] 40 219s > 219s > ## *************** 2SLS (methodResidCov="noDfCor", singleEqSigma=F) ************* 219s > fit2sls1rs <- systemfit( system, "2SLS", data = Kmenta, inst = inst, 219s + methodResidCov = "noDfCor", singleEqSigma = FALSE, useMatrix = useMatrix ) 219s > print( summary( fit2sls1rs ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 33 162 2.97 0.697 0.525 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 65.7 3.87 1.97 0.755 0.726 219s supply 20 16 96.6 6.04 2.46 0.640 0.572 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.29 3.59 219s supply 3.59 4.83 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.902 219s supply 0.902 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.6333 8.1158 11.66 1.6e-09 *** 219s price -0.2436 0.0989 -2.46 0.025 * 219s income 0.3140 0.0481 6.53 5.2e-06 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.966 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 219s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 49.5324 9.8463 5.03 0.00012 *** 219s price 0.2401 0.0819 2.93 0.00980 ** 219s farmPrice 0.2556 0.0387 6.60 6.1e-06 *** 219s trend 0.2529 0.0817 3.10 0.00694 ** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.458 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 219s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 219s 219s > nobs( fit2sls1rs ) 219s [1] 40 219s > 219s > ## ********************* 2SLS with restriction ******************** 219s > ## **************** 2SLS with restriction (default)******************** 219s > fit2sls2 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 219s + inst = inst, useMatrix = useMatrix ) 219s > print( summary( fit2sls2 ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 34 166 3.6 0.691 0.553 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 67.4 3.97 1.99 0.749 0.719 219s supply 20 16 98.2 6.13 2.48 0.634 0.565 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.97 4.55 219s supply 4.55 6.13 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.923 219s supply 0.923 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 219s price -0.2247 0.1034 -2.17 0.037 * 219s income 0.2983 0.0454 6.57 1.6e-07 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.991 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 219s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 219s price 0.2427 0.0896 2.71 0.011 * 219s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 219s trend 0.2983 0.0454 6.57 1.6e-07 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.477 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 219s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 219s 219s > nobs( fit2sls2 ) 219s [1] 40 219s > # the same with symbolically specified restrictions 219s > fit2sls2Sym <- systemfit( system, "2SLS", data = Kmenta, 219s + restrict.matrix = restrict, inst = inst, useMatrix = useMatrix ) 219s > all.equal( fit2sls2, fit2sls2Sym ) 219s [1] "Component “call”: target, current do not match when deparsed" 219s > nobs( fit2sls2Sym ) 219s [1] 40 219s > 219s > ## ************* 2SLS with restriction (singleEqSigma=T) ***************** 219s > fit2sls2s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 219s + inst = inst, singleEqSigma = TRUE, x = TRUE, 219s + useMatrix = useMatrix ) 219s > print( summary( fit2sls2s ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 34 166 3.6 0.691 0.553 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 67.4 3.97 1.99 0.749 0.719 219s supply 20 16 98.2 6.13 2.48 0.634 0.565 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.97 4.55 219s supply 4.55 6.13 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.923 219s supply 0.923 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.2816 8.0090 11.77 1.5e-13 *** 219s price -0.2247 0.0946 -2.37 0.023 * 219s income 0.2983 0.0430 6.94 5.3e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.991 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 219s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 48.1843 11.8001 4.08 0.00025 *** 219s price 0.2427 0.1006 2.41 0.02135 * 219s farmPrice 0.2619 0.0459 5.70 2.1e-06 *** 219s trend 0.2983 0.0430 6.94 5.3e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.477 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 219s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 219s 219s > nobs( fit2sls2s ) 219s [1] 40 219s > 219s > ## ********************* 2SLS with restriction (useDfSys=T) ************** 219s > print( summary( fit2sls2, useDfSys = TRUE ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 34 166 3.6 0.691 0.553 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 67.4 3.97 1.99 0.749 0.719 219s supply 20 16 98.2 6.13 2.48 0.634 0.565 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.97 4.55 219s supply 4.55 6.13 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.923 219s supply 0.923 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 219s price -0.2247 0.1034 -2.17 0.037 * 219s income 0.2983 0.0454 6.57 1.6e-07 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.991 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 219s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 219s price 0.2427 0.0896 2.71 0.011 * 219s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 219s trend 0.2983 0.0454 6.57 1.6e-07 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.477 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 219s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 219s 219s > nobs( fit2sls2 ) 219s [1] 40 219s > 219s > ## ********************* 2SLS with restriction (methodResidCov = "noDfCor") ************** 219s > fit2sls2r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 219s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 219s > print( summary( fit2sls2r ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 34 166 2.45 0.691 0.526 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 67.4 3.97 1.99 0.749 0.719 219s supply 20 16 98.2 6.13 2.48 0.634 0.565 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.37 3.75 219s supply 3.75 4.91 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.923 219s supply 0.923 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.2816 8.1771 11.53 2.7e-13 *** 219s price -0.2247 0.0954 -2.36 0.024 * 219s income 0.2983 0.0419 7.13 3.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.991 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 219s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 48.1843 9.7159 4.96 1.9e-05 *** 219s price 0.2427 0.0826 2.94 0.0059 ** 219s farmPrice 0.2619 0.0379 6.92 5.7e-08 *** 219s trend 0.2983 0.0419 7.13 3.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.477 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 219s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 219s 219s > nobs( fit2sls2r ) 219s [1] 40 219s > 219s > ## ******** 2SLS with restriction (methodResidCov="noDfCor", singleEqSigma=TRUE) ********* 219s > fit2sls2rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 219s + inst = inst, methodResidCov = "noDfCor", singleEqSigma = TRUE, 219s + useMatrix = useMatrix ) 219s > print( summary( fit2sls2rs ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 34 166 2.45 0.691 0.526 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 67.4 3.97 1.99 0.749 0.719 219s supply 20 16 98.2 6.13 2.48 0.634 0.565 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.37 3.75 219s supply 3.75 4.91 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.923 219s supply 0.923 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.2816 7.3834 12.77 1.6e-14 *** 219s price -0.2247 0.0871 -2.58 0.014 * 219s income 0.2983 0.0394 7.57 8.5e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.991 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 219s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 48.1843 10.5574 4.56 6.3e-05 *** 219s price 0.2427 0.0900 2.70 0.011 * 219s farmPrice 0.2619 0.0411 6.37 2.8e-07 *** 219s trend 0.2983 0.0394 7.57 8.5e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.477 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 219s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 219s 219s > nobs( fit2sls2rs ) 219s [1] 40 219s > 219s > ## ********************* 2SLS with restriction via restrict.regMat ****************** 219s > ## *************** 2SLS with restriction via restrict.regMat (default )*************** 219s > fit2sls3 <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 219s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 219s > print( summary( fit2sls3, useDfSys = TRUE ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 34 166 2.45 0.691 0.526 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 67.4 3.97 1.99 0.749 0.719 219s supply 20 16 98.2 6.13 2.48 0.634 0.565 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.37 3.75 219s supply 3.75 4.91 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.923 219s supply 0.923 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 94.2816 8.1771 11.53 2.7e-13 *** 219s price -0.2247 0.0954 -2.36 0.024 * 219s income 0.2983 0.0419 7.13 3.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.991 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 219s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 48.1843 9.7159 4.96 1.9e-05 *** 219s price 0.2427 0.0826 2.94 0.0059 ** 219s farmPrice 0.2619 0.0379 6.92 5.7e-08 *** 219s trend 0.2983 0.0419 7.13 3.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.477 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 219s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 219s 219s > nobs( fit2sls3 ) 219s [1] 40 219s > 219s > 219s > ## ***************** 2SLS with 2 restrictions ******************* 219s > ## ************** 2SLS with 2 restrictions (default) ************** 219s > fit2sls4 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 219s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 219s > print( summary( fit2sls4 ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 3.78 0.69 0.568 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.89 4.53 219s supply 4.53 6.25 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 219s price -0.2433 0.0663 -3.67 0.00081 *** 219s income 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 219s price 0.2567 0.0663 3.87 0.00045 *** 219s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 219s trend 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls4 ) 219s [1] 40 219s > # the same with symbolically specified restrictions 219s > fit2sls4Sym <- systemfit( system, "2SLS", data = Kmenta, 219s + restrict.matrix = restrict2, inst = inst, useMatrix = useMatrix ) 219s > all.equal( fit2sls4, fit2sls4Sym ) 219s [1] "Component “call”: target, current do not match when deparsed" 219s > nobs( fit2sls4Sym ) 219s [1] 40 219s > 219s > ## ************ 2SLS with 2 restrictions (singleEqSigma=T) ************** 219s > fit2sls4s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 219s + restrict.rhs = restr2q, inst = inst, singleEqSigma = TRUE, 219s + useMatrix = useMatrix ) 219s > print( summary( fit2sls4s ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 3.78 0.69 0.568 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.89 4.53 219s supply 4.53 6.25 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 219s price -0.2433 0.0684 -3.56 0.0011 ** 219s income 0.3027 0.0394 7.69 5.1e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 219s price 0.2567 0.0684 3.75 0.00064 *** 219s farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 219s trend 0.3027 0.0394 7.69 5.1e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls4s ) 219s [1] 40 219s > 219s > ## ***************** 2SLS with 2 restrictions (useDfSys=T) ************** 219s > print( summary( fit2sls4, useDfSys = TRUE ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 3.78 0.69 0.568 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.89 4.53 219s supply 4.53 6.25 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 219s price -0.2433 0.0663 -3.67 0.00081 *** 219s income 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 219s price 0.2567 0.0663 3.87 0.00045 *** 219s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 219s trend 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls4 ) 219s [1] 40 219s > 219s > ## ***************** 2SLS with 2 restrictions (methodResidCov="noDfCor") ************** 219s > fit2sls4r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 219s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 219s + x = TRUE, useMatrix = useMatrix ) 219s > print( summary( fit2sls4r ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 2.57 0.69 0.54 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.30 3.73 219s supply 3.73 5.00 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 219s price -0.2433 0.0621 -3.92 0.00039 *** 219s income 0.3027 0.0382 7.93 2.5e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 219s price 0.2567 0.0621 4.14 0.00021 *** 219s farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 219s trend 0.3027 0.0382 7.93 2.5e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls4r ) 219s [1] 40 219s > 219s > ## ***** 2SLS with 2 restrictions (methodResidCov="noDfCor", singleEqSigma=T) ******* 219s > fit2sls4rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr2m, 219s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 219s + singleEqSigma = TRUE, useMatrix = useMatrix ) 219s > print( summary( fit2sls4rs ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 2.57 0.69 0.54 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.30 3.73 219s supply 3.73 5.00 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 5.7579 16.62 < 2e-16 *** 219s price -0.2433 0.0621 -3.92 4e-04 *** 219s income 0.3027 0.0360 8.40 6.6e-10 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.5360 6.18 4.5e-07 *** 219s price 0.2567 0.0621 4.13 0.00021 *** 219s farmPrice 0.2637 0.0407 6.47 1.8e-07 *** 219s trend 0.3027 0.0360 8.40 6.6e-10 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls4rs ) 219s [1] 40 219s > 219s > ## ************* 2SLS with 2 restrictions via R and restrict.regMat ****************** 219s > ## ******** 2SLS with 2 restrictions via R and restrict.regMat (default) ************* 219s > fit2sls5 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 219s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 219s + useMatrix = useMatrix ) 219s > print( summary( fit2sls5 ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 3.78 0.69 0.568 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.89 4.53 219s supply 4.53 6.25 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 219s price -0.2433 0.0663 -3.67 0.00081 *** 219s income 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 219s price 0.2567 0.0663 3.87 0.00045 *** 219s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 219s trend 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls5 ) 219s [1] 40 219s > # the same with symbolically specified restrictions 219s > fit2sls5Sym <- systemfit( system, "2SLS", data = Kmenta, 219s + restrict.matrix = restrict3, restrict.regMat = tc, inst = inst, 219s + useMatrix = useMatrix ) 219s > all.equal( fit2sls5, fit2sls5Sym ) 219s [1] "Component “call”: target, current do not match when deparsed" 219s > nobs( fit2sls5Sym ) 219s [1] 40 219s > 219s > ## ******* 2SLS with 2 restrictions via R and restrict.regMat (singleEqSigma=T) ****** 219s > fit2sls5s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 219s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 219s + singleEqSigma = TRUE, useMatrix = useMatrix ) 219s > print( summary( fit2sls5s ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 3.78 0.69 0.568 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.89 4.53 219s supply 4.53 6.25 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 219s price -0.2433 0.0684 -3.56 0.0011 ** 219s income 0.3027 0.0394 7.69 5.1e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 219s price 0.2567 0.0684 3.75 0.00064 *** 219s farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 219s trend 0.3027 0.0394 7.69 5.1e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls5s ) 219s [1] 40 219s > 219s > ## ********** 2SLS with 2 restrictions via R and restrict.regMat (useDfSys=T) ******* 219s > print( summary( fit2sls5, useDfSys = TRUE ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 3.78 0.69 0.568 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.89 4.53 219s supply 4.53 6.25 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.4189 14.91 < 2e-16 *** 219s price -0.2433 0.0663 -3.67 0.00081 *** 219s income 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.8941 5.90 1.1e-06 *** 219s price 0.2567 0.0663 3.87 0.00045 *** 219s farmPrice 0.2637 0.0398 6.62 1.2e-07 *** 219s trend 0.3027 0.0408 7.42 1.1e-08 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls5 ) 219s [1] 40 219s > 219s > ## ************* 2SLS with 2 restrictions via R and restrict.regMat (methodResidCov="noDfCor") ********* 219s > fit2sls5r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 219s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 219s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 219s > print( summary( fit2sls5r ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 2.57 0.69 0.54 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.30 3.73 219s supply 3.73 5.00 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 219s price -0.2433 0.0621 -3.92 0.00039 *** 219s income 0.3027 0.0382 7.93 2.5e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 219s price 0.2567 0.0621 4.14 0.00021 *** 219s farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 219s trend 0.3027 0.0382 7.93 2.5e-09 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls5r ) 219s [1] 40 219s > 219s > ## ** 2SLS with 2 restrictions via R and restrict.regMat (methodResidCov="noDfCor", singleEqSigma=T) ** 219s > fit2sls5rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restr3m, 219s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 219s + methodResidCov = "noDfCor", singleEqSigma = TRUE, 219s + x = TRUE, useMatrix = useMatrix ) 219s > print( summary( fit2sls5rs ) ) 219s 219s systemfit results 219s method: 2SLS 219s 219s N DF SSR detRCov OLS-R2 McElroy-R2 219s system 40 35 166 2.57 0.69 0.54 219s 219s N DF SSR MSE RMSE R2 Adj R2 219s demand 20 17 66.1 3.89 1.97 0.754 0.725 219s supply 20 16 100.0 6.25 2.50 0.627 0.557 219s 219s The covariance matrix of the residuals 219s demand supply 219s demand 3.30 3.73 219s supply 3.73 5.00 219s 219s The correlations of the residuals 219s demand supply 219s demand 1.000 0.919 219s supply 0.919 1.000 219s 219s 219s 2SLS estimates for 'demand' (equation 1) 219s Model Formula: consump ~ price + income 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 95.7059 5.7579 16.62 < 2e-16 *** 219s price -0.2433 0.0621 -3.92 4e-04 *** 219s income 0.3027 0.0360 8.40 6.6e-10 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 1.972 on 17 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 17 219s SSR: 66.081 MSE: 3.887 Root MSE: 1.972 219s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 219s 219s 219s 2SLS estimates for 'supply' (equation 2) 219s Model Formula: consump ~ price + farmPrice + trend 219s Instruments: ~income + farmPrice + trend 219s 219s Estimate Std. Error t value Pr(>|t|) 219s (Intercept) 46.5637 7.5360 6.18 4.5e-07 *** 219s price 0.2567 0.0621 4.13 0.00021 *** 219s farmPrice 0.2637 0.0407 6.47 1.8e-07 *** 219s trend 0.3027 0.0360 8.40 6.6e-10 *** 219s --- 219s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 219s 219s Residual standard error: 2.5 on 16 degrees of freedom 219s Number of observations: 20 Degrees of Freedom: 16 219s SSR: 99.971 MSE: 6.248 Root MSE: 2.5 219s Multiple R-Squared: 0.627 Adjusted R-Squared: 0.557 219s 219s > nobs( fit2sls5rs ) 219s [1] 40 219s > 219s > ## *********** 2SLS estimation with different instruments ************** 219s > ## ******* 2SLS estimation with different instruments (default) ********* 219s > fit2slsd1 <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 219s + useMatrix = useMatrix ) 219s > print( summary( fit2slsd1 ) ) 219s 219s systemfit results 219s method: 2SLS 219s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 164 9.25 0.694 0.512 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.748 0.719 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.97 3.84 220s supply 3.84 6.04 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.784 220s supply 0.784 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 220s price -0.4116 0.1448 -2.84 0.011 * 220s income 0.3617 0.0564 6.41 6.4e-06 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.992 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 220s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 220s price 0.2401 0.0999 2.40 0.0288 * 220s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 220s trend 0.2529 0.0997 2.54 0.0219 * 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.458 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 220s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 220s 220s > nobs( fit2slsd1 ) 220s [1] 40 220s > 220s > ## *********** 2SLS estimation with different instruments (singleEqSigma=F)***** 220s > fit2slsd1s <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 220s + singleEqSigma = FALSE, useMatrix = useMatrix ) 220s > print( summary( fit2slsd1s ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 164 9.25 0.694 0.512 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.748 0.719 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.97 3.84 220s supply 3.84 6.04 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.784 220s supply 0.784 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 106.7894 12.4749 8.56 1.4e-07 *** 220s price -0.4116 0.1622 -2.54 0.021 * 220s income 0.3617 0.0631 5.73 2.5e-05 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.992 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 220s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 49.5324 10.8976 4.55 0.00033 *** 220s price 0.2401 0.0907 2.65 0.01755 * 220s farmPrice 0.2556 0.0429 5.96 2e-05 *** 220s trend 0.2529 0.0904 2.80 0.01292 * 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.458 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 220s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 220s 220s > nobs( fit2slsd1s ) 220s [1] 40 220s > 220s > ## ********* 2SLS estimation with different instruments (useDfSys=T) ******* 220s > print( summary( fit2slsd1, useDfSys = TRUE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 164 9.25 0.694 0.512 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.748 0.719 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.97 3.84 220s supply 3.84 6.04 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.784 220s supply 0.784 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 220s price -0.4116 0.1448 -2.84 0.0076 ** 220s income 0.3617 0.0564 6.41 2.9e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.992 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 220s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 220s price 0.2401 0.0999 2.40 0.02208 * 220s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 220s trend 0.2529 0.0997 2.54 0.01605 * 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.458 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 220s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 220s 220s > nobs( fit2slsd1 ) 220s [1] 40 220s > 220s > ## ********* 2SLS estimation with different instruments (methodResidCov="noDfCor") ****** 220s > fit2slsd1r <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 220s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 220s > print( summary( fit2slsd1r ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 164 6.29 0.694 0.5 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.748 0.719 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.37 3.16 220s supply 3.16 4.83 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.784 220s supply 0.784 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 106.789 10.274 10.39 8.8e-09 *** 220s price -0.412 0.134 -3.08 0.0068 ** 220s income 0.362 0.052 6.95 2.3e-06 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.992 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 220s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 220s price 0.2401 0.0894 2.69 0.01623 * 220s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 220s trend 0.2529 0.0891 2.84 0.01188 * 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.458 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 220s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 220s 220s > nobs( fit2slsd1r ) 220s [1] 40 220s > 220s > ## 2SLS estimation with different instruments (methodResidCov="noDfCor",singleEqSigma=F) 220s > fit2slsd1r <- systemfit( system, "2SLS", data = Kmenta, inst = instlist, 220s + methodResidCov = "noDfCor", singleEqSigma = FALSE, 220s + useMatrix = useMatrix ) 220s > print( summary( fit2slsd1r ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 164 6.29 0.694 0.5 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.748 0.719 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.37 3.16 220s supply 3.16 4.83 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.784 220s supply 0.784 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 106.7894 11.3309 9.42 3.7e-08 *** 220s price -0.4116 0.1473 -2.79 0.012 * 220s income 0.3617 0.0574 6.31 7.9e-06 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.992 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 220s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 49.5324 9.8982 5.00 0.00013 *** 220s price 0.2401 0.0824 2.92 0.01012 * 220s farmPrice 0.2556 0.0389 6.56 6.5e-06 *** 220s trend 0.2529 0.0821 3.08 0.00718 ** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.458 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 220s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 220s 220s > nobs( fit2slsd1r ) 220s [1] 40 220s > 220s > ## **** 2SLS estimation with different instruments and restriction ******* 220s > ## ** 2SLS estimation with different instruments and restriction (default) **** 220s > fit2slsd2 <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 220s + inst = instlist, useMatrix = useMatrix ) 220s > print( summary( fit2slsd2 ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 4.89 0.693 0.56 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.79 4.35 220s supply 4.35 6.27 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.891 220s supply 0.891 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 220s price -0.3449 0.1455 -2.37 0.024 * 220s income 0.3260 0.0511 6.38 2.8e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.947 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 220s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 220s price 0.2443 0.0894 2.73 0.0099 ** 220s farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 220s trend 0.3260 0.0511 6.38 2.8e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.504 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 220s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 220s 220s > nobs( fit2slsd2 ) 220s [1] 40 220s > 220s > ## 2SLS estimation with different instruments and restriction (singleEqSigma=T) 220s > fit2slsd2s <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 220s + inst = instlist, singleEqSigma = TRUE, useMatrix = useMatrix ) 220s > print( summary( fit2slsd2s ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 4.89 0.693 0.56 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.79 4.35 220s supply 4.35 6.27 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.891 220s supply 0.891 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 103.5936 10.6344 9.74 2.3e-11 *** 220s price -0.3449 0.1327 -2.60 0.014 * 220s income 0.3260 0.0485 6.73 9.9e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.947 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 220s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 47.3592 11.9466 3.96 0.00036 *** 220s price 0.2443 0.1017 2.40 0.02188 * 220s farmPrice 0.2657 0.0465 5.71 2.0e-06 *** 220s trend 0.3260 0.0485 6.73 9.9e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.504 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 220s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 220s 220s > nobs( fit2slsd2s ) 220s [1] 40 220s > 220s > ## **** 2SLS estimation with different instruments and restriction (useDfSys=F) 220s > print( summary( fit2slsd2, useDfSys = FALSE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 4.89 0.693 0.56 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.79 4.35 220s supply 4.35 6.27 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.891 220s supply 0.891 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 103.5936 11.8930 8.71 1.1e-07 *** 220s price -0.3449 0.1455 -2.37 0.03 * 220s income 0.3260 0.0511 6.38 6.9e-06 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.947 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 220s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 47.3592 10.5362 4.49 0.00037 *** 220s price 0.2443 0.0894 2.73 0.01475 * 220s farmPrice 0.2657 0.0411 6.47 7.8e-06 *** 220s trend 0.3260 0.0511 6.38 9.1e-06 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.504 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 220s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 220s 220s > nobs( fit2slsd2 ) 220s [1] 40 220s > 220s > ## **** 2SLS estimation with different instruments and restriction (methodResidCov="noDfCor") 220s > fit2slsd2r <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 220s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 220s > print( summary( fit2slsd2r ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 3.32 0.693 0.537 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.22 3.58 220s supply 3.58 5.02 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.891 220s supply 0.891 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 220s price -0.3449 0.1341 -2.57 0.015 * 220s income 0.3260 0.0471 6.92 5.7e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.947 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 220s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 220s price 0.2443 0.0824 2.96 0.0055 ** 220s farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 220s trend 0.3260 0.0471 6.92 5.7e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.504 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 220s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 220s 220s > nobs( fit2slsd2r ) 220s [1] 40 220s > 220s > ## 2SLS estimation with different instr. and restr. (methodResidCov="noDfCor", singleEqSigma=T) 220s > fit2slsd2rs <- systemfit( system, "2SLS", data = Kmenta, restrict.matrix = restrm, 220s + inst = instlist, methodResidCov = "noDfCor", singleEqSigma = TRUE, 220s + useMatrix = useMatrix ) 220s > print( summary( fit2slsd2rs ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 3.32 0.693 0.537 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.22 3.58 220s supply 3.58 5.02 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.891 220s supply 0.891 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 103.5936 9.7929 10.58 2.7e-12 *** 220s price -0.3449 0.1220 -2.83 0.0078 ** 220s income 0.3260 0.0444 7.35 1.6e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.947 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 220s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 47.3592 10.6890 4.43 9.3e-05 *** 220s price 0.2443 0.0910 2.69 0.011 * 220s farmPrice 0.2657 0.0416 6.38 2.8e-07 *** 220s trend 0.3260 0.0444 7.35 1.6e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.504 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 220s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 220s 220s > nobs( fit2slsd2rs ) 220s [1] 40 220s > 220s > ## **** 2SLS estimation with different instruments and restriction via restrict.regMat * 220s > ## 2SLS estimation with different instruments and restriction via restrict.regMat (default) 220s > fit2slsd3 <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 220s + inst = instlist, useMatrix = useMatrix ) 220s > print( summary( fit2slsd3 ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 4.89 0.693 0.56 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.79 4.35 220s supply 4.35 6.27 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.891 220s supply 0.891 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 220s price -0.3449 0.1455 -2.37 0.024 * 220s income 0.3260 0.0511 6.38 2.8e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.947 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 220s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 220s price 0.2443 0.0894 2.73 0.0099 ** 220s farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 220s trend 0.3260 0.0511 6.38 2.8e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.504 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 220s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 220s 220s > nobs( fit2slsd3 ) 220s [1] 40 220s > 220s > ## **** 2SLS estimation with different instr. and restr. via restrict.regMat (methodResidCov="noDfCor") 220s > fit2slsd3r <- systemfit( system, "2SLS", data = Kmenta, restrict.regMat = tc, 220s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 220s > print( summary( fit2slsd3r ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 3.32 0.693 0.537 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.22 3.58 220s supply 3.58 5.02 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.891 220s supply 0.891 1.000 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 220s price -0.3449 0.1341 -2.57 0.015 * 220s income 0.3260 0.0471 6.92 5.7e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.947 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 64.445 MSE: 3.791 Root MSE: 1.947 220s Multiple R-Squared: 0.76 Adjusted R-Squared: 0.731 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 220s price 0.2443 0.0824 2.96 0.0055 ** 220s farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 220s trend 0.3260 0.0471 6.92 5.7e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.504 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 100.321 MSE: 6.27 Root MSE: 2.504 220s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 220s 220s > nobs( fit2slsd3r ) 220s [1] 40 220s > 220s > 220s > ## *********** estimations with a single regressor ************ 220s > fit2slsS1 <- systemfit( 220s + list( consump ~ price - 1, price ~ consump + trend ), "2SLS", 220s + data = Kmenta, inst = ~ farmPrice + trend + income, useMatrix = useMatrix ) 220s > print( summary( fit2slsS1 ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 36 1544 179 -0.65 0.852 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s eq1 20 19 861 45.3 6.73 -2.213 -2.213 220s eq2 20 17 682 40.1 6.33 -0.022 -0.143 220s 220s The covariance matrix of the residuals 220s eq1 eq2 220s eq1 45.3 -40.5 220s eq2 -40.5 40.1 220s 220s The correlations of the residuals 220s eq1 eq2 220s eq1 1.00 -0.95 220s eq2 -0.95 1.00 220s 220s 220s 2SLS estimates for 'eq1' (equation 1) 220s Model Formula: consump ~ price - 1 220s Instruments: ~farmPrice + trend + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s price 1.006 0.015 66.9 <2e-16 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 6.734 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 220s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 220s 220s 220s 2SLS estimates for 'eq2' (equation 2) 220s Model Formula: price ~ consump + trend 220s Instruments: ~farmPrice + trend + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 55.5365 46.2668 1.20 0.25 220s consump 0.4453 0.4622 0.96 0.35 220s trend -0.0426 0.2496 -0.17 0.87 220s 220s Residual standard error: 6.335 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 220s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 220s 220s > nobs( fit2slsS1 ) 220s [1] 40 220s > fit2slsS2 <- systemfit( 220s + list( consump ~ price - 1, consump ~ trend - 1 ), "2SLS", 220s + data = Kmenta, inst = ~ farmPrice + price + income, useMatrix = useMatrix ) 220s > print( summary( fit2slsS2 ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 38 47456 111148 -87.5 -5.28 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s eq1 20 19 861 45.3 6.73 -2.21 -2.21 220s eq2 20 19 46595 2452.3 49.52 -172.79 -172.79 220s 220s The covariance matrix of the residuals 220s eq1 eq2 220s eq1 45.34 -6.33 220s eq2 -6.33 2452.34 220s 220s The correlations of the residuals 220s eq1 eq2 220s eq1 1.0000 -0.0448 220s eq2 -0.0448 1.0000 220s 220s 220s 2SLS estimates for 'eq1' (equation 1) 220s Model Formula: consump ~ price - 1 220s Instruments: ~farmPrice + price + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s price 1.006 0.015 66.9 <2e-16 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 6.733 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 220s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 220s 220s 220s 2SLS estimates for 'eq2' (equation 2) 220s Model Formula: consump ~ trend - 1 220s Instruments: ~farmPrice + price + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s trend 7.578 0.934 8.11 1.4e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 49.521 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 46594.549 MSE: 2452.345 Root MSE: 49.521 220s Multiple R-Squared: -172.786 Adjusted R-Squared: -172.786 220s 220s > nobs( fit2slsS2 ) 220s [1] 40 220s > fit2slsS3 <- systemfit( 220s + list( consump ~ trend - 1, price ~ trend - 1 ), "2SLS", 220s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 220s > print( summary( fit2slsS3 ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 38 97978 687515 -104 -10.6 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s eq1 20 19 50950 2682 51.8 -189.0 -189.0 220s eq2 20 19 47028 2475 49.8 -69.5 -69.5 220s 220s The covariance matrix of the residuals 220s eq1 eq2 220s eq1 2682 2439 220s eq2 2439 2475 220s 220s The correlations of the residuals 220s eq1 eq2 220s eq1 1.000 0.989 220s eq2 0.989 1.000 220s 220s 220s 2SLS estimates for 'eq1' (equation 1) 220s Model Formula: consump ~ trend - 1 220s Instruments: ~income + farmPrice 220s 220s Estimate Std. Error t value Pr(>|t|) 220s trend 8.65 1.05 8.27 1e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 51.784 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 50949.985 MSE: 2681.578 Root MSE: 51.784 220s Multiple R-Squared: -189.031 Adjusted R-Squared: -189.031 220s 220s 220s 2SLS estimates for 'eq2' (equation 2) 220s Model Formula: price ~ trend - 1 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s trend 7.318 0.929 7.88 2.1e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 49.751 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 220s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 220s 220s > nobs( fit2slsS3 ) 220s [1] 40 220s > fit2slsS4 <- systemfit( 220s + list( consump ~ trend - 1, price ~ trend - 1 ), "2SLS", 220s + data = Kmenta, inst = ~ farmPrice + trend + income, 220s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 220s > print( summary( fit2slsS4 ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 39 93548 111736 -99 -1.03 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s eq1 20 19 46514 2448 49.5 -172.5 -172.5 220s eq2 20 19 47033 2475 49.8 -69.5 -69.5 220s 220s The covariance matrix of the residuals 220s eq1 eq2 220s eq1 2448 2439 220s eq2 2439 2475 220s 220s The correlations of the residuals 220s eq1 eq2 220s eq1 1.000 0.988 220s eq2 0.988 1.000 220s 220s 220s 2SLS estimates for 'eq1' (equation 1) 220s Model Formula: consump ~ trend - 1 220s Instruments: ~farmPrice + trend + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s trend 7.362 0.646 11.4 5.7e-14 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 49.478 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 46514.283 MSE: 2448.12 Root MSE: 49.478 220s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 220s 220s 220s 2SLS estimates for 'eq2' (equation 2) 220s Model Formula: price ~ trend - 1 220s Instruments: ~farmPrice + trend + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s trend 7.362 0.646 11.4 5.7e-14 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 49.754 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 47033.469 MSE: 2475.446 Root MSE: 49.754 220s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 220s 220s > nobs( fit2slsS4 ) 220s [1] 40 220s > fit2slsS5 <- systemfit( 220s + list( consump ~ 1, price ~ 1 ), "2SLS", 220s + data = Kmenta, inst = ~ farmPrice, useMatrix = useMatrix ) 220s > print( summary( fit2slsS1 ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 36 1544 179 -0.65 0.852 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s eq1 20 19 861 45.3 6.73 -2.213 -2.213 220s eq2 20 17 682 40.1 6.33 -0.022 -0.143 220s 220s The covariance matrix of the residuals 220s eq1 eq2 220s eq1 45.3 -40.5 220s eq2 -40.5 40.1 220s 220s The correlations of the residuals 220s eq1 eq2 220s eq1 1.00 -0.95 220s eq2 -0.95 1.00 220s 220s 220s 2SLS estimates for 'eq1' (equation 1) 220s Model Formula: consump ~ price - 1 220s Instruments: ~farmPrice + trend + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s price 1.006 0.015 66.9 <2e-16 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 6.734 on 19 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 19 220s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 220s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 220s 220s 220s 2SLS estimates for 'eq2' (equation 2) 220s Model Formula: price ~ consump + trend 220s Instruments: ~farmPrice + trend + income 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 55.5365 46.2668 1.20 0.25 220s consump 0.4453 0.4622 0.96 0.35 220s trend -0.0426 0.2496 -0.17 0.87 220s 220s Residual standard error: 6.335 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 220s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 220s 220s > 220s > 220s > ## **************** shorter summaries ********************** 220s > print( summary( fit2sls1, useDfSys = TRUE, residCov = FALSE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 162 4.36 0.697 0.548 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 65.7 3.87 1.97 0.755 0.726 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 220s price -0.2436 0.0965 -2.52 0.017 * 220s income 0.3140 0.0469 6.69 1.3e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.966 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 220s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 220s price 0.2401 0.0999 2.40 0.02208 * 220s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 220s trend 0.2529 0.0997 2.54 0.01605 * 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.458 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 220s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 220s 220s > 220s > print( summary( fit2sls1, equations = FALSE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 162 4.36 0.697 0.548 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 65.7 3.87 1.97 0.755 0.726 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.87 4.36 220s supply 4.36 6.04 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.902 220s supply 0.902 1.000 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 220s demand_price -0.2436 0.0965 -2.52 0.0218 * 220s demand_income 0.3140 0.0469 6.69 3.8e-06 *** 220s supply_(Intercept) 49.5324 12.0105 4.12 0.0008 *** 220s supply_price 0.2401 0.0999 2.40 0.0288 * 220s supply_farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 220s supply_trend 0.2529 0.0997 2.54 0.0219 * 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2sls1rs, residCov = FALSE, equations = FALSE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 162 2.97 0.697 0.525 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 65.7 3.87 1.97 0.755 0.726 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 94.6333 8.1158 11.66 1.6e-09 *** 220s demand_price -0.2436 0.0989 -2.46 0.02471 * 220s demand_income 0.3140 0.0481 6.53 5.2e-06 *** 220s supply_(Intercept) 49.5324 9.8463 5.03 0.00012 *** 220s supply_price 0.2401 0.0819 2.93 0.00980 ** 220s supply_farmPrice 0.2556 0.0387 6.60 6.1e-06 *** 220s supply_trend 0.2529 0.0817 3.10 0.00694 ** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2sls2Sym, useDfSys = FALSE ), equations = FALSE ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 166 3.6 0.691 0.553 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.749 0.719 220s supply 20 16 98.2 6.13 2.48 0.634 0.565 220s 220s The covariance matrix of the residuals 220s demand supply 220s demand 3.97 4.55 220s supply 4.55 6.13 220s 220s The correlations of the residuals 220s demand supply 220s demand 1.000 0.923 220s supply 0.923 1.000 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 94.2816 8.8693 10.63 6.3e-09 *** 220s demand_price -0.2247 0.1034 -2.17 0.04425 * 220s demand_income 0.2983 0.0454 6.57 4.8e-06 *** 220s supply_(Intercept) 48.1843 10.5384 4.57 0.00031 *** 220s supply_price 0.2427 0.0896 2.71 0.01551 * 220s supply_farmPrice 0.2619 0.0411 6.38 9.1e-06 *** 220s supply_trend 0.2983 0.0454 6.57 6.4e-06 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2sls2 ), residCov = FALSE ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 166 3.6 0.691 0.553 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.749 0.719 220s supply 20 16 98.2 6.13 2.48 0.634 0.565 220s 220s 220s 2SLS estimates for 'demand' (equation 1) 220s Model Formula: consump ~ price + income 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 94.2816 8.8693 10.63 2.4e-12 *** 220s price -0.2247 0.1034 -2.17 0.037 * 220s income 0.2983 0.0454 6.57 1.6e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 1.991 on 17 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 17 220s SSR: 67.418 MSE: 3.966 Root MSE: 1.991 220s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.719 220s 220s 220s 2SLS estimates for 'supply' (equation 2) 220s Model Formula: consump ~ price + farmPrice + trend 220s Instruments: ~income + farmPrice + trend 220s 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 48.1843 10.5384 4.57 6.1e-05 *** 220s price 0.2427 0.0896 2.71 0.011 * 220s farmPrice 0.2619 0.0411 6.38 2.8e-07 *** 220s trend 0.2983 0.0454 6.57 1.6e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s 220s Residual standard error: 2.477 on 16 degrees of freedom 220s Number of observations: 20 Degrees of Freedom: 16 220s SSR: 98.155 MSE: 6.135 Root MSE: 2.477 220s Multiple R-Squared: 0.634 Adjusted R-Squared: 0.565 220s 220s > 220s > print( summary( fit2sls3, useDfSys = FALSE, residCov = FALSE, 220s + equations = FALSE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 166 2.45 0.691 0.526 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.749 0.719 220s supply 20 16 98.2 6.13 2.48 0.634 0.565 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 94.2816 8.1771 11.53 1.8e-09 *** 220s demand_price -0.2247 0.0954 -2.36 0.03071 * 220s demand_income 0.2983 0.0419 7.13 1.7e-06 *** 220s supply_(Intercept) 48.1843 9.7159 4.96 0.00014 *** 220s supply_price 0.2427 0.0826 2.94 0.00966 ** 220s supply_farmPrice 0.2619 0.0379 6.92 3.5e-06 *** 220s supply_trend 0.2983 0.0419 7.13 2.4e-06 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2sls4s ), equations = FALSE, residCov = FALSE ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 35 166 3.78 0.69 0.568 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 66.1 3.89 1.97 0.754 0.725 220s supply 20 16 100.0 6.25 2.50 0.627 0.557 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 95.7059 6.3056 15.18 < 2e-16 *** 220s demand_price -0.2433 0.0684 -3.56 0.00110 ** 220s demand_income 0.3027 0.0394 7.69 5.1e-09 *** 220s supply_(Intercept) 46.5637 8.3296 5.59 2.7e-06 *** 220s supply_price 0.2567 0.0684 3.75 0.00064 *** 220s supply_farmPrice 0.2637 0.0455 5.79 1.5e-06 *** 220s supply_trend 0.3027 0.0394 7.69 5.1e-09 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2sls5r, equations = FALSE, residCov = FALSE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 35 166 2.57 0.69 0.54 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 66.1 3.89 1.97 0.754 0.725 220s supply 20 16 100.0 6.25 2.50 0.627 0.557 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 95.7059 6.0044 15.94 < 2e-16 *** 220s demand_price -0.2433 0.0621 -3.92 0.00039 *** 220s demand_income 0.3027 0.0382 7.93 2.5e-09 *** 220s supply_(Intercept) 46.5637 7.3842 6.31 3.1e-07 *** 220s supply_price 0.2567 0.0621 4.14 0.00021 *** 220s supply_farmPrice 0.2637 0.0373 7.08 3.0e-08 *** 220s supply_trend 0.3027 0.0382 7.93 2.5e-09 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2slsd1s ), residCov = FALSE, equations = FALSE ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 33 164 9.25 0.694 0.512 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 67.4 3.97 1.99 0.748 0.719 220s supply 20 16 96.6 6.04 2.46 0.640 0.572 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 106.7894 12.4749 8.56 1.4e-07 *** 220s demand_price -0.4116 0.1622 -2.54 0.02121 * 220s demand_income 0.3617 0.0631 5.73 2.5e-05 *** 220s supply_(Intercept) 49.5324 10.8976 4.55 0.00033 *** 220s supply_price 0.2401 0.0907 2.65 0.01755 * 220s supply_farmPrice 0.2556 0.0429 5.96 2.0e-05 *** 220s supply_trend 0.2529 0.0904 2.80 0.01292 * 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2slsd2, residCov = FALSE, equations = FALSE ) ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 4.89 0.693 0.56 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 103.5936 11.8930 8.71 3.5e-10 *** 220s demand_price -0.3449 0.1455 -2.37 0.0236 * 220s demand_income 0.3260 0.0511 6.38 2.8e-07 *** 220s supply_(Intercept) 47.3592 10.5362 4.49 7.7e-05 *** 220s supply_price 0.2443 0.0894 2.73 0.0099 ** 220s supply_farmPrice 0.2657 0.0411 6.47 2.1e-07 *** 220s supply_trend 0.3260 0.0511 6.38 2.8e-07 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > print( summary( fit2slsd3r ), residCov = FALSE, equations = FALSE ) 220s 220s systemfit results 220s method: 2SLS 220s 220s N DF SSR detRCov OLS-R2 McElroy-R2 220s system 40 34 165 3.32 0.693 0.537 220s 220s N DF SSR MSE RMSE R2 Adj R2 220s demand 20 17 64.4 3.79 1.95 0.760 0.731 220s supply 20 16 100.3 6.27 2.50 0.626 0.556 220s 220s 220s Coefficients: 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 103.5936 10.9648 9.45 4.9e-11 *** 220s demand_price -0.3449 0.1341 -2.57 0.0147 * 220s demand_income 0.3260 0.0471 6.92 5.7e-08 *** 220s supply_(Intercept) 47.3592 9.7139 4.88 2.5e-05 *** 220s supply_price 0.2443 0.0824 2.96 0.0055 ** 220s supply_farmPrice 0.2657 0.0379 7.01 4.3e-08 *** 220s supply_trend 0.3260 0.0471 6.92 5.7e-08 *** 220s --- 220s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 220s > 220s > 220s > ## ****************** residuals ************************** 220s > print( residuals( fit2sls1 ) ) 220s demand supply 220s 1 0.843 -0.4348 220s 2 -0.698 -1.2131 220s 3 2.359 1.7090 220s 4 1.490 0.7956 220s 5 2.139 1.5942 220s 6 1.277 0.6595 220s 7 1.571 1.4346 220s 8 -3.066 -4.8724 220s 9 -1.125 -2.3975 220s 10 2.492 3.1427 220s 11 -0.108 0.0689 220s 12 -2.292 -1.3978 220s 13 -1.598 -1.1136 220s 14 -0.271 1.1684 220s 15 1.958 3.4865 220s 16 -3.430 -3.8285 220s 17 -0.313 0.6793 220s 18 -2.151 -2.7713 220s 19 1.592 2.6668 220s 20 -0.668 0.6235 220s > print( residuals( fit2sls1$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 220s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 220s 12 13 14 15 16 17 18 19 20 220s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 220s > 220s > print( residuals( fit2sls2s ) ) 220s demand supply 220s 1 0.678 -0.0135 220s 2 -0.777 -0.8544 220s 3 2.281 2.0245 220s 4 1.416 1.0692 220s 5 2.213 1.7598 220s 6 1.334 0.7923 220s 7 1.640 1.5342 220s 8 -2.994 -4.8544 220s 9 -1.072 -2.3959 220s 10 2.522 3.1637 220s 11 -0.330 0.1628 220s 12 -2.593 -1.2864 220s 13 -1.856 -1.0729 220s 14 -0.356 1.1087 220s 15 2.138 3.2597 220s 16 -3.282 -4.1265 220s 17 -0.076 0.3331 220s 18 -2.119 -3.0961 220s 19 1.690 2.3122 220s 20 -0.458 0.1799 220s > print( residuals( fit2sls2s$eq[[ 2 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 220s -0.0135 -0.8544 2.0245 1.0692 1.7598 0.7923 1.5342 -4.8544 -2.3959 3.1637 220s 11 12 13 14 15 16 17 18 19 20 220s 0.1628 -1.2864 -1.0729 1.1087 3.2597 -4.1265 0.3331 -3.0961 2.3122 0.1799 220s > 220s > print( residuals( fit2sls3 ) ) 220s demand supply 220s 1 0.678 -0.0135 220s 2 -0.777 -0.8544 220s 3 2.281 2.0245 220s 4 1.416 1.0692 220s 5 2.213 1.7598 220s 6 1.334 0.7923 220s 7 1.640 1.5342 220s 8 -2.994 -4.8544 220s 9 -1.072 -2.3959 220s 10 2.522 3.1637 220s 11 -0.330 0.1628 220s 12 -2.593 -1.2864 220s 13 -1.856 -1.0729 220s 14 -0.356 1.1087 220s 15 2.138 3.2597 220s 16 -3.282 -4.1265 220s 17 -0.076 0.3331 220s 18 -2.119 -3.0961 220s 19 1.690 2.3122 220s 20 -0.458 0.1799 220s > print( residuals( fit2sls3$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 220s 0.678 -0.777 2.281 1.416 2.213 1.334 1.640 -2.994 -1.072 2.522 -0.330 220s 12 13 14 15 16 17 18 19 20 220s -2.593 -1.856 -0.356 2.138 -3.282 -0.076 -2.119 1.690 -0.458 220s > 220s > print( residuals( fit2sls4r ) ) 220s demand supply 220s 1 0.729 0.0219 220s 2 -0.698 -0.8806 220s 3 2.349 2.0055 220s 4 1.496 1.0326 220s 5 2.165 1.7870 220s 6 1.310 0.7993 220s 7 1.635 1.5189 220s 8 -2.951 -4.9334 220s 9 -1.134 -2.3609 220s 10 2.397 3.2818 220s 11 -0.359 0.2857 220s 12 -2.524 -1.2257 220s 13 -1.745 -1.0782 220s 14 -0.349 1.1382 220s 15 2.022 3.2981 220s 16 -3.345 -4.1440 220s 17 -0.322 0.4686 220s 18 -2.075 -3.1779 220s 19 1.738 2.2072 220s 20 -0.339 -0.0444 220s > print( residuals( fit2sls4r$eq[[ 2 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 220s 0.0219 -0.8806 2.0055 1.0326 1.7870 0.7993 1.5189 -4.9334 -2.3609 3.2818 220s 11 12 13 14 15 16 17 18 19 20 220s 0.2857 -1.2257 -1.0782 1.1382 3.2981 -4.1440 0.4686 -3.1779 2.2072 -0.0444 220s > 220s > print( residuals( fit2sls5rs ) ) 220s demand supply 220s 1 0.729 0.0219 220s 2 -0.698 -0.8806 220s 3 2.349 2.0055 220s 4 1.496 1.0326 220s 5 2.165 1.7870 220s 6 1.310 0.7993 220s 7 1.635 1.5189 220s 8 -2.951 -4.9334 220s 9 -1.134 -2.3609 220s 10 2.397 3.2818 220s 11 -0.359 0.2857 220s 12 -2.524 -1.2257 220s 13 -1.745 -1.0782 220s 14 -0.349 1.1382 220s 15 2.022 3.2981 220s 16 -3.345 -4.1440 220s 17 -0.322 0.4686 220s 18 -2.075 -3.1779 220s 19 1.738 2.2072 220s 20 -0.339 -0.0444 220s > print( residuals( fit2sls5rs$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 220s 0.729 -0.698 2.349 1.496 2.165 1.310 1.635 -2.951 -1.134 2.397 -0.359 220s 12 13 14 15 16 17 18 19 20 220s -2.524 -1.745 -0.349 2.022 -3.345 -0.322 -2.075 1.738 -0.339 220s > 220s > print( residuals( fit2slsd1 ) ) 220s demand supply 220s 1 1.3775 -0.4348 220s 2 0.0125 -1.2131 220s 3 2.9728 1.7090 220s 4 2.2121 0.7956 220s 5 1.6920 1.5942 220s 6 1.0407 0.6595 220s 7 1.4768 1.4346 220s 8 -2.7583 -4.8724 220s 9 -1.6807 -2.3975 220s 10 1.4265 3.1427 220s 11 -0.2029 0.0689 220s 12 -1.5123 -1.3978 220s 13 -0.4958 -1.1136 220s 14 -0.1528 1.1684 220s 15 0.8692 3.4865 220s 16 -4.0547 -3.8285 220s 17 -2.5309 0.6793 220s 18 -1.8070 -2.7713 220s 19 1.9299 2.6668 220s 20 0.1853 0.6235 220s > print( residuals( fit2slsd1$eq[[ 2 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 220s -0.4348 -1.2131 1.7090 0.7956 1.5942 0.6595 1.4346 -4.8724 -2.3975 3.1427 220s 11 12 13 14 15 16 17 18 19 20 220s 0.0689 -1.3978 -1.1136 1.1684 3.4865 -3.8285 0.6793 -2.7713 2.6668 0.6235 220s > 220s > print( residuals( fit2slsd2r ) ) 220s demand supply 220s 1 0.996 0.2444 220s 2 -0.268 -0.6349 220s 3 2.715 2.2177 220s 4 1.936 1.2367 220s 5 1.907 1.8612 220s 6 1.184 0.8736 220s 7 1.609 1.5951 220s 8 -2.709 -4.8434 220s 9 -1.476 -2.3949 220s 10 1.705 3.1765 220s 11 -0.540 0.2202 220s 12 -2.167 -1.2182 220s 13 -1.150 -1.0480 220s 14 -0.316 1.0722 220s 15 1.395 3.1209 220s 16 -3.680 -4.3088 220s 17 -1.669 0.1212 220s 18 -1.829 -3.2948 220s 19 2.016 2.0952 220s 20 0.341 -0.0916 220s > print( residuals( fit2slsd2r$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 220s 0.996 -0.268 2.715 1.936 1.907 1.184 1.609 -2.709 -1.476 1.705 -0.540 220s 12 13 14 15 16 17 18 19 20 220s -2.167 -1.150 -0.316 1.395 -3.680 -1.669 -1.829 2.016 0.341 220s > 220s > 220s > ## *************** coefficients ********************* 220s > print( round( coef( fit2sls1s ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 94.633 -0.244 0.314 49.532 220s supply_price supply_farmPrice supply_trend 220s 0.240 0.256 0.253 220s > print( round( coef( fit2sls1s$eq[[ 1 ]] ), digits = 6 ) ) 220s (Intercept) price income 220s 94.633 -0.244 0.314 220s > 220s > print( round( coef( fit2sls2 ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 94.282 -0.225 0.298 48.184 220s supply_price supply_farmPrice supply_trend 220s 0.243 0.262 0.298 220s > print( round( coef( fit2sls2$eq[[ 2 ]] ), digits = 6 ) ) 220s (Intercept) price farmPrice trend 220s 48.184 0.243 0.262 0.298 220s > 220s > print( round( coef( fit2sls3 ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 94.282 -0.225 0.298 48.184 220s supply_price supply_farmPrice supply_trend 220s 0.243 0.262 0.298 220s > print( round( coef( fit2sls3, modified.regMat = TRUE ), digits = 6 ) ) 220s C1 C2 C3 C4 C5 C6 220s 94.282 -0.225 0.298 48.184 0.243 0.262 220s > print( round( coef( fit2sls3$eq[[ 1 ]] ), digits = 6 ) ) 220s (Intercept) price income 220s 94.282 -0.225 0.298 220s > 220s > print( round( coef( fit2sls4s ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 95.706 -0.243 0.303 46.564 220s supply_price supply_farmPrice supply_trend 220s 0.257 0.264 0.303 220s > print( round( coef( fit2sls4s$eq[[ 2 ]] ), digits = 6 ) ) 220s (Intercept) price farmPrice trend 220s 46.564 0.257 0.264 0.303 220s > 220s > print( round( coef( fit2sls5r ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 95.706 -0.243 0.303 46.564 220s supply_price supply_farmPrice supply_trend 220s 0.257 0.264 0.303 220s > print( round( coef( fit2sls5r, modified.regMat = TRUE ), digits = 6 ) ) 220s C1 C2 C3 C4 C5 C6 220s 95.706 -0.243 0.303 46.564 0.257 0.264 220s > print( round( coef( fit2sls5r$eq[[ 2 ]] ), digits = 6 ) ) 220s (Intercept) price farmPrice trend 220s 46.564 0.257 0.264 0.303 220s > 220s > 220s > ## *************** coefficients with stats ********************* 220s > print( round( coef( summary( fit2sls1s ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 94.633 8.9352 10.59 0.000000 220s demand_price -0.244 0.1088 -2.24 0.038916 220s demand_income 0.314 0.0530 5.93 0.000016 220s supply_(Intercept) 49.532 10.8404 4.57 0.000315 220s supply_price 0.240 0.0902 2.66 0.017058 220s supply_farmPrice 0.256 0.0426 5.99 0.000019 220s supply_trend 0.253 0.0899 2.81 0.012528 220s > print( round( coef( summary( fit2sls1s$eq[[ 1 ]] ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 94.633 8.935 10.59 0.000000 220s price -0.244 0.109 -2.24 0.038916 220s income 0.314 0.053 5.93 0.000016 220s > 220s > print( round( coef( summary( fit2sls2, useDfSys = FALSE ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 94.282 8.8693 10.63 0.000000 220s demand_price -0.225 0.1034 -2.17 0.044246 220s demand_income 0.298 0.0454 6.57 0.000005 220s supply_(Intercept) 48.184 10.5384 4.57 0.000313 220s supply_price 0.243 0.0896 2.71 0.015508 220s supply_farmPrice 0.262 0.0411 6.38 0.000009 220s supply_trend 0.298 0.0454 6.57 0.000006 220s > print( round( coef( summary( fit2sls2$eq[[ 2 ]], useDfSys = FALSE ) ), 220s + digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 48.184 10.5384 4.57 0.000313 220s price 0.243 0.0896 2.71 0.015508 220s farmPrice 0.262 0.0411 6.38 0.000009 220s trend 0.298 0.0454 6.57 0.000006 220s > 220s > print( round( coef( summary( fit2sls3 ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 94.282 8.1771 11.53 0.000000 220s demand_price -0.225 0.0954 -2.36 0.024352 220s demand_income 0.298 0.0419 7.13 0.000000 220s supply_(Intercept) 48.184 9.7159 4.96 0.000019 220s supply_price 0.243 0.0826 2.94 0.005903 220s supply_farmPrice 0.262 0.0379 6.92 0.000000 220s supply_trend 0.298 0.0419 7.13 0.000000 220s > print( round( coef( summary( fit2sls3 ), modified.regMat = TRUE ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s C1 94.282 8.1771 11.53 0.000000 220s C2 -0.225 0.0954 -2.36 0.024352 220s C3 0.298 0.0419 7.13 0.000000 220s C4 48.184 9.7159 4.96 0.000019 220s C5 0.243 0.0826 2.94 0.005903 220s C6 0.262 0.0379 6.92 0.000000 220s > print( round( coef( summary( fit2sls3$eq[[ 1 ]] ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 94.282 8.1771 11.53 0.0000 220s price -0.225 0.0954 -2.36 0.0244 220s income 0.298 0.0419 7.13 0.0000 220s > 220s > print( round( coef( summary( fit2sls4s ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 95.706 6.3056 15.18 0.000000 220s demand_price -0.243 0.0684 -3.56 0.001104 220s demand_income 0.303 0.0394 7.69 0.000000 220s supply_(Intercept) 46.564 8.3296 5.59 0.000003 220s supply_price 0.257 0.0684 3.75 0.000635 220s supply_farmPrice 0.264 0.0455 5.79 0.000001 220s supply_trend 0.303 0.0394 7.69 0.000000 220s > print( round( coef( summary( fit2sls4s$eq[[ 2 ]] ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 46.564 8.3296 5.59 0.000003 220s price 0.257 0.0684 3.75 0.000635 220s farmPrice 0.264 0.0455 5.79 0.000001 220s trend 0.303 0.0394 7.69 0.000000 220s > 220s > print( round( coef( summary( fit2sls5r, useDfSys = FALSE ) ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s demand_(Intercept) 95.706 6.0044 15.94 0.000000 220s demand_price -0.243 0.0621 -3.92 0.001102 220s demand_income 0.303 0.0382 7.93 0.000000 220s supply_(Intercept) 46.564 7.3842 6.31 0.000010 220s supply_price 0.257 0.0621 4.14 0.000774 220s supply_farmPrice 0.264 0.0373 7.08 0.000003 220s supply_trend 0.303 0.0382 7.93 0.000001 220s > print( round( coef( summary( fit2sls5r, useDfSys = FALSE ), 220s + modified.regMat = TRUE ), digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s C1 95.706 6.0044 15.94 NA 220s C2 -0.243 0.0621 -3.92 NA 220s C3 0.303 0.0382 7.93 NA 220s C4 46.564 7.3842 6.31 NA 220s C5 0.257 0.0621 4.14 NA 220s C6 0.264 0.0373 7.08 NA 220s > print( round( coef( summary( fit2sls5r$eq[[ 2 ]], useDfSys = FALSE ) ), 220s + digits = 6 ) ) 220s Estimate Std. Error t value Pr(>|t|) 220s (Intercept) 46.564 7.3842 6.31 0.000010 220s price 0.257 0.0621 4.14 0.000774 220s farmPrice 0.264 0.0373 7.08 0.000003 220s trend 0.303 0.0382 7.93 0.000001 220s > 220s > 220s > ## *********** variance covariance matrix of the coefficients ******* 220s > print( round( vcov( fit2sls1s ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 79.8371 -0.85694 0.06274 220s demand_price -0.8569 0.01185 -0.00336 220s demand_income 0.0627 -0.00336 0.00280 220s supply_(Intercept) 0.0000 0.00000 0.00000 220s supply_price 0.0000 0.00000 0.00000 220s supply_farmPrice 0.0000 0.00000 0.00000 220s supply_trend 0.0000 0.00000 0.00000 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 0.000 0.000000 0.000000 220s demand_price 0.000 0.000000 0.000000 220s demand_income 0.000 0.000000 0.000000 220s supply_(Intercept) 117.514 -0.892363 -0.263795 220s supply_price -0.892 0.008136 0.000763 220s supply_farmPrice -0.264 0.000763 0.001819 220s supply_trend -0.241 0.000472 0.001122 220s supply_trend 220s demand_(Intercept) 0.000000 220s demand_price 0.000000 220s demand_income 0.000000 220s supply_(Intercept) -0.240505 220s supply_price 0.000472 220s supply_farmPrice 0.001122 220s supply_trend 0.008090 220s > print( round( vcov( fit2sls1s$eq[[ 1 ]] ), digits = 6 ) ) 220s (Intercept) price income 220s (Intercept) 79.8371 -0.85694 0.06274 220s price -0.8569 0.01185 -0.00336 220s income 0.0627 -0.00336 0.00280 220s > 220s > print( round( vcov( fit2sls1r ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 53.3287 -0.57241 0.04191 220s demand_price -0.5724 0.00791 -0.00225 220s demand_income 0.0419 -0.00225 0.00187 220s supply_(Intercept) 0.0000 0.00000 0.00000 220s supply_price 0.0000 0.00000 0.00000 220s supply_farmPrice 0.0000 0.00000 0.00000 220s supply_trend 0.0000 0.00000 0.00000 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 0.000 0.000000 0.000000 220s demand_price 0.000 0.000000 0.000000 220s demand_income 0.000 0.000000 0.000000 220s supply_(Intercept) 115.402 -0.876328 -0.259055 220s supply_price -0.876 0.007989 0.000749 220s supply_farmPrice -0.259 0.000749 0.001786 220s supply_trend -0.236 0.000463 0.001101 220s supply_trend 220s demand_(Intercept) 0.000000 220s demand_price 0.000000 220s demand_income 0.000000 220s supply_(Intercept) -0.236183 220s supply_price 0.000463 220s supply_farmPrice 0.001101 220s supply_trend 0.007945 220s > print( round( vcov( fit2sls1r$eq[[ 2 ]] ), digits = 6 ) ) 220s (Intercept) price farmPrice trend 220s (Intercept) 115.402 -0.876328 -0.259055 -0.236183 220s price -0.876 0.007989 0.000749 0.000463 220s farmPrice -0.259 0.000749 0.001786 0.001101 220s trend -0.236 0.000463 0.001101 0.007945 220s > 220s > print( round( vcov( fit2sls2 ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 78.66379 -0.829021 0.046112 220s demand_price -0.82902 0.010698 -0.002471 220s demand_income 0.04611 -0.002471 0.002061 220s supply_(Intercept) -1.37081 0.073457 -0.061273 220s supply_price 0.00269 -0.000144 0.000120 220s supply_farmPrice 0.00639 -0.000343 0.000286 220s supply_trend 0.04611 -0.002471 0.002061 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) -1.3708 0.002689 0.006393 220s demand_price 0.0735 -0.000144 -0.000343 220s demand_income -0.0613 0.000120 0.000286 220s supply_(Intercept) 111.0580 -0.872938 -0.236592 220s supply_price -0.8729 0.008032 0.000707 220s supply_farmPrice -0.2366 0.000707 0.001686 220s supply_trend -0.0613 0.000120 0.000286 220s supply_trend 220s demand_(Intercept) 0.046112 220s demand_price -0.002471 220s demand_income 0.002061 220s supply_(Intercept) -0.061273 220s supply_price 0.000120 220s supply_farmPrice 0.000286 220s supply_trend 0.002061 220s > print( round( vcov( fit2sls2$eq[[ 1 ]] ), digits = 6 ) ) 220s (Intercept) price income 220s (Intercept) 78.6638 -0.82902 0.04611 220s price -0.8290 0.01070 -0.00247 220s income 0.0461 -0.00247 0.00206 220s > 220s > print( round( vcov( fit2sls3 ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 66.86423 -0.704668 0.039196 220s demand_price -0.70467 0.009094 -0.002100 220s demand_income 0.03920 -0.002100 0.001752 220s supply_(Intercept) -1.16519 0.062438 -0.052082 220s supply_price 0.00229 -0.000122 0.000102 220s supply_farmPrice 0.00543 -0.000291 0.000243 220s supply_trend 0.03920 -0.002100 0.001752 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) -1.1652 0.002285 0.005434 220s demand_price 0.0624 -0.000122 -0.000291 220s demand_income -0.0521 0.000102 0.000243 220s supply_(Intercept) 94.3993 -0.741997 -0.201104 220s supply_price -0.7420 0.006827 0.000601 220s supply_farmPrice -0.2011 0.000601 0.001433 220s supply_trend -0.0521 0.000102 0.000243 220s supply_trend 220s demand_(Intercept) 0.039196 220s demand_price -0.002100 220s demand_income 0.001752 220s supply_(Intercept) -0.052082 220s supply_price 0.000102 220s supply_farmPrice 0.000243 220s supply_trend 0.001752 220s > print( round( vcov( fit2sls3, modified.regMat = TRUE ), digits = 6 ) ) 220s C1 C2 C3 C4 C5 C6 220s C1 66.86423 -0.704668 0.039196 -1.1652 0.002285 0.005434 220s C2 -0.70467 0.009094 -0.002100 0.0624 -0.000122 -0.000291 220s C3 0.03920 -0.002100 0.001752 -0.0521 0.000102 0.000243 220s C4 -1.16519 0.062438 -0.052082 94.3993 -0.741997 -0.201104 220s C5 0.00229 -0.000122 0.000102 -0.7420 0.006827 0.000601 220s C6 0.00543 -0.000291 0.000243 -0.2011 0.000601 0.001433 220s > print( round( vcov( fit2sls3$eq[[ 2 ]] ), digits = 6 ) ) 220s (Intercept) price farmPrice trend 220s (Intercept) 94.3993 -0.741997 -0.201104 -0.052082 220s price -0.7420 0.006827 0.000601 0.000102 220s farmPrice -0.2011 0.000601 0.001433 0.000243 220s trend -0.0521 0.000102 0.000243 0.001752 220s > 220s > print( round( vcov( fit2sls4s ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 39.7610 -0.358128 -0.03842 220s demand_price -0.3581 0.004681 -0.00113 220s demand_income -0.0384 -0.001129 0.00155 220s supply_(Intercept) 39.6949 -0.480685 0.08595 220s supply_price -0.3581 0.004681 -0.00113 220s supply_farmPrice -0.0359 0.000252 0.00011 220s supply_trend -0.0384 -0.001129 0.00155 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 39.6949 -0.358128 -0.035932 220s demand_price -0.4807 0.004681 0.000252 220s demand_income 0.0859 -0.001129 0.000110 220s supply_(Intercept) 69.3817 -0.480685 -0.226588 220s supply_price -0.4807 0.004681 0.000252 220s supply_farmPrice -0.2266 0.000252 0.002072 220s supply_trend 0.0859 -0.001129 0.000110 220s supply_trend 220s demand_(Intercept) -0.03842 220s demand_price -0.00113 220s demand_income 0.00155 220s supply_(Intercept) 0.08595 220s supply_price -0.00113 220s supply_farmPrice 0.00011 220s supply_trend 0.00155 220s > print( round( vcov( fit2sls4s$eq[[ 1 ]] ), digits = 6 ) ) 220s (Intercept) price income 220s (Intercept) 39.7610 -0.35813 -0.03842 220s price -0.3581 0.00468 -0.00113 220s income -0.0384 -0.00113 0.00155 220s > 220s > print( round( vcov( fit2sls5r ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 36.0523 -0.302514 -0.057288 220s demand_price -0.3025 0.003851 -0.000847 220s demand_income -0.0573 -0.000847 0.001456 220s supply_(Intercept) 34.1121 -0.397307 0.057684 220s supply_price -0.3025 0.003851 -0.000847 220s supply_farmPrice -0.0337 0.000218 0.000122 220s supply_trend -0.0573 -0.000847 0.001456 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 34.1121 -0.302514 -0.033671 220s demand_price -0.3973 0.003851 0.000218 220s demand_income 0.0577 -0.000847 0.000122 220s supply_(Intercept) 54.5267 -0.397307 -0.157170 220s supply_price -0.3973 0.003851 0.000218 220s supply_farmPrice -0.1572 0.000218 0.001388 220s supply_trend 0.0577 -0.000847 0.000122 220s supply_trend 220s demand_(Intercept) -0.057288 220s demand_price -0.000847 220s demand_income 0.001456 220s supply_(Intercept) 0.057684 220s supply_price -0.000847 220s supply_farmPrice 0.000122 220s supply_trend 0.001456 220s > print( round( vcov( fit2sls5r, modified.regMat = TRUE ), digits = 6 ) ) 220s C1 C2 C3 C4 C5 C6 220s C1 36.0523 -0.302514 -0.057288 34.1121 -0.302514 -0.033671 220s C2 -0.3025 0.003851 -0.000847 -0.3973 0.003851 0.000218 220s C3 -0.0573 -0.000847 0.001456 0.0577 -0.000847 0.000122 220s C4 34.1121 -0.397307 0.057684 54.5267 -0.397307 -0.157170 220s C5 -0.3025 0.003851 -0.000847 -0.3973 0.003851 0.000218 220s C6 -0.0337 0.000218 0.000122 -0.1572 0.000218 0.001388 220s > print( round( vcov( fit2sls5r$eq[[ 2 ]] ), digits = 6 ) ) 220s (Intercept) price farmPrice trend 220s (Intercept) 54.5267 -0.397307 -0.157170 0.057684 220s price -0.3973 0.003851 0.000218 -0.000847 220s farmPrice -0.1572 0.000218 0.001388 0.000122 220s trend 0.0577 -0.000847 0.000122 0.001456 220s > 220s > print( round( vcov( fit2slsd1 ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 124.179 -1.51767 0.28519 220s demand_price -1.518 0.02098 -0.00595 220s demand_income 0.285 -0.00595 0.00318 220s supply_(Intercept) 0.000 0.00000 0.00000 220s supply_price 0.000 0.00000 0.00000 220s supply_farmPrice 0.000 0.00000 0.00000 220s supply_trend 0.000 0.00000 0.00000 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 0.000 0.000000 0.000000 220s demand_price 0.000 0.000000 0.000000 220s demand_income 0.000 0.000000 0.000000 220s supply_(Intercept) 144.253 -1.095410 -0.323818 220s supply_price -1.095 0.009987 0.000936 220s supply_farmPrice -0.324 0.000936 0.002233 220s supply_trend -0.295 0.000579 0.001377 220s supply_trend 220s demand_(Intercept) 0.000000 220s demand_price 0.000000 220s demand_income 0.000000 220s supply_(Intercept) -0.295229 220s supply_price 0.000579 220s supply_farmPrice 0.001377 220s supply_trend 0.009931 220s > print( round( vcov( fit2slsd1$eq[[ 1 ]] ), digits = 6 ) ) 220s (Intercept) price income 220s (Intercept) 124.179 -1.51767 0.28519 220s price -1.518 0.02098 -0.00595 220s income 0.285 -0.00595 0.00318 220s > 220s > print( round( vcov( fit2slsd2rs ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 95.9017 -1.129212 0.176368 220s demand_price -1.1292 0.014881 -0.003682 220s demand_income 0.1764 -0.003682 0.001968 220s supply_(Intercept) -5.2430 0.109460 -0.058492 220s supply_price 0.0103 -0.000215 0.000115 220s supply_farmPrice 0.0245 -0.000510 0.000273 220s supply_trend 0.1764 -0.003682 0.001968 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) -5.2430 0.010284 0.024451 220s demand_price 0.1095 -0.000215 -0.000510 220s demand_income -0.0585 0.000115 0.000273 220s supply_(Intercept) 114.2555 -0.898881 -0.243056 220s supply_price -0.8989 0.008273 0.000727 220s supply_farmPrice -0.2431 0.000727 0.001733 220s supply_trend -0.0585 0.000115 0.000273 220s supply_trend 220s demand_(Intercept) 0.176368 220s demand_price -0.003682 220s demand_income 0.001968 220s supply_(Intercept) -0.058492 220s supply_price 0.000115 220s supply_farmPrice 0.000273 220s supply_trend 0.001968 220s > print( round( vcov( fit2slsd2rs$eq[[ 2 ]] ), digits = 6 ) ) 220s (Intercept) price farmPrice trend 220s (Intercept) 114.2555 -0.898881 -0.243056 -0.058492 220s price -0.8989 0.008273 0.000727 0.000115 220s farmPrice -0.2431 0.000727 0.001733 0.000273 220s trend -0.0585 0.000115 0.000273 0.001968 220s > 220s > print( round( vcov( fit2slsd3 ), digits = 6 ) ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 141.4425 -1.640068 0.234151 220s demand_price -1.6401 0.021165 -0.004888 220s demand_income 0.2342 -0.004888 0.002612 220s supply_(Intercept) -6.9607 0.145321 -0.077656 220s supply_price 0.0137 -0.000285 0.000152 220s supply_farmPrice 0.0325 -0.000678 0.000362 220s supply_trend 0.2342 -0.004888 0.002612 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) -6.9607 0.013653 0.032462 220s demand_price 0.1453 -0.000285 -0.000678 220s demand_income -0.0777 0.000152 0.000362 220s supply_(Intercept) 111.0123 -0.869653 -0.237751 220s supply_price -0.8697 0.007995 0.000708 220s supply_farmPrice -0.2378 0.000708 0.001688 220s supply_trend -0.0777 0.000152 0.000362 220s supply_trend 220s demand_(Intercept) 0.234151 220s demand_price -0.004888 220s demand_income 0.002612 220s supply_(Intercept) -0.077656 220s supply_price 0.000152 220s supply_farmPrice 0.000362 220s supply_trend 0.002612 220s > print( round( vcov( fit2slsd3, modified.regMat = TRUE ), digits = 6 ) ) 220s C1 C2 C3 C4 C5 C6 220s C1 141.4425 -1.640068 0.234151 -6.9607 0.013653 0.032462 220s C2 -1.6401 0.021165 -0.004888 0.1453 -0.000285 -0.000678 220s C3 0.2342 -0.004888 0.002612 -0.0777 0.000152 0.000362 220s C4 -6.9607 0.145321 -0.077656 111.0123 -0.869653 -0.237751 220s C5 0.0137 -0.000285 0.000152 -0.8697 0.007995 0.000708 220s C6 0.0325 -0.000678 0.000362 -0.2378 0.000708 0.001688 220s > print( round( vcov( fit2slsd3$eq[[ 1 ]] ), digits = 6 ) ) 220s (Intercept) price income 220s (Intercept) 141.442 -1.64007 0.23415 220s price -1.640 0.02116 -0.00489 220s income 0.234 -0.00489 0.00261 220s > 220s > 220s > ## *********** confidence intervals of coefficients ************* 220s > print( confint( fit2sls1 ) ) 220s 2.5 % 97.5 % 220s demand_(Intercept) 77.922 111.345 220s demand_price -0.447 -0.040 220s demand_income 0.215 0.413 220s supply_(Intercept) 24.071 74.994 220s supply_price 0.028 0.452 220s supply_farmPrice 0.155 0.356 220s supply_trend 0.042 0.464 220s > print( confint( fit2sls1$eq[[ 1 ]], level = 0.9 ) ) 220s 5 % 95 % 220s (Intercept) 80.854 108.412 220s price -0.411 -0.076 220s income 0.232 0.396 220s > 220s > print( confint( fit2sls2s, level = 0.9 ) ) 220s 5 % 95 % 220s demand_(Intercept) 78.005 110.558 220s demand_price -0.417 -0.032 220s demand_income 0.211 0.386 220s supply_(Intercept) 24.204 72.165 220s supply_price 0.038 0.447 220s supply_farmPrice 0.169 0.355 220s supply_trend 0.211 0.386 220s > print( confint( fit2sls2s$eq[[ 2 ]], level = 0.99 ) ) 220s 0.5 % 99.5 % 220s (Intercept) 15.989 80.380 220s price -0.032 0.517 220s farmPrice 0.137 0.387 220s trend 0.181 0.416 220s > 220s > print( confint( fit2sls3, level = 0.99, useDfSys = TRUE ) ) 220s 0.5 % 99.5 % 220s demand_(Intercept) 77.664 110.899 220s demand_price -0.419 -0.031 220s demand_income 0.213 0.383 220s supply_(Intercept) 28.439 67.929 220s supply_price 0.075 0.411 220s supply_farmPrice 0.185 0.339 220s supply_trend 0.213 0.383 220s > print( confint( fit2sls3$eq[[ 1 ]], level = 0.5, useDfSys = TRUE ) ) 220s 25 % 75 % 220s (Intercept) 88.71 99.857 220s price -0.29 -0.160 220s income 0.27 0.327 220s > 220s > print( confint( fit2sls4r, level = 0.5 ) ) 220s 25 % 75 % 220s demand_(Intercept) 83.516 107.895 220s demand_price -0.369 -0.117 220s demand_income 0.225 0.380 220s supply_(Intercept) 31.573 61.554 220s supply_price 0.131 0.383 220s supply_farmPrice 0.188 0.339 220s supply_trend 0.225 0.380 220s > print( confint( fit2sls4r$eq[[ 2 ]], level = 0.25 ) ) 220s 37.5 % 62.5 % 220s (Intercept) 44.192 48.935 220s price 0.237 0.277 220s farmPrice 0.252 0.276 220s trend 0.290 0.315 220s > 220s > print( confint( fit2sls5rs, level = 0.25 ) ) 220s 37.5 % 62.5 % 220s demand_(Intercept) 84.017 107.395 220s demand_price -0.369 -0.117 220s demand_income 0.230 0.376 220s supply_(Intercept) 31.265 61.863 220s supply_price 0.131 0.383 220s supply_farmPrice 0.181 0.346 220s supply_trend 0.230 0.376 220s > print( confint( fit2sls5rs$eq[[ 1 ]], level = 0.975 ) ) 220s 1.3 % 98.8 % 220s (Intercept) 82.221 109.191 220s price -0.389 -0.098 220s income 0.218 0.387 220s > 220s > print( confint( fit2slsd1, level = 0.975, useDfSys = TRUE ) ) 220s 1.3 % 98.8 % 220s demand_(Intercept) 84.118 129.461 220s demand_price -0.706 -0.117 220s demand_income 0.247 0.476 220s supply_(Intercept) 25.097 73.968 220s supply_price 0.037 0.443 220s supply_farmPrice 0.159 0.352 220s supply_trend 0.050 0.456 220s > print( confint( fit2slsd1$eq[[ 2 ]], level = 0.999, useDfSys = TRUE ) ) 220s 0.1 % 100 % 220s (Intercept) 6.163 92.901 220s price -0.121 0.601 220s farmPrice 0.085 0.426 220s trend -0.107 0.613 220s > 220s > print( confint( fit2slsd2r, level = 0.999 ) ) 220s 0.1 % 100 % 220s demand_(Intercept) 81.311 125.877 220s demand_price -0.617 -0.072 220s demand_income 0.230 0.422 220s supply_(Intercept) 27.618 67.100 220s supply_price 0.077 0.412 220s supply_farmPrice 0.189 0.343 220s supply_trend 0.230 0.422 220s > print( confint( fit2slsd2r$eq[[ 1 ]] ) ) 220s 2.5 % 97.5 % 220s (Intercept) 81.311 125.877 220s price -0.617 -0.072 220s income 0.230 0.422 220s > 220s > 220s > ## *********** fitted values ************* 220s > print( fitted( fit2sls1, se.fit = TRUE, interval = "prediction" ) ) 220s demand supply 220s 1 97.6 98.9 220s 2 99.9 100.4 220s 3 99.8 100.5 220s 4 100.0 100.7 220s 5 102.1 102.6 220s 6 102.0 102.6 220s 7 102.4 102.6 220s 8 103.0 104.8 220s 9 101.5 102.7 220s 10 100.3 99.7 220s 11 95.5 95.4 220s 12 94.7 93.8 220s 13 96.1 95.6 220s 14 99.0 97.6 220s 15 103.8 102.3 220s 16 103.7 104.1 220s 17 103.8 102.8 220s 18 102.1 102.7 220s 19 103.6 102.6 220s 20 106.9 105.6 220s > print( fitted( fit2sls1$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 12 13 220s 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 220s 14 15 16 17 18 19 20 220s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 220s > 220s > print( fitted( fit2sls2s ) ) 220s demand supply 220s 1 97.8 98.5 220s 2 100.0 100.0 220s 3 99.9 100.1 220s 4 100.1 100.4 220s 5 102.0 102.5 220s 6 101.9 102.5 220s 7 102.4 102.5 220s 8 102.9 104.8 220s 9 101.4 102.7 220s 10 100.3 99.7 220s 11 95.8 95.3 220s 12 95.0 93.7 220s 13 96.4 95.6 220s 14 99.1 97.6 220s 15 103.7 102.5 220s 16 103.5 104.4 220s 17 103.6 103.2 220s 18 102.0 103.0 220s 19 103.5 102.9 220s 20 106.7 106.1 220s > print( fitted( fit2sls2s$eq[[ 2 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 12 13 220s 98.5 100.0 100.1 100.4 102.5 102.5 102.5 104.8 102.7 99.7 95.3 93.7 95.6 220s 14 15 16 17 18 19 20 220s 97.6 102.5 104.4 103.2 103.0 102.9 106.1 220s > 220s > print( fitted( fit2sls3 ) ) 220s demand supply 220s 1 97.8 98.5 220s 2 100.0 100.0 220s 3 99.9 100.1 220s 4 100.1 100.4 220s 5 102.0 102.5 220s 6 101.9 102.5 220s 7 102.4 102.5 220s 8 102.9 104.8 220s 9 101.4 102.7 220s 10 100.3 99.7 220s 11 95.8 95.3 220s 12 95.0 93.7 220s 13 96.4 95.6 220s 14 99.1 97.6 220s 15 103.7 102.5 220s 16 103.5 104.4 220s 17 103.6 103.2 220s 18 102.0 103.0 220s 19 103.5 102.9 220s 20 106.7 106.1 220s > print( fitted( fit2sls3$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 12 13 220s 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 220s 14 15 16 17 18 19 20 220s 99.1 103.7 103.5 103.6 102.0 103.5 106.7 220s > 220s > print( fitted( fit2sls4r ) ) 220s demand supply 220s 1 97.8 98.5 220s 2 99.9 100.1 220s 3 99.8 100.2 220s 4 100.0 100.5 220s 5 102.1 102.5 220s 6 101.9 102.4 220s 7 102.4 102.5 220s 8 102.9 104.8 220s 9 101.5 102.7 220s 10 100.4 99.5 220s 11 95.8 95.1 220s 12 94.9 93.6 220s 13 96.3 95.6 220s 14 99.1 97.6 220s 15 103.8 102.5 220s 16 103.6 104.4 220s 17 103.8 103.1 220s 18 102.0 103.1 220s 19 103.5 103.0 220s 20 106.6 106.3 220s > print( fitted( fit2sls4r$eq[[ 2 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 12 13 220s 98.5 100.1 100.2 100.5 102.5 102.4 102.5 104.8 102.7 99.5 95.1 93.6 95.6 220s 14 15 16 17 18 19 20 220s 97.6 102.5 104.4 103.1 103.1 103.0 106.3 220s > 220s > print( fitted( fit2sls5rs ) ) 220s demand supply 220s 1 97.8 98.5 220s 2 99.9 100.1 220s 3 99.8 100.2 220s 4 100.0 100.5 220s 5 102.1 102.5 220s 6 101.9 102.4 220s 7 102.4 102.5 220s 8 102.9 104.8 220s 9 101.5 102.7 220s 10 100.4 99.5 220s 11 95.8 95.1 220s 12 94.9 93.6 220s 13 96.3 95.6 220s 14 99.1 97.6 220s 15 103.8 102.5 220s 16 103.6 104.4 220s 17 103.8 103.1 220s 18 102.0 103.1 220s 19 103.5 103.0 220s 20 106.6 106.3 220s > print( fitted( fit2sls5rs$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 12 13 220s 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 220s 14 15 16 17 18 19 20 220s 99.1 103.8 103.6 103.8 102.0 103.5 106.6 220s > 220s > print( fitted( fit2slsd1 ) ) 220s demand supply 220s 1 97.1 98.9 220s 2 99.2 100.4 220s 3 99.2 100.5 220s 4 99.3 100.7 220s 5 102.5 102.6 220s 6 102.2 102.6 220s 7 102.5 102.6 220s 8 102.7 104.8 220s 9 102.0 102.7 220s 10 101.4 99.7 220s 11 95.6 95.4 220s 12 93.9 93.8 220s 13 95.0 95.6 220s 14 98.9 97.6 220s 15 104.9 102.3 220s 16 104.3 104.1 220s 17 106.1 102.8 220s 18 101.7 102.7 220s 19 103.3 102.6 220s 20 106.0 105.6 220s > print( fitted( fit2slsd1$eq[[ 2 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 12 13 220s 98.9 100.4 100.5 100.7 102.6 102.6 102.6 104.8 102.7 99.7 95.4 93.8 95.6 220s 14 15 16 17 18 19 20 220s 97.6 102.3 104.1 102.8 102.7 102.6 105.6 220s > 220s > print( fitted( fit2slsd2r ) ) 220s demand supply 220s 1 97.5 98.2 220s 2 99.5 99.8 220s 3 99.4 99.9 220s 4 99.6 100.3 220s 5 102.3 102.4 220s 6 102.1 102.4 220s 7 102.4 102.4 220s 8 102.6 104.7 220s 9 101.8 102.7 220s 10 101.1 99.6 220s 11 96.0 95.2 220s 12 94.6 93.6 220s 13 95.7 95.6 220s 14 99.1 97.7 220s 15 104.4 102.7 220s 16 103.9 104.5 220s 17 105.2 103.4 220s 18 101.8 103.2 220s 19 103.2 103.1 220s 20 105.9 106.3 220s > print( fitted( fit2slsd2r$eq[[ 1 ]] ) ) 220s 1 2 3 4 5 6 7 8 9 10 11 12 13 220s 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 220s 14 15 16 17 18 19 20 220s 99.1 104.4 103.9 105.2 101.8 103.2 105.9 220s > 220s > 220s > ## *********** predicted values ************* 220s > predictData <- Kmenta 220s > predictData$consump <- NULL 220s > predictData$price <- Kmenta$price * 0.9 220s > predictData$income <- Kmenta$income * 1.1 220s > 220s > print( predict( fit2sls1, se.fit = TRUE, interval = "prediction" ) ) 220s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 220s 1 97.6 0.661 93.3 102.0 98.9 1.079 220s 2 99.9 0.600 95.5 104.2 100.4 1.064 220s 3 99.8 0.564 95.5 104.1 100.5 0.962 220s 4 100.0 0.605 95.7 104.4 100.7 0.938 220s 5 102.1 0.516 97.8 106.4 102.6 0.914 220s 6 102.0 0.474 97.7 106.2 102.6 0.808 220s 7 102.4 0.493 98.1 106.7 102.6 0.736 220s 8 103.0 0.615 98.6 107.3 104.8 0.994 220s 9 101.5 0.544 97.2 105.8 102.7 0.808 220s 10 100.3 0.822 95.8 104.8 99.7 1.023 220s 11 95.5 0.963 90.9 100.2 95.4 1.228 220s 12 94.7 1.006 90.1 99.4 93.8 1.428 220s 13 96.1 0.915 91.6 100.7 95.6 1.272 220s 14 99.0 0.518 94.7 103.3 97.6 0.917 220s 15 103.8 0.793 99.4 108.3 102.3 0.899 220s 16 103.7 0.636 99.3 108.0 104.1 0.936 220s 17 103.8 1.348 98.8 108.9 102.8 1.665 220s 18 102.1 0.549 97.8 106.4 102.7 0.988 220s 19 103.6 0.695 99.2 108.0 102.6 1.129 220s 20 106.9 1.306 101.9 111.9 105.6 1.733 220s supply.lwr supply.upr 220s 1 93.2 104.6 220s 2 94.7 106.1 220s 3 94.9 106.0 220s 4 95.1 106.3 220s 5 97.1 108.2 220s 6 97.1 108.1 220s 7 97.1 108.0 220s 8 99.2 110.4 220s 9 97.3 108.2 220s 10 94.0 105.3 220s 11 89.5 101.2 220s 12 87.8 99.8 220s 13 89.8 101.5 220s 14 92.0 103.1 220s 15 96.8 107.9 220s 16 98.5 109.6 220s 17 96.5 109.1 220s 18 97.1 108.3 220s 19 96.8 108.3 220s 20 99.2 112.0 220s > print( predict( fit2sls1$eq[[ 1 ]], se.fit = TRUE, interval = "prediction" ) ) 220s fit se.fit lwr upr 220s 1 97.6 0.661 93.3 102.0 220s 2 99.9 0.600 95.5 104.2 220s 3 99.8 0.564 95.5 104.1 220s 4 100.0 0.605 95.7 104.4 220s 5 102.1 0.516 97.8 106.4 220s 6 102.0 0.474 97.7 106.2 220s 7 102.4 0.493 98.1 106.7 220s 8 103.0 0.615 98.6 107.3 220s 9 101.5 0.544 97.2 105.8 220s 10 100.3 0.822 95.8 104.8 220s 11 95.5 0.963 90.9 100.2 220s 12 94.7 1.006 90.1 99.4 220s 13 96.1 0.915 91.6 100.7 220s 14 99.0 0.518 94.7 103.3 220s 15 103.8 0.793 99.4 108.3 220s 16 103.7 0.636 99.3 108.0 220s 17 103.8 1.348 98.8 108.9 220s 18 102.1 0.549 97.8 106.4 220s 19 103.6 0.695 99.2 108.0 220s 20 106.9 1.306 101.9 111.9 220s > 220s > print( predict( fit2sls2s, se.pred = TRUE, interval = "confidence", 220s + level = 0.999, newdata = predictData ) ) 220s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 220s 1 102.7 2.23 99.1 106 96.1 2.75 220s 2 105.2 2.23 101.6 109 97.5 2.64 220s 3 105.1 2.24 101.4 109 97.6 2.65 220s 4 105.4 2.23 101.8 109 97.9 2.62 220s 5 107.2 2.52 101.7 113 100.1 2.83 220s 6 107.1 2.46 101.9 112 100.0 2.77 220s 7 107.7 2.45 102.6 113 100.0 2.70 220s 8 108.5 2.41 103.6 113 102.2 2.65 220s 9 106.5 2.53 100.9 112 100.4 2.87 220s 10 105.0 2.66 98.7 111 97.4 3.10 220s 11 100.1 2.42 95.1 105 93.0 3.17 220s 12 99.5 2.22 96.0 103 91.3 3.14 220s 13 101.2 2.13 98.5 104 93.1 2.95 220s 14 104.0 2.32 99.7 108 95.3 2.91 220s 15 108.9 2.74 102.1 116 100.2 2.92 220s 16 108.9 2.62 102.7 115 102.0 2.79 220s 17 108.4 3.09 99.9 117 101.1 3.37 220s 18 107.5 2.36 102.9 112 100.5 2.65 220s 19 109.2 2.44 104.1 114 100.3 2.64 220s 20 113.0 2.67 106.6 119 103.3 2.58 220s supply.lwr supply.upr 220s 1 91.8 100.4 220s 2 94.3 100.8 220s 3 94.2 101.0 220s 4 94.8 101.0 220s 5 95.2 105.0 220s 6 95.6 104.5 220s 7 96.1 103.9 220s 8 98.9 105.6 220s 9 95.2 105.6 220s 10 90.7 104.1 220s 11 85.9 100.2 220s 12 84.4 98.3 220s 13 87.3 98.9 220s 14 89.7 100.8 220s 15 94.7 105.8 220s 16 97.3 106.6 220s 17 92.9 109.3 220s 18 97.1 103.9 220s 19 97.1 103.6 220s 20 100.7 105.9 220s > print( predict( fit2sls2s$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 220s + level = 0.999, newdata = predictData ) ) 220s fit se.pred lwr upr 220s 1 96.1 2.75 91.8 100.4 220s 2 97.5 2.64 94.3 100.8 220s 3 97.6 2.65 94.2 101.0 220s 4 97.9 2.62 94.8 101.0 220s 5 100.1 2.83 95.2 105.0 220s 6 100.0 2.77 95.6 104.5 220s 7 100.0 2.70 96.1 103.9 220s 8 102.2 2.65 98.9 105.6 220s 9 100.4 2.87 95.2 105.6 220s 10 97.4 3.10 90.7 104.1 220s 11 93.0 3.17 85.9 100.2 220s 12 91.3 3.14 84.4 98.3 220s 13 93.1 2.95 87.3 98.9 220s 14 95.3 2.91 89.7 100.8 220s 15 100.2 2.92 94.7 105.8 220s 16 102.0 2.79 97.3 106.6 220s 17 101.1 3.37 92.9 109.3 220s 18 100.5 2.65 97.1 103.9 220s 19 100.3 2.64 97.1 103.6 220s 20 103.3 2.58 100.7 105.9 220s > 220s > print( predict( fit2sls3, se.pred = TRUE, interval = "prediction", 220s + level = 0.975, useDfSys = TRUE ) ) 220s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 220s 1 97.8 2.09 92.9 103 98.5 2.55 220s 2 100.0 2.08 95.1 105 100.0 2.57 220s 3 99.9 2.07 95.0 105 100.1 2.55 220s 4 100.1 2.08 95.2 105 100.4 2.56 220s 5 102.0 2.06 97.2 107 102.5 2.58 220s 6 101.9 2.05 97.1 107 102.5 2.56 220s 7 102.4 2.05 97.5 107 102.5 2.55 220s 8 102.9 2.09 98.0 108 104.8 2.61 220s 9 101.4 2.07 96.6 106 102.7 2.57 220s 10 100.3 2.17 95.2 105 99.7 2.62 220s 11 95.8 2.20 90.6 101 95.3 2.67 220s 12 95.0 2.20 89.9 100 93.7 2.74 220s 13 96.4 2.17 91.3 101 95.6 2.69 220s 14 99.1 2.06 94.3 104 97.6 2.59 220s 15 103.7 2.14 98.7 109 102.5 2.56 220s 16 103.5 2.08 98.6 108 104.4 2.55 220s 17 103.6 2.40 98.0 109 103.2 2.78 220s 18 102.0 2.07 97.2 107 103.0 2.56 220s 19 103.5 2.11 98.6 108 102.9 2.59 220s 20 106.7 2.38 101.1 112 106.1 2.78 220s supply.lwr supply.upr 220s 1 92.5 104 220s 2 94.0 106 220s 3 94.1 106 220s 4 94.4 106 220s 5 96.4 109 220s 6 96.5 108 220s 7 96.5 108 220s 8 98.6 111 220s 9 96.7 109 220s 10 93.5 106 220s 11 89.0 102 220s 12 87.3 100 220s 13 89.3 102 220s 14 91.6 104 220s 15 96.5 109 220s 16 98.4 110 220s 17 96.7 110 220s 18 97.0 109 220s 19 96.8 109 220s 20 99.5 113 220s > print( predict( fit2sls3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 220s + level = 0.975, useDfSys = TRUE ) ) 220s fit se.pred lwr upr 220s 1 97.8 2.09 92.9 103 220s 2 100.0 2.08 95.1 105 220s 3 99.9 2.07 95.0 105 220s 4 100.1 2.08 95.2 105 220s 5 102.0 2.06 97.2 107 220s 6 101.9 2.05 97.1 107 220s 7 102.4 2.05 97.5 107 220s 8 102.9 2.09 98.0 108 220s 9 101.4 2.07 96.6 106 220s 10 100.3 2.17 95.2 105 220s 11 95.8 2.20 90.6 101 220s 12 95.0 2.20 89.9 100 220s 13 96.4 2.17 91.3 101 220s 14 99.1 2.06 94.3 104 220s 15 103.7 2.14 98.7 109 220s 16 103.5 2.08 98.6 108 220s 17 103.6 2.40 98.0 109 220s 18 102.0 2.07 97.2 107 220s 19 103.5 2.11 98.6 108 220s 20 106.7 2.38 101.1 112 220s > 220s > print( predict( fit2sls4r, se.fit = TRUE, interval = "confidence", 220s + level = 0.25 ) ) 220s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 220s 1 97.8 0.602 97.6 97.9 98.5 0.586 220s 2 99.9 0.526 99.7 100.1 100.1 0.672 220s 3 99.8 0.508 99.7 100.0 100.2 0.621 220s 4 100.0 0.530 99.8 100.2 100.5 0.632 220s 5 102.1 0.488 101.9 102.2 102.5 0.704 220s 6 101.9 0.474 101.8 102.1 102.4 0.636 220s 7 102.4 0.498 102.2 102.5 102.5 0.587 220s 8 102.9 0.604 102.7 103.0 104.8 0.764 220s 9 101.5 0.502 101.3 101.6 102.7 0.656 220s 10 100.4 0.696 100.2 100.6 99.5 0.710 220s 11 95.8 0.928 95.5 96.1 95.1 0.885 220s 12 94.9 0.889 94.7 95.2 93.6 1.146 220s 13 96.3 0.739 96.0 96.5 95.6 1.052 220s 14 99.1 0.519 98.9 99.3 97.6 0.746 220s 15 103.8 0.626 103.6 104.0 102.5 0.637 220s 16 103.6 0.566 103.4 103.8 104.4 0.615 220s 17 103.8 0.942 103.5 104.1 103.1 1.153 220s 18 102.0 0.540 101.8 102.2 103.1 0.556 220s 19 103.5 0.677 103.3 103.7 103.0 0.631 220s 20 106.6 1.226 106.2 107.0 106.3 0.900 220s supply.lwr supply.upr 220s 1 98.3 98.7 220s 2 99.9 100.3 220s 3 100.0 100.4 220s 4 100.3 100.7 220s 5 102.2 102.7 220s 6 102.2 102.6 220s 7 102.3 102.7 220s 8 104.6 105.1 220s 9 102.5 102.9 220s 10 99.3 99.8 220s 11 94.9 95.4 220s 12 93.3 94.0 220s 13 95.3 96.0 220s 14 97.4 97.9 220s 15 102.3 102.7 220s 16 104.2 104.6 220s 17 102.7 103.4 220s 18 102.9 103.3 220s 19 102.8 103.2 220s 20 106.0 106.6 220s > print( predict( fit2sls4r$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 220s + level = 0.25 ) ) 220s fit se.fit lwr upr 220s 1 98.5 0.586 98.3 98.7 220s 2 100.1 0.672 99.9 100.3 220s 3 100.2 0.621 100.0 100.4 220s 4 100.5 0.632 100.3 100.7 220s 5 102.5 0.704 102.2 102.7 220s 6 102.4 0.636 102.2 102.6 220s 7 102.5 0.587 102.3 102.7 220s 8 104.8 0.764 104.6 105.1 220s 9 102.7 0.656 102.5 102.9 220s 10 99.5 0.710 99.3 99.8 220s 11 95.1 0.885 94.9 95.4 220s 12 93.6 1.146 93.3 94.0 220s 13 95.6 1.052 95.3 96.0 220s 14 97.6 0.746 97.4 97.9 220s 15 102.5 0.637 102.3 102.7 220s 16 104.4 0.615 104.2 104.6 220s 17 103.1 1.153 102.7 103.4 220s 18 103.1 0.556 102.9 103.3 220s 19 103.0 0.631 102.8 103.2 220s 20 106.3 0.900 106.0 106.6 220s > 220s > print( predict( fit2sls5rs, se.fit = TRUE, se.pred = TRUE, 220s + interval = "prediction", level = 0.5, newdata = predictData ) ) 220s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 220s 1 102.8 0.713 2.10 101.4 104 95.9 220s 2 105.4 0.742 2.11 103.9 107 97.4 220s 3 105.3 0.751 2.11 103.8 107 97.5 220s 4 105.5 0.749 2.11 104.1 107 97.8 220s 5 107.5 1.080 2.25 105.9 109 99.9 220s 6 107.4 1.031 2.23 105.9 109 99.9 220s 7 107.9 1.040 2.23 106.4 109 99.9 220s 8 108.7 1.044 2.23 107.1 110 102.1 220s 9 106.8 1.073 2.24 105.2 108 100.2 220s 10 105.3 1.188 2.30 103.8 107 97.2 220s 11 100.3 1.013 2.22 98.8 102 92.8 220s 12 99.7 0.770 2.12 98.2 101 91.1 220s 13 101.3 0.584 2.06 99.9 103 93.0 220s 14 104.3 0.833 2.14 102.8 106 95.1 220s 15 109.2 1.310 2.37 107.6 111 100.1 220s 16 109.1 1.214 2.32 107.6 111 101.8 220s 17 108.9 1.582 2.53 107.1 111 100.8 220s 18 107.7 0.958 2.19 106.2 109 100.4 220s 19 109.4 1.111 2.26 107.9 111 100.3 220s 20 113.2 1.529 2.50 111.5 115 103.4 220s supply.se.fit supply.se.pred supply.lwr supply.upr 220s 1 0.746 2.61 94.1 97.7 220s 2 0.628 2.58 95.6 99.1 220s 3 0.642 2.58 95.7 99.3 220s 4 0.607 2.57 96.0 99.5 220s 5 0.978 2.68 98.1 101.8 220s 6 0.881 2.65 98.1 101.7 220s 7 0.786 2.62 98.1 101.7 220s 8 0.780 2.62 100.4 103.9 220s 9 1.031 2.70 98.4 102.1 220s 10 1.212 2.78 95.3 99.1 220s 11 1.339 2.84 90.8 94.7 220s 12 1.478 2.90 89.1 93.1 220s 13 1.292 2.81 91.1 94.9 220s 14 1.123 2.74 93.2 97.0 220s 15 1.105 2.73 98.2 101.9 220s 16 0.996 2.69 100.0 103.7 220s 17 1.636 2.99 98.8 102.9 220s 18 0.777 2.62 98.7 102.2 220s 19 0.775 2.62 98.5 102.1 220s 20 0.600 2.57 101.6 105.1 220s > print( predict( fit2sls5rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 220s + interval = "prediction", level = 0.5, newdata = predictData ) ) 220s fit se.fit se.pred lwr upr 220s 1 102.8 0.713 2.10 101.4 104 220s 2 105.4 0.742 2.11 103.9 107 220s 3 105.3 0.751 2.11 103.8 107 220s 4 105.5 0.749 2.11 104.1 107 220s 5 107.5 1.080 2.25 105.9 109 220s 6 107.4 1.031 2.23 105.9 109 220s 7 107.9 1.040 2.23 106.4 109 220s 8 108.7 1.044 2.23 107.1 110 220s 9 106.8 1.073 2.24 105.2 108 220s 10 105.3 1.188 2.30 103.8 107 220s 11 100.3 1.013 2.22 98.8 102 220s 12 99.7 0.770 2.12 98.2 101 220s 13 101.3 0.584 2.06 99.9 103 220s 14 104.3 0.833 2.14 102.8 106 220s 15 109.2 1.310 2.37 107.6 111 220s 16 109.1 1.214 2.32 107.6 111 220s 17 108.9 1.582 2.53 107.1 111 220s 18 107.7 0.958 2.19 106.2 109 220s 19 109.4 1.111 2.26 107.9 111 220s 20 113.2 1.529 2.50 111.5 115 220s > 220s > print( predict( fit2slsd1, se.fit = TRUE, se.pred = TRUE, 220s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 220s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 220s 1 97.1 0.751 2.13 95.1 99.2 98.9 220s 2 99.2 0.757 2.13 97.1 101.2 100.4 220s 3 99.2 0.692 2.11 97.3 101.1 100.5 220s 4 99.3 0.766 2.13 97.2 101.4 100.7 220s 5 102.5 0.595 2.08 100.9 104.2 102.6 220s 6 102.2 0.503 2.05 100.8 103.6 102.6 220s 7 102.5 0.503 2.05 101.1 103.9 102.6 220s 8 102.7 0.653 2.10 100.9 104.4 104.8 220s 9 102.0 0.655 2.10 100.2 103.8 102.7 220s 10 101.4 1.074 2.26 98.5 104.3 99.7 220s 11 95.6 0.978 2.22 93.0 98.3 95.4 220s 12 93.9 1.134 2.29 90.8 97.0 93.8 220s 13 95.0 1.162 2.31 91.9 98.2 95.6 220s 14 98.9 0.530 2.06 97.5 100.4 97.6 220s 15 104.9 1.061 2.26 102.0 107.8 102.3 220s 16 104.3 0.757 2.13 102.2 106.3 104.1 220s 17 106.1 1.963 2.80 100.7 111.4 102.8 220s 18 101.7 0.597 2.08 100.1 103.4 102.7 220s 19 103.3 0.736 2.12 101.3 105.3 102.6 220s 20 106.0 1.430 2.45 102.1 110.0 105.6 220s supply.se.fit supply.se.pred supply.lwr supply.upr 220s 1 1.079 2.68 96.0 101.9 220s 2 1.064 2.68 97.5 103.3 220s 3 0.962 2.64 97.8 103.1 220s 4 0.938 2.63 98.1 103.3 220s 5 0.914 2.62 100.1 105.1 220s 6 0.808 2.59 100.4 104.8 220s 7 0.736 2.57 100.5 104.6 220s 8 0.994 2.65 102.1 107.5 220s 9 0.808 2.59 100.5 105.0 220s 10 1.023 2.66 96.9 102.5 220s 11 1.228 2.75 92.0 98.7 220s 12 1.428 2.84 89.9 97.7 220s 13 1.272 2.77 92.2 99.1 220s 14 0.917 2.62 95.1 100.1 220s 15 0.899 2.62 99.9 104.8 220s 16 0.936 2.63 101.5 106.6 220s 17 1.665 2.97 98.3 107.4 220s 18 0.988 2.65 100.0 105.4 220s 19 1.129 2.70 99.5 105.6 220s 20 1.733 3.01 100.9 110.3 220s > print( predict( fit2slsd1$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 220s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 220s fit se.fit se.pred lwr upr 220s 1 98.9 1.079 2.68 96.0 101.9 220s 2 100.4 1.064 2.68 97.5 103.3 220s 3 100.5 0.962 2.64 97.8 103.1 220s 4 100.7 0.938 2.63 98.1 103.3 220s 5 102.6 0.914 2.62 100.1 105.1 220s 6 102.6 0.808 2.59 100.4 104.8 220s 7 102.6 0.736 2.57 100.5 104.6 220s 8 104.8 0.994 2.65 102.1 107.5 220s 9 102.7 0.808 2.59 100.5 105.0 220s 10 99.7 1.023 2.66 96.9 102.5 220s 11 95.4 1.228 2.75 92.0 98.7 220s 12 93.8 1.428 2.84 89.9 97.7 220s 13 95.6 1.272 2.77 92.2 99.1 220s 14 97.6 0.917 2.62 95.1 100.1 220s 15 102.3 0.899 2.62 99.9 104.8 220s 16 104.1 0.936 2.63 101.5 106.6 220s 17 102.8 1.665 2.97 98.3 107.4 220s 18 102.7 0.988 2.65 100.0 105.4 220s 19 102.6 1.129 2.70 99.5 105.6 220s 20 105.6 1.733 3.01 100.9 110.3 220s > 220s > print( predict( fit2slsd2r, se.fit = TRUE, interval = "prediction", 220s + level = 0.9, newdata = predictData ) ) 220s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 220s 1 104 1.34 99.8 108 95.8 1.026 220s 2 106 1.27 102.3 110 97.3 0.786 220s 3 106 1.32 102.2 110 97.4 0.804 220s 4 106 1.27 102.4 110 97.7 0.734 220s 5 109 2.06 104.2 114 100.0 1.130 220s 6 109 1.92 104.1 113 99.9 1.014 220s 7 109 1.86 104.7 114 99.9 0.893 220s 8 110 1.67 105.4 114 102.2 0.765 220s 9 108 2.12 103.4 113 100.4 1.187 220s 10 107 2.45 101.9 112 97.4 1.525 220s 11 102 1.85 97.1 106 92.9 1.627 220s 12 101 1.26 96.6 104 91.2 1.587 220s 13 102 0.98 98.3 106 93.1 1.314 220s 14 105 1.63 101.1 110 95.3 1.253 220s 15 111 2.53 105.6 116 100.4 1.269 220s 16 111 2.23 105.7 116 102.1 1.075 220s 17 111 3.28 104.9 118 101.3 1.888 220s 18 109 1.59 104.5 113 100.7 0.796 220s 19 110 1.70 106.1 115 100.5 0.772 220s 20 114 1.87 109.4 119 103.6 0.656 220s supply.lwr supply.upr 220s 1 91.2 100.4 220s 2 92.8 101.7 220s 3 93.0 101.9 220s 4 93.3 102.1 220s 5 95.3 104.6 220s 6 95.4 104.5 220s 7 95.4 104.4 220s 8 97.8 106.6 220s 9 95.7 105.1 220s 10 92.5 102.4 220s 11 87.9 98.0 220s 12 86.2 96.2 220s 13 88.3 97.9 220s 14 90.5 100.0 220s 15 95.6 105.1 220s 16 97.5 106.7 220s 17 96.0 106.6 220s 18 96.2 105.1 220s 19 96.1 105.0 220s 20 99.2 107.9 220s > print( predict( fit2slsd2r$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 220s + level = 0.9, newdata = predictData ) ) 220s fit se.fit lwr upr 220s 1 104 1.34 99.8 108 220s 2 106 1.27 102.3 110 220s 3 106 1.32 102.2 110 220s 4 106 1.27 102.4 110 220s 5 109 2.06 104.2 114 220s 6 109 1.92 104.1 113 220s 7 109 1.86 104.7 114 220s 8 110 1.67 105.4 114 220s 9 108 2.12 103.4 113 220s 10 107 2.45 101.9 112 220s 11 102 1.85 97.1 106 220s 12 101 1.26 96.6 104 220s 13 102 0.98 98.3 106 220s 14 105 1.63 101.1 110 220s 15 111 2.53 105.6 116 220s 16 111 2.23 105.7 116 220s 17 111 3.28 104.9 118 220s 18 109 1.59 104.5 113 220s 19 110 1.70 106.1 115 220s 20 114 1.87 109.4 119 220s > 220s > # predict just one observation 220s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 220s + trend = 25 ) 220s > 220s > print( predict( fit2sls1rs, newdata = smallData ) ) 220s demand.pred supply.pred 220s 1 110 118 220s > print( predict( fit2sls1rs$eq[[ 1 ]], newdata = smallData ) ) 220s fit 220s 1 110 220s > 220s > print( predict( fit2sls2, se.fit = TRUE, level = 0.9, 220s + newdata = smallData ) ) 220s demand.pred demand.se.fit supply.pred supply.se.fit 220s 1 110 2.79 119 3.18 220s > print( predict( fit2sls2$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 220s + newdata = smallData ) ) 220s fit se.pred 220s 1 110 3.42 220s > 220s > print( predict( fit2sls3, interval = "prediction", level = 0.975, 220s + newdata = smallData ) ) 220s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 220s 1 110 102 117 119 110 128 220s > print( predict( fit2sls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 220s + newdata = smallData ) ) 220s fit lwr upr 220s 1 110 106 113 220s > 220s > print( predict( fit2sls4r, se.fit = TRUE, interval = "confidence", 220s + level = 0.999, newdata = smallData ) ) 220s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 220s 1 109 2.24 101 118 119 2.09 220s supply.lwr supply.upr 220s 1 112 127 220s > print( predict( fit2sls4r$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 220s + level = 0.75, newdata = smallData ) ) 220s fit se.pred lwr upr 220s 1 119 3.26 115 123 220s > 220s > print( predict( fit2sls5s, se.fit = TRUE, interval = "prediction", 220s + newdata = smallData ) ) 220s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 220s 1 109 2.26 103 116 119 2.33 220s supply.lwr supply.upr 220s 1 112 126 220s > print( predict( fit2sls5s$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 220s + newdata = smallData ) ) 220s fit se.pred lwr upr 220s 1 109 3 105 114 220s > 220s > print( predict( fit2slsd3, se.fit = TRUE, se.pred = TRUE, 220s + interval = "prediction", level = 0.5, newdata = smallData ) ) 220s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 220s 1 108 3.33 3.86 105 110 119 220s supply.se.fit supply.se.pred supply.lwr supply.upr 220s 1 3.2 4.07 116 122 220s > print( predict( fit2slsd3$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 220s + interval = "confidence", level = 0.25, newdata = smallData ) ) 220s fit se.fit se.pred lwr upr 220s 1 108 3.33 3.86 107 109 220s > 220s > 220s > ## ************ correlation of predicted values *************** 220s > print( correlation.systemfit( fit2sls1, 1, 2 ) ) 220s [,1] 220s [1,] 0 220s [2,] 0 220s [3,] 0 220s [4,] 0 220s [5,] 0 220s [6,] 0 220s [7,] 0 220s [8,] 0 220s [9,] 0 220s [10,] 0 220s [11,] 0 220s [12,] 0 220s [13,] 0 220s [14,] 0 220s [15,] 0 220s [16,] 0 220s [17,] 0 220s [18,] 0 220s [19,] 0 220s [20,] 0 220s > 220s > print( correlation.systemfit( fit2sls2s, 2, 1 ) ) 220s [,1] 220s [1,] 0.413453 220s [2,] 0.153759 220s [3,] 0.152962 220s [4,] 0.112671 220s [5,] -0.071442 220s [6,] -0.053943 220s [7,] -0.050961 220s [8,] -0.005442 220s [9,] -0.000476 220s [10,] -0.001894 220s [11,] 0.047351 220s [12,] 0.064973 220s [13,] 0.024591 220s [14,] -0.028036 220s [15,] 0.175326 220s [16,] 0.254878 220s [17,] 0.104540 220s [18,] 0.065579 220s [19,] 0.147008 220s [20,] 0.124593 220s > 220s > print( correlation.systemfit( fit2sls3, 1, 2 ) ) 220s [,1] 220s [1,] 0.44877 220s [2,] 0.16875 220s [3,] 0.16850 220s [4,] 0.12519 220s [5,] -0.08079 220s [6,] -0.06096 220s [7,] -0.05780 220s [8,] -0.00618 220s [9,] -0.00054 220s [10,] -0.00214 220s [11,] 0.05454 220s [12,] 0.07607 220s [13,] 0.02868 220s [14,] -0.03197 220s [15,] 0.19899 220s [16,] 0.28551 220s [17,] 0.11838 220s [18,] 0.07184 220s [19,] 0.16271 220s [20,] 0.13995 220s > 220s > print( correlation.systemfit( fit2sls4r, 2, 1 ) ) 220s [,1] 220s [1,] 0.4078 220s [2,] 0.2866 220s [3,] 0.2528 220s [4,] 0.2836 220s [5,] -0.0300 220s [6,] -0.0537 220s [7,] -0.0627 220s [8,] 0.1044 220s [9,] 0.1003 220s [10,] 0.4530 220s [11,] 0.1293 220s [12,] 0.0184 220s [13,] 0.0449 220s [14,] -0.0409 220s [15,] 0.4229 220s [16,] 0.2649 220s [17,] 0.6554 220s [18,] 0.2693 220s [19,] 0.3831 220s [20,] 0.5784 220s > 220s > print( correlation.systemfit( fit2sls5rs, 1, 2 ) ) 220s [,1] 220s [1,] 0.38438 220s [2,] 0.30697 220s [3,] 0.26690 220s [4,] 0.30163 220s [5,] -0.02768 220s [6,] -0.05086 220s [7,] -0.05895 220s [8,] 0.10102 220s [9,] 0.10072 220s [10,] 0.45547 220s [11,] 0.10817 220s [12,] 0.00552 220s [13,] 0.04219 220s [14,] -0.04054 220s [15,] 0.42100 220s [16,] 0.24974 220s [17,] 0.65722 220s [18,] 0.24286 220s [19,] 0.34336 220s [20,] 0.54717 220s > 220s > print( correlation.systemfit( fit2slsd1, 2, 1 ) ) 220s [,1] 220s [1,] 0 220s [2,] 0 220s [3,] 0 220s [4,] 0 220s [5,] 0 220s [6,] 0 220s [7,] 0 220s [8,] 0 220s [9,] 0 220s [10,] 0 220s [11,] 0 220s [12,] 0 220s [13,] 0 220s [14,] 0 220s [15,] 0 220s [16,] 0 220s [17,] 0 220s [18,] 0 220s [19,] 0 220s [20,] 0 220s > 220s > print( correlation.systemfit( fit2slsd2r, 1, 2 ) ) 220s [,1] 220s [1,] 0.51320 220s [2,] 0.27263 220s [3,] 0.26221 220s [4,] 0.21307 220s [5,] -0.11973 220s [6,] -0.08282 220s [7,] -0.06158 220s [8,] -0.00225 220s [9,] -0.00103 220s [10,] -0.00892 220s [11,] 0.04576 220s [12,] 0.08710 220s [13,] 0.03423 220s [14,] -0.03425 220s [15,] 0.25625 220s [16,] 0.35070 220s [17,] 0.17505 220s [18,] -0.02443 220s [19,] 0.07277 220s [20,] 0.05142 220s > 220s > 220s > ## ************ Log-Likelihood values *************** 220s > print( logLik( fit2sls1 ) ) 220s 'log Lik.' -67.6 (df=8) 220s > print( logLik( fit2sls1, residCovDiag = TRUE ) ) 220s 'log Lik.' -84.4 (df=8) 220s > 220s > print( logLik( fit2sls2s ) ) 220s 'log Lik.' -65.7 (df=7) 220s > print( logLik( fit2sls2s, residCovDiag = TRUE ) ) 220s 'log Lik.' -84.8 (df=7) 220s > 220s > print( logLik( fit2sls3 ) ) 220s 'log Lik.' -65.7 (df=7) 220s > print( logLik( fit2sls3, residCovDiag = TRUE ) ) 220s 'log Lik.' -84.8 (df=7) 220s > 220s > print( logLik( fit2sls4r ) ) 220s 'log Lik.' -66.2 (df=6) 220s > print( logLik( fit2sls4r, residCovDiag = TRUE ) ) 220s 'log Lik.' -84.8 (df=6) 220s > 220s > print( logLik( fit2sls5rs ) ) 220s 'log Lik.' -66.2 (df=6) 220s > print( logLik( fit2sls5rs, residCovDiag = TRUE ) ) 220s 'log Lik.' -84.8 (df=6) 220s > 220s > print( logLik( fit2slsd1 ) ) 220s 'log Lik.' -75.1 (df=8) 220s > print( logLik( fit2slsd1, residCovDiag = TRUE ) ) 220s 'log Lik.' -84.7 (df=8) 220s > 220s > print( logLik( fit2slsd2r ) ) 220s 'log Lik.' -68.8 (df=7) 220s > print( logLik( fit2slsd2r, residCovDiag = TRUE ) ) 220s 'log Lik.' -84.6 (df=7) 220s > 220s > 220s > ## ************** F tests **************** 220s > # testing first restriction 220s > print( linearHypothesis( fit2sls1, restrm ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.06 0.8 220s > linearHypothesis( fit2sls1, restrict ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.06 0.8 220s > 220s > print( linearHypothesis( fit2sls1s, restrm ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1s 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.07 0.79 220s > linearHypothesis( fit2sls1s, restrict ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1s 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.07 0.79 220s > 220s > print( linearHypothesis( fit2sls1, restrm ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.06 0.8 220s > linearHypothesis( fit2sls1, restrict ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.06 0.8 220s > 220s > print( linearHypothesis( fit2sls1r, restrm ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1r 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.08 0.78 220s > linearHypothesis( fit2sls1r, restrict ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1r 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0.08 0.78 220s > 220s > # testing second restriction 220s > restrOnly2m <- matrix(0,1,7) 220s > restrOnly2q <- 0.5 220s > restrOnly2m[1,2] <- -1 220s > restrOnly2m[1,5] <- 1 220s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 220s > # first restriction not imposed 220s > print( linearHypothesis( fit2sls1, restrOnly2m, restrOnly2q ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0 0.96 220s > linearHypothesis( fit2sls1, restrictOnly2 ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 34 220s 2 33 1 0 0.96 220s > 220s > # first restriction imposed 220s > print( linearHypothesis( fit2sls2, restrOnly2m, restrOnly2q ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 34 1 0.01 0.92 220s > linearHypothesis( fit2sls2, restrictOnly2 ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 34 1 0.01 0.92 220s > 220s > print( linearHypothesis( fit2sls2r, restrOnly2m, restrOnly2q ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2r 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 34 1 0.01 0.91 220s > linearHypothesis( fit2sls2r, restrictOnly2 ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2r 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 34 1 0.01 0.91 220s > 220s > print( linearHypothesis( fit2sls3, restrOnly2m, restrOnly2q ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls3 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 34 1 0.01 0.91 220s > linearHypothesis( fit2sls3, restrictOnly2 ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls3 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 34 1 0.01 0.91 220s > 220s > # testing both of the restrictions 220s > print( linearHypothesis( fit2sls1, restr2m, restr2q ) ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 33 2 0.04 0.97 220s > linearHypothesis( fit2sls1, restrict2 ) 220s Linear hypothesis test (Theil's F test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df F Pr(>F) 220s 1 35 220s 2 33 2 0.04 0.97 220s > 220s > 220s > ## ************** Wald tests **************** 220s > # testing first restriction 220s > print( linearHypothesis( fit2sls1, restrm, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.31 0.58 220s > linearHypothesis( fit2sls1, restrict, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.31 0.58 220s > 220s > print( linearHypothesis( fit2sls1s, restrm, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1s 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.34 0.56 220s > linearHypothesis( fit2sls1s, restrict, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1s 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.34 0.56 220s > 220s > print( linearHypothesis( fit2sls1, restrm, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.31 0.58 220s > linearHypothesis( fit2sls1, restrict, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.31 0.58 220s > 220s > print( linearHypothesis( fit2sls1r, restrm, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1r 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.38 0.54 220s > linearHypothesis( fit2sls1r, restrict, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s 220s Model 1: restricted model 220s Model 2: fit2sls1r 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.38 0.54 220s > 220s > # testing second restriction 220s > # first restriction not imposed 220s > print( linearHypothesis( fit2sls1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.01 0.91 220s > linearHypothesis( fit2sls1, restrictOnly2, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 34 220s 2 33 1 0.01 0.91 220s > # first restriction imposed 220s > print( linearHypothesis( fit2sls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 34 1 0.06 0.81 220s > linearHypothesis( fit2sls2, restrictOnly2, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 34 1 0.06 0.81 220s > 220s > print( linearHypothesis( fit2sls2r, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2r 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 34 1 0.07 0.8 220s > linearHypothesis( fit2sls2r, restrictOnly2, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls2r 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 34 1 0.07 0.8 220s > 220s > print( linearHypothesis( fit2sls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls3 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 34 1 0.07 0.8 220s > linearHypothesis( fit2sls3, restrictOnly2, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls3 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 34 1 0.07 0.8 220s > 220s > # testing both of the restrictions 220s > print( linearHypothesis( fit2sls1, restr2m, restr2q, test = "Chisq" ) ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 33 2 0.35 0.84 220s > linearHypothesis( fit2sls1, restrict2, test = "Chisq" ) 220s Linear hypothesis test (Chi^2 statistic of a Wald test) 220s 220s Hypothesis: 220s demand_income - supply_trend = 0 220s - demand_price + supply_price = 0.5 220s 220s Model 1: restricted model 220s Model 2: fit2sls1 220s 220s Res.Df Df Chisq Pr(>Chisq) 220s 1 35 220s 2 33 2 0.35 0.84 220s > 220s > 220s > ## **************** model frame ************************ 220s > print( mf <- model.frame( fit2sls1 ) ) 220s consump price income farmPrice trend 220s 1 98.5 100.3 87.4 98.0 1 220s 2 99.2 104.3 97.6 99.1 2 220s 3 102.2 103.4 96.7 99.1 3 220s 4 101.5 104.5 98.2 98.1 4 220s 5 104.2 98.0 99.8 110.8 5 220s 6 103.2 99.5 100.5 108.2 6 220s 7 104.0 101.1 103.2 105.6 7 220s 8 99.9 104.8 107.8 109.8 8 220s 9 100.3 96.4 96.6 108.7 9 220s 10 102.8 91.2 88.9 100.6 10 220s 11 95.4 93.1 75.1 81.0 11 220s 12 92.4 98.8 76.9 68.6 12 220s 13 94.5 102.9 84.6 70.9 13 220s 14 98.8 98.8 90.6 81.4 14 220s 15 105.8 95.1 103.1 102.3 15 220s 16 100.2 98.5 105.1 105.0 16 220s 17 103.5 86.5 96.4 110.5 17 220s 18 99.9 104.0 104.4 92.5 18 220s 19 105.2 105.8 110.7 89.3 19 220s 20 106.2 113.5 127.1 93.0 20 220s > print( mf1 <- model.frame( fit2sls1$eq[[ 1 ]] ) ) 220s consump price income 220s 1 98.5 100.3 87.4 220s 2 99.2 104.3 97.6 220s 3 102.2 103.4 96.7 220s 4 101.5 104.5 98.2 220s 5 104.2 98.0 99.8 220s 6 103.2 99.5 100.5 220s 7 104.0 101.1 103.2 220s 8 99.9 104.8 107.8 220s 9 100.3 96.4 96.6 220s 10 102.8 91.2 88.9 220s 11 95.4 93.1 75.1 220s 12 92.4 98.8 76.9 220s 13 94.5 102.9 84.6 220s 14 98.8 98.8 90.6 220s 15 105.8 95.1 103.1 220s 16 100.2 98.5 105.1 220s 17 103.5 86.5 96.4 220s 18 99.9 104.0 104.4 220s 19 105.2 105.8 110.7 220s 20 106.2 113.5 127.1 220s > print( attributes( mf1 )$terms ) 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s > print( mf2 <- model.frame( fit2sls1$eq[[ 2 ]] ) ) 220s consump price farmPrice trend 220s 1 98.5 100.3 98.0 1 220s 2 99.2 104.3 99.1 2 220s 3 102.2 103.4 99.1 3 220s 4 101.5 104.5 98.1 4 220s 5 104.2 98.0 110.8 5 220s 6 103.2 99.5 108.2 6 220s 7 104.0 101.1 105.6 7 220s 8 99.9 104.8 109.8 8 220s 9 100.3 96.4 108.7 9 220s 10 102.8 91.2 100.6 10 220s 11 95.4 93.1 81.0 11 220s 12 92.4 98.8 68.6 12 220s 13 94.5 102.9 70.9 13 220s 14 98.8 98.8 81.4 14 220s 15 105.8 95.1 102.3 15 220s 16 100.2 98.5 105.0 16 220s 17 103.5 86.5 110.5 17 220s 18 99.9 104.0 92.5 18 220s 19 105.2 105.8 89.3 19 220s 20 106.2 113.5 93.0 20 220s > print( attributes( mf2 )$terms ) 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s > 220s > print( all.equal( mf, model.frame( fit2sls2s ) ) ) 220s [1] TRUE 220s > print( all.equal( mf2, model.frame( fit2sls2s$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > 220s > print( all.equal( mf, model.frame( fit2sls3 ) ) ) 220s [1] TRUE 220s > print( all.equal( mf1, model.frame( fit2sls3$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > 220s > print( all.equal( mf, model.frame( fit2sls4r ) ) ) 220s [1] TRUE 220s > print( all.equal( mf2, model.frame( fit2sls4r$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > 220s > print( all.equal( mf, model.frame( fit2sls5rs ) ) ) 220s [1] TRUE 220s > print( all.equal( mf1, model.frame( fit2sls5rs$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > 220s > fit2sls1$eq[[ 1 ]]$modelInst 220s income farmPrice trend 220s 1 87.4 98.0 1 220s 2 97.6 99.1 2 220s 3 96.7 99.1 3 220s 4 98.2 98.1 4 220s 5 99.8 110.8 5 220s 6 100.5 108.2 6 220s 7 103.2 105.6 7 220s 8 107.8 109.8 8 220s 9 96.6 108.7 9 220s 10 88.9 100.6 10 220s 11 75.1 81.0 11 220s 12 76.9 68.6 12 220s 13 84.6 70.9 13 220s 14 90.6 81.4 14 220s 15 103.1 102.3 15 220s 16 105.1 105.0 16 220s 17 96.4 110.5 17 220s 18 104.4 92.5 18 220s 19 110.7 89.3 19 220s 20 127.1 93.0 20 220s > fit2sls1$eq[[ 2 ]]$modelInst 220s income farmPrice trend 220s 1 87.4 98.0 1 220s 2 97.6 99.1 2 220s 3 96.7 99.1 3 220s 4 98.2 98.1 4 220s 5 99.8 110.8 5 220s 6 100.5 108.2 6 220s 7 103.2 105.6 7 220s 8 107.8 109.8 8 220s 9 96.6 108.7 9 220s 10 88.9 100.6 10 220s 11 75.1 81.0 11 220s 12 76.9 68.6 12 220s 13 84.6 70.9 13 220s 14 90.6 81.4 14 220s 15 103.1 102.3 15 220s 16 105.1 105.0 16 220s 17 96.4 110.5 17 220s 18 104.4 92.5 18 220s 19 110.7 89.3 19 220s 20 127.1 93.0 20 220s > 220s > fit2sls2s$eq[[ 1 ]]$modelInst 220s income farmPrice trend 220s 1 87.4 98.0 1 220s 2 97.6 99.1 2 220s 3 96.7 99.1 3 220s 4 98.2 98.1 4 220s 5 99.8 110.8 5 220s 6 100.5 108.2 6 220s 7 103.2 105.6 7 220s 8 107.8 109.8 8 220s 9 96.6 108.7 9 220s 10 88.9 100.6 10 220s 11 75.1 81.0 11 220s 12 76.9 68.6 12 220s 13 84.6 70.9 13 220s 14 90.6 81.4 14 220s 15 103.1 102.3 15 220s 16 105.1 105.0 16 220s 17 96.4 110.5 17 220s 18 104.4 92.5 18 220s 19 110.7 89.3 19 220s 20 127.1 93.0 20 220s > fit2sls2s$eq[[ 2 ]]$modelInst 220s income farmPrice trend 220s 1 87.4 98.0 1 220s 2 97.6 99.1 2 220s 3 96.7 99.1 3 220s 4 98.2 98.1 4 220s 5 99.8 110.8 5 220s 6 100.5 108.2 6 220s 7 103.2 105.6 7 220s 8 107.8 109.8 8 220s 9 96.6 108.7 9 220s 10 88.9 100.6 10 220s 11 75.1 81.0 11 220s 12 76.9 68.6 12 220s 13 84.6 70.9 13 220s 14 90.6 81.4 14 220s 15 103.1 102.3 15 220s 16 105.1 105.0 16 220s 17 96.4 110.5 17 220s 18 104.4 92.5 18 220s 19 110.7 89.3 19 220s 20 127.1 93.0 20 220s > 220s > fit2sls5rs$eq[[ 1 ]]$modelInst 220s income farmPrice trend 220s 1 87.4 98.0 1 220s 2 97.6 99.1 2 220s 3 96.7 99.1 3 220s 4 98.2 98.1 4 220s 5 99.8 110.8 5 220s 6 100.5 108.2 6 220s 7 103.2 105.6 7 220s 8 107.8 109.8 8 220s 9 96.6 108.7 9 220s 10 88.9 100.6 10 220s 11 75.1 81.0 11 220s 12 76.9 68.6 12 220s 13 84.6 70.9 13 220s 14 90.6 81.4 14 220s 15 103.1 102.3 15 220s 16 105.1 105.0 16 220s 17 96.4 110.5 17 220s 18 104.4 92.5 18 220s 19 110.7 89.3 19 220s 20 127.1 93.0 20 220s > fit2sls5rs$eq[[ 2 ]]$modelInst 220s income farmPrice trend 220s 1 87.4 98.0 1 220s 2 97.6 99.1 2 220s 3 96.7 99.1 3 220s 4 98.2 98.1 4 220s 5 99.8 110.8 5 220s 6 100.5 108.2 6 220s 7 103.2 105.6 7 220s 8 107.8 109.8 8 220s 9 96.6 108.7 9 220s 10 88.9 100.6 10 220s 11 75.1 81.0 11 220s 12 76.9 68.6 12 220s 13 84.6 70.9 13 220s 14 90.6 81.4 14 220s 15 103.1 102.3 15 220s 16 105.1 105.0 16 220s 17 96.4 110.5 17 220s 18 104.4 92.5 18 220s 19 110.7 89.3 19 220s 20 127.1 93.0 20 220s > 220s > 220s > ## **************** model matrix ************************ 220s > # with x (returnModelMatrix) = TRUE 220s > print( !is.null( fit2sls1$eq[[ 1 ]]$x ) ) 220s [1] TRUE 220s > print( mm <- model.matrix( fit2sls1 ) ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s demand_1 1 100.3 87.4 0 220s demand_2 1 104.3 97.6 0 220s demand_3 1 103.4 96.7 0 220s demand_4 1 104.5 98.2 0 220s demand_5 1 98.0 99.8 0 220s demand_6 1 99.5 100.5 0 220s demand_7 1 101.1 103.2 0 220s demand_8 1 104.8 107.8 0 220s demand_9 1 96.4 96.6 0 220s demand_10 1 91.2 88.9 0 220s demand_11 1 93.1 75.1 0 220s demand_12 1 98.8 76.9 0 220s demand_13 1 102.9 84.6 0 220s demand_14 1 98.8 90.6 0 220s demand_15 1 95.1 103.1 0 220s demand_16 1 98.5 105.1 0 220s demand_17 1 86.5 96.4 0 220s demand_18 1 104.0 104.4 0 220s demand_19 1 105.8 110.7 0 220s demand_20 1 113.5 127.1 0 220s supply_1 0 0.0 0.0 1 220s supply_2 0 0.0 0.0 1 220s supply_3 0 0.0 0.0 1 220s supply_4 0 0.0 0.0 1 220s supply_5 0 0.0 0.0 1 220s supply_6 0 0.0 0.0 1 220s supply_7 0 0.0 0.0 1 220s supply_8 0 0.0 0.0 1 220s supply_9 0 0.0 0.0 1 220s supply_10 0 0.0 0.0 1 220s supply_11 0 0.0 0.0 1 220s supply_12 0 0.0 0.0 1 220s supply_13 0 0.0 0.0 1 220s supply_14 0 0.0 0.0 1 220s supply_15 0 0.0 0.0 1 220s supply_16 0 0.0 0.0 1 220s supply_17 0 0.0 0.0 1 220s supply_18 0 0.0 0.0 1 220s supply_19 0 0.0 0.0 1 220s supply_20 0 0.0 0.0 1 220s supply_price supply_farmPrice supply_trend 220s demand_1 0.0 0.0 0 220s demand_2 0.0 0.0 0 220s demand_3 0.0 0.0 0 220s demand_4 0.0 0.0 0 220s demand_5 0.0 0.0 0 220s demand_6 0.0 0.0 0 220s demand_7 0.0 0.0 0 220s demand_8 0.0 0.0 0 220s demand_9 0.0 0.0 0 220s demand_10 0.0 0.0 0 220s demand_11 0.0 0.0 0 220s demand_12 0.0 0.0 0 220s demand_13 0.0 0.0 0 220s demand_14 0.0 0.0 0 220s demand_15 0.0 0.0 0 220s demand_16 0.0 0.0 0 220s demand_17 0.0 0.0 0 220s demand_18 0.0 0.0 0 220s demand_19 0.0 0.0 0 220s demand_20 0.0 0.0 0 220s supply_1 100.3 98.0 1 220s supply_2 104.3 99.1 2 220s supply_3 103.4 99.1 3 220s supply_4 104.5 98.1 4 220s supply_5 98.0 110.8 5 220s supply_6 99.5 108.2 6 220s supply_7 101.1 105.6 7 220s supply_8 104.8 109.8 8 220s supply_9 96.4 108.7 9 220s supply_10 91.2 100.6 10 220s supply_11 93.1 81.0 11 220s supply_12 98.8 68.6 12 220s supply_13 102.9 70.9 13 220s supply_14 98.8 81.4 14 220s supply_15 95.1 102.3 15 220s supply_16 98.5 105.0 16 220s supply_17 86.5 110.5 17 220s supply_18 104.0 92.5 18 220s supply_19 105.8 89.3 19 220s supply_20 113.5 93.0 20 220s > print( mm1 <- model.matrix( fit2sls1$eq[[ 1 ]] ) ) 220s (Intercept) price income 220s 1 1 100.3 87.4 220s 2 1 104.3 97.6 220s 3 1 103.4 96.7 220s 4 1 104.5 98.2 220s 5 1 98.0 99.8 220s 6 1 99.5 100.5 220s 7 1 101.1 103.2 220s 8 1 104.8 107.8 220s 9 1 96.4 96.6 220s 10 1 91.2 88.9 220s 11 1 93.1 75.1 220s 12 1 98.8 76.9 220s 13 1 102.9 84.6 220s 14 1 98.8 90.6 220s 15 1 95.1 103.1 220s 16 1 98.5 105.1 220s 17 1 86.5 96.4 220s 18 1 104.0 104.4 220s 19 1 105.8 110.7 220s 20 1 113.5 127.1 220s attr(,"assign") 220s [1] 0 1 2 220s > print( mm2 <- model.matrix( fit2sls1$eq[[ 2 ]] ) ) 220s (Intercept) price farmPrice trend 220s 1 1 100.3 98.0 1 220s 2 1 104.3 99.1 2 220s 3 1 103.4 99.1 3 220s 4 1 104.5 98.1 4 220s 5 1 98.0 110.8 5 220s 6 1 99.5 108.2 6 220s 7 1 101.1 105.6 7 220s 8 1 104.8 109.8 8 220s 9 1 96.4 108.7 9 220s 10 1 91.2 100.6 10 220s 11 1 93.1 81.0 11 220s 12 1 98.8 68.6 12 220s 13 1 102.9 70.9 13 220s 14 1 98.8 81.4 14 220s 15 1 95.1 102.3 15 220s 16 1 98.5 105.0 16 220s 17 1 86.5 110.5 17 220s 18 1 104.0 92.5 18 220s 19 1 105.8 89.3 19 220s 20 1 113.5 93.0 20 220s attr(,"assign") 220s [1] 0 1 2 3 220s > 220s > # with x (returnModelMatrix) = FALSE 220s > print( all.equal( mm, model.matrix( fit2sls1s ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls1s$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls1s$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > print( !is.null( fit2sls1s$eq[[ 1 ]]$x ) ) 220s [1] FALSE 220s > 220s > # with x (returnModelMatrix) = TRUE 220s > print( !is.null( fit2sls2s$eq[[ 1 ]]$x ) ) 220s [1] TRUE 220s > print( all.equal( mm, model.matrix( fit2sls2s ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls2s$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls2s$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > 220s > # with x (returnModelMatrix) = FALSE 220s > print( all.equal( mm, model.matrix( fit2sls2Sym ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls2Sym$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls2Sym$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > print( !is.null( fit2sls2Sym$eq[[ 1 ]]$x ) ) 220s [1] FALSE 220s > 220s > # with x (returnModelMatrix) = FALSE 220s > print( all.equal( mm, model.matrix( fit2sls3 ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls3$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls3$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > print( !is.null( fit2sls3$eq[[ 1 ]]$x ) ) 220s [1] FALSE 220s > 220s > # with x (returnModelMatrix) = TRUE 220s > print( !is.null( fit2sls4r$eq[[ 1 ]]$x ) ) 220s [1] TRUE 220s > print( all.equal( mm, model.matrix( fit2sls4r ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls4r$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls4r$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > 220s > # with x (returnModelMatrix) = FALSE 220s > print( all.equal( mm, model.matrix( fit2sls4s ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls4s$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls4s$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > print( !is.null( fit2sls4s$eq[[ 1 ]]$x ) ) 220s [1] FALSE 220s > 220s > # with x (returnModelMatrix) = TRUE 220s > print( !is.null( fit2sls5rs$eq[[ 1 ]]$x ) ) 220s [1] TRUE 220s > print( all.equal( mm, model.matrix( fit2sls5rs ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls5rs$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls5rs$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > 220s > # with x (returnModelMatrix) = FALSE 220s > print( all.equal( mm, model.matrix( fit2sls5r ) ) ) 220s [1] TRUE 220s > print( all.equal( mm1, model.matrix( fit2sls5r$eq[[ 1 ]] ) ) ) 220s [1] TRUE 220s > print( all.equal( mm2, model.matrix( fit2sls5r$eq[[ 2 ]] ) ) ) 220s [1] TRUE 220s > print( !is.null( fit2sls5r$eq[[ 1 ]]$x ) ) 220s [1] FALSE 220s > 220s > # matrices of instrumental variables 220s > model.matrix( fit2sls1, which = "z" ) 220s demand_(Intercept) demand_income demand_farmPrice demand_trend 220s demand_1 1 87.4 98.0 1 220s demand_2 1 97.6 99.1 2 220s demand_3 1 96.7 99.1 3 220s demand_4 1 98.2 98.1 4 220s demand_5 1 99.8 110.8 5 220s demand_6 1 100.5 108.2 6 220s demand_7 1 103.2 105.6 7 220s demand_8 1 107.8 109.8 8 220s demand_9 1 96.6 108.7 9 220s demand_10 1 88.9 100.6 10 220s demand_11 1 75.1 81.0 11 220s demand_12 1 76.9 68.6 12 220s demand_13 1 84.6 70.9 13 220s demand_14 1 90.6 81.4 14 220s demand_15 1 103.1 102.3 15 220s demand_16 1 105.1 105.0 16 220s demand_17 1 96.4 110.5 17 220s demand_18 1 104.4 92.5 18 220s demand_19 1 110.7 89.3 19 220s demand_20 1 127.1 93.0 20 220s supply_1 0 0.0 0.0 0 220s supply_2 0 0.0 0.0 0 220s supply_3 0 0.0 0.0 0 220s supply_4 0 0.0 0.0 0 220s supply_5 0 0.0 0.0 0 220s supply_6 0 0.0 0.0 0 220s supply_7 0 0.0 0.0 0 220s supply_8 0 0.0 0.0 0 220s supply_9 0 0.0 0.0 0 220s supply_10 0 0.0 0.0 0 220s supply_11 0 0.0 0.0 0 220s supply_12 0 0.0 0.0 0 220s supply_13 0 0.0 0.0 0 220s supply_14 0 0.0 0.0 0 220s supply_15 0 0.0 0.0 0 220s supply_16 0 0.0 0.0 0 220s supply_17 0 0.0 0.0 0 220s supply_18 0 0.0 0.0 0 220s supply_19 0 0.0 0.0 0 220s supply_20 0 0.0 0.0 0 220s supply_(Intercept) supply_income supply_farmPrice supply_trend 220s demand_1 0 0.0 0.0 0 220s demand_2 0 0.0 0.0 0 220s demand_3 0 0.0 0.0 0 220s demand_4 0 0.0 0.0 0 220s demand_5 0 0.0 0.0 0 220s demand_6 0 0.0 0.0 0 220s demand_7 0 0.0 0.0 0 220s demand_8 0 0.0 0.0 0 220s demand_9 0 0.0 0.0 0 220s demand_10 0 0.0 0.0 0 220s demand_11 0 0.0 0.0 0 220s demand_12 0 0.0 0.0 0 220s demand_13 0 0.0 0.0 0 220s demand_14 0 0.0 0.0 0 220s demand_15 0 0.0 0.0 0 220s demand_16 0 0.0 0.0 0 220s demand_17 0 0.0 0.0 0 220s demand_18 0 0.0 0.0 0 220s demand_19 0 0.0 0.0 0 220s demand_20 0 0.0 0.0 0 220s supply_1 1 87.4 98.0 1 220s supply_2 1 97.6 99.1 2 220s supply_3 1 96.7 99.1 3 220s supply_4 1 98.2 98.1 4 220s supply_5 1 99.8 110.8 5 220s supply_6 1 100.5 108.2 6 220s supply_7 1 103.2 105.6 7 220s supply_8 1 107.8 109.8 8 220s supply_9 1 96.6 108.7 9 220s supply_10 1 88.9 100.6 10 220s supply_11 1 75.1 81.0 11 220s supply_12 1 76.9 68.6 12 220s supply_13 1 84.6 70.9 13 220s supply_14 1 90.6 81.4 14 220s supply_15 1 103.1 102.3 15 220s supply_16 1 105.1 105.0 16 220s supply_17 1 96.4 110.5 17 220s supply_18 1 104.4 92.5 18 220s supply_19 1 110.7 89.3 19 220s supply_20 1 127.1 93.0 20 220s > model.matrix( fit2sls1$eq[[ 1 ]], which = "z" ) 220s (Intercept) income farmPrice trend 220s 1 1 87.4 98.0 1 220s 2 1 97.6 99.1 2 220s 3 1 96.7 99.1 3 220s 4 1 98.2 98.1 4 220s 5 1 99.8 110.8 5 220s 6 1 100.5 108.2 6 220s 7 1 103.2 105.6 7 220s 8 1 107.8 109.8 8 220s 9 1 96.6 108.7 9 220s 10 1 88.9 100.6 10 220s 11 1 75.1 81.0 11 220s 12 1 76.9 68.6 12 220s 13 1 84.6 70.9 13 220s 14 1 90.6 81.4 14 220s 15 1 103.1 102.3 15 220s 16 1 105.1 105.0 16 220s 17 1 96.4 110.5 17 220s 18 1 104.4 92.5 18 220s 19 1 110.7 89.3 19 220s 20 1 127.1 93.0 20 220s attr(,"assign") 220s [1] 0 1 2 3 220s > model.matrix( fit2sls1$eq[[ 2 ]], which = "z" ) 220s (Intercept) income farmPrice trend 220s 1 1 87.4 98.0 1 220s 2 1 97.6 99.1 2 220s 3 1 96.7 99.1 3 220s 4 1 98.2 98.1 4 220s 5 1 99.8 110.8 5 220s 6 1 100.5 108.2 6 220s 7 1 103.2 105.6 7 220s 8 1 107.8 109.8 8 220s 9 1 96.6 108.7 9 220s 10 1 88.9 100.6 10 220s 11 1 75.1 81.0 11 220s 12 1 76.9 68.6 12 220s 13 1 84.6 70.9 13 220s 14 1 90.6 81.4 14 220s 15 1 103.1 102.3 15 220s 16 1 105.1 105.0 16 220s 17 1 96.4 110.5 17 220s 18 1 104.4 92.5 18 220s 19 1 110.7 89.3 19 220s 20 1 127.1 93.0 20 220s attr(,"assign") 220s [1] 0 1 2 3 220s > 220s > # matrices of fitted regressors 220s > model.matrix( fit2sls5r, which = "xHat" ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s demand_1 1 99.6 87.4 0 220s demand_2 1 105.1 97.6 0 220s demand_3 1 103.8 96.7 0 220s demand_4 1 104.5 98.2 0 220s demand_5 1 98.7 99.8 0 220s demand_6 1 99.6 100.5 0 220s demand_7 1 102.0 103.2 0 220s demand_8 1 102.2 107.8 0 220s demand_9 1 94.6 96.6 0 220s demand_10 1 92.7 88.9 0 220s demand_11 1 92.4 75.1 0 220s demand_12 1 98.9 76.9 0 220s demand_13 1 102.2 84.6 0 220s demand_14 1 100.3 90.6 0 220s demand_15 1 97.6 103.1 0 220s demand_16 1 96.9 105.1 0 220s demand_17 1 87.7 96.4 0 220s demand_18 1 101.1 104.4 0 220s demand_19 1 106.1 110.7 0 220s demand_20 1 114.4 127.1 0 220s supply_1 0 0.0 0.0 1 220s supply_2 0 0.0 0.0 1 220s supply_3 0 0.0 0.0 1 220s supply_4 0 0.0 0.0 1 220s supply_5 0 0.0 0.0 1 220s supply_6 0 0.0 0.0 1 220s supply_7 0 0.0 0.0 1 220s supply_8 0 0.0 0.0 1 220s supply_9 0 0.0 0.0 1 220s supply_10 0 0.0 0.0 1 220s supply_11 0 0.0 0.0 1 220s supply_12 0 0.0 0.0 1 220s supply_13 0 0.0 0.0 1 220s supply_14 0 0.0 0.0 1 220s supply_15 0 0.0 0.0 1 220s supply_16 0 0.0 0.0 1 220s supply_17 0 0.0 0.0 1 220s supply_18 0 0.0 0.0 1 220s supply_19 0 0.0 0.0 1 220s supply_20 0 0.0 0.0 1 220s supply_price supply_farmPrice supply_trend 220s demand_1 0.0 0.0 0 220s demand_2 0.0 0.0 0 220s demand_3 0.0 0.0 0 220s demand_4 0.0 0.0 0 220s demand_5 0.0 0.0 0 220s demand_6 0.0 0.0 0 220s demand_7 0.0 0.0 0 220s demand_8 0.0 0.0 0 220s demand_9 0.0 0.0 0 220s demand_10 0.0 0.0 0 220s demand_11 0.0 0.0 0 220s demand_12 0.0 0.0 0 220s demand_13 0.0 0.0 0 220s demand_14 0.0 0.0 0 220s demand_15 0.0 0.0 0 220s demand_16 0.0 0.0 0 220s demand_17 0.0 0.0 0 220s demand_18 0.0 0.0 0 220s demand_19 0.0 0.0 0 220s demand_20 0.0 0.0 0 220s supply_1 99.6 98.0 1 220s supply_2 105.1 99.1 2 220s supply_3 103.8 99.1 3 220s supply_4 104.5 98.1 4 220s supply_5 98.7 110.8 5 220s supply_6 99.6 108.2 6 220s supply_7 102.0 105.6 7 220s supply_8 102.2 109.8 8 220s supply_9 94.6 108.7 9 220s supply_10 92.7 100.6 10 220s supply_11 92.4 81.0 11 220s supply_12 98.9 68.6 12 220s supply_13 102.2 70.9 13 220s supply_14 100.3 81.4 14 220s supply_15 97.6 102.3 15 220s supply_16 96.9 105.0 16 220s supply_17 87.7 110.5 17 220s supply_18 101.1 92.5 18 220s supply_19 106.1 89.3 19 220s supply_20 114.4 93.0 20 220s > model.matrix( fit2sls5r$eq[[ 1 ]], which = "xHat" ) 220s (Intercept) price income 220s 1 1 99.6 87.4 220s 2 1 105.1 97.6 220s 3 1 103.8 96.7 220s 4 1 104.5 98.2 220s 5 1 98.7 99.8 220s 6 1 99.6 100.5 220s 7 1 102.0 103.2 220s 8 1 102.2 107.8 220s 9 1 94.6 96.6 220s 10 1 92.7 88.9 220s 11 1 92.4 75.1 220s 12 1 98.9 76.9 220s 13 1 102.2 84.6 220s 14 1 100.3 90.6 220s 15 1 97.6 103.1 220s 16 1 96.9 105.1 220s 17 1 87.7 96.4 220s 18 1 101.1 104.4 220s 19 1 106.1 110.7 220s 20 1 114.4 127.1 220s > model.matrix( fit2sls5r$eq[[ 2 ]], which = "xHat" ) 220s (Intercept) price farmPrice trend 220s 1 1 99.6 98.0 1 220s 2 1 105.1 99.1 2 220s 3 1 103.8 99.1 3 220s 4 1 104.5 98.1 4 220s 5 1 98.7 110.8 5 220s 6 1 99.6 108.2 6 220s 7 1 102.0 105.6 7 220s 8 1 102.2 109.8 8 220s 9 1 94.6 108.7 9 220s 10 1 92.7 100.6 10 220s 11 1 92.4 81.0 11 220s 12 1 98.9 68.6 12 220s 13 1 102.2 70.9 13 220s 14 1 100.3 81.4 14 220s 15 1 97.6 102.3 15 220s 16 1 96.9 105.0 16 220s 17 1 87.7 110.5 17 220s 18 1 101.1 92.5 18 220s 19 1 106.1 89.3 19 220s 20 1 114.4 93.0 20 220s > 220s > 220s > ## **************** formulas ************************ 220s > formula( fit2sls1 ) 220s $demand 220s consump ~ price + income 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s 220s > formula( fit2sls1$eq[[ 1 ]] ) 220s consump ~ price + income 220s > 220s > formula( fit2sls2s ) 220s $demand 220s consump ~ price + income 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s 220s > formula( fit2sls2s$eq[[ 2 ]] ) 220s consump ~ price + farmPrice + trend 220s > 220s > formula( fit2sls3 ) 220s $demand 220s consump ~ price + income 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s 220s > formula( fit2sls3$eq[[ 1 ]] ) 220s consump ~ price + income 220s > 220s > formula( fit2sls4r ) 220s $demand 220s consump ~ price + income 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s 220s > formula( fit2sls4r$eq[[ 2 ]] ) 220s consump ~ price + farmPrice + trend 220s > 220s > formula( fit2sls5rs ) 220s $demand 220s consump ~ price + income 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s 220s > formula( fit2sls5rs$eq[[ 1 ]] ) 220s consump ~ price + income 220s > 220s > formula( fit2slsd1 ) 220s $demand 220s consump ~ price + income 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s 220s > formula( fit2slsd1$eq[[ 2 ]] ) 220s consump ~ price + farmPrice + trend 220s > 220s > formula( fit2slsd2r ) 220s $demand 220s consump ~ price + income 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s 220s > formula( fit2slsd2r$eq[[ 1 ]] ) 220s consump ~ price + income 220s > 220s > 220s > ## **************** model terms ******************* 220s > terms( fit2sls1 ) 220s $demand 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s 220s > terms( fit2sls1$eq[[ 1 ]] ) 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s > 220s > terms( fit2sls2s ) 220s $demand 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s 220s > terms( fit2sls2s$eq[[ 2 ]] ) 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s > 220s > terms( fit2sls3 ) 220s $demand 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s 220s > terms( fit2sls3$eq[[ 1 ]] ) 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s > 220s > terms( fit2sls4r ) 220s $demand 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s 220s > terms( fit2sls4r$eq[[ 2 ]] ) 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s > 220s > terms( fit2sls5rs ) 220s $demand 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s 220s > terms( fit2sls5rs$eq[[ 1 ]] ) 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s > 220s > terms( fit2slsd1 ) 220s $demand 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s 220s > terms( fit2slsd1$eq[[ 2 ]] ) 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s > 220s > terms( fit2slsd2r ) 220s $demand 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s 220s $supply 220s consump ~ price + farmPrice + trend 220s attr(,"variables") 220s list(consump, price, farmPrice, trend) 220s attr(,"factors") 220s price farmPrice trend 220s consump 0 0 0 220s price 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "price" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, farmPrice, trend) 220s attr(,"dataClasses") 220s consump price farmPrice trend 220s "numeric" "numeric" "numeric" "numeric" 220s 220s > terms( fit2slsd2r$eq[[ 1 ]] ) 220s consump ~ price + income 220s attr(,"variables") 220s list(consump, price, income) 220s attr(,"factors") 220s price income 220s consump 0 0 220s price 1 0 220s income 0 1 220s attr(,"term.labels") 220s [1] "price" "income" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 1 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(consump, price, income) 220s attr(,"dataClasses") 220s consump price income 220s "numeric" "numeric" "numeric" 220s > 220s > 220s > ## **************** terms of instruments ******************* 220s > fit2sls1$eq[[ 1 ]]$termsInst 220s ~income + farmPrice + trend 220s attr(,"variables") 220s list(income, farmPrice, trend) 220s attr(,"factors") 220s income farmPrice trend 220s income 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "income" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 0 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(income, farmPrice, trend) 220s attr(,"dataClasses") 220s income farmPrice trend 220s "numeric" "numeric" "numeric" 220s > 220s > fit2sls2s$eq[[ 2 ]]$termsInst 220s ~income + farmPrice + trend 220s attr(,"variables") 220s list(income, farmPrice, trend) 220s attr(,"factors") 220s income farmPrice trend 220s income 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "income" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 0 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(income, farmPrice, trend) 220s attr(,"dataClasses") 220s income farmPrice trend 220s "numeric" "numeric" "numeric" 220s > 220s > fit2sls3$eq[[ 1 ]]$termsInst 220s ~income + farmPrice + trend 220s attr(,"variables") 220s list(income, farmPrice, trend) 220s attr(,"factors") 220s income farmPrice trend 220s income 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "income" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 0 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(income, farmPrice, trend) 220s attr(,"dataClasses") 220s income farmPrice trend 220s "numeric" "numeric" "numeric" 220s > 220s > fit2sls4r$eq[[ 2 ]]$termsInst 220s ~income + farmPrice + trend 220s attr(,"variables") 220s list(income, farmPrice, trend) 220s attr(,"factors") 220s income farmPrice trend 220s income 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "income" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 0 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(income, farmPrice, trend) 220s attr(,"dataClasses") 220s income farmPrice trend 220s "numeric" "numeric" "numeric" 220s > 220s > fit2sls5rs$eq[[ 1 ]]$termsInst 220s ~income + farmPrice + trend 220s attr(,"variables") 220s list(income, farmPrice, trend) 220s attr(,"factors") 220s income farmPrice trend 220s income 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "income" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 0 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(income, farmPrice, trend) 220s attr(,"dataClasses") 220s income farmPrice trend 220s "numeric" "numeric" "numeric" 220s > 220s > fit2slsd1$eq[[ 2 ]]$termsInst 220s ~income + farmPrice + trend 220s attr(,"variables") 220s list(income, farmPrice, trend) 220s attr(,"factors") 220s income farmPrice trend 220s income 1 0 0 220s farmPrice 0 1 0 220s trend 0 0 1 220s attr(,"term.labels") 220s [1] "income" "farmPrice" "trend" 220s attr(,"order") 220s [1] 1 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 0 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(income, farmPrice, trend) 220s attr(,"dataClasses") 220s income farmPrice trend 220s "numeric" "numeric" "numeric" 220s > 220s > fit2slsd2r$eq[[ 1 ]]$termsInst 220s ~income + farmPrice 220s attr(,"variables") 220s list(income, farmPrice) 220s attr(,"factors") 220s income farmPrice 220s income 1 0 220s farmPrice 0 1 220s attr(,"term.labels") 220s [1] "income" "farmPrice" 220s attr(,"order") 220s [1] 1 1 220s attr(,"intercept") 220s [1] 1 220s attr(,"response") 220s [1] 0 220s attr(,".Environment") 220s 220s attr(,"predvars") 220s list(income, farmPrice) 220s attr(,"dataClasses") 220s income farmPrice 220s "numeric" "numeric" 220s > 220s > 220s > ## **************** estfun ************************ 220s > library( "sandwich" ) 220s > 220s > estfun( fit2sls1 ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s demand_1 0.6738 67.13 58.89 0.000 220s demand_2 -0.4897 -51.48 -47.80 0.000 220s demand_3 2.4440 253.65 236.33 0.000 220s demand_4 1.4958 156.35 146.88 0.000 220s demand_5 2.2975 226.65 229.29 0.000 220s demand_6 1.3235 131.89 133.02 0.000 220s demand_7 1.7917 182.70 184.90 0.000 220s demand_8 -3.6818 -376.41 -396.90 0.000 220s demand_9 -1.5729 -148.80 -151.94 0.000 220s demand_10 2.8552 264.73 253.83 0.000 220s demand_11 -0.2736 -25.29 -20.55 0.000 220s demand_12 -2.2634 -223.89 -174.06 0.000 220s demand_13 -1.7795 -181.80 -150.55 0.000 220s demand_14 0.0991 9.93 8.98 0.000 220s demand_15 2.5674 250.64 264.70 0.000 220s demand_16 -3.8102 -369.18 -400.45 0.000 220s demand_17 -0.0206 -1.81 -1.99 0.000 220s demand_18 -2.8715 -290.19 -299.78 0.000 220s demand_19 1.6632 176.41 184.12 0.000 220s demand_20 -0.4478 -51.23 -56.92 0.000 220s supply_1 0.0000 0.00 0.00 -0.268 220s supply_2 0.0000 0.00 0.00 -1.418 220s supply_3 0.0000 0.00 0.00 1.625 220s supply_4 0.0000 0.00 0.00 0.790 220s supply_5 0.0000 0.00 0.00 1.438 220s supply_6 0.0000 0.00 0.00 0.613 220s supply_7 0.0000 0.00 0.00 1.217 220s supply_8 0.0000 0.00 0.00 -4.265 220s supply_9 0.0000 0.00 0.00 -1.956 220s supply_10 0.0000 0.00 0.00 2.785 220s supply_11 0.0000 0.00 0.00 0.233 220s supply_12 0.0000 0.00 0.00 -1.426 220s supply_13 0.0000 0.00 0.00 -0.935 220s supply_14 0.0000 0.00 0.00 0.803 220s supply_15 0.0000 0.00 0.00 2.886 220s supply_16 0.0000 0.00 0.00 -3.454 220s supply_17 0.0000 0.00 0.00 0.391 220s supply_18 0.0000 0.00 0.00 -2.061 220s supply_19 0.0000 0.00 0.00 2.596 220s supply_20 0.0000 0.00 0.00 0.406 220s supply_price supply_farmPrice supply_trend 220s demand_1 0.0 0.0 0.000 220s demand_2 0.0 0.0 0.000 220s demand_3 0.0 0.0 0.000 220s demand_4 0.0 0.0 0.000 220s demand_5 0.0 0.0 0.000 220s demand_6 0.0 0.0 0.000 220s demand_7 0.0 0.0 0.000 220s demand_8 0.0 0.0 0.000 220s demand_9 0.0 0.0 0.000 220s demand_10 0.0 0.0 0.000 220s demand_11 0.0 0.0 0.000 220s demand_12 0.0 0.0 0.000 220s demand_13 0.0 0.0 0.000 220s demand_14 0.0 0.0 0.000 220s demand_15 0.0 0.0 0.000 220s demand_16 0.0 0.0 0.000 220s demand_17 0.0 0.0 0.000 220s demand_18 0.0 0.0 0.000 220s demand_19 0.0 0.0 0.000 220s demand_20 0.0 0.0 0.000 220s supply_1 -26.7 -26.3 -0.268 220s supply_2 -149.1 -140.5 -2.836 220s supply_3 168.7 161.1 4.876 220s supply_4 82.6 77.5 3.159 220s supply_5 141.9 159.3 7.190 220s supply_6 61.1 66.4 3.680 220s supply_7 124.1 128.5 8.520 220s supply_8 -436.1 -468.3 -34.122 220s supply_9 -185.0 -212.6 -17.602 220s supply_10 258.2 280.1 27.848 220s supply_11 21.5 18.8 2.558 220s supply_12 -141.0 -97.8 -17.107 220s supply_13 -95.5 -66.3 -12.152 220s supply_14 80.6 65.4 11.246 220s supply_15 281.7 295.2 43.286 220s supply_16 -334.7 -362.7 -55.267 220s supply_17 34.3 43.2 6.650 220s supply_18 -208.3 -190.7 -37.106 220s supply_19 275.4 231.8 49.327 220s supply_20 46.5 37.8 8.122 220s > round( colSums( estfun( fit2sls1 ) ), digits = 7 ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 0 0 0 0 220s supply_price supply_farmPrice supply_trend 220s 0 0 0 220s > 220s > estfun( fit2sls1s ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s demand_1 0.6738 67.13 58.89 0.000 220s demand_2 -0.4897 -51.48 -47.80 0.000 220s demand_3 2.4440 253.65 236.33 0.000 220s demand_4 1.4958 156.35 146.88 0.000 220s demand_5 2.2975 226.65 229.29 0.000 220s demand_6 1.3235 131.89 133.02 0.000 220s demand_7 1.7917 182.70 184.90 0.000 220s demand_8 -3.6818 -376.41 -396.90 0.000 220s demand_9 -1.5729 -148.80 -151.94 0.000 220s demand_10 2.8552 264.73 253.83 0.000 220s demand_11 -0.2736 -25.29 -20.55 0.000 220s demand_12 -2.2634 -223.89 -174.06 0.000 220s demand_13 -1.7795 -181.80 -150.55 0.000 220s demand_14 0.0991 9.93 8.98 0.000 220s demand_15 2.5674 250.64 264.70 0.000 220s demand_16 -3.8102 -369.18 -400.45 0.000 220s demand_17 -0.0206 -1.81 -1.99 0.000 220s demand_18 -2.8715 -290.19 -299.78 0.000 220s demand_19 1.6632 176.41 184.12 0.000 220s demand_20 -0.4478 -51.23 -56.92 0.000 220s supply_1 0.0000 0.00 0.00 -0.268 220s supply_2 0.0000 0.00 0.00 -1.418 220s supply_3 0.0000 0.00 0.00 1.625 220s supply_4 0.0000 0.00 0.00 0.790 220s supply_5 0.0000 0.00 0.00 1.438 220s supply_6 0.0000 0.00 0.00 0.613 220s supply_7 0.0000 0.00 0.00 1.217 220s supply_8 0.0000 0.00 0.00 -4.265 220s supply_9 0.0000 0.00 0.00 -1.956 220s supply_10 0.0000 0.00 0.00 2.785 220s supply_11 0.0000 0.00 0.00 0.233 220s supply_12 0.0000 0.00 0.00 -1.426 220s supply_13 0.0000 0.00 0.00 -0.935 220s supply_14 0.0000 0.00 0.00 0.803 220s supply_15 0.0000 0.00 0.00 2.886 220s supply_16 0.0000 0.00 0.00 -3.454 220s supply_17 0.0000 0.00 0.00 0.391 220s supply_18 0.0000 0.00 0.00 -2.061 220s supply_19 0.0000 0.00 0.00 2.596 220s supply_20 0.0000 0.00 0.00 0.406 220s supply_price supply_farmPrice supply_trend 220s demand_1 0.0 0.0 0.000 220s demand_2 0.0 0.0 0.000 220s demand_3 0.0 0.0 0.000 220s demand_4 0.0 0.0 0.000 220s demand_5 0.0 0.0 0.000 220s demand_6 0.0 0.0 0.000 220s demand_7 0.0 0.0 0.000 220s demand_8 0.0 0.0 0.000 220s demand_9 0.0 0.0 0.000 220s demand_10 0.0 0.0 0.000 220s demand_11 0.0 0.0 0.000 220s demand_12 0.0 0.0 0.000 220s demand_13 0.0 0.0 0.000 220s demand_14 0.0 0.0 0.000 220s demand_15 0.0 0.0 0.000 220s demand_16 0.0 0.0 0.000 220s demand_17 0.0 0.0 0.000 220s demand_18 0.0 0.0 0.000 220s demand_19 0.0 0.0 0.000 220s demand_20 0.0 0.0 0.000 220s supply_1 -26.7 -26.3 -0.268 220s supply_2 -149.1 -140.5 -2.836 220s supply_3 168.7 161.1 4.876 220s supply_4 82.6 77.5 3.159 220s supply_5 141.9 159.3 7.190 220s supply_6 61.1 66.4 3.680 220s supply_7 124.1 128.5 8.520 220s supply_8 -436.1 -468.3 -34.122 220s supply_9 -185.0 -212.6 -17.602 220s supply_10 258.2 280.1 27.848 220s supply_11 21.5 18.8 2.558 220s supply_12 -141.0 -97.8 -17.107 220s supply_13 -95.5 -66.3 -12.152 220s supply_14 80.6 65.4 11.246 220s supply_15 281.7 295.2 43.286 220s supply_16 -334.7 -362.7 -55.267 220s supply_17 34.3 43.2 6.650 220s supply_18 -208.3 -190.7 -37.106 220s supply_19 275.4 231.8 49.327 220s supply_20 46.5 37.8 8.122 220s > round( colSums( estfun( fit2sls1s ) ), digits = 7 ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 0 0 0 0 220s supply_price supply_farmPrice supply_trend 220s 0 0 0 220s > 220s > estfun( fit2sls1r ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s demand_1 0.6738 67.13 58.89 0.000 220s demand_2 -0.4897 -51.48 -47.80 0.000 220s demand_3 2.4440 253.65 236.33 0.000 220s demand_4 1.4958 156.35 146.88 0.000 220s demand_5 2.2975 226.65 229.29 0.000 220s demand_6 1.3235 131.89 133.02 0.000 220s demand_7 1.7917 182.70 184.90 0.000 220s demand_8 -3.6818 -376.41 -396.90 0.000 220s demand_9 -1.5729 -148.80 -151.94 0.000 220s demand_10 2.8552 264.73 253.83 0.000 220s demand_11 -0.2736 -25.29 -20.55 0.000 220s demand_12 -2.2634 -223.89 -174.06 0.000 220s demand_13 -1.7795 -181.80 -150.55 0.000 220s demand_14 0.0991 9.93 8.98 0.000 220s demand_15 2.5674 250.64 264.70 0.000 220s demand_16 -3.8102 -369.18 -400.45 0.000 220s demand_17 -0.0206 -1.81 -1.99 0.000 220s demand_18 -2.8715 -290.19 -299.78 0.000 220s demand_19 1.6632 176.41 184.12 0.000 220s demand_20 -0.4478 -51.23 -56.92 0.000 220s supply_1 0.0000 0.00 0.00 -0.268 220s supply_2 0.0000 0.00 0.00 -1.418 220s supply_3 0.0000 0.00 0.00 1.625 220s supply_4 0.0000 0.00 0.00 0.790 220s supply_5 0.0000 0.00 0.00 1.438 220s supply_6 0.0000 0.00 0.00 0.613 220s supply_7 0.0000 0.00 0.00 1.217 220s supply_8 0.0000 0.00 0.00 -4.265 220s supply_9 0.0000 0.00 0.00 -1.956 220s supply_10 0.0000 0.00 0.00 2.785 220s supply_11 0.0000 0.00 0.00 0.233 220s supply_12 0.0000 0.00 0.00 -1.426 220s supply_13 0.0000 0.00 0.00 -0.935 220s supply_14 0.0000 0.00 0.00 0.803 220s supply_15 0.0000 0.00 0.00 2.886 220s supply_16 0.0000 0.00 0.00 -3.454 220s supply_17 0.0000 0.00 0.00 0.391 220s supply_18 0.0000 0.00 0.00 -2.061 220s supply_19 0.0000 0.00 0.00 2.596 220s supply_20 0.0000 0.00 0.00 0.406 220s supply_price supply_farmPrice supply_trend 220s demand_1 0.0 0.0 0.000 220s demand_2 0.0 0.0 0.000 220s demand_3 0.0 0.0 0.000 220s demand_4 0.0 0.0 0.000 220s demand_5 0.0 0.0 0.000 220s demand_6 0.0 0.0 0.000 220s demand_7 0.0 0.0 0.000 220s demand_8 0.0 0.0 0.000 220s demand_9 0.0 0.0 0.000 220s demand_10 0.0 0.0 0.000 220s demand_11 0.0 0.0 0.000 220s demand_12 0.0 0.0 0.000 220s demand_13 0.0 0.0 0.000 220s demand_14 0.0 0.0 0.000 220s demand_15 0.0 0.0 0.000 220s demand_16 0.0 0.0 0.000 220s demand_17 0.0 0.0 0.000 220s demand_18 0.0 0.0 0.000 220s demand_19 0.0 0.0 0.000 220s demand_20 0.0 0.0 0.000 220s supply_1 -26.7 -26.3 -0.268 220s supply_2 -149.1 -140.5 -2.836 220s supply_3 168.7 161.1 4.876 220s supply_4 82.6 77.5 3.159 220s supply_5 141.9 159.3 7.190 220s supply_6 61.1 66.4 3.680 220s supply_7 124.1 128.5 8.520 220s supply_8 -436.1 -468.3 -34.122 220s supply_9 -185.0 -212.6 -17.602 220s supply_10 258.2 280.1 27.848 220s supply_11 21.5 18.8 2.558 220s supply_12 -141.0 -97.8 -17.107 220s supply_13 -95.5 -66.3 -12.152 220s supply_14 80.6 65.4 11.246 220s supply_15 281.7 295.2 43.286 220s supply_16 -334.7 -362.7 -55.267 220s supply_17 34.3 43.2 6.650 220s supply_18 -208.3 -190.7 -37.106 220s supply_19 275.4 231.8 49.327 220s supply_20 46.5 37.8 8.122 220s > round( colSums( estfun( fit2sls1r ) ), digits = 7 ) 220s demand_(Intercept) demand_price demand_income supply_(Intercept) 220s 0 0 0 0 220s supply_price supply_farmPrice supply_trend 220s 0 0 0 220s > 220s > 220s > ## **************** bread ************************ 220s > bread( fit2sls1 ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 649.07 -6.9669 0.5100 220s demand_price -6.97 0.0963 -0.0273 220s demand_income 0.51 -0.0273 0.0228 220s supply_(Intercept) 0.00 0.0000 0.0000 220s supply_price 0.00 0.0000 0.0000 220s supply_farmPrice 0.00 0.0000 0.0000 220s supply_trend 0.00 0.0000 0.0000 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 0.00 0.00000 0.00000 220s demand_price 0.00 0.00000 0.00000 220s demand_income 0.00 0.00000 0.00000 220s supply_(Intercept) 955.38 -7.25488 -2.14464 220s supply_price -7.25 0.06614 0.00620 220s supply_farmPrice -2.14 0.00620 0.01479 220s supply_trend -1.96 0.00384 0.00912 220s supply_trend 220s demand_(Intercept) 0.00000 220s demand_price 0.00000 220s demand_income 0.00000 220s supply_(Intercept) -1.95529 220s supply_price 0.00384 220s supply_farmPrice 0.00912 220s supply_trend 0.06577 220s > 220s > bread( fit2sls1s ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 649.07 -6.9669 0.5100 220s demand_price -6.97 0.0963 -0.0273 220s demand_income 0.51 -0.0273 0.0228 220s supply_(Intercept) 0.00 0.0000 0.0000 220s supply_price 0.00 0.0000 0.0000 220s supply_farmPrice 0.00 0.0000 0.0000 220s supply_trend 0.00 0.0000 0.0000 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 0.00 0.00000 0.00000 220s demand_price 0.00 0.00000 0.00000 220s demand_income 0.00 0.00000 0.00000 220s supply_(Intercept) 955.38 -7.25488 -2.14464 220s supply_price -7.25 0.06614 0.00620 220s supply_farmPrice -2.14 0.00620 0.01479 220s supply_trend -1.96 0.00384 0.00912 220s supply_trend 220s demand_(Intercept) 0.00000 220s demand_price 0.00000 220s demand_income 0.00000 220s supply_(Intercept) -1.95529 220s supply_price 0.00384 220s supply_farmPrice 0.00912 220s supply_trend 0.06577 220s > 220s > bread( fit2sls1r ) 220s demand_(Intercept) demand_price demand_income 220s demand_(Intercept) 649.07 -6.9669 0.5100 220s demand_price -6.97 0.0963 -0.0273 220s demand_income 0.51 -0.0273 0.0228 220s supply_(Intercept) 0.00 0.0000 0.0000 220s supply_price 0.00 0.0000 0.0000 220s supply_farmPrice 0.00 0.0000 0.0000 220s supply_trend 0.00 0.0000 0.0000 220s supply_(Intercept) supply_price supply_farmPrice 220s demand_(Intercept) 0.00 0.00000 0.00000 220s demand_price 0.00 0.00000 0.00000 220s demand_income 0.00 0.00000 0.00000 220s supply_(Intercept) 955.38 -7.25488 -2.14464 220s supply_price -7.25 0.06614 0.00620 220s supply_farmPrice -2.14 0.00620 0.01479 220s supply_trend -1.96 0.00384 0.00912 220s supply_trend 220s demand_(Intercept) 0.00000 220s demand_price 0.00000 220s demand_income 0.00000 220s supply_(Intercept) -1.95529 220s supply_price 0.00384 220s supply_farmPrice 0.00912 220s supply_trend 0.06577 220s > 220s BEGIN TEST test_3sls.R 220s 220s R version 4.3.2 (2023-10-31) -- "Eye Holes" 220s Copyright (C) 2023 The R Foundation for Statistical Computing 220s Platform: aarch64-unknown-linux-gnu (64-bit) 220s 220s R is free software and comes with ABSOLUTELY NO WARRANTY. 220s You are welcome to redistribute it under certain conditions. 220s Type 'license()' or 'licence()' for distribution details. 220s 220s R is a collaborative project with many contributors. 220s Type 'contributors()' for more information and 220s 'citation()' on how to cite R or R packages in publications. 220s 220s Type 'demo()' for some demos, 'help()' for on-line help, or 220s 'help.start()' for an HTML browser interface to help. 220s Type 'q()' to quit R. 220s 220s > library( systemfit ) 220s Loading required package: Matrix 221s Loading required package: car 221s Loading required package: carData 221s Loading required package: lmtest 221s Loading required package: zoo 221s 221s Attaching package: ‘zoo’ 221s 221s The following objects are masked from ‘package:base’: 221s 221s as.Date, as.Date.numeric 221s 221s 221s Please cite the 'systemfit' package as: 221s 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/. 221s 221s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 221s https://r-forge.r-project.org/projects/systemfit/ 221s > options( digits = 3 ) 221s > 221s > data( "Kmenta" ) 221s > useMatrix <- FALSE 221s > 221s > demand <- consump ~ price + income 221s > supply <- consump ~ price + farmPrice + trend 221s > inst <- ~ income + farmPrice + trend 221s > inst1 <- ~ income + farmPrice 221s > instlist <- list( inst1, inst ) 221s > system <- list( demand = demand, supply = supply ) 221s > restrm <- matrix(0,1,7) # restriction matrix "R" 221s > restrm[1,3] <- 1 221s > restrm[1,7] <- -1 221s > restrict <- "demand_income - supply_trend = 0" 221s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 221s > restr2m[1,3] <- 1 221s > restr2m[1,7] <- -1 221s > restr2m[2,2] <- -1 221s > restr2m[2,5] <- 1 221s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 221s > restrict2 <- c( "demand_income - supply_trend = 0", 221s + "- demand_price + supply_price = 0.5" ) 221s > tc <- matrix(0,7,6) 221s > tc[1,1] <- 1 221s > tc[2,2] <- 1 221s > tc[3,3] <- 1 221s > tc[4,4] <- 1 221s > tc[5,5] <- 1 221s > tc[6,6] <- 1 221s > tc[7,3] <- 1 221s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 221s > restr3m[1,2] <- -1 221s > restr3m[1,5] <- 1 221s > restr3q <- c( 0.5 ) # restriction vector "q" 2 221s > restrict3 <- "- C2 + C5 = 0.5" 221s > 221s > 221s > ## *************** 3SLS estimation ************************ 221s > fit3sls <- list() 221s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 221s > for( i in seq( along = formulas ) ) { 221s + fit3sls[[ i ]] <- list() 221s + 221s + print( "***************************************************" ) 221s + print( paste( "3SLS formula:", formulas[ i ] ) ) 221s + print( "************* 3SLS *********************************" ) 221s + fit3sls[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, method3sls = formulas[ i ], useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e1 ) ) 221s + 221s + print( "********************* 3SLS EViews-like *****************" ) 221s + fit3sls[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e1e, useDfSys = TRUE ) ) 221s + 221s + print( "********************* 3SLS with methodResidCov = Theil *****************" ) 221s + fit3sls[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 221s + x = TRUE, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e1c, useDfSys = TRUE ) ) 221s + 221s + print( "*************** W3SLS with methodResidCov = Theil *****************" ) 221s + fit3sls[[ i ]]$e1wc <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 221s + residCovWeighted = TRUE, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e1wc, useDfSys = TRUE ) ) 221s + 221s + 221s + print( "*************** 3SLS with restriction *****************" ) 221s + fit3sls[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 221s + x = TRUE, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e2 ) ) 221s + # the same with symbolically specified restrictions 221s + fit3sls[[ i ]]$e2Sym <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.matrix = restrict, method3sls = formulas[ i ], 221s + x = TRUE, useMatrix = useMatrix ) 221s + print( all.equal( fit3sls[[ i ]]$e2, fit3sls[[ i ]]$e2Sym ) ) 221s + 221s + print( "************** 3SLS with restriction (EViews-like) *****************" ) 221s + fit3sls[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 221s + method3sls = formulas[ i ], useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e2e, useDfSys = TRUE ) ) 221s + print( nobs( fit3sls[[i]]$e2e )) 221s + 221s + print( "*************** W3SLS with restriction *****************" ) 221s + fit3sls[[ i ]]$e2w <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 221s + residCovWeighted = TRUE, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e2w ) ) 221s + 221s + 221s + print( "*************** 3SLS with restriction via restrict.regMat ********************" ) 221s + fit3sls[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e3 ) ) 221s + 221s + print( "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" ) 221s + fit3sls[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 221s + method3sls = formulas[ i ], x = TRUE, 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e3e, useDfSys = TRUE ) ) 221s + 221s + print( "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" ) 221s + fit3sls[[ i ]]$e3we <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 221s + method3sls = formulas[ i ], residCovWeighted = TRUE, 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e3we, useDfSys = TRUE ) ) 221s + 221s + 221s + print( "*************** 3SLS with 2 restrictions **********************" ) 221s + fit3sls[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.matrix = restr2m, restrict.rhs = restr2q, 221s + method3sls = formulas[ i ], x = TRUE, 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e4 ) ) 221s + # the same with symbolically specified restrictions 221s + fit3sls[[ i ]]$e4Sym <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.matrix = restrict2, method3sls = formulas[ i ], 221s + x = TRUE, useMatrix = useMatrix ) 221s + print( all.equal( fit3sls[[ i ]]$e4, fit3sls[[ i ]]$e4Sym ) ) 221s + 221s + print( "*************** 3SLS with 2 restrictions (EViews-like) ************" ) 221s + fit3sls[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 221s + restrict.rhs = restr2q, method3sls = formulas[ i ], 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e4e, useDfSys = TRUE ) ) 221s + 221s + print( "********** W3SLS with 2 (symbolic) restrictions ***************" ) 221s + fit3sls[[ i ]]$e4wSym <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.matrix = restrict2, method3sls = formulas[ i ], 221s + residCovWeighted = TRUE, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e4wSym ) ) 221s + 221s + 221s + print( "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" ) 221s + fit3sls[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 221s + restrict.rhs = restr3q, method3sls = formulas[ i ], 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e5 ) ) 221s + # the same with symbolically specified restrictions 221s + fit3sls[[ i ]]$e5Sym <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.regMat = tc, restrict.matrix = restrict3, 221s + method3sls = formulas[ i ], useMatrix = useMatrix ) 221s + print( all.equal( fit3sls[[ i ]]$e5, fit3sls[[ i ]]$e5Sym ) ) 221s + 221s + print( "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" ) 221s + fit3sls[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 221s + restrict.matrix = restr3m, restrict.rhs = restr3q, 221s + method3sls = formulas[ i ], x = TRUE, 221s + useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e5e, useDfSys = TRUE ) ) 221s + 221s + print( "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" ) 221s + fit3sls[[ i ]]$e5we <- systemfit( system, "3SLS", data = Kmenta, 221s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 221s + restrict.matrix = restr3m, restrict.rhs = restr3q, method3sls = formulas[ i ], 221s + residCovWeighted = TRUE, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$e5we, useDfSys = TRUE ) ) 221s + 221s + ## *********** estimations with a single regressor ************ 221s + fit3sls[[ i ]]$S1 <- systemfit( 221s + list( farmPrice ~ consump - 1, price ~ consump + trend ), "3SLS", 221s + data = Kmenta, inst = ~ trend + income, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$S1 ) ) 221s + fit3sls[[ i ]]$S2 <- systemfit( 221s + list( consump ~ farmPrice - 1, consump ~ trend - 1 ), "3SLS", 221s + data = Kmenta, inst = ~ price + income, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$S2 ) ) 221s + fit3sls[[ i ]]$S3 <- systemfit( 221s + list( consump ~ trend - 1, farmPrice ~ trend - 1 ), "3SLS", 221s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$S3 ) ) 221s + fit3sls[[ i ]]$S4 <- systemfit( 221s + list( consump ~ farmPrice - 1, price ~ trend - 1 ), "3SLS", 221s + data = Kmenta, inst = ~ farmPrice + trend + income, 221s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$S4 ) ) 221s + fit3sls[[ i ]]$S5 <- systemfit( 221s + list( consump ~ 1, price ~ 1 ), "3SLS", 221s + data = Kmenta, inst = ~ income, useMatrix = useMatrix ) 221s + print( summary( fit3sls[[ i ]]$S5 ) ) 221s + } 222s [1] "***************************************************" 222s [1] "3SLS formula: GLS" 222s [1] "************* 3SLS *********************************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 1.03 0.676 0.786 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 107.9 6.75 2.60 0.598 0.522 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.36 222s supply 4.36 6.04 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.00 222s supply 5.00 6.74 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.00 0.98 222s supply 0.98 1.00 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 222s price -0.2436 0.0965 -2.52 0.022 * 222s income 0.3140 0.0469 6.69 3.8e-06 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 222s price 0.2286 0.0997 2.29 0.03571 * 222s farmPrice 0.2282 0.0440 5.19 9e-05 *** 222s trend 0.3611 0.0729 4.95 0.00014 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.597 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 222s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 222s 222s [1] "********************* 3SLS EViews-like *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 173 0.719 0.677 0.748 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 107.2 6.70 2.59 0.600 0.525 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.29 3.59 222s supply 3.59 4.83 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.29 4.11 222s supply 4.11 5.36 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.979 222s supply 0.979 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 222s price -0.2436 0.0890 -2.74 0.0099 ** 222s income 0.3140 0.0433 7.25 2.5e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 222s price 0.2289 0.0892 2.57 0.015 * 222s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 222s trend 0.3579 0.0652 5.49 4.3e-06 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.589 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 222s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 222s 222s [1] "********************* 3SLS with methodResidCov = Theil *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 -0.718 0.675 0.922 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 108.7 6.79 2.61 0.594 0.518 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.50 222s supply 4.50 6.04 222s 222s warning: this covariance matrix is NOT positive semidefinit! 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.2 222s supply 5.20 6.8 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.981 222s supply 0.981 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 222s price -0.2436 0.0965 -2.52 0.017 * 222s income 0.3140 0.0469 6.69 1.3e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 222s price 0.2282 0.0997 2.29 0.02855 * 222s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 222s trend 0.3648 0.0707 5.16 1.1e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.607 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 222s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 222s 222s [1] "*************** W3SLS with methodResidCov = Theil *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 -0.718 0.675 0.922 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 108.7 6.79 2.61 0.594 0.518 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.50 222s supply 4.50 6.04 222s 222s warning: this covariance matrix is NOT positive semidefinit! 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.2 222s supply 5.20 6.8 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.981 222s supply 0.981 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 222s price -0.2436 0.0965 -2.52 0.017 * 222s income 0.3140 0.0469 6.69 1.3e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 222s price 0.2282 0.0997 2.29 0.02855 * 222s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 222s trend 0.3648 0.0707 5.16 1.1e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.607 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 222s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 222s 222s [1] "*************** 3SLS with restriction *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.27 0.678 0.722 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.8 3.99 2.00 0.747 0.717 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.97 4.55 222s supply 4.55 6.13 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.99 4.98 222s supply 4.98 6.55 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 222s price -0.222 0.096 -2.31 0.027 * 222s income 0.296 0.045 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.997 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 222s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 222s price 0.2193 0.1002 2.19 0.036 * 222s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 222s trend 0.2956 0.0450 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "************** 3SLS with restriction (EViews-like) *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 171 0.887 0.68 0.678 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.5 3.97 1.99 0.748 0.719 222s supply 20 16 104.0 6.50 2.55 0.612 0.539 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.37 3.75 222s supply 3.75 4.91 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.37 4.08 222s supply 4.08 5.20 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.974 222s supply 0.974 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 222s price -0.2243 0.0888 -2.53 0.016 * 222s income 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.992 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 222s price 0.2207 0.0896 2.46 0.019 * 222s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 222s trend 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.55 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 222s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 222s 222s [1] 40 222s [1] "*************** W3SLS with restriction *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.24 0.677 0.725 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 68.1 4.00 2.00 0.746 0.716 222s supply 20 16 105.2 6.57 2.56 0.608 0.534 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.93 4.56 222s supply 4.56 6.15 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 4.00 5.01 222s supply 5.01 6.57 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.976 222s supply 0.976 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 222s price -0.2194 0.0954 -2.3 0.028 * 222s income 0.2938 0.0445 6.6 1.4e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.001 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 222s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 222s price 0.2184 0.1003 2.18 0.036 * 222s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 222s trend 0.2938 0.0445 6.60 1.4e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.564 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 222s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 222s 222s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.27 0.678 0.722 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.8 3.99 2.00 0.747 0.717 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.97 4.55 222s supply 4.55 6.13 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.99 4.98 222s supply 4.98 6.55 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 222s price -0.222 0.096 -2.31 0.027 * 222s income 0.296 0.045 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.997 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 222s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 222s price 0.2193 0.1002 2.19 0.036 * 222s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 222s trend 0.2956 0.0450 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 171 0.887 0.68 0.678 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.5 3.97 1.99 0.748 0.719 222s supply 20 16 104.0 6.50 2.55 0.612 0.539 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.37 3.75 222s supply 3.75 4.91 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.37 4.08 222s supply 4.08 5.20 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.974 222s supply 0.974 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 222s price -0.2243 0.0888 -2.53 0.016 * 222s income 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.992 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 222s price 0.2207 0.0896 2.46 0.019 * 222s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 222s trend 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.55 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 222s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 222s 222s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 172 0.873 0.679 0.681 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.7 3.98 2.00 0.748 0.718 222s supply 20 16 104.3 6.52 2.55 0.611 0.538 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.35 3.76 222s supply 3.76 4.92 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.38 4.10 222s supply 4.10 5.22 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 222s price -0.2225 0.0883 -2.52 0.017 * 222s income 0.2964 0.0416 7.13 3.1e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.995 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 222s price 0.2201 0.0897 2.45 0.019 * 222s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 222s trend 0.2964 0.0416 7.13 3.1e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.553 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 222s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 222s 222s [1] "*************** 3SLS with 2 restrictions **********************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 171 1.74 0.681 0.696 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.8 3.87 1.97 0.755 0.726 222s supply 20 16 105.4 6.59 2.57 0.607 0.533 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.89 4.53 222s supply 4.53 6.25 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 4.87 222s supply 4.87 6.59 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 222s price -0.2457 0.0891 -2.76 0.0092 ** 222s income 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.967 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 222s price 0.2543 0.0891 2.85 0.0072 ** 222s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 222s trend 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.566 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 222s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.683 0.658 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.96 0.755 0.727 222s supply 20 16 104.6 6.54 2.56 0.610 0.537 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.73 222s supply 3.73 5.00 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.23 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 222s price -0.2494 0.0812 -3.07 0.0041 ** 222s income 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.964 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 222s price 0.2506 0.0812 3.09 0.0039 ** 222s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 222s trend 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.557 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 222s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 222s 222s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 172 1.74 0.68 0.697 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.9 3.88 1.97 0.754 0.725 222s supply 20 16 105.7 6.60 2.57 0.606 0.532 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.88 4.55 222s supply 4.55 6.27 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.88 4.88 222s supply 4.88 6.60 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 222s price -0.2443 0.0892 -2.74 0.0096 ** 222s income 0.3234 0.0229 14.14 4.4e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.969 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 222s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 222s price 0.2557 0.0892 2.87 0.0069 ** 222s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 222s trend 0.3234 0.0229 14.14 4.4e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.57 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 222s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 222s 222s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 171 1.74 0.681 0.696 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.8 3.87 1.97 0.755 0.726 222s supply 20 16 105.4 6.59 2.57 0.607 0.533 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.89 4.53 222s supply 4.53 6.25 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 4.87 222s supply 4.87 6.59 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 222s price -0.2457 0.0891 -2.76 0.0092 ** 222s income 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.967 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 222s price 0.2543 0.0891 2.85 0.0072 ** 222s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 222s trend 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.566 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 222s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.683 0.658 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.96 0.755 0.727 222s supply 20 16 104.6 6.54 2.56 0.610 0.537 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.73 222s supply 3.73 5.00 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.23 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 222s price -0.2494 0.0812 -3.07 0.0041 ** 222s income 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.964 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 222s price 0.2506 0.0812 3.09 0.0039 ** 222s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 222s trend 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.557 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 222s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 222s 222s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.682 0.659 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.97 0.755 0.726 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.75 222s supply 3.75 5.01 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.24 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 222s price -0.2484 0.0812 -3.06 0.0042 ** 222s income 0.3246 0.0205 15.81 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.965 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 222s price 0.2516 0.0812 3.10 0.0038 ** 222s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 222s trend 0.3246 0.0205 15.81 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 36 3690 5613 0.012 0.368 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 2132 112.2 10.59 0.305 0.305 222s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 112.2 -44.8 222s eq2 -44.8 56.8 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 112.2 -68.3 222s eq2 -68.3 91.7 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 -0.674 222s eq2 -0.674 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: farmPrice ~ consump - 1 222s Instruments: ~trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s consump 0.9588 0.0235 40.9 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 10.592 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 222s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: price ~ consump + trend 222s Instruments: ~trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) -92.192 49.896 -1.85 0.0821 . 222s consump 1.953 0.499 3.92 0.0011 ** 222s trend -0.469 0.247 -1.90 0.0743 . 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 9.574 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 222s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 38 56326 283068 -104 -10.6 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 2313 122 11.0 -7.63 -7.63 222s eq2 20 19 54013 2843 53.3 -200.46 -200.46 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 121 -255 222s eq2 -255 2953 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 122 -251 222s eq2 -251 2843 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 -0.433 222s eq2 -0.433 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ farmPrice - 1 222s Instruments: ~price + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 11.034 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 222s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: consump ~ trend - 1 222s Instruments: ~price + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 9.02 1.13 8 1.7e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 53.318 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 222s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 38 167069 397886 -49.1 -0.82 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 76692 4036 63.5 -285.0 -285.0 222s eq2 20 19 90377 4757 69.0 -28.5 -28.5 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 2682 2547 222s eq2 2547 2741 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 4036 4336 222s eq2 4336 4757 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 0.928 222s eq2 0.928 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ trend - 1 222s Instruments: ~income + farmPrice 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 4.162 0.723 5.75 1.5e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 63.533 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 222s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: farmPrice ~ trend - 1 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 3.274 0.676 4.84 0.00011 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 68.969 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 222s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 39 161126 1162329 -171 -17.4 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 3553 187 13.7 -12.3 -12.3 222s eq2 20 19 157573 8293 91.1 -235.2 -235.2 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 208 -731 222s eq2 -731 8271 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 187 -623 222s eq2 -623 8293 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 -0.121 222s eq2 -0.121 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ farmPrice - 1 222s Instruments: ~farmPrice + trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 13.675 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 222s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: price ~ trend - 1 222s Instruments: ~farmPrice + trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 1.1122 0.0272 40.8 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 91.068 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 222s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 38 935 491 0 0 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 268 14.1 3.76 0 0 222s eq2 20 19 667 35.1 5.93 0 0 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 14.11 2.18 222s eq2 2.18 35.12 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 14.11 2.18 222s eq2 2.18 35.12 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.0000 0.0981 222s eq2 0.0981 1.0000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ 1 222s Instruments: ~income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 100.90 0.84 120 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 3.756 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 222s Multiple R-Squared: 0 Adjusted R-Squared: 0 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: price ~ 1 222s Instruments: ~income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 100.02 1.33 75.5 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 5.926 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 222s Multiple R-Squared: 0 Adjusted R-Squared: 0 222s 222s [1] "***************************************************" 222s [1] "3SLS formula: IV" 222s [1] "************* 3SLS *********************************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 1.03 0.676 0.786 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 107.9 6.75 2.60 0.598 0.522 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.36 222s supply 4.36 6.04 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.00 222s supply 5.00 6.74 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.00 0.98 222s supply 0.98 1.00 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 222s price -0.2436 0.0965 -2.52 0.022 * 222s income 0.3140 0.0469 6.69 3.8e-06 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 222s price 0.2286 0.0997 2.29 0.03571 * 222s farmPrice 0.2282 0.0440 5.19 9e-05 *** 222s trend 0.3611 0.0729 4.95 0.00014 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.597 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 222s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 222s 222s [1] "********************* 3SLS EViews-like *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 173 0.719 0.677 0.748 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 107.2 6.70 2.59 0.600 0.525 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.29 3.59 222s supply 3.59 4.83 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.29 4.11 222s supply 4.11 5.36 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.979 222s supply 0.979 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 222s price -0.2436 0.0890 -2.74 0.0099 ** 222s income 0.3140 0.0433 7.25 2.5e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 222s price 0.2289 0.0892 2.57 0.015 * 222s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 222s trend 0.3579 0.0652 5.49 4.3e-06 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.589 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 222s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 222s 222s [1] "********************* 3SLS with methodResidCov = Theil *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 -0.718 0.675 0.922 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 108.7 6.79 2.61 0.594 0.518 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.50 222s supply 4.50 6.04 222s 222s warning: this covariance matrix is NOT positive semidefinit! 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.2 222s supply 5.20 6.8 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.981 222s supply 0.981 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 222s price -0.2436 0.0965 -2.52 0.017 * 222s income 0.3140 0.0469 6.69 1.3e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 222s price 0.2282 0.0997 2.29 0.02855 * 222s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 222s trend 0.3648 0.0707 5.16 1.1e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.607 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 222s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 222s 222s [1] "*************** W3SLS with methodResidCov = Theil *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 -0.718 0.675 0.922 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 108.7 6.79 2.61 0.594 0.518 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.50 222s supply 4.50 6.04 222s 222s warning: this covariance matrix is NOT positive semidefinit! 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.2 222s supply 5.20 6.8 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.981 222s supply 0.981 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 222s price -0.2436 0.0965 -2.52 0.017 * 222s income 0.3140 0.0469 6.69 1.3e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 222s price 0.2282 0.0997 2.29 0.02855 * 222s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 222s trend 0.3648 0.0707 5.16 1.1e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.607 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 222s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 222s 222s [1] "*************** 3SLS with restriction *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.27 0.678 0.722 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.8 3.99 2.00 0.747 0.717 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.97 4.55 222s supply 4.55 6.13 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.99 4.98 222s supply 4.98 6.55 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 222s price -0.222 0.096 -2.31 0.027 * 222s income 0.296 0.045 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.997 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 222s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 222s price 0.2193 0.1002 2.19 0.036 * 222s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 222s trend 0.2956 0.0450 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "************** 3SLS with restriction (EViews-like) *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 171 0.887 0.68 0.678 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.5 3.97 1.99 0.748 0.719 222s supply 20 16 104.0 6.50 2.55 0.612 0.539 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.37 3.75 222s supply 3.75 4.91 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.37 4.08 222s supply 4.08 5.20 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.974 222s supply 0.974 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 222s price -0.2243 0.0888 -2.53 0.016 * 222s income 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.992 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 222s price 0.2207 0.0896 2.46 0.019 * 222s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 222s trend 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.55 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 222s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 222s 222s [1] 40 222s [1] "*************** W3SLS with restriction *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.24 0.677 0.725 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 68.1 4.00 2.00 0.746 0.716 222s supply 20 16 105.2 6.57 2.56 0.608 0.534 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.93 4.56 222s supply 4.56 6.15 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 4.00 5.01 222s supply 5.01 6.57 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.976 222s supply 0.976 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 222s price -0.2194 0.0954 -2.3 0.028 * 222s income 0.2938 0.0445 6.6 1.4e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.001 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 222s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 222s price 0.2184 0.1003 2.18 0.036 * 222s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 222s trend 0.2938 0.0445 6.60 1.4e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.564 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 222s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 222s 222s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.27 0.678 0.722 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.8 3.99 2.00 0.747 0.717 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.97 4.55 222s supply 4.55 6.13 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.99 4.98 222s supply 4.98 6.55 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 222s price -0.222 0.096 -2.31 0.027 * 222s income 0.296 0.045 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.997 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 222s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 222s price 0.2193 0.1002 2.19 0.036 * 222s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 222s trend 0.2956 0.0450 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 171 0.887 0.68 0.678 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.5 3.97 1.99 0.748 0.719 222s supply 20 16 104.0 6.50 2.55 0.612 0.539 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.37 3.75 222s supply 3.75 4.91 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.37 4.08 222s supply 4.08 5.20 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.974 222s supply 0.974 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 222s price -0.2243 0.0888 -2.53 0.016 * 222s income 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.992 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 222s price 0.2207 0.0896 2.46 0.019 * 222s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 222s trend 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.55 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 222s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 222s 222s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 172 0.873 0.679 0.681 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.7 3.98 2.00 0.748 0.718 222s supply 20 16 104.3 6.52 2.55 0.611 0.538 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.35 3.76 222s supply 3.76 4.92 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.38 4.10 222s supply 4.10 5.22 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 222s price -0.2225 0.0883 -2.52 0.017 * 222s income 0.2964 0.0416 7.13 3.1e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.995 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 222s price 0.2201 0.0897 2.45 0.019 * 222s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 222s trend 0.2964 0.0416 7.13 3.1e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.553 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 222s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 222s 222s [1] "*************** 3SLS with 2 restrictions **********************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 171 1.74 0.681 0.696 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.8 3.87 1.97 0.755 0.726 222s supply 20 16 105.4 6.59 2.57 0.607 0.533 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.89 4.53 222s supply 4.53 6.25 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 4.87 222s supply 4.87 6.59 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 222s price -0.2457 0.0891 -2.76 0.0092 ** 222s income 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.967 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 222s price 0.2543 0.0891 2.85 0.0072 ** 222s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 222s trend 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.566 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 222s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.683 0.658 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.96 0.755 0.727 222s supply 20 16 104.6 6.54 2.56 0.610 0.537 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.73 222s supply 3.73 5.00 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.23 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 222s price -0.2494 0.0812 -3.07 0.0041 ** 222s income 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.964 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 222s price 0.2506 0.0812 3.09 0.0039 ** 222s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 222s trend 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.557 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 222s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 222s 222s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 172 1.74 0.68 0.697 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.9 3.88 1.97 0.754 0.725 222s supply 20 16 105.7 6.60 2.57 0.606 0.532 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.88 4.55 222s supply 4.55 6.27 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.88 4.88 222s supply 4.88 6.60 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 222s price -0.2443 0.0892 -2.74 0.0096 ** 222s income 0.3234 0.0229 14.14 4.4e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.969 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 222s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 222s price 0.2557 0.0892 2.87 0.0069 ** 222s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 222s trend 0.3234 0.0229 14.14 4.4e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.57 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 222s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 222s 222s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 171 1.74 0.681 0.696 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.8 3.87 1.97 0.755 0.726 222s supply 20 16 105.4 6.59 2.57 0.607 0.533 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.89 4.53 222s supply 4.53 6.25 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 4.87 222s supply 4.87 6.59 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 222s price -0.2457 0.0891 -2.76 0.0092 ** 222s income 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.967 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 222s price 0.2543 0.0891 2.85 0.0072 ** 222s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 222s trend 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.566 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 222s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.683 0.658 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.96 0.755 0.727 222s supply 20 16 104.6 6.54 2.56 0.610 0.537 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.73 222s supply 3.73 5.00 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.23 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 222s price -0.2494 0.0812 -3.07 0.0041 ** 222s income 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.964 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 222s price 0.2506 0.0812 3.09 0.0039 ** 222s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 222s trend 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.557 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 222s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 222s 222s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.682 0.659 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.97 0.755 0.726 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.75 222s supply 3.75 5.01 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.24 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 222s price -0.2484 0.0812 -3.06 0.0042 ** 222s income 0.3246 0.0205 15.81 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.965 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 222s price 0.2516 0.0812 3.10 0.0038 ** 222s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 222s trend 0.3246 0.0205 15.81 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 36 3690 5613 0.012 0.368 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 2132 112.2 10.59 0.305 0.305 222s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 112.2 -44.8 222s eq2 -44.8 56.8 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 112.2 -68.3 222s eq2 -68.3 91.7 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 -0.674 222s eq2 -0.674 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: farmPrice ~ consump - 1 222s Instruments: ~trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s consump 0.9588 0.0235 40.9 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 10.592 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 222s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: price ~ consump + trend 222s Instruments: ~trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) -92.192 49.896 -1.85 0.0821 . 222s consump 1.953 0.499 3.92 0.0011 ** 222s trend -0.469 0.247 -1.90 0.0743 . 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 9.574 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 222s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 38 56326 283068 -104 -10.6 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 2313 122 11.0 -7.63 -7.63 222s eq2 20 19 54013 2843 53.3 -200.46 -200.46 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 121 -255 222s eq2 -255 2953 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 122 -251 222s eq2 -251 2843 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 -0.433 222s eq2 -0.433 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ farmPrice - 1 222s Instruments: ~price + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 11.034 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 222s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: consump ~ trend - 1 222s Instruments: ~price + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 9.02 1.13 8 1.7e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 53.318 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 222s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 38 167069 397886 -49.1 -0.82 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 76692 4036 63.5 -285.0 -285.0 222s eq2 20 19 90377 4757 69.0 -28.5 -28.5 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 2682 2547 222s eq2 2547 2741 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 4036 4336 222s eq2 4336 4757 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 0.928 222s eq2 0.928 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ trend - 1 222s Instruments: ~income + farmPrice 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 4.162 0.723 5.75 1.5e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 63.533 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 222s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: farmPrice ~ trend - 1 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 3.274 0.676 4.84 0.00011 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 68.969 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 222s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 39 161126 1162329 -171 -17.4 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 3553 187 13.7 -12.3 -12.3 222s eq2 20 19 157573 8293 91.1 -235.2 -235.2 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 208 -731 222s eq2 -731 8271 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 187 -623 222s eq2 -623 8293 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.000 -0.121 222s eq2 -0.121 1.000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ farmPrice - 1 222s Instruments: ~farmPrice + trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 13.675 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 222s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: price ~ trend - 1 222s Instruments: ~farmPrice + trend + income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s trend 1.1122 0.0272 40.8 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 91.068 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 222s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 222s 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 38 935 491 0 0 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s eq1 20 19 268 14.1 3.76 0 0 222s eq2 20 19 667 35.1 5.93 0 0 222s 222s The covariance matrix of the residuals used for estimation 222s eq1 eq2 222s eq1 14.11 2.18 222s eq2 2.18 35.12 222s 222s The covariance matrix of the residuals 222s eq1 eq2 222s eq1 14.11 2.18 222s eq2 2.18 35.12 222s 222s The correlations of the residuals 222s eq1 eq2 222s eq1 1.0000 0.0981 222s eq2 0.0981 1.0000 222s 222s 222s 3SLS estimates for 'eq1' (equation 1) 222s Model Formula: consump ~ 1 222s Instruments: ~income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 100.90 0.84 120 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 3.756 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 222s Multiple R-Squared: 0 Adjusted R-Squared: 0 222s 222s 222s 3SLS estimates for 'eq2' (equation 2) 222s Model Formula: price ~ 1 222s Instruments: ~income 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 100.02 1.33 75.5 <2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 5.926 on 19 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 19 222s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 222s Multiple R-Squared: 0 Adjusted R-Squared: 0 222s 222s [1] "***************************************************" 222s [1] "3SLS formula: Schmidt" 222s [1] "************* 3SLS *********************************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 1.03 0.676 0.786 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 107.9 6.75 2.60 0.598 0.522 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.36 222s supply 4.36 6.04 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.00 222s supply 5.00 6.74 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.00 0.98 222s supply 0.98 1.00 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 222s price -0.2436 0.0965 -2.52 0.022 * 222s income 0.3140 0.0469 6.69 3.8e-06 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 222s price 0.2286 0.0997 2.29 0.03571 * 222s farmPrice 0.2282 0.0440 5.19 9e-05 *** 222s trend 0.3611 0.0729 4.95 0.00014 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.597 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 222s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 222s 222s [1] "********************* 3SLS EViews-like *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 173 0.719 0.677 0.748 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 107.2 6.70 2.59 0.600 0.525 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.29 3.59 222s supply 3.59 4.83 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.29 4.11 222s supply 4.11 5.36 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.979 222s supply 0.979 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 222s price -0.2436 0.0890 -2.74 0.0099 ** 222s income 0.3140 0.0433 7.25 2.5e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 222s price 0.2289 0.0892 2.57 0.015 * 222s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 222s trend 0.3579 0.0652 5.49 4.3e-06 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.589 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 222s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 222s 222s [1] "********************* 3SLS with methodResidCov = Theil *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 -0.718 0.675 0.922 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 108.7 6.79 2.61 0.594 0.518 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.50 222s supply 4.50 6.04 222s 222s warning: this covariance matrix is NOT positive semidefinit! 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.2 222s supply 5.20 6.8 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.981 222s supply 0.981 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 222s price -0.2436 0.0965 -2.52 0.017 * 222s income 0.3140 0.0469 6.69 1.3e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 222s price 0.2282 0.0997 2.29 0.02855 * 222s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 222s trend 0.3648 0.0707 5.16 1.1e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.607 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 222s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 222s 222s [1] "*************** W3SLS with methodResidCov = Theil *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 33 174 -0.718 0.675 0.922 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.7 3.87 1.97 0.755 0.726 222s supply 20 16 108.7 6.79 2.61 0.594 0.518 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.87 4.50 222s supply 4.50 6.04 222s 222s warning: this covariance matrix is NOT positive semidefinit! 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 5.2 222s supply 5.20 6.8 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.981 222s supply 0.981 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 222s price -0.2436 0.0965 -2.52 0.017 * 222s income 0.3140 0.0469 6.69 1.3e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.966 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 222s price 0.2282 0.0997 2.29 0.02855 * 222s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 222s trend 0.3648 0.0707 5.16 1.1e-05 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.607 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 222s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 222s 222s [1] "*************** 3SLS with restriction *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.27 0.678 0.722 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.8 3.99 2.00 0.747 0.717 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.97 4.55 222s supply 4.55 6.13 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.99 4.98 222s supply 4.98 6.55 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 222s price -0.222 0.096 -2.31 0.027 * 222s income 0.296 0.045 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.997 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 222s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 222s price 0.2193 0.1002 2.19 0.036 * 222s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 222s trend 0.2956 0.0450 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "************** 3SLS with restriction (EViews-like) *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 171 0.887 0.68 0.678 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.5 3.97 1.99 0.748 0.719 222s supply 20 16 104.0 6.50 2.55 0.612 0.539 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.37 3.75 222s supply 3.75 4.91 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.37 4.08 222s supply 4.08 5.20 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.974 222s supply 0.974 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 222s price -0.2243 0.0888 -2.53 0.016 * 222s income 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.992 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 222s price 0.2207 0.0896 2.46 0.019 * 222s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 222s trend 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.55 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 222s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 222s 222s [1] 40 222s [1] "*************** W3SLS with restriction *****************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.24 0.677 0.725 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 68.1 4.00 2.00 0.746 0.716 222s supply 20 16 105.2 6.57 2.56 0.608 0.534 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.93 4.56 222s supply 4.56 6.15 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 4.00 5.01 222s supply 5.01 6.57 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.976 222s supply 0.976 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 222s price -0.2194 0.0954 -2.3 0.028 * 222s income 0.2938 0.0445 6.6 1.4e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.001 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 222s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 222s price 0.2184 0.1003 2.18 0.036 * 222s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 222s trend 0.2938 0.0445 6.60 1.4e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.564 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 222s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 222s 222s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 173 1.27 0.678 0.722 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.8 3.99 2.00 0.747 0.717 222s supply 20 16 104.8 6.55 2.56 0.609 0.536 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.97 4.55 222s supply 4.55 6.13 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.99 4.98 222s supply 4.98 6.55 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 222s price -0.222 0.096 -2.31 0.027 * 222s income 0.296 0.045 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.997 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 222s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 222s price 0.2193 0.1002 2.19 0.036 * 222s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 222s trend 0.2956 0.0450 6.57 1.6e-07 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.559 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 222s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 222s 222s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 171 0.887 0.68 0.678 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.5 3.97 1.99 0.748 0.719 222s supply 20 16 104.0 6.50 2.55 0.612 0.539 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.37 3.75 222s supply 3.75 4.91 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.37 4.08 222s supply 4.08 5.20 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.974 222s supply 0.974 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 222s price -0.2243 0.0888 -2.53 0.016 * 222s income 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.992 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 222s price 0.2207 0.0896 2.46 0.019 * 222s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 222s trend 0.2979 0.0420 7.10 3.4e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.55 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 222s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 222s 222s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 34 172 0.873 0.679 0.681 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 67.7 3.98 2.00 0.748 0.718 222s supply 20 16 104.3 6.52 2.55 0.611 0.538 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.35 3.76 222s supply 3.76 4.92 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.38 4.10 222s supply 4.10 5.22 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.975 222s supply 0.975 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 222s price -0.2225 0.0883 -2.52 0.017 * 222s income 0.2964 0.0416 7.13 3.1e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.995 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 222s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 222s price 0.2201 0.0897 2.45 0.019 * 222s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 222s trend 0.2964 0.0416 7.13 3.1e-08 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.553 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 222s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 222s 222s [1] "*************** 3SLS with 2 restrictions **********************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 171 1.74 0.681 0.696 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.8 3.87 1.97 0.755 0.726 222s supply 20 16 105.4 6.59 2.57 0.607 0.533 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.89 4.53 222s supply 4.53 6.25 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 4.87 222s supply 4.87 6.59 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 222s price -0.2457 0.0891 -2.76 0.0092 ** 222s income 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.967 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 222s price 0.2543 0.0891 2.85 0.0072 ** 222s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 222s trend 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.566 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 222s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.683 0.658 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.96 0.755 0.727 222s supply 20 16 104.6 6.54 2.56 0.610 0.537 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.73 222s supply 3.73 5.00 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.23 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 222s price -0.2494 0.0812 -3.07 0.0041 ** 222s income 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.964 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 222s price 0.2506 0.0812 3.09 0.0039 ** 222s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 222s trend 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.557 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 222s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 222s 222s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 172 1.74 0.68 0.697 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.9 3.88 1.97 0.754 0.725 222s supply 20 16 105.7 6.60 2.57 0.606 0.532 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.88 4.55 222s supply 4.55 6.27 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.88 4.88 222s supply 4.88 6.60 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 222s price -0.2443 0.0892 -2.74 0.0096 ** 222s income 0.3234 0.0229 14.14 4.4e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.969 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 222s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 222s price 0.2557 0.0892 2.87 0.0069 ** 222s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 222s trend 0.3234 0.0229 14.14 4.4e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.57 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 222s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 222s 222s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 171 1.74 0.681 0.696 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.8 3.87 1.97 0.755 0.726 222s supply 20 16 105.4 6.59 2.57 0.607 0.533 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.89 4.53 222s supply 4.53 6.25 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.87 4.87 222s supply 4.87 6.59 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 222s price -0.2457 0.0891 -2.76 0.0092 ** 222s income 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.967 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 222s price 0.2543 0.0891 2.85 0.0072 ** 222s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 222s trend 0.3236 0.0233 13.91 8.9e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.566 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 222s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 222s 222s [1] "Component “call”: target, current do not match when deparsed" 222s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.683 0.658 222s 222s N DF SSR MSE RMSE R2 Adj R2 222s demand 20 17 65.6 3.86 1.96 0.755 0.727 222s supply 20 16 104.6 6.54 2.56 0.610 0.537 222s 222s The covariance matrix of the residuals used for estimation 222s demand supply 222s demand 3.30 3.73 222s supply 3.73 5.00 222s 222s The covariance matrix of the residuals 222s demand supply 222s demand 3.28 4.00 222s supply 4.00 5.23 222s 222s The correlations of the residuals 222s demand supply 222s demand 1.000 0.965 222s supply 0.965 1.000 222s 222s 222s 3SLS estimates for 'demand' (equation 1) 222s Model Formula: consump ~ price + income 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 222s price -0.2494 0.0812 -3.07 0.0041 ** 222s income 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 1.964 on 17 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 17 222s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 222s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 222s 222s 222s 3SLS estimates for 'supply' (equation 2) 222s Model Formula: consump ~ price + farmPrice + trend 222s Instruments: ~income + farmPrice + trend 222s 222s Estimate Std. Error t value Pr(>|t|) 222s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 222s price 0.2506 0.0812 3.09 0.0039 ** 222s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 222s trend 0.3248 0.0209 15.57 < 2e-16 *** 222s --- 222s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 222s 222s Residual standard error: 2.557 on 16 degrees of freedom 222s Number of observations: 20 Degrees of Freedom: 16 222s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 222s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 222s 222s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 222s 222s systemfit results 222s method: 3SLS 222s 222s N DF SSR detRCov OLS-R2 McElroy-R2 222s system 40 35 170 1.19 0.682 0.659 222s 222s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.6 3.86 1.97 0.755 0.726 223s supply 20 16 104.8 6.55 2.56 0.609 0.536 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.30 3.75 223s supply 3.75 5.01 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.28 4.00 223s supply 4.00 5.24 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.965 223s supply 0.965 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 223s price -0.2484 0.0812 -3.06 0.0042 ** 223s income 0.3246 0.0205 15.81 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.965 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 223s price 0.2516 0.0812 3.10 0.0038 ** 223s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 223s trend 0.3246 0.0205 15.81 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.559 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 223s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 36 3690 5613 0.012 0.368 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 2132 112.2 10.59 0.305 0.305 223s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 112.2 -44.8 223s eq2 -44.8 56.8 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 112.2 -68.3 223s eq2 -68.3 91.7 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.674 223s eq2 -0.674 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: farmPrice ~ consump - 1 223s Instruments: ~trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s consump 0.9588 0.0235 40.9 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 10.592 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 223s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ consump + trend 223s Instruments: ~trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) -92.192 49.896 -1.85 0.0821 . 223s consump 1.953 0.499 3.92 0.0011 ** 223s trend -0.469 0.247 -1.90 0.0743 . 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 9.574 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 223s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 56326 283068 -104 -10.6 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 2313 122 11.0 -7.63 -7.63 223s eq2 20 19 54013 2843 53.3 -200.46 -200.46 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 121 -255 223s eq2 -255 2953 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 122 -251 223s eq2 -251 2843 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.433 223s eq2 -0.433 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ farmPrice - 1 223s Instruments: ~price + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 11.034 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 223s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: consump ~ trend - 1 223s Instruments: ~price + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 9.02 1.13 8 1.7e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 53.318 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 223s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 167069 397886 -49.1 -0.82 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 76692 4036 63.5 -285.0 -285.0 223s eq2 20 19 90377 4757 69.0 -28.5 -28.5 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 2682 2547 223s eq2 2547 2741 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 4036 4336 223s eq2 4336 4757 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 0.928 223s eq2 0.928 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ trend - 1 223s Instruments: ~income + farmPrice 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 4.162 0.723 5.75 1.5e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 63.533 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 223s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: farmPrice ~ trend - 1 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 3.274 0.676 4.84 0.00011 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 68.969 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 223s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 39 161126 1162329 -171 -17.4 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 3553 187 13.7 -12.3 -12.3 223s eq2 20 19 157573 8293 91.1 -235.2 -235.2 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 208 -731 223s eq2 -731 8271 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 187 -623 223s eq2 -623 8293 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.121 223s eq2 -0.121 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ farmPrice - 1 223s Instruments: ~farmPrice + trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 13.675 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 223s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ trend - 1 223s Instruments: ~farmPrice + trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 1.1122 0.0272 40.8 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 91.068 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 223s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 935 491 0 0 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 268 14.1 3.76 0 0 223s eq2 20 19 667 35.1 5.93 0 0 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 14.11 2.18 223s eq2 2.18 35.12 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 14.11 2.18 223s eq2 2.18 35.12 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.0000 0.0981 223s eq2 0.0981 1.0000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ 1 223s Instruments: ~income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 100.90 0.84 120 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.756 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 223s Multiple R-Squared: 0 Adjusted R-Squared: 0 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ 1 223s Instruments: ~income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 100.02 1.33 75.5 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 5.926 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 223s Multiple R-Squared: 0 Adjusted R-Squared: 0 223s 223s [1] "***************************************************" 223s [1] "3SLS formula: GMM" 223s [1] "************* 3SLS *********************************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 174 1.03 0.676 0.786 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 107.9 6.75 2.60 0.598 0.522 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 4.36 223s supply 4.36 6.04 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.00 223s supply 5.00 6.74 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.00 0.98 223s supply 0.98 1.00 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 223s price -0.2436 0.0965 -2.52 0.022 * 223s income 0.3140 0.0469 6.69 3.8e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 223s price 0.2286 0.0997 2.29 0.03571 * 223s farmPrice 0.2282 0.0440 5.19 9e-05 *** 223s trend 0.3611 0.0729 4.95 0.00014 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.597 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 223s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 223s 223s [1] "********************* 3SLS EViews-like *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 173 0.719 0.677 0.748 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 107.2 6.70 2.59 0.600 0.525 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.29 3.59 223s supply 3.59 4.83 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.29 4.11 223s supply 4.11 5.36 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.979 223s supply 0.979 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 223s price -0.2436 0.0890 -2.74 0.0099 ** 223s income 0.3140 0.0433 7.25 2.5e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 223s price 0.2289 0.0892 2.57 0.015 * 223s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 223s trend 0.3579 0.0652 5.49 4.3e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.589 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 223s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 223s 223s [1] "********************* 3SLS with methodResidCov = Theil *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 174 -0.718 0.675 0.922 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 108.7 6.79 2.61 0.594 0.518 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 4.50 223s supply 4.50 6.04 223s 223s warning: this covariance matrix is NOT positive semidefinit! 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.2 223s supply 5.20 6.8 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.981 223s supply 0.981 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 223s price -0.2436 0.0965 -2.52 0.017 * 223s income 0.3140 0.0469 6.69 1.3e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 223s price 0.2282 0.0997 2.29 0.02855 * 223s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 223s trend 0.3648 0.0707 5.16 1.1e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.607 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 223s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 223s 223s [1] "*************** W3SLS with methodResidCov = Theil *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 174 -0.718 0.675 0.922 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 108.7 6.79 2.61 0.594 0.518 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 4.50 223s supply 4.50 6.04 223s 223s warning: this covariance matrix is NOT positive semidefinit! 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.2 223s supply 5.20 6.8 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.981 223s supply 0.981 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 223s price -0.2436 0.0965 -2.52 0.017 * 223s income 0.3140 0.0469 6.69 1.3e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 223s price 0.2282 0.0997 2.29 0.02855 * 223s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 223s trend 0.3648 0.0707 5.16 1.1e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.607 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 223s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 223s 223s [1] "*************** 3SLS with restriction *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 173 1.27 0.678 0.722 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.8 3.99 2.00 0.747 0.717 223s supply 20 16 104.8 6.55 2.56 0.609 0.536 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.97 4.55 223s supply 4.55 6.13 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.99 4.98 223s supply 4.98 6.55 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.975 223s supply 0.975 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 223s price -0.222 0.096 -2.31 0.027 * 223s income 0.296 0.045 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.997 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 223s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 223s price 0.2193 0.1002 2.19 0.036 * 223s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 223s trend 0.2956 0.0450 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.559 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 223s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 223s 223s [1] "Component “call”: target, current do not match when deparsed" 223s [1] "************** 3SLS with restriction (EViews-like) *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 171 0.887 0.68 0.678 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.5 3.97 1.99 0.748 0.719 223s supply 20 16 104.0 6.50 2.55 0.612 0.539 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.37 3.75 223s supply 3.75 4.91 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.37 4.08 223s supply 4.08 5.20 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.974 223s supply 0.974 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 223s price -0.2243 0.0888 -2.53 0.016 * 223s income 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.992 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 223s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 223s price 0.2207 0.0896 2.46 0.019 * 223s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 223s trend 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.55 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 223s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 223s 223s [1] 40 223s [1] "*************** W3SLS with restriction *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 173 1.24 0.677 0.725 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 68.1 4.00 2.00 0.746 0.716 223s supply 20 16 105.2 6.57 2.56 0.608 0.534 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.93 4.56 223s supply 4.56 6.15 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.00 5.01 223s supply 5.01 6.57 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.976 223s supply 0.976 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 223s price -0.2194 0.0954 -2.3 0.028 * 223s income 0.2938 0.0445 6.6 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.001 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 223s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 223s price 0.2184 0.1003 2.18 0.036 * 223s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 223s trend 0.2938 0.0445 6.60 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.564 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 223s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 223s 223s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 173 1.27 0.678 0.722 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.8 3.99 2.00 0.747 0.717 223s supply 20 16 104.8 6.55 2.56 0.609 0.536 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.97 4.55 223s supply 4.55 6.13 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.99 4.98 223s supply 4.98 6.55 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.975 223s supply 0.975 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 223s price -0.222 0.096 -2.31 0.027 * 223s income 0.296 0.045 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.997 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 223s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 223s price 0.2193 0.1002 2.19 0.036 * 223s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 223s trend 0.2956 0.0450 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.559 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 223s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 223s 223s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 171 0.887 0.68 0.678 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.5 3.97 1.99 0.748 0.719 223s supply 20 16 104.0 6.50 2.55 0.612 0.539 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.37 3.75 223s supply 3.75 4.91 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.37 4.08 223s supply 4.08 5.20 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.974 223s supply 0.974 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 223s price -0.2243 0.0888 -2.53 0.016 * 223s income 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.992 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 223s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 223s price 0.2207 0.0896 2.46 0.019 * 223s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 223s trend 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.55 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 223s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 223s 223s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 172 0.873 0.679 0.681 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.7 3.98 2.00 0.748 0.718 223s supply 20 16 104.3 6.52 2.55 0.611 0.538 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.35 3.76 223s supply 3.76 4.92 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.38 4.10 223s supply 4.10 5.22 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.975 223s supply 0.975 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 223s price -0.2225 0.0883 -2.52 0.017 * 223s income 0.2964 0.0416 7.13 3.1e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.995 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 223s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 223s price 0.2201 0.0897 2.45 0.019 * 223s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 223s trend 0.2964 0.0416 7.13 3.1e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.553 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 223s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 223s 223s [1] "*************** 3SLS with 2 restrictions **********************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 171 1.74 0.681 0.696 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.8 3.87 1.97 0.755 0.726 223s supply 20 16 105.4 6.59 2.57 0.607 0.533 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.89 4.53 223s supply 4.53 6.25 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 4.87 223s supply 4.87 6.59 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.965 223s supply 0.965 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 223s price -0.2457 0.0891 -2.76 0.0092 ** 223s income 0.3236 0.0233 13.91 8.9e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.967 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 223s price 0.2543 0.0891 2.85 0.0072 ** 223s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 223s trend 0.3236 0.0233 13.91 8.9e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.566 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 223s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 223s 223s [1] "Component “call”: target, current do not match when deparsed" 223s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 170 1.19 0.683 0.658 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.6 3.86 1.96 0.755 0.727 223s supply 20 16 104.6 6.54 2.56 0.610 0.537 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.30 3.73 223s supply 3.73 5.00 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.28 4.00 223s supply 4.00 5.23 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.965 223s supply 0.965 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 223s price -0.2494 0.0812 -3.07 0.0041 ** 223s income 0.3248 0.0209 15.57 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.964 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 223s price 0.2506 0.0812 3.09 0.0039 ** 223s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 223s trend 0.3248 0.0209 15.57 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.557 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 223s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 223s 223s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 172 1.74 0.68 0.697 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.9 3.88 1.97 0.754 0.725 223s supply 20 16 105.7 6.60 2.57 0.606 0.532 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.88 4.55 223s supply 4.55 6.27 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.88 4.88 223s supply 4.88 6.60 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.965 223s supply 0.965 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 223s price -0.2443 0.0892 -2.74 0.0096 ** 223s income 0.3234 0.0229 14.14 4.4e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.969 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.907 MSE: 3.877 Root MSE: 1.969 223s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 223s price 0.2557 0.0892 2.87 0.0069 ** 223s farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 223s trend 0.3234 0.0229 14.14 4.4e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.57 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 105.659 MSE: 6.604 Root MSE: 2.57 223s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 223s 223s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 171 1.74 0.681 0.696 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.8 3.87 1.97 0.755 0.726 223s supply 20 16 105.4 6.59 2.57 0.607 0.533 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.89 4.53 223s supply 4.53 6.25 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 4.87 223s supply 4.87 6.59 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.965 223s supply 0.965 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 223s price -0.2457 0.0891 -2.76 0.0092 ** 223s income 0.3236 0.0233 13.91 8.9e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.967 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 223s price 0.2543 0.0891 2.85 0.0072 ** 223s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 223s trend 0.3236 0.0233 13.91 8.9e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.566 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 223s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 223s 223s [1] "Component “call”: target, current do not match when deparsed" 223s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 170 1.19 0.683 0.658 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.6 3.86 1.96 0.755 0.727 223s supply 20 16 104.6 6.54 2.56 0.610 0.537 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.30 3.73 223s supply 3.73 5.00 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.28 4.00 223s supply 4.00 5.23 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.965 223s supply 0.965 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.1703 7.3154 12.87 7.8e-15 *** 223s price -0.2494 0.0812 -3.07 0.0041 ** 223s income 0.3248 0.0209 15.57 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.964 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.577 MSE: 3.857 Root MSE: 1.964 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.727 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 50.0853 7.5503 6.63 1.1e-07 *** 223s price 0.2506 0.0812 3.09 0.0039 ** 223s farmPrice 0.2312 0.0212 10.88 8.9e-13 *** 223s trend 0.3248 0.0209 15.57 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.557 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.607 MSE: 6.538 Root MSE: 2.557 223s Multiple R-Squared: 0.61 Adjusted R-Squared: 0.537 223s 223s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 170 1.19 0.682 0.659 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.6 3.86 1.97 0.755 0.726 223s supply 20 16 104.8 6.55 2.56 0.609 0.536 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.30 3.75 223s supply 3.75 5.01 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.28 4.00 223s supply 4.00 5.24 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.965 223s supply 0.965 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.0830 7.3058 12.88 7.5e-15 *** 223s price -0.2484 0.0812 -3.06 0.0042 ** 223s income 0.3246 0.0205 15.81 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.965 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.646 MSE: 3.862 Root MSE: 1.965 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 50.0190 7.5314 6.64 1.1e-07 *** 223s price 0.2516 0.0812 3.10 0.0038 ** 223s farmPrice 0.2309 0.0209 11.05 5.9e-13 *** 223s trend 0.3246 0.0205 15.81 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.559 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.795 MSE: 6.55 Root MSE: 2.559 223s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 36 3690 5613 0.012 0.368 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 2132 112.2 10.59 0.305 0.305 223s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 112.2 -44.8 223s eq2 -44.8 56.8 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 112.2 -68.3 223s eq2 -68.3 91.7 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.674 223s eq2 -0.674 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: farmPrice ~ consump - 1 223s Instruments: ~trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s consump 0.9588 0.0235 40.9 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 10.592 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 223s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ consump + trend 223s Instruments: ~trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) -92.192 49.896 -1.85 0.0821 . 223s consump 1.953 0.499 3.92 0.0011 ** 223s trend -0.469 0.247 -1.90 0.0743 . 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 9.574 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 223s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 56326 283068 -104 -10.6 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 2313 122 11.0 -7.63 -7.63 223s eq2 20 19 54013 2843 53.3 -200.46 -200.46 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 121 -255 223s eq2 -255 2953 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 122 -251 223s eq2 -251 2843 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.433 223s eq2 -0.433 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ farmPrice - 1 223s Instruments: ~price + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 11.034 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 223s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: consump ~ trend - 1 223s Instruments: ~price + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 9.02 1.13 8 1.7e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 53.318 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 223s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 167069 397886 -49.1 -0.82 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 76692 4036 63.5 -285.0 -285.0 223s eq2 20 19 90377 4757 69.0 -28.5 -28.5 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 2682 2547 223s eq2 2547 2741 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 4036 4336 223s eq2 4336 4757 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 0.928 223s eq2 0.928 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ trend - 1 223s Instruments: ~income + farmPrice 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 4.162 0.723 5.75 1.5e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 63.533 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 223s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: farmPrice ~ trend - 1 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 3.274 0.676 4.84 0.00011 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 68.969 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 223s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 39 161126 1162329 -171 -17.4 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 3553 187 13.7 -12.3 -12.3 223s eq2 20 19 157573 8293 91.1 -235.2 -235.2 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 208 -731 223s eq2 -731 8271 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 187 -623 223s eq2 -623 8293 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.121 223s eq2 -0.121 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ farmPrice - 1 223s Instruments: ~farmPrice + trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 13.675 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 223s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ trend - 1 223s Instruments: ~farmPrice + trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 1.1122 0.0272 40.8 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 91.068 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 223s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 935 491 0 0 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 268 14.1 3.76 0 0 223s eq2 20 19 667 35.1 5.93 0 0 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 14.11 2.18 223s eq2 2.18 35.12 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 14.11 2.18 223s eq2 2.18 35.12 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.0000 0.0981 223s eq2 0.0981 1.0000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ 1 223s Instruments: ~income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 100.90 0.84 120 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.756 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 223s Multiple R-Squared: 0 Adjusted R-Squared: 0 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ 1 223s Instruments: ~income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 100.02 1.33 75.5 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 5.926 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 223s Multiple R-Squared: 0 Adjusted R-Squared: 0 223s 223s [1] "***************************************************" 223s [1] "3SLS formula: EViews" 223s [1] "************* 3SLS *********************************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 174 1.03 0.676 0.786 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 107.9 6.75 2.60 0.598 0.522 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 4.36 223s supply 4.36 6.04 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.00 223s supply 5.00 6.74 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.00 0.98 223s supply 0.98 1.00 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 223s price -0.2436 0.0965 -2.52 0.022 * 223s income 0.3140 0.0469 6.69 3.8e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.1972 11.8934 4.39 0.00046 *** 223s price 0.2286 0.0997 2.29 0.03571 * 223s farmPrice 0.2282 0.0440 5.19 9e-05 *** 223s trend 0.3611 0.0729 4.95 0.00014 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.597 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 107.914 MSE: 6.745 Root MSE: 2.597 223s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.522 223s 223s [1] "********************* 3SLS EViews-like *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 173 0.719 0.677 0.748 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 107.2 6.70 2.59 0.600 0.525 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.29 3.59 223s supply 3.59 4.83 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.29 4.11 223s supply 4.11 5.36 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.979 223s supply 0.979 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 223s price -0.2436 0.0890 -2.74 0.0099 ** 223s income 0.3140 0.0433 7.25 2.5e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.1176 10.6378 4.90 2.5e-05 *** 223s price 0.2289 0.0892 2.57 0.015 * 223s farmPrice 0.2290 0.0393 5.82 1.6e-06 *** 223s trend 0.3579 0.0652 5.49 4.3e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.589 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 107.216 MSE: 6.701 Root MSE: 2.589 223s Multiple R-Squared: 0.6 Adjusted R-Squared: 0.525 223s 223s [1] "********************* 3SLS with methodResidCov = Theil *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 174 -0.718 0.675 0.922 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 108.7 6.79 2.61 0.594 0.518 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 4.50 223s supply 4.50 6.04 223s 223s warning: this covariance matrix is NOT positive semidefinit! 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.2 223s supply 5.20 6.8 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.981 223s supply 0.981 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 223s price -0.2436 0.0965 -2.52 0.017 * 223s income 0.3140 0.0469 6.69 1.3e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 223s price 0.2282 0.0997 2.29 0.02855 * 223s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 223s trend 0.3648 0.0707 5.16 1.1e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.607 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 223s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 223s 223s [1] "*************** W3SLS with methodResidCov = Theil *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 174 -0.718 0.675 0.922 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 108.7 6.79 2.61 0.594 0.518 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 4.50 223s supply 4.50 6.04 223s 223s warning: this covariance matrix is NOT positive semidefinit! 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.2 223s supply 5.20 6.8 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.981 223s supply 0.981 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 223s price -0.2436 0.0965 -2.52 0.017 * 223s income 0.3140 0.0469 6.69 1.3e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.2869 11.8853 4.40 0.00011 *** 223s price 0.2282 0.0997 2.29 0.02855 * 223s farmPrice 0.2272 0.0438 5.19 1.0e-05 *** 223s trend 0.3648 0.0707 5.16 1.1e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.607 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 108.727 MSE: 6.795 Root MSE: 2.607 223s Multiple R-Squared: 0.594 Adjusted R-Squared: 0.518 223s 223s [1] "*************** 3SLS with restriction *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 173 1.27 0.678 0.722 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.8 3.99 2.00 0.747 0.717 223s supply 20 16 104.8 6.55 2.56 0.609 0.536 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.97 4.55 223s supply 4.55 6.13 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.99 4.98 223s supply 4.98 6.55 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.975 223s supply 0.975 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 223s price -0.222 0.096 -2.31 0.027 * 223s income 0.296 0.045 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.997 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 223s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 223s price 0.2193 0.1002 2.19 0.036 * 223s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 223s trend 0.2956 0.0450 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.559 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 223s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 223s 223s [1] "Component “call”: target, current do not match when deparsed" 223s [1] "************** 3SLS with restriction (EViews-like) *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 171 0.887 0.68 0.678 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.5 3.97 1.99 0.748 0.719 223s supply 20 16 104.0 6.50 2.55 0.612 0.539 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.37 3.75 223s supply 3.75 4.91 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.37 4.08 223s supply 4.08 5.20 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.974 223s supply 0.974 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 223s price -0.2243 0.0888 -2.53 0.016 * 223s income 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.992 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 223s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 223s price 0.2207 0.0896 2.46 0.019 * 223s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 223s trend 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.55 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 223s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 223s 223s [1] 40 223s [1] "*************** W3SLS with restriction *****************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 173 1.24 0.677 0.725 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 68.1 4.00 2.00 0.746 0.716 223s supply 20 16 105.2 6.57 2.56 0.608 0.534 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.93 4.56 223s supply 4.56 6.15 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.00 5.01 223s supply 5.01 6.57 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.976 223s supply 0.976 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.1823 7.9793 11.8 1.4e-13 *** 223s price -0.2194 0.0954 -2.3 0.028 * 223s income 0.2938 0.0445 6.6 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.001 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 68.057 MSE: 4.003 Root MSE: 2.001 223s Multiple R-Squared: 0.746 Adjusted R-Squared: 0.716 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 56.2541 11.5687 4.86 2.6e-05 *** 223s price 0.2184 0.1003 2.18 0.036 * 223s farmPrice 0.2040 0.0401 5.09 1.3e-05 *** 223s trend 0.2938 0.0445 6.60 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.564 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 105.161 MSE: 6.573 Root MSE: 2.564 223s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 223s 223s [1] "*************** 3SLS with restriction via restrict.regMat ********************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 173 1.27 0.678 0.722 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.8 3.99 2.00 0.747 0.717 223s supply 20 16 104.8 6.55 2.56 0.609 0.536 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.97 4.55 223s supply 4.55 6.13 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.99 4.98 223s supply 4.98 6.55 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.975 223s supply 0.975 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.222 8.015 11.76 1.6e-13 *** 223s price -0.222 0.096 -2.31 0.027 * 223s income 0.296 0.045 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.997 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 223s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.9604 11.5777 4.83 2.8e-05 *** 223s price 0.2193 0.1002 2.19 0.036 * 223s farmPrice 0.2060 0.0403 5.11 1.3e-05 *** 223s trend 0.2956 0.0450 6.57 1.6e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.559 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 223s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 223s 223s [1] "*************** 3SLS with restriction via restrict.regMat (EViews-like) *******" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 171 0.887 0.68 0.678 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.5 3.97 1.99 0.748 0.719 223s supply 20 16 104.0 6.50 2.55 0.612 0.539 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.37 3.75 223s supply 3.75 4.91 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.37 4.08 223s supply 4.08 5.20 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.974 223s supply 0.974 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 223s price -0.2243 0.0888 -2.53 0.016 * 223s income 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.992 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 223s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 223s price 0.2207 0.0896 2.46 0.019 * 223s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 223s trend 0.2979 0.0420 7.10 3.4e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.55 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 223s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 223s 223s [1] "**** W3SLS with restriction via restrict.regMat (EViews-like) ****" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 172 0.873 0.679 0.681 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 67.7 3.98 2.00 0.748 0.718 223s supply 20 16 104.3 6.52 2.55 0.611 0.538 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.35 3.76 223s supply 3.76 4.92 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.38 4.10 223s supply 4.10 5.22 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.975 223s supply 0.975 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.2409 7.3617 12.80 1.5e-14 *** 223s price -0.2225 0.0883 -2.52 0.017 * 223s income 0.2964 0.0416 7.13 3.1e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.995 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 67.672 MSE: 3.981 Root MSE: 1.995 223s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 55.6925 10.3937 5.36 5.9e-06 *** 223s price 0.2201 0.0897 2.45 0.019 * 223s farmPrice 0.2078 0.0364 5.71 2.0e-06 *** 223s trend 0.2964 0.0416 7.13 3.1e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.553 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 104.312 MSE: 6.519 Root MSE: 2.553 223s Multiple R-Squared: 0.611 Adjusted R-Squared: 0.538 223s 223s [1] "*************** 3SLS with 2 restrictions **********************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 442 31.1 0.176 -0.052 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 164 9.66 3.11 0.388 0.316 223s supply 20 16 278 17.36 4.17 -0.036 -0.230 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.89 4.53 223s supply 4.53 6.25 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 9.66 11.7 223s supply 11.69 17.4 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.903 223s supply 0.903 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 91.2986 7.9234 11.52 1.8e-13 *** 223s price -0.4494 0.0891 -5.04 1.4e-05 *** 223s income 0.5592 0.0233 24.04 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.108 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 164.177 MSE: 9.657 Root MSE: 3.108 223s Multiple R-Squared: 0.388 Adjusted R-Squared: 0.316 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) -1.8394 8.1797 -0.22 0.82 223s price 0.5506 0.0891 6.18 4.5e-07 *** 223s farmPrice 0.4325 0.0241 17.95 < 2e-16 *** 223s trend 0.5592 0.0233 24.04 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 4.167 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 277.77 MSE: 17.361 Root MSE: 4.167 223s Multiple R-Squared: -0.036 Adjusted R-Squared: -0.23 223s 223s [1] "Component “call”: target, current do not match when deparsed" 223s [1] "*************** 3SLS with 2 restrictions (EViews-like) ************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 439 21.3 0.18 -0.18 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 169 9.93 3.15 0.370 0.296 223s supply 20 16 271 16.91 4.11 -0.009 -0.198 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.30 3.73 223s supply 3.73 5.00 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 8.44 9.64 223s supply 9.64 13.53 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.902 223s supply 0.902 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 223s price -0.4781 0.0812 -5.89 1.1e-06 *** 223s income 0.5683 0.0209 27.24 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.152 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 168.882 MSE: 9.934 Root MSE: 3.152 223s Multiple R-Squared: 0.37 Adjusted R-Squared: 0.296 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 0.6559 7.5503 0.09 0.93 223s price 0.5219 0.0812 6.43 2.1e-07 *** 223s farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 223s trend 0.5683 0.0209 27.24 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 4.112 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 270.595 MSE: 16.912 Root MSE: 4.112 223s Multiple R-Squared: -0.009 Adjusted R-Squared: -0.198 223s 223s [1] "********** W3SLS with 2 (symbolic) restrictions ***************" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 448 31.2 0.165 -0.057 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 166 9.77 3.13 0.38 0.307 223s supply 20 16 281 17.59 4.19 -0.05 -0.246 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.88 4.55 223s supply 4.55 6.27 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 9.77 11.9 223s supply 11.86 17.6 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.905 223s supply 0.905 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 90.6391 7.9088 11.46 2.1e-13 *** 223s price -0.4438 0.0892 -4.98 1.7e-05 *** 223s income 0.5603 0.0229 24.50 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.126 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 166.148 MSE: 9.773 Root MSE: 3.126 223s Multiple R-Squared: 0.38 Adjusted R-Squared: 0.307 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) -2.5480 8.1522 -0.31 0.76 223s price 0.5562 0.0892 6.24 3.7e-07 *** 223s farmPrice 0.4340 0.0237 18.33 < 2e-16 *** 223s trend 0.5603 0.0229 24.50 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 4.194 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 281.4 MSE: 17.587 Root MSE: 4.194 223s Multiple R-Squared: -0.05 Adjusted R-Squared: -0.246 223s 223s [1] "*************** 3SLS with 2 restrictions via R and restrict.regMat **********" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 442 31.1 0.176 -0.052 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 164 9.66 3.11 0.388 0.316 223s supply 20 16 278 17.36 4.17 -0.036 -0.230 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.89 4.53 223s supply 4.53 6.25 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 9.66 11.7 223s supply 11.69 17.4 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.903 223s supply 0.903 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 91.2986 7.9234 11.52 1.8e-13 *** 223s price -0.4494 0.0891 -5.04 1.4e-05 *** 223s income 0.5592 0.0233 24.04 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.108 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 164.177 MSE: 9.657 Root MSE: 3.108 223s Multiple R-Squared: 0.388 Adjusted R-Squared: 0.316 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) -1.8394 8.1797 -0.22 0.82 223s price 0.5506 0.0891 6.18 4.5e-07 *** 223s farmPrice 0.4325 0.0241 17.95 < 2e-16 *** 223s trend 0.5592 0.0233 24.04 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 4.167 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 277.77 MSE: 17.361 Root MSE: 4.167 223s Multiple R-Squared: -0.036 Adjusted R-Squared: -0.23 223s 223s [1] "Component “call”: target, current do not match when deparsed" 223s [1] "******** 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)*****" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 439 21.3 0.18 -0.18 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 169 9.93 3.15 0.370 0.296 223s supply 20 16 271 16.91 4.11 -0.009 -0.198 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.30 3.73 223s supply 3.73 5.00 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 8.44 9.64 223s supply 9.64 13.53 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.902 223s supply 0.902 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 223s price -0.4781 0.0812 -5.89 1.1e-06 *** 223s income 0.5683 0.0209 27.24 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.152 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 168.882 MSE: 9.934 Root MSE: 3.152 223s Multiple R-Squared: 0.37 Adjusted R-Squared: 0.296 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 0.6559 7.5503 0.09 0.93 223s price 0.5219 0.0812 6.43 2.1e-07 *** 223s farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 223s trend 0.5683 0.0209 27.24 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 4.112 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 270.595 MSE: 16.912 Root MSE: 4.112 223s Multiple R-Squared: -0.009 Adjusted R-Squared: -0.198 223s 223s [1] "*** W3SLS with 2 restrictions via R and restrict.regMat (EViews-like) ***" 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 444 21.3 0.172 -0.188 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 171 10.0 3.17 0.363 0.289 223s supply 20 16 274 17.1 4.13 -0.020 -0.212 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.30 3.75 223s supply 3.75 5.01 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 8.53 9.77 223s supply 9.77 13.68 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.904 223s supply 0.904 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.7628 7.3058 12.70 1.2e-14 *** 223s price -0.4740 0.0812 -5.84 1.3e-06 *** 223s income 0.5694 0.0205 27.74 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.168 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 170.659 MSE: 10.039 Root MSE: 3.168 223s Multiple R-Squared: 0.363 Adjusted R-Squared: 0.289 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 0.0845 7.5314 0.01 0.99 223s price 0.5260 0.0812 6.48 1.8e-07 *** 223s farmPrice 0.4370 0.0209 20.91 < 2e-16 *** 223s trend 0.5694 0.0205 27.74 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 4.135 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 273.568 MSE: 17.098 Root MSE: 4.135 223s Multiple R-Squared: -0.02 Adjusted R-Squared: -0.212 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 36 3690 5613 0.012 0.368 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 2132 112.2 10.59 0.305 0.305 223s eq2 20 17 1558 91.7 9.57 -1.335 -1.610 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 112.2 -44.8 223s eq2 -44.8 56.8 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 112.2 -68.3 223s eq2 -68.3 91.7 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.674 223s eq2 -0.674 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: farmPrice ~ consump - 1 223s Instruments: ~trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s consump 0.9588 0.0235 40.9 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 10.592 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 2131.725 MSE: 112.196 Root MSE: 10.592 223s Multiple R-Squared: 0.305 Adjusted R-Squared: 0.305 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ consump + trend 223s Instruments: ~trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) -92.192 49.896 -1.85 0.0821 . 223s consump 1.953 0.499 3.92 0.0011 ** 223s trend -0.469 0.247 -1.90 0.0743 . 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 9.574 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 1558.311 MSE: 91.665 Root MSE: 9.574 223s Multiple R-Squared: -1.335 Adjusted R-Squared: -1.61 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 56326 283068 -104 -10.6 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 2313 122 11.0 -7.63 -7.63 223s eq2 20 19 54013 2843 53.3 -200.46 -200.46 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 121 -255 223s eq2 -255 2953 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 122 -251 223s eq2 -251 2843 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.433 223s eq2 -0.433 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ farmPrice - 1 223s Instruments: ~price + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s farmPrice 1.0417 0.0253 41.2 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 11.034 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 2313.073 MSE: 121.741 Root MSE: 11.034 223s Multiple R-Squared: -7.627 Adjusted R-Squared: -7.627 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: consump ~ trend - 1 223s Instruments: ~price + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 9.02 1.13 8 1.7e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 53.318 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 54013.367 MSE: 2842.809 Root MSE: 53.318 223s Multiple R-Squared: -200.456 Adjusted R-Squared: -200.456 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 167069 397886 -49.1 -0.82 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 76692 4036 63.5 -285.0 -285.0 223s eq2 20 19 90377 4757 69.0 -28.5 -28.5 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 2682 2547 223s eq2 2547 2741 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 4036 4336 223s eq2 4336 4757 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 0.928 223s eq2 0.928 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ trend - 1 223s Instruments: ~income + farmPrice 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 4.162 0.723 5.75 1.5e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 63.533 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 76691.636 MSE: 4036.402 Root MSE: 63.533 223s Multiple R-Squared: -285.041 Adjusted R-Squared: -285.041 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: farmPrice ~ trend - 1 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 3.274 0.676 4.84 0.00011 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 68.969 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 90377.499 MSE: 4756.71 Root MSE: 68.969 223s Multiple R-Squared: -28.451 Adjusted R-Squared: -28.451 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 39 161126 1162329 -171 -17.4 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 3553 187 13.7 -12.3 -12.3 223s eq2 20 19 157573 8293 91.1 -235.2 -235.2 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 208 -731 223s eq2 -731 8271 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 187 -623 223s eq2 -623 8293 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.000 -0.121 223s eq2 -0.121 1.000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ farmPrice - 1 223s Instruments: ~farmPrice + trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s farmPrice 1.1122 0.0272 40.8 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 13.675 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 3553.118 MSE: 187.006 Root MSE: 13.675 223s Multiple R-Squared: -12.252 Adjusted R-Squared: -12.252 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ trend - 1 223s Instruments: ~farmPrice + trend + income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s trend 1.1122 0.0272 40.8 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 91.068 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 157573.328 MSE: 8293.333 Root MSE: 91.068 223s Multiple R-Squared: -235.153 Adjusted R-Squared: -235.153 223s 223s 223s systemfit results 223s method: 3SLS 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 38 935 491 0 0 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s eq1 20 19 268 14.1 3.76 0 0 223s eq2 20 19 667 35.1 5.93 0 0 223s 223s The covariance matrix of the residuals used for estimation 223s eq1 eq2 223s eq1 14.11 2.18 223s eq2 2.18 35.12 223s 223s The covariance matrix of the residuals 223s eq1 eq2 223s eq1 14.11 2.18 223s eq2 2.18 35.12 223s 223s The correlations of the residuals 223s eq1 eq2 223s eq1 1.0000 0.0981 223s eq2 0.0981 1.0000 223s 223s 223s 3SLS estimates for 'eq1' (equation 1) 223s Model Formula: consump ~ 1 223s Instruments: ~income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 100.90 0.84 120 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 3.756 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 223s Multiple R-Squared: 0 Adjusted R-Squared: 0 223s 223s 223s 3SLS estimates for 'eq2' (equation 2) 223s Model Formula: price ~ 1 223s Instruments: ~income 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 100.02 1.33 75.5 <2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 5.926 on 19 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 19 223s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 223s Multiple R-Squared: 0 Adjusted R-Squared: 0 223s 223s > 223s > ## ******************** iterated 3SLS ********************** 223s > fit3slsi <- list() 223s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 223s > for( i in seq( along = formulas ) ) { 223s + fit3slsi[[ i ]] <- list() 223s + 223s + print( "***************************************************" ) 223s + print( paste( "3SLS formula:", formulas[ i ] ) ) 223s + print( "************* 3SLS *********************************" ) 223s + fit3slsi[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, method3sls = formulas[ i ], maxiter = 100, 223s + useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e1 ) ) 223s + 223s + print( "********************* iterated 3SLS EViews-like ****************" ) 223s + fit3slsi[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 223s + maxiter = 100, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e1e, useDfSys = TRUE ) ) 223s + 223s + print( "************** iterated 3SLS with methodResidCov = Theil **************" ) 223s + fit3slsi[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "Theil", method3sls = formulas[ i ], 223s + maxiter = 100, x = TRUE, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e1c, useDfSys = TRUE ) ) 223s + 223s + print( "**************** iterated W3SLS EViews-like ****************" ) 223s + fit3slsi[[ i ]]$e1we <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "noDfCor", method3sls = formulas[ i ], 223s + maxiter = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e1we, useDfSys = TRUE ) ) 223s + 223s + 223s + print( "******* iterated 3SLS with restriction *****************" ) 223s + fit3slsi[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, restrict.matrix = restrm, method3sls = formulas[ i ], 223s + maxiter = 100, x = TRUE, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e2 ) ) 223s + 223s + print( "********* iterated 3SLS with restriction (EViews-like) *********" ) 223s + fit3slsi[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 223s + method3sls = formulas[ i ], maxiter = 100, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e2e, useDfSys = TRUE ) ) 223s + 223s + print( "******** iterated W3SLS with restriction (EViews-like) *********" ) 223s + fit3slsi[[ i ]]$e2we <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restrm, 223s + method3sls = formulas[ i ], maxiter = 100, residCovWeighted = TRUE, 223s + useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e2we, useDfSys = TRUE ) ) 223s + 223s + 223s + print( "********* iterated 3SLS with restriction via restrict.regMat *****************" ) 223s + fit3slsi[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], 223s + maxiter = 100, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e3 ) ) 223s + 223s + print( "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" ) 223s + fit3slsi[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "noDfCor", restrict.regMat = tc, 223s + method3sls = formulas[ i ], maxiter = 100, x = TRUE, 223s + useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e3e, useDfSys = TRUE ) ) 223s + 223s + print( "***** iterated W3SLS with restriction via restrict.regMat ********" ) 223s + fit3slsi[[ i ]]$e3w <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, restrict.regMat = tc, method3sls = formulas[ i ], maxiter = 100, 223s + residCovWeighted = TRUE, x = TRUE, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e3w ) ) 223s + 223s + 223s + print( "******** iterated 3SLS with 2 restrictions *********************" ) 223s + fit3slsi[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, restrict.matrix = restr2m, restrict.rhs = restr2q, 223s + method3sls = formulas[ i ], maxiter = 100, x = TRUE, 223s + useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e4 ) ) 223s + 223s + print( "********* iterated 3SLS with 2 restrictions (EViews-like) *******" ) 223s + fit3slsi[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 223s + restrict.rhs = restr2q, method3sls = formulas[ i ], maxiter = 100, 223s + useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e4e, useDfSys = TRUE ) ) 223s + 223s + print( "******** iterated W3SLS with 2 restrictions (EViews-like) *******" ) 223s + fit3slsi[[ i ]]$e4we <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, methodResidCov = "noDfCor", restrict.matrix = restr2m, 223s + restrict.rhs = restr2q, method3sls = formulas[ i ], maxiter = 100, 223s + residCovWeighted = TRUE, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e4we, useDfSys = TRUE ) ) 223s + 223s + 223s + print( "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" ) 223s + fit3slsi[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 223s + restrict.rhs = restr3q, method3sls = formulas[ i ], maxiter = 100, 223s + useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e5 ) ) 223s + 223s + print( "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" ) 223s + fit3slsi[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, restrict.regMat = tc, methodResidCov = "noDfCor", 223s + restrict.matrix = restr3m, restrict.rhs = restr3q, 223s + method3sls = formulas[ i ], maxiter = 100, useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e5e, useDfSys = TRUE ) ) 223s + 223s + print( "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" ) 223s + fit3slsi[[ i ]]$e5w <- systemfit( system, "3SLS", data = Kmenta, 223s + inst = inst, restrict.regMat = tc, restrict.matrix = restr3m, 223s + restrict.rhs = restr3q, method3sls = formulas[ i ], maxiter = 100, 223s + residCovWeighted = TRUE, x = TRUE, 223s + useMatrix = useMatrix ) 223s + print( summary( fit3slsi[[ i ]]$e5w ) ) 223s + } 223s [1] "***************************************************" 223s [1] "3SLS formula: GLS" 223s [1] "************* 3SLS *********************************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 178 0.983 0.668 0.814 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 112.4 7.03 2.65 0.581 0.502 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 5.12 223s supply 5.12 7.03 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.12 223s supply 5.12 7.03 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 223s price -0.2436 0.0965 -2.52 0.022 * 223s income 0.3140 0.0469 6.69 3.8e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 223s price 0.2266 0.1075 2.11 0.05110 . 223s farmPrice 0.2234 0.0468 4.78 0.00021 *** 223s trend 0.3800 0.0720 5.28 7.5e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.651 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 223s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 223s 223s [1] "********************* iterated 3SLS EViews-like ****************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 177 0.667 0.67 0.782 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 111.3 6.96 2.64 0.585 0.507 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 223s price -0.2436 0.0890 -2.74 0.0099 ** 223s income 0.3140 0.0433 7.25 2.5e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 223s price 0.2271 0.0956 2.37 0.024 * 223s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 223s trend 0.3756 0.0641 5.86 1.5e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.637 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 223s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 223s 223s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 179 -0.818 0.665 0.957 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 113.8 7.11 2.67 0.576 0.496 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 5.32 223s supply 5.32 7.11 223s 223s warning: this covariance matrix is NOT positive semidefinit! 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.32 223s supply 5.32 7.11 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 223s price -0.2436 0.0965 -2.52 0.017 * 223s income 0.3140 0.0469 6.69 1.3e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 223s price 0.2261 0.1081 2.09 0.04425 * 223s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 223s trend 0.3851 0.0693 5.55 3.6e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.667 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 223s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 223s 223s [1] "**************** iterated W3SLS EViews-like ****************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 177 0.667 0.67 0.782 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 111.3 6.96 2.64 0.585 0.507 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 223s price -0.2436 0.0890 -2.74 0.0099 ** 223s income 0.3140 0.0433 7.25 2.5e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 223s price 0.2271 0.0956 2.37 0.024 * 223s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 223s trend 0.3756 0.0641 5.86 1.5e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.637 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 223s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 223s 223s [1] "******* iterated 3SLS with restriction *****************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 17 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 240 0.56 0.553 0.819 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 98.4 5.79 2.41 0.633 0.590 223s supply 20 16 141.1 8.82 2.97 0.474 0.375 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 223s price -0.1064 0.1023 -1.04 0.31 223s income 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.406 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 223s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 223s price 0.1833 0.1189 1.54 0.13 223s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 223s trend 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.97 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 223s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 223s 223s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 20 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 237 0.364 0.557 0.755 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 99.3 5.84 2.42 0.630 0.586 223s supply 20 16 138.1 8.63 2.94 0.485 0.388 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 223s price -0.1043 0.0958 -1.09 0.28 223s income 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.417 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 223s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 223s price 0.1851 0.1053 1.76 0.088 . 223s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 223s trend 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.938 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 223s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 223s 223s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 20 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 237 0.364 0.557 0.755 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 99.3 5.84 2.42 0.630 0.586 223s supply 20 16 138.1 8.63 2.94 0.485 0.388 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 223s price -0.1043 0.0958 -1.09 0.28 223s income 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.417 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 223s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 223s price 0.1851 0.1053 1.76 0.088 . 223s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 223s trend 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.938 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 223s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 223s 223s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 17 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 240 0.56 0.553 0.819 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 98.4 5.79 2.41 0.633 0.590 223s supply 20 16 141.1 8.82 2.97 0.474 0.375 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 223s price -0.1064 0.1023 -1.04 0.31 223s income 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.406 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 223s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 223s price 0.1833 0.1189 1.54 0.13 223s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 223s trend 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.97 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 223s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 223s 223s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 20 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 237 0.364 0.557 0.755 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 99.3 5.84 2.42 0.630 0.586 223s supply 20 16 138.1 8.63 2.94 0.485 0.388 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 223s price -0.1043 0.0958 -1.09 0.28 223s income 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.417 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 223s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 223s price 0.1851 0.1053 1.76 0.088 . 223s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 223s trend 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.938 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 223s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 223s 223s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 17 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 240 0.56 0.553 0.819 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 98.4 5.79 2.41 0.633 0.590 223s supply 20 16 141.1 8.82 2.97 0.474 0.375 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 223s price -0.1064 0.1023 -1.04 0.31 223s income 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.406 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 223s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 223s price 0.1833 0.1189 1.54 0.13 223s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 223s trend 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.97 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 223s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 223s 223s [1] "******** iterated 3SLS with 2 restrictions *********************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 9 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 185 1.76 0.655 0.71 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 69.9 4.11 2.03 0.739 0.709 223s supply 20 16 114.8 7.18 2.68 0.572 0.491 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.11 5.27 223s supply 5.27 7.18 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.11 5.27 223s supply 5.27 7.18 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.00 0.97 223s supply 0.97 1.00 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 223s price -0.2007 0.0920 -2.18 0.036 * 223s income 0.3159 0.0192 16.42 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.028 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 223s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 223s price 0.2993 0.0920 3.25 0.0025 ** 223s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 223s trend 0.3159 0.0192 16.42 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.679 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 223s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 223s 223s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 8 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 179 1.19 0.666 0.668 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 68.3 4.02 2.00 0.745 0.715 223s supply 20 16 110.8 6.92 2.63 0.587 0.509 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.41 4.21 223s supply 4.21 5.54 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.41 4.21 223s supply 4.21 5.54 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.968 223s supply 0.968 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 223s price -0.2168 0.0835 -2.6 0.014 * 223s income 0.3199 0.0168 19.1 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.004 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 223s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 223s price 0.2832 0.0835 3.39 0.0017 ** 223s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 223s trend 0.3199 0.0168 19.07 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.631 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 223s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 223s 223s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 8 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 179 1.19 0.666 0.668 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 68.3 4.02 2.00 0.745 0.715 223s supply 20 16 110.8 6.92 2.63 0.587 0.509 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.41 4.21 223s supply 4.21 5.54 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.41 4.21 223s supply 4.21 5.54 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.968 223s supply 0.968 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 223s price -0.2168 0.0835 -2.6 0.014 * 223s income 0.3199 0.0168 19.1 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.004 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 223s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 223s price 0.2832 0.0835 3.39 0.0017 ** 223s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 223s trend 0.3199 0.0168 19.07 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.631 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 223s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 223s 223s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 9 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 185 1.76 0.655 0.71 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 69.9 4.11 2.03 0.739 0.709 223s supply 20 16 114.8 7.18 2.68 0.572 0.491 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.11 5.27 223s supply 5.27 7.18 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.11 5.27 223s supply 5.27 7.18 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.00 0.97 223s supply 0.97 1.00 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 223s price -0.2007 0.0920 -2.18 0.036 * 223s income 0.3159 0.0192 16.42 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.028 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 223s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 223s price 0.2993 0.0920 3.25 0.0025 ** 223s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 223s trend 0.3159 0.0192 16.42 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.679 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 223s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 223s 223s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 8 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 179 1.19 0.666 0.668 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 68.3 4.02 2.00 0.745 0.715 223s supply 20 16 110.8 6.92 2.63 0.587 0.509 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.41 4.21 223s supply 4.21 5.54 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.41 4.21 223s supply 4.21 5.54 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.968 223s supply 0.968 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 223s price -0.2168 0.0835 -2.6 0.014 * 223s income 0.3199 0.0168 19.1 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.004 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 223s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 223s price 0.2832 0.0835 3.39 0.0017 ** 223s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 223s trend 0.3199 0.0168 19.07 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.631 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 223s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 223s 223s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 9 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 35 185 1.76 0.655 0.71 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 69.9 4.11 2.03 0.739 0.709 223s supply 20 16 114.8 7.18 2.68 0.572 0.491 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.11 5.27 223s supply 5.27 7.18 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.11 5.27 223s supply 5.27 7.18 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.00 0.97 223s supply 0.97 1.00 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 223s price -0.2007 0.0920 -2.18 0.036 * 223s income 0.3159 0.0192 16.42 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.028 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 223s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 223s price 0.2993 0.0920 3.25 0.0025 ** 223s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 223s trend 0.3159 0.0192 16.42 < 2e-16 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.679 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 223s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 223s 223s [1] "***************************************************" 223s [1] "3SLS formula: IV" 223s [1] "************* 3SLS *********************************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 178 0.983 0.668 0.814 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 112.4 7.03 2.65 0.581 0.502 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 5.12 223s supply 5.12 7.03 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.12 223s supply 5.12 7.03 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 223s price -0.2436 0.0965 -2.52 0.022 * 223s income 0.3140 0.0469 6.69 3.8e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 223s price 0.2266 0.1075 2.11 0.05110 . 223s farmPrice 0.2234 0.0468 4.78 0.00021 *** 223s trend 0.3800 0.0720 5.28 7.5e-05 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.651 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 223s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 223s 223s [1] "********************* iterated 3SLS EViews-like ****************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 177 0.667 0.67 0.782 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 111.3 6.96 2.64 0.585 0.507 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 223s price -0.2436 0.0890 -2.74 0.0099 ** 223s income 0.3140 0.0433 7.25 2.5e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 223s price 0.2271 0.0956 2.37 0.024 * 223s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 223s trend 0.3756 0.0641 5.86 1.5e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.637 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 223s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 223s 223s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 179 -0.818 0.665 0.957 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 113.8 7.11 2.67 0.576 0.496 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.87 5.32 223s supply 5.32 7.11 223s 223s warning: this covariance matrix is NOT positive semidefinit! 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.87 5.32 223s supply 5.32 7.11 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 223s price -0.2436 0.0965 -2.52 0.017 * 223s income 0.3140 0.0469 6.69 1.3e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 223s price 0.2261 0.1081 2.09 0.04425 * 223s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 223s trend 0.3851 0.0693 5.55 3.6e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.667 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 223s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 223s 223s [1] "**************** iterated W3SLS EViews-like ****************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 6 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 33 177 0.667 0.67 0.782 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 65.7 3.87 1.97 0.755 0.726 223s supply 20 16 111.3 6.96 2.64 0.585 0.507 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 3.29 4.20 223s supply 4.20 5.57 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.982 223s supply 0.982 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 223s price -0.2436 0.0890 -2.74 0.0099 ** 223s income 0.3140 0.0433 7.25 2.5e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 1.966 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 223s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 223s price 0.2271 0.0956 2.37 0.024 * 223s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 223s trend 0.3756 0.0641 5.86 1.5e-06 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.637 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 223s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 223s 223s [1] "******* iterated 3SLS with restriction *****************" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 17 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 240 0.56 0.553 0.819 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 98.4 5.79 2.41 0.633 0.590 223s supply 20 16 141.1 8.82 2.97 0.474 0.375 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 5.79 7.11 223s supply 7.11 8.82 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 223s price -0.1064 0.1023 -1.04 0.31 223s income 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.406 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 223s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 223s price 0.1833 0.1189 1.54 0.13 223s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 223s trend 0.1996 0.0297 6.73 9.9e-08 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.97 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 223s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 223s 223s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 20 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 237 0.364 0.557 0.755 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 99.3 5.84 2.42 0.630 0.586 223s supply 20 16 138.1 8.63 2.94 0.485 0.388 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 223s price -0.1043 0.0958 -1.09 0.28 223s income 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.417 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 223s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 223s price 0.1851 0.1053 1.76 0.088 . 223s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 223s trend 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.938 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 223s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 223s 223s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 223s 223s systemfit results 223s method: iterated 3SLS 223s 223s convergence achieved after 20 iterations 223s 223s N DF SSR detRCov OLS-R2 McElroy-R2 223s system 40 34 237 0.364 0.557 0.755 223s 223s N DF SSR MSE RMSE R2 Adj R2 223s demand 20 17 99.3 5.84 2.42 0.630 0.586 223s supply 20 16 138.1 8.63 2.94 0.485 0.388 223s 223s The covariance matrix of the residuals used for estimation 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The covariance matrix of the residuals 223s demand supply 223s demand 4.96 5.82 223s supply 5.82 6.90 223s 223s The correlations of the residuals 223s demand supply 223s demand 1.000 0.995 223s supply 0.995 1.000 223s 223s 223s 3SLS estimates for 'demand' (equation 1) 223s Model Formula: consump ~ price + income 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 223s price -0.1043 0.0958 -1.09 0.28 223s income 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.417 on 17 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 17 223s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 223s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 223s 223s 223s 3SLS estimates for 'supply' (equation 2) 223s Model Formula: consump ~ price + farmPrice + trend 223s Instruments: ~income + farmPrice + trend 223s 223s Estimate Std. Error t value Pr(>|t|) 223s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 223s price 0.1851 0.1053 1.76 0.088 . 223s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 223s trend 0.1979 0.0299 6.61 1.4e-07 *** 223s --- 223s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 223s 223s Residual standard error: 2.938 on 16 degrees of freedom 223s Number of observations: 20 Degrees of Freedom: 16 223s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 223s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 223s 223s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "******** iterated 3SLS with 2 restrictions *********************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "***************************************************" 224s [1] "3SLS formula: Schmidt" 224s [1] "************* 3SLS *********************************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 178 0.983 0.668 0.814 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 112.4 7.03 2.65 0.581 0.502 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.87 5.12 224s supply 5.12 7.03 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.87 5.12 224s supply 5.12 7.03 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 224s price -0.2436 0.0965 -2.52 0.022 * 224s income 0.3140 0.0469 6.69 3.8e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 224s price 0.2266 0.1075 2.11 0.05110 . 224s farmPrice 0.2234 0.0468 4.78 0.00021 *** 224s trend 0.3800 0.0720 5.28 7.5e-05 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.651 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 224s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 224s 224s [1] "********************* iterated 3SLS EViews-like ****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 177 0.667 0.67 0.782 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 111.3 6.96 2.64 0.585 0.507 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 224s price -0.2436 0.0890 -2.74 0.0099 ** 224s income 0.3140 0.0433 7.25 2.5e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 224s price 0.2271 0.0956 2.37 0.024 * 224s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 224s trend 0.3756 0.0641 5.86 1.5e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.637 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 224s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 224s 224s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 179 -0.818 0.665 0.957 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 113.8 7.11 2.67 0.576 0.496 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.87 5.32 224s supply 5.32 7.11 224s 224s warning: this covariance matrix is NOT positive semidefinit! 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.87 5.32 224s supply 5.32 7.11 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 224s price -0.2436 0.0965 -2.52 0.017 * 224s income 0.3140 0.0469 6.69 1.3e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 224s price 0.2261 0.1081 2.09 0.04425 * 224s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 224s trend 0.3851 0.0693 5.55 3.6e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.667 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 224s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 224s 224s [1] "**************** iterated W3SLS EViews-like ****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 177 0.667 0.67 0.782 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 111.3 6.96 2.64 0.585 0.507 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 224s price -0.2436 0.0890 -2.74 0.0099 ** 224s income 0.3140 0.0433 7.25 2.5e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 224s price 0.2271 0.0956 2.37 0.024 * 224s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 224s trend 0.3756 0.0641 5.86 1.5e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.637 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 224s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 224s 224s [1] "******* iterated 3SLS with restriction *****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "******** iterated 3SLS with 2 restrictions *********************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "***************************************************" 224s [1] "3SLS formula: GMM" 224s [1] "************* 3SLS *********************************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 178 0.983 0.668 0.814 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 112.4 7.03 2.65 0.581 0.502 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.87 5.12 224s supply 5.12 7.03 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.87 5.12 224s supply 5.12 7.03 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 224s price -0.2436 0.0965 -2.52 0.022 * 224s income 0.3140 0.0469 6.69 3.8e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 224s price 0.2266 0.1075 2.11 0.05110 . 224s farmPrice 0.2234 0.0468 4.78 0.00021 *** 224s trend 0.3800 0.0720 5.28 7.5e-05 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.651 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 224s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 224s 224s [1] "********************* iterated 3SLS EViews-like ****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 177 0.667 0.67 0.782 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 111.3 6.96 2.64 0.585 0.507 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 224s price -0.2436 0.0890 -2.74 0.0099 ** 224s income 0.3140 0.0433 7.25 2.5e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 224s price 0.2271 0.0956 2.37 0.024 * 224s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 224s trend 0.3756 0.0641 5.86 1.5e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.637 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 224s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 224s 224s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 179 -0.818 0.665 0.957 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 113.8 7.11 2.67 0.576 0.496 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.87 5.32 224s supply 5.32 7.11 224s 224s warning: this covariance matrix is NOT positive semidefinit! 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.87 5.32 224s supply 5.32 7.11 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 224s price -0.2436 0.0965 -2.52 0.017 * 224s income 0.3140 0.0469 6.69 1.3e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 224s price 0.2261 0.1081 2.09 0.04425 * 224s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 224s trend 0.3851 0.0693 5.55 3.6e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.667 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 224s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 224s 224s [1] "**************** iterated W3SLS EViews-like ****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 177 0.667 0.67 0.782 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 111.3 6.96 2.64 0.585 0.507 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 224s price -0.2436 0.0890 -2.74 0.0099 ** 224s income 0.3140 0.0433 7.25 2.5e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 224s price 0.2271 0.0956 2.37 0.024 * 224s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 224s trend 0.3756 0.0641 5.86 1.5e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.637 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 224s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 224s 224s [1] "******* iterated 3SLS with restriction *****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "******** iterated 3SLS with 2 restrictions *********************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 8 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 179 1.19 0.666 0.668 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 68.3 4.02 2.00 0.745 0.715 224s supply 20 16 110.8 6.92 2.63 0.587 0.509 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.41 4.21 224s supply 4.21 5.54 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.968 224s supply 0.968 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 91.3901 7.3161 12.5 1.9e-14 *** 224s price -0.2168 0.0835 -2.6 0.014 * 224s income 0.3199 0.0168 19.1 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.004 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 68.293 MSE: 4.017 Root MSE: 2.004 224s Multiple R-Squared: 0.745 Adjusted R-Squared: 0.715 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 47.5787 7.4268 6.41 2.3e-07 *** 224s price 0.2832 0.0835 3.39 0.0017 ** 224s farmPrice 0.2240 0.0168 13.36 2.7e-15 *** 224s trend 0.3199 0.0168 19.07 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.631 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 110.791 MSE: 6.924 Root MSE: 2.631 224s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.509 224s 224s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 9 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 185 1.76 0.655 0.71 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 69.9 4.11 2.03 0.739 0.709 224s supply 20 16 114.8 7.18 2.68 0.572 0.491 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.11 5.27 224s supply 5.27 7.18 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.00 0.97 224s supply 0.97 1.00 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 90.1569 7.9174 11.39 2.5e-13 *** 224s price -0.2007 0.0920 -2.18 0.036 * 224s income 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.028 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 69.917 MSE: 4.113 Root MSE: 2.028 224s Multiple R-Squared: 0.739 Adjusted R-Squared: 0.709 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 46.4810 8.0104 5.80 1.4e-06 *** 224s price 0.2993 0.0920 3.25 0.0025 ** 224s farmPrice 0.2190 0.0196 11.20 4.0e-13 *** 224s trend 0.3159 0.0192 16.42 < 2e-16 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.679 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 114.83 MSE: 7.177 Root MSE: 2.679 224s Multiple R-Squared: 0.572 Adjusted R-Squared: 0.491 224s 224s [1] "***************************************************" 224s [1] "3SLS formula: EViews" 224s [1] "************* 3SLS *********************************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 178 0.983 0.668 0.814 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 112.4 7.03 2.65 0.581 0.502 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.87 5.12 224s supply 5.12 7.03 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.87 5.12 224s supply 5.12 7.03 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 224s price -0.2436 0.0965 -2.52 0.022 * 224s income 0.3140 0.0469 6.69 3.8e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.6618 12.8051 4.11 0.00081 *** 224s price 0.2266 0.1075 2.11 0.05110 . 224s farmPrice 0.2234 0.0468 4.78 0.00021 *** 224s trend 0.3800 0.0720 5.28 7.5e-05 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.651 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 112.431 MSE: 7.027 Root MSE: 2.651 224s Multiple R-Squared: 0.581 Adjusted R-Squared: 0.502 224s 224s [1] "********************* iterated 3SLS EViews-like ****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 177 0.667 0.67 0.782 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 111.3 6.96 2.64 0.585 0.507 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 224s price -0.2436 0.0890 -2.74 0.0099 ** 224s income 0.3140 0.0433 7.25 2.5e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 224s price 0.2271 0.0956 2.37 0.024 * 224s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 224s trend 0.3756 0.0641 5.86 1.5e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.637 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 224s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 224s 224s [1] "************** iterated 3SLS with methodResidCov = Theil **************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 179 -0.818 0.665 0.957 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 113.8 7.11 2.67 0.576 0.496 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.87 5.32 224s supply 5.32 7.11 224s 224s warning: this covariance matrix is NOT positive semidefinit! 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.87 5.32 224s supply 5.32 7.11 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.9208 11.95 1.6e-13 *** 224s price -0.2436 0.0965 -2.52 0.017 * 224s income 0.3140 0.0469 6.69 1.3e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.7863 12.8707 4.10 0.00025 *** 224s price 0.2261 0.1081 2.09 0.04425 * 224s farmPrice 0.2221 0.0467 4.75 3.8e-05 *** 224s trend 0.3851 0.0693 5.55 3.6e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.667 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 113.77 MSE: 7.111 Root MSE: 2.667 224s Multiple R-Squared: 0.576 Adjusted R-Squared: 0.496 224s 224s [1] "**************** iterated W3SLS EViews-like ****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 6 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 33 177 0.667 0.67 0.782 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 65.7 3.87 1.97 0.755 0.726 224s supply 20 16 111.3 6.96 2.64 0.585 0.507 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 3.29 4.20 224s supply 4.20 5.57 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.982 224s supply 0.982 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 224s price -0.2436 0.0890 -2.74 0.0099 ** 224s income 0.3140 0.0433 7.25 2.5e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 1.966 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 224s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 52.5527 11.3956 4.61 5.8e-05 *** 224s price 0.2271 0.0956 2.37 0.024 * 224s farmPrice 0.2245 0.0416 5.39 5.8e-06 *** 224s trend 0.3756 0.0641 5.86 1.5e-06 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.637 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 111.302 MSE: 6.956 Root MSE: 2.637 224s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 224s 224s [1] "******* iterated 3SLS with restriction *****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "********* iterated 3SLS with restriction (EViews-like) *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "******** iterated W3SLS with restriction (EViews-like) *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "********* iterated 3SLS with restriction via restrict.regMat *****************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "********* iterated 3SLS with restriction via restrict.regMat (EViews-like) ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 20 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 237 0.364 0.557 0.755 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 99.3 5.84 2.42 0.630 0.586 224s supply 20 16 138.1 8.63 2.94 0.485 0.388 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 4.96 5.82 224s supply 5.82 6.90 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 224s price -0.1043 0.0958 -1.09 0.28 224s income 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.417 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 99.297 MSE: 5.841 Root MSE: 2.417 224s Multiple R-Squared: 0.63 Adjusted R-Squared: 0.586 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 224s price 0.1851 0.1053 1.76 0.088 . 224s farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 224s trend 0.1979 0.0299 6.61 1.4e-07 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.938 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 138.088 MSE: 8.63 Root MSE: 2.938 224s Multiple R-Squared: 0.485 Adjusted R-Squared: 0.388 224s 224s [1] "***** iterated W3SLS with restriction via restrict.regMat ********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 17 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 34 240 0.56 0.553 0.819 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 98.4 5.79 2.41 0.633 0.590 224s supply 20 16 141.1 8.82 2.97 0.474 0.375 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 5.79 7.11 224s supply 7.11 8.82 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.995 224s supply 0.995 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 92.0742 9.6303 9.56 3.6e-11 *** 224s price -0.1064 0.1023 -1.04 0.31 224s income 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.406 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 98.435 MSE: 5.79 Root MSE: 2.406 224s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.59 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.8551 12.4839 5.52 3.7e-06 *** 224s price 0.1833 0.1189 1.54 0.13 224s farmPrice 0.1202 0.0260 4.63 5.1e-05 *** 224s trend 0.1996 0.0297 6.73 9.9e-08 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.97 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 141.147 MSE: 8.822 Root MSE: 2.97 224s Multiple R-Squared: 0.474 Adjusted R-Squared: 0.375 224s 224s [1] "******** iterated 3SLS with 2 restrictions *********************" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s warning: convergence not achieved after 100 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 1194 34.7 -1.23 0.688 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 274 16.1 4.02 -0.024 -0.144 224s supply 20 16 920 57.5 7.58 -2.431 -3.074 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 16.1 29.9 224s supply 29.9 57.5 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 16.1 29.9 224s supply 29.9 57.5 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.981 224s supply 0.981 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 224s price 0.2553 0.1380 1.85 0.07275 . 224s income 0.3264 0.0424 7.71 4.8e-09 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 4.018 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 224s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) -49.0143 9.6115 -5.10 1.2e-05 *** 224s price 1.2553 0.1380 9.10 9.5e-11 *** 224s farmPrice 0.2166 0.0573 3.78 0.00058 *** 224s trend 0.3264 0.0424 7.71 4.8e-09 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 7.582 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 919.812 MSE: 57.488 Root MSE: 7.582 224s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 224s 224s [1] "********* iterated 3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 66 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 615 20.5 -0.147 0.48 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 151 8.87 2.98 0.437 0.371 224s supply 20 16 464 29.00 5.38 -0.731 -1.055 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 7.54 12.4 224s supply 12.43 23.2 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 7.54 12.4 224s supply 12.43 23.2 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.939 224s supply 0.939 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 224s price -0.0907 0.1236 -0.73 0.47 224s income 0.4263 0.0385 11.08 5.4e-13 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.979 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 224s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) -27.3424 9.5498 -2.86 0.007 ** 224s price 0.9093 0.1236 7.36 1.3e-08 *** 224s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 224s trend 0.4263 0.0385 11.08 5.4e-13 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 5.385 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 224s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 224s 224s [1] "******** iterated W3SLS with 2 restrictions (EViews-like) *******" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 66 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 615 20.5 -0.147 0.48 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 151 8.87 2.98 0.437 0.371 224s supply 20 16 464 29.00 5.38 -0.731 -1.055 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 7.54 12.4 224s supply 12.43 23.2 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 7.54 12.4 224s supply 12.43 23.2 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.939 224s supply 0.939 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 224s price -0.0907 0.1236 -0.73 0.47 224s income 0.4263 0.0385 11.08 5.4e-13 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.979 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 224s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) -27.3423 9.5498 -2.86 0.007 ** 224s price 0.9093 0.1236 7.36 1.3e-08 *** 224s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 224s trend 0.4263 0.0385 11.08 5.4e-13 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 5.385 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 224s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 224s 224s [1] "******** iterated 3SLS with 2 restrictions via R and restrict.regMat *********" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s warning: convergence not achieved after 100 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 1194 34.7 -1.23 0.688 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 274 16.1 4.02 -0.024 -0.144 224s supply 20 16 920 57.5 7.58 -2.431 -3.074 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 16.1 29.9 224s supply 29.9 57.5 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 16.1 29.9 224s supply 29.9 57.5 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.981 224s supply 0.981 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 224s price 0.2553 0.1380 1.85 0.07275 . 224s income 0.3264 0.0424 7.71 4.8e-09 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 4.018 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 224s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) -49.0143 9.6115 -5.10 1.2e-05 *** 224s price 1.2553 0.1380 9.10 9.5e-11 *** 224s farmPrice 0.2166 0.0573 3.78 0.00058 *** 224s trend 0.3264 0.0424 7.71 4.8e-09 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 7.582 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 919.812 MSE: 57.488 Root MSE: 7.582 224s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 224s 224s [1] "*** iterated 3SLS with 2 restrictions via R and restrict.regMat (EViews-like)**" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s convergence achieved after 66 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 615 20.5 -0.147 0.48 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 151 8.87 2.98 0.437 0.371 224s supply 20 16 464 29.00 5.38 -0.731 -1.055 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 7.54 12.4 224s supply 12.43 23.2 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 7.54 12.4 224s supply 12.43 23.2 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.939 224s supply 0.939 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 68.3925 9.6792 7.07 3.1e-08 *** 224s price -0.0907 0.1236 -0.73 0.47 224s income 0.4263 0.0385 11.08 5.4e-13 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 2.979 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 150.821 MSE: 8.872 Root MSE: 2.979 224s Multiple R-Squared: 0.437 Adjusted R-Squared: 0.371 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) -27.3424 9.5498 -2.86 0.007 ** 224s price 0.9093 0.1236 7.36 1.3e-08 *** 224s farmPrice 0.3396 0.0498 6.82 6.5e-08 *** 224s trend 0.4263 0.0385 11.08 5.4e-13 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 5.385 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 464.036 MSE: 29.002 Root MSE: 5.385 224s Multiple R-Squared: -0.731 Adjusted R-Squared: -1.055 224s 224s [1] "** iterated W3SLS with 2 restrictions via R and restrict.regMat ***" 224s 224s systemfit results 224s method: iterated 3SLS 224s 224s warning: convergence not achieved after 100 iterations 224s 224s N DF SSR detRCov OLS-R2 McElroy-R2 224s system 40 35 1194 34.7 -1.23 0.688 224s 224s N DF SSR MSE RMSE R2 Adj R2 224s demand 20 17 274 16.1 4.02 -0.024 -0.144 224s supply 20 16 920 57.5 7.58 -2.431 -3.074 224s 224s The covariance matrix of the residuals used for estimation 224s demand supply 224s demand 16.1 29.9 224s supply 29.9 57.5 224s 224s The covariance matrix of the residuals 224s demand supply 224s demand 16.1 29.9 224s supply 29.9 57.5 224s 224s The correlations of the residuals 224s demand supply 224s demand 1.000 0.981 224s supply 0.981 1.000 224s 224s 224s 3SLS estimates for 'demand' (equation 1) 224s Model Formula: consump ~ price + income 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) 43.5261 10.3602 4.20 0.00017 *** 224s price 0.2553 0.1380 1.85 0.07275 . 224s income 0.3264 0.0424 7.71 4.8e-09 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 4.018 on 17 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 17 224s SSR: 274.43 MSE: 16.143 Root MSE: 4.018 224s Multiple R-Squared: -0.024 Adjusted R-Squared: -0.144 224s 224s 224s 3SLS estimates for 'supply' (equation 2) 224s Model Formula: consump ~ price + farmPrice + trend 224s Instruments: ~income + farmPrice + trend 224s 224s Estimate Std. Error t value Pr(>|t|) 224s (Intercept) -49.0142 9.6115 -5.10 1.2e-05 *** 224s price 1.2553 0.1380 9.10 9.5e-11 *** 224s farmPrice 0.2166 0.0573 3.78 0.00058 *** 224s trend 0.3264 0.0424 7.71 4.8e-09 *** 224s --- 224s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 224s 224s Residual standard error: 7.582 on 16 degrees of freedom 224s Number of observations: 20 Degrees of Freedom: 16 224s SSR: 919.811 MSE: 57.488 Root MSE: 7.582 224s Multiple R-Squared: -2.431 Adjusted R-Squared: -3.074 224s 224s > 224s > ## **************** 3SLS with different instruments ************* 224s > fit3slsd <- list() 224s > formulas <- c( "GLS", "IV", "Schmidt", "GMM", "EViews" ) 224s > for( i in seq( along = formulas ) ) { 224s + fit3slsd[[ i ]] <- list() 224s + 224s + print( "***************************************************" ) 224s + print( paste( "3SLS formula:", formulas[ i ] ) ) 224s + print( "************* 3SLS with different instruments **************" ) 224s + fit3slsd[[ i ]]$e1 <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, method3sls = formulas[ i ], useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e1 ) ) 224s + 224s + print( "******* 3SLS with different instruments (EViews-like) **********" ) 224s + fit3slsd[[ i ]]$e1e <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, methodResidCov = "noDfCor", method3sls = formulas[ i ], 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e1e, useDfSys = TRUE ) ) 224s + 224s + print( "**** 3SLS with different instruments and methodResidCov = Theil ***" ) 224s + fit3slsd[[ i ]]$e1c <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, methodResidCov = "Theil", method3sls = formulas[ i ], 224s + x = TRUE, useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e1c, useDfSys = TRUE ) ) 224s + 224s + print( "************* W3SLS with different instruments **************" ) 224s + fit3slsd[[ i ]]$e1w <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, method3sls = formulas[ i ], residCovWeighted = TRUE, 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e1w ) ) 224s + 224s + 224s + print( "******* 3SLS with different instruments and restriction ********" ) 224s + fit3slsd[[ i ]]$e2 <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.matrix = restrm, method3sls = formulas[ i ], 224s + x = TRUE, useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e2 ) ) 224s + 224s + print( "** 3SLS with different instruments and restriction (EViews-like) *" ) 224s + fit3slsd[[ i ]]$e2e <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restrm, 224s + method3sls = formulas[ i ], useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e2e, useDfSys = TRUE ) ) 224s + 224s + print( "** W3SLS with different instruments and restriction (EViews-like) *" ) 224s + fit3slsd[[ i ]]$e2we <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restrm, 224s + method3sls = formulas[ i ], residCovWeighted = TRUE, 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e2we, useDfSys = TRUE ) ) 224s + 224s + 224s + print( "** 3SLS with different instruments and restriction via restrict.regMat *******" ) 224s + fit3slsd[[ i ]]$e3 <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.regMat = tc, method3sls = formulas[ i ], 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e3 ) ) 224s + 224s + print( "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" ) 224s + fit3slsd[[ i ]]$e3e <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, methodResidCov = "noDfCor", restrict.regMat = tc, 224s + method3sls = formulas[ i ], x = TRUE, 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e3e, useDfSys = TRUE ) ) 224s + 224s + print( "** W3SLS with different instr. and restr. via restrict.regMat ****" ) 224s + fit3slsd[[ i ]]$e3w <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.regMat = tc, method3sls = formulas[ i ], 224s + residCovWeighted = TRUE, x = TRUE, 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e3w ) ) 224s + 224s + 224s + print( "****** 3SLS with different instruments and 2 restrictions *********" ) 224s + fit3slsd[[ i ]]$e4 <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.matrix = restr2m, restrict.rhs = restr2q, 224s + method3sls = formulas[ i ], x = TRUE, 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e4 ) ) 224s + 224s + print( "** 3SLS with different instruments and 2 restrictions (EViews-like) *" ) 224s + fit3slsd[[ i ]]$e4e <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, methodResidCov = "noDfCor", restrict.matrix = restr2m, 224s + restrict.rhs = restr2q, method3sls = formulas[ i ], 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e4e, useDfSys = TRUE ) ) 224s + 224s + print( "**** W3SLS with different instruments and 2 restrictions *********" ) 224s + fit3slsd[[ i ]]$e4w <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.matrix = restr2m, restrict.rhs = restr2q, 224s + method3sls = formulas[ i ], residCovWeighted = TRUE, 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e4w ) ) 224s + 224s + 224s + print( " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" ) 224s + fit3slsd[[ i ]]$e5 <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.regMat = tc, restrict.matrix = restr3m, 224s + restrict.rhs = restr3q, method3sls = formulas[ i ], 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e5 ) ) 224s + 224s + print( "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" ) 224s + fit3slsd[[ i ]]$e5e <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.regMat = tc, methodResidCov = "noDfCor", 224s + restrict.matrix = restr3m, restrict.rhs = restr3q, 224s + method3sls = formulas[ i ], x = TRUE, 224s + useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e5e, useDfSys = TRUE ) ) 224s + 224s + print( "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" ) 224s + fit3slsd[[ i ]]$e5we <- systemfit( system, "3SLS", data = Kmenta, 224s + inst = instlist, restrict.regMat = tc, methodResidCov = "noDfCor", 224s + restrict.matrix = restr3m, restrict.rhs = restr3q, method3sls = formulas[ i ], 224s + residCovWeighted = TRUE, useMatrix = useMatrix ) 224s + print( summary( fit3slsd[[ i ]]$e5we, useDfSys = TRUE ) ) 224s + } 225s [1] "***************************************************" 225s [1] "3SLS formula: GLS" 225s [1] "************* 3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 170 13.4 0.683 0.52 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 102.4 6.40 2.53 0.618 0.546 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.47 225s supply 3.47 6.40 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.688 225s supply 0.688 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 46.9385 11.5390 4.07 0.0009 *** 225s price 0.2744 0.0897 3.06 0.0075 ** 225s farmPrice 0.2521 0.0470 5.36 6.4e-05 *** 225s trend 0.2048 0.0781 2.62 0.0185 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.53 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.443 MSE: 6.403 Root MSE: 2.53 225s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 225s 225s [1] "******* 3SLS with different instruments (EViews-like) **********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 170 9 0.684 0.511 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 102.2 6.39 2.53 0.619 0.547 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.37 3.16 225s supply 3.16 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.37 2.87 225s supply 2.87 5.11 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.691 225s supply 0.691 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 225s price -0.412 0.134 -3.08 0.0041 ** 225s income 0.362 0.052 6.95 6.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 47.0160 10.3208 4.56 6.8e-05 *** 225s price 0.2734 0.0802 3.41 0.0017 ** 225s farmPrice 0.2522 0.0421 6.00 9.8e-07 *** 225s trend 0.2062 0.0699 2.95 0.0058 ** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.527 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.203 MSE: 6.388 Root MSE: 2.527 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 225s 225s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 170 12.7 0.683 0.502 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 102.7 6.42 2.53 0.617 0.545 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.96 225s supply 3.96 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.57 225s supply 3.57 6.42 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.685 225s supply 0.685 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 225s price -0.4116 0.1448 -2.84 0.0076 ** 225s income 0.3617 0.0564 6.41 2.9e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 46.8512 11.5060 4.07 0.00027 *** 225s price 0.2756 0.0889 3.10 0.00395 ** 225s farmPrice 0.2520 0.0470 5.36 6.4e-06 *** 225s trend 0.2032 0.0765 2.66 0.01204 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.534 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.718 MSE: 6.42 Root MSE: 2.534 225s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.545 225s 225s [1] "************* W3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 170 13.4 0.683 0.52 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 102.4 6.40 2.53 0.618 0.546 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.47 225s supply 3.47 6.40 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.688 225s supply 0.688 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 46.9385 11.5390 4.07 0.0009 *** 225s price 0.2744 0.0897 3.06 0.0075 ** 225s farmPrice 0.2521 0.0470 5.36 6.4e-05 *** 225s trend 0.2048 0.0781 2.62 0.0185 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.53 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.443 MSE: 6.403 Root MSE: 2.53 225s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 225s 225s [1] "******* 3SLS with different instruments and restriction ********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 201 2.72 0.626 0.685 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 72.3 4.25 2.06 0.730 0.699 225s supply 20 16 128.3 8.02 2.83 0.521 0.432 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.25 5.60 225s supply 5.60 8.02 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 88.9456 6.3475 14.01 1.1e-15 *** 225s price -0.1778 0.0812 -2.19 0.036 * 225s income 0.3049 0.0474 6.43 2.4e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.062 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 72.262 MSE: 4.251 Root MSE: 2.062 225s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.699 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 40.2918 11.2022 3.60 0.001 ** 225s price 0.3613 0.0785 4.60 5.6e-05 *** 225s farmPrice 0.2201 0.0453 4.86 2.6e-05 *** 225s trend 0.3049 0.0474 6.43 2.4e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.832 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 128.304 MSE: 8.019 Root MSE: 2.832 225s Multiple R-Squared: 0.521 Adjusted R-Squared: 0.432 225s 225s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 200 1.75 0.627 0.651 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 72.7 4.28 2.07 0.729 0.697 225s supply 20 16 127.0 7.94 2.82 0.526 0.437 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.64 4.62 225s supply 4.62 6.35 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.961 225s supply 0.961 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 88.7634 5.8428 15.19 < 2e-16 *** 225s price -0.1738 0.0737 -2.36 0.024 * 225s income 0.3027 0.0432 7.00 4.5e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.068 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 72.717 MSE: 4.277 Root MSE: 2.068 225s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 40.8177 10.0564 4.06 0.00027 *** 225s price 0.3569 0.0705 5.06 1.4e-05 *** 225s farmPrice 0.2195 0.0403 5.45 4.4e-06 *** 225s trend 0.3027 0.0432 7.00 4.5e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.818 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 127.044 MSE: 7.94 Root MSE: 2.818 225s Multiple R-Squared: 0.526 Adjusted R-Squared: 0.437 225s 225s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 199 1.77 0.629 0.65 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 72.4 4.26 2.06 0.730 0.698 225s supply 20 16 126.7 7.92 2.81 0.527 0.439 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.24 3.60 225s supply 3.60 5.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.62 4.60 225s supply 4.60 6.34 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.961 225s supply 0.961 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 88.9298 5.9083 15.05 < 2e-16 *** 225s price -0.1760 0.0746 -2.36 0.024 * 225s income 0.3032 0.0434 6.99 4.6e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.064 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 72.435 MSE: 4.261 Root MSE: 2.064 225s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.698 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 40.8325 10.1094 4.04 0.00029 *** 225s price 0.3562 0.0711 5.01 1.7e-05 *** 225s farmPrice 0.2200 0.0405 5.43 4.8e-06 *** 225s trend 0.3032 0.0434 6.99 4.6e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.814 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 126.74 MSE: 7.921 Root MSE: 2.814 225s Multiple R-Squared: 0.527 Adjusted R-Squared: 0.439 225s 225s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 201 2.72 0.626 0.685 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 72.3 4.25 2.06 0.730 0.699 225s supply 20 16 128.3 8.02 2.83 0.521 0.432 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.25 5.60 225s supply 5.60 8.02 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 88.9456 6.3475 14.01 1.1e-15 *** 225s price -0.1778 0.0812 -2.19 0.036 * 225s income 0.3049 0.0474 6.43 2.4e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.062 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 72.262 MSE: 4.251 Root MSE: 2.062 225s Multiple R-Squared: 0.73 Adjusted R-Squared: 0.699 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 40.2918 11.2022 3.60 0.001 ** 225s price 0.3613 0.0785 4.60 5.6e-05 *** 225s farmPrice 0.2201 0.0453 4.86 2.6e-05 *** 225s trend 0.3049 0.0474 6.43 2.4e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.832 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 128.304 MSE: 8.019 Root MSE: 2.832 225s Multiple R-Squared: 0.521 Adjusted R-Squared: 0.432 225s 225s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 200 1.75 0.627 0.651 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 72.7 4.28 2.07 0.729 0.697 225s supply 20 16 127.0 7.94 2.82 0.526 0.437 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.64 4.62 225s supply 4.62 6.35 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.961 225s supply 0.961 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 88.7634 5.8428 15.19 < 2e-16 *** 225s price -0.1738 0.0737 -2.36 0.024 * 225s income 0.3027 0.0432 7.00 4.5e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.068 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 72.717 MSE: 4.277 Root MSE: 2.068 225s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 40.8177 10.0564 4.06 0.00027 *** 225s price 0.3569 0.0705 5.06 1.4e-05 *** 225s farmPrice 0.2195 0.0403 5.45 4.4e-06 *** 225s trend 0.3027 0.0432 7.00 4.5e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.818 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 127.044 MSE: 7.94 Root MSE: 2.818 225s Multiple R-Squared: 0.526 Adjusted R-Squared: 0.437 225s 225s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 200 2.75 0.627 0.684 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 71.9 4.23 2.06 0.732 0.700 225s supply 20 16 127.9 8.00 2.83 0.523 0.433 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.81 4.36 225s supply 4.36 6.34 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.23 5.58 225s supply 5.58 7.99 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.958 225s supply 0.958 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 89.1391 6.4318 13.86 1.6e-15 *** 225s price -0.1803 0.0823 -2.19 0.035 * 225s income 0.3055 0.0476 6.42 2.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.057 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 71.945 MSE: 4.232 Root MSE: 2.057 225s Multiple R-Squared: 0.732 Adjusted R-Squared: 0.7 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 40.3187 11.2699 3.58 0.0011 ** 225s price 0.3604 0.0792 4.55 6.5e-05 *** 225s farmPrice 0.2207 0.0456 4.84 2.8e-05 *** 225s trend 0.3055 0.0476 6.42 2.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.828 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 127.918 MSE: 7.995 Root MSE: 2.828 225s Multiple R-Squared: 0.523 Adjusted R-Squared: 0.433 225s 225s [1] "****** 3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 211 2.1 0.606 0.71 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 77.9 4.58 2.14 0.709 0.675 225s supply 20 16 133.2 8.32 2.88 0.503 0.410 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.58 6.01 225s supply 6.01 8.32 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.972 225s supply 0.972 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 86.4443 5.3770 16.08 <2e-16 *** 225s price -0.1371 0.0504 -2.72 0.01 * 225s income 0.2888 0.0182 15.89 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.141 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 77.945 MSE: 4.585 Root MSE: 2.141 225s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 41.8618 5.4316 7.71 4.8e-09 *** 225s price 0.3629 0.0504 7.20 2.1e-08 *** 225s farmPrice 0.2040 0.0205 9.96 9.4e-12 *** 225s trend 0.2888 0.0182 15.89 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.885 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 133.177 MSE: 8.324 Root MSE: 2.885 225s Multiple R-Squared: 0.503 Adjusted R-Squared: 0.41 225s 225s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 210 1.42 0.609 0.668 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 77.9 4.58 2.14 0.709 0.675 225s supply 20 16 132.0 8.25 2.87 0.508 0.415 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.90 4.93 225s supply 4.93 6.60 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.972 225s supply 0.972 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 86.3521 4.9704 17.4 <2e-16 *** 225s price -0.1376 0.0458 -3.0 0.0049 ** 225s income 0.2902 0.0168 17.3 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.141 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 77.912 MSE: 4.583 Root MSE: 2.141 225s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 41.6089 4.9950 8.33 8.0e-10 *** 225s price 0.3624 0.0458 7.91 2.6e-09 *** 225s farmPrice 0.2069 0.0184 11.27 3.4e-13 *** 225s trend 0.2902 0.0168 17.27 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.872 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 131.997 MSE: 8.25 Root MSE: 2.872 225s Multiple R-Squared: 0.508 Adjusted R-Squared: 0.415 225s 225s [1] "**** W3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 214 2.1 0.601 0.713 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 78.9 4.64 2.15 0.706 0.671 225s supply 20 16 135.2 8.45 2.91 0.496 0.401 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.75 4.46 225s supply 4.46 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.64 6.09 225s supply 6.09 8.45 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.973 225s supply 0.973 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 85.9516 5.1136 16.81 <2e-16 *** 225s price -0.1318 0.0479 -2.75 0.0093 ** 225s income 0.2884 0.0171 16.86 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.154 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 78.853 MSE: 4.638 Root MSE: 2.154 225s Multiple R-Squared: 0.706 Adjusted R-Squared: 0.671 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 41.4498 5.1591 8.03 1.9e-09 *** 225s price 0.3682 0.0479 7.69 5.0e-09 *** 225s farmPrice 0.2028 0.0193 10.50 2.3e-12 *** 225s trend 0.2884 0.0171 16.86 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.907 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 135.215 MSE: 8.451 Root MSE: 2.907 225s Multiple R-Squared: 0.496 Adjusted R-Squared: 0.401 225s 225s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 211 2.1 0.606 0.71 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 77.9 4.58 2.14 0.709 0.675 225s supply 20 16 133.2 8.32 2.88 0.503 0.410 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.58 6.01 225s supply 6.01 8.32 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.972 225s supply 0.972 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 86.4443 5.3770 16.08 <2e-16 *** 225s price -0.1371 0.0504 -2.72 0.01 * 225s income 0.2888 0.0182 15.89 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.141 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 77.945 MSE: 4.585 Root MSE: 2.141 225s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 41.8618 5.4316 7.71 4.8e-09 *** 225s price 0.3629 0.0504 7.20 2.1e-08 *** 225s farmPrice 0.2040 0.0205 9.96 9.4e-12 *** 225s trend 0.2888 0.0182 15.89 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.885 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 133.177 MSE: 8.324 Root MSE: 2.885 225s Multiple R-Squared: 0.503 Adjusted R-Squared: 0.41 225s 225s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 210 1.42 0.609 0.668 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 77.9 4.58 2.14 0.709 0.675 225s supply 20 16 132.0 8.25 2.87 0.508 0.415 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.90 4.93 225s supply 4.93 6.60 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.972 225s supply 0.972 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 86.3521 4.9704 17.4 <2e-16 *** 225s price -0.1376 0.0458 -3.0 0.0049 ** 225s income 0.2902 0.0168 17.3 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.141 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 77.912 MSE: 4.583 Root MSE: 2.141 225s Multiple R-Squared: 0.709 Adjusted R-Squared: 0.675 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 41.6089 4.9950 8.33 8.0e-10 *** 225s price 0.3624 0.0458 7.91 2.6e-09 *** 225s farmPrice 0.2069 0.0184 11.27 3.4e-13 *** 225s trend 0.2902 0.0168 17.27 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.872 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 131.997 MSE: 8.25 Root MSE: 2.872 225s Multiple R-Squared: 0.508 Adjusted R-Squared: 0.415 225s 225s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 212 1.42 0.604 0.671 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 78.7 4.63 2.15 0.706 0.672 225s supply 20 16 133.7 8.36 2.89 0.501 0.408 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.19 3.68 225s supply 3.68 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.94 4.99 225s supply 4.99 6.69 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.973 225s supply 0.973 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 85.9108 4.7598 18.05 <2e-16 *** 225s price -0.1329 0.0438 -3.03 0.0045 ** 225s income 0.2900 0.0159 18.18 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.152 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 78.713 MSE: 4.63 Root MSE: 2.152 225s Multiple R-Squared: 0.706 Adjusted R-Squared: 0.672 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 41.2362 4.7784 8.63 3.5e-10 *** 225s price 0.3671 0.0438 8.38 7.0e-10 *** 225s farmPrice 0.2060 0.0174 11.81 9.1e-14 *** 225s trend 0.2900 0.0159 18.18 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.891 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 133.715 MSE: 8.357 Root MSE: 2.891 225s Multiple R-Squared: 0.501 Adjusted R-Squared: 0.408 225s 225s [1] "***************************************************" 225s [1] "3SLS formula: IV" 225s [1] "************* 3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 174 2.12 0.675 0.659 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 106.6 6.66 2.58 0.602 0.528 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 4.93 225s supply 4.93 6.66 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.2953 11.7078 4.89 0.00016 *** 225s price 0.1373 0.0979 1.40 0.17978 225s farmPrice 0.2660 0.0483 5.51 4.8e-05 *** 225s trend 0.3970 0.0672 5.91 2.2e-05 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.582 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 225s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 225s 225s [1] "******* 3SLS with different instruments (EViews-like) **********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 173 1.51 0.677 0.612 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 105.7 6.61 2.57 0.606 0.532 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.37 3.16 225s supply 3.16 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.37 4.04 225s supply 4.04 5.29 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.957 225s supply 0.957 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 225s price -0.412 0.134 -3.08 0.0041 ** 225s income 0.362 0.052 6.95 6.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.0636 10.4717 5.45 4.9e-06 *** 225s price 0.1403 0.0875 1.60 0.12 225s farmPrice 0.2657 0.0432 6.15 6.2e-07 *** 225s trend 0.3927 0.0601 6.53 2.0e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.571 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 105.735 MSE: 6.608 Root MSE: 2.571 225s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 225s 225s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 175 0.321 0.673 0.655 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 107.7 6.73 2.59 0.598 0.523 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.96 225s supply 3.96 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 5.14 225s supply 5.14 6.73 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.962 225s supply 0.962 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 225s price -0.4116 0.1448 -2.84 0.0076 ** 225s income 0.3617 0.0564 6.41 2.9e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.5567 11.6867 4.92 2.3e-05 *** 225s price 0.1338 0.0977 1.37 0.18 225s farmPrice 0.2664 0.0484 5.51 4.1e-06 *** 225s trend 0.4018 0.0644 6.24 4.8e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.594 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 107.679 MSE: 6.73 Root MSE: 2.594 225s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 225s 225s [1] "************* W3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 174 2.12 0.675 0.659 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 106.6 6.66 2.58 0.602 0.528 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 4.93 225s supply 4.93 6.66 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.2953 11.7078 4.89 0.00016 *** 225s price 0.1373 0.0979 1.40 0.17978 225s farmPrice 0.2660 0.0483 5.51 4.8e-05 *** 225s trend 0.3970 0.0672 5.91 2.2e-05 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.582 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 225s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 225s 225s [1] "******* 3SLS with different instruments and restriction ********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 397 11.4 0.26 -0.128 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 175 10.3 3.20 0.349 0.273 225s supply 20 16 223 13.9 3.73 0.170 0.014 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 10.3 11.5 225s supply 11.5 13.9 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 137.2061 12.4591 11.01 9.3e-13 *** 225s price -0.8101 0.1734 -4.67 4.5e-05 *** 225s income 0.4585 0.0659 6.96 5.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.204 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 174.513 MSE: 10.265 Root MSE: 3.204 225s Multiple R-Squared: 0.349 Adjusted R-Squared: 0.273 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 81.1339 9.1968 8.82 2.6e-10 *** 225s price -0.1765 0.0892 -1.98 0.056 . 225s farmPrice 0.3374 0.0591 5.71 2.1e-06 *** 225s trend 0.4585 0.0659 6.96 5.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.73 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 222.562 MSE: 13.91 Root MSE: 3.73 225s Multiple R-Squared: 0.17 Adjusted R-Squared: 0.014 225s 225s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 365 7.14 0.319 -0.166 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 163 9.57 3.09 0.393 0.322 225s supply 20 16 202 12.65 3.56 0.245 0.104 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.13 8.67 225s supply 8.67 10.12 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.956 225s supply 0.956 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 134.9751 11.3086 11.94 1.0e-13 *** 225s price -0.7834 0.1565 -5.01 1.7e-05 *** 225s income 0.4539 0.0598 7.60 8.0e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.093 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 162.635 MSE: 9.567 Root MSE: 3.093 225s Multiple R-Squared: 0.393 Adjusted R-Squared: 0.322 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 78.1824 8.5029 9.19 9.6e-11 *** 225s price -0.1415 0.0807 -1.75 0.089 . 225s farmPrice 0.3322 0.0524 6.34 3.1e-07 *** 225s trend 0.4539 0.0598 7.60 8.0e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.557 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 202.39 MSE: 12.649 Root MSE: 3.557 225s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.104 225s 225s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 351 6.72 0.345 -0.118 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 156 9.18 3.03 0.418 0.349 225s supply 20 16 195 12.20 3.49 0.272 0.135 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.24 3.60 225s supply 3.60 5.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 7.81 8.34 225s supply 8.34 9.76 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.955 225s supply 0.955 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 133.7954 11.2810 11.86 1.2e-13 *** 225s price -0.7678 0.1558 -4.93 2.1e-05 *** 225s income 0.4501 0.0595 7.56 8.8e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.031 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 156.133 MSE: 9.184 Root MSE: 3.031 225s Multiple R-Squared: 0.418 Adjusted R-Squared: 0.349 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 77.4097 8.6219 8.98 1.7e-10 *** 225s price -0.1304 0.0814 -1.60 0.12 225s farmPrice 0.3292 0.0523 6.29 3.6e-07 *** 225s trend 0.4501 0.0595 7.56 8.8e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.493 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 195.256 MSE: 12.204 Root MSE: 3.493 225s Multiple R-Squared: 0.272 Adjusted R-Squared: 0.135 225s 225s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 397 11.4 0.26 -0.128 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 175 10.3 3.20 0.349 0.273 225s supply 20 16 223 13.9 3.73 0.170 0.014 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 10.3 11.5 225s supply 11.5 13.9 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 137.2061 12.4591 11.01 9.3e-13 *** 225s price -0.8101 0.1734 -4.67 4.5e-05 *** 225s income 0.4585 0.0659 6.96 5.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.204 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 174.513 MSE: 10.265 Root MSE: 3.204 225s Multiple R-Squared: 0.349 Adjusted R-Squared: 0.273 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 81.1339 9.1968 8.82 2.6e-10 *** 225s price -0.1765 0.0892 -1.98 0.056 . 225s farmPrice 0.3374 0.0591 5.71 2.1e-06 *** 225s trend 0.4585 0.0659 6.96 5.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.73 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 222.562 MSE: 13.91 Root MSE: 3.73 225s Multiple R-Squared: 0.17 Adjusted R-Squared: 0.014 225s 225s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 365 7.14 0.319 -0.166 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 163 9.57 3.09 0.393 0.322 225s supply 20 16 202 12.65 3.56 0.245 0.104 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.13 8.67 225s supply 8.67 10.12 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.956 225s supply 0.956 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 134.9751 11.3086 11.94 1.0e-13 *** 225s price -0.7834 0.1565 -5.01 1.7e-05 *** 225s income 0.4539 0.0598 7.60 8.0e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.093 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 162.635 MSE: 9.567 Root MSE: 3.093 225s Multiple R-Squared: 0.393 Adjusted R-Squared: 0.322 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 78.1824 8.5029 9.19 9.6e-11 *** 225s price -0.1415 0.0807 -1.75 0.089 . 225s farmPrice 0.3322 0.0524 6.34 3.1e-07 *** 225s trend 0.4539 0.0598 7.60 8.0e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.557 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 202.39 MSE: 12.649 Root MSE: 3.557 225s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.104 225s 225s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 378 10.5 0.295 -0.071 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 166 9.74 3.12 0.382 0.309 225s supply 20 16 212 13.26 3.64 0.209 0.060 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.81 4.36 225s supply 4.36 6.34 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 9.75 10.9 225s supply 10.89 13.3 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.958 225s supply 0.958 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 135.6740 12.4146 10.93 1.1e-12 *** 225s price -0.7901 0.1723 -4.59 5.9e-05 *** 225s income 0.4537 0.0655 6.92 5.6e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.122 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 165.668 MSE: 9.745 Root MSE: 3.122 225s Multiple R-Squared: 0.382 Adjusted R-Squared: 0.309 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 80.0613 9.3724 8.54 5.6e-10 *** 225s price -0.1614 0.0902 -1.79 0.082 . 225s farmPrice 0.3335 0.0590 5.65 2.4e-06 *** 225s trend 0.4537 0.0655 6.92 5.6e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.642 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 212.177 MSE: 13.261 Root MSE: 3.642 225s Multiple R-Squared: 0.209 Adjusted R-Squared: 0.06 225s 225s [1] "****** 3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 362 6.33 0.325 0.259 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 149 8.79 2.96 0.443 0.377 225s supply 20 16 213 13.30 3.65 0.206 0.058 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.79 10.5 225s supply 10.51 13.3 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.973 225s supply 0.973 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 135.467 10.955 12.37 2.5e-14 *** 225s price -0.727 0.116 -6.27 3.4e-07 *** 225s income 0.391 0.018 21.77 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.964 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 149.387 MSE: 8.787 Root MSE: 2.964 225s Multiple R-Squared: 0.443 Adjusted R-Squared: 0.377 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 92.2897 11.0352 8.36 7.3e-10 *** 225s price -0.2272 0.1160 -1.96 0.058 . 225s farmPrice 0.2817 0.0209 13.47 2.0e-15 *** 225s trend 0.3913 0.0180 21.77 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.647 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 212.786 MSE: 13.299 Root MSE: 3.647 225s Multiple R-Squared: 0.206 Adjusted R-Squared: 0.058 225s 225s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 306 3.37 0.43 0.248 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 127 7.5 2.74 0.525 0.469 225s supply 20 16 178 11.2 3.34 0.334 0.210 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 6.37 7.31 225s supply 7.31 8.92 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.97 225s supply 0.97 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 130.7296 9.6847 13.50 2.0e-15 *** 225s price -0.6671 0.1009 -6.61 1.2e-07 *** 225s income 0.3782 0.0159 23.74 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.738 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 127.413 MSE: 7.495 Root MSE: 2.738 225s Multiple R-Squared: 0.525 Adjusted R-Squared: 0.469 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 87.4510 9.7547 8.96 1.4e-10 *** 225s price -0.1671 0.1009 -1.66 0.11 225s farmPrice 0.2710 0.0183 14.81 < 2e-16 *** 225s trend 0.3782 0.0159 23.74 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.34 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 178.456 MSE: 11.154 Root MSE: 3.34 225s Multiple R-Squared: 0.334 Adjusted R-Squared: 0.21 225s 225s [1] "**** W3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 467 8.98 0.128 0.113 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 193 11.3 3.37 0.282 0.197 225s supply 20 16 275 17.2 4.14 -0.025 -0.217 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.75 4.46 225s supply 4.46 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 11.3 13.6 225s supply 13.6 17.2 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.977 225s supply 0.977 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 143.4678 11.2566 12.75 1.0e-14 *** 225s price -0.8203 0.1194 -6.87 5.6e-08 *** 225s income 0.4047 0.0168 24.13 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.366 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 192.561 MSE: 11.327 Root MSE: 3.366 225s Multiple R-Squared: 0.282 Adjusted R-Squared: 0.197 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 100.3734 11.3093 8.88 1.7e-10 *** 225s price -0.3203 0.1194 -2.68 0.011 * 225s farmPrice 0.2930 0.0198 14.79 < 2e-16 *** 225s trend 0.4047 0.0168 24.13 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 4.144 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 274.775 MSE: 17.173 Root MSE: 4.144 225s Multiple R-Squared: -0.025 Adjusted R-Squared: -0.217 225s 225s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 362 6.33 0.325 0.259 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 149 8.79 2.96 0.443 0.377 225s supply 20 16 213 13.30 3.65 0.206 0.058 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.79 10.5 225s supply 10.51 13.3 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.973 225s supply 0.973 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 135.467 10.955 12.37 2.5e-14 *** 225s price -0.727 0.116 -6.27 3.4e-07 *** 225s income 0.391 0.018 21.77 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.964 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 149.387 MSE: 8.787 Root MSE: 2.964 225s Multiple R-Squared: 0.443 Adjusted R-Squared: 0.377 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 92.2897 11.0352 8.36 7.3e-10 *** 225s price -0.2272 0.1160 -1.96 0.058 . 225s farmPrice 0.2817 0.0209 13.47 2.0e-15 *** 225s trend 0.3913 0.0180 21.77 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.647 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 212.786 MSE: 13.299 Root MSE: 3.647 225s Multiple R-Squared: 0.206 Adjusted R-Squared: 0.058 225s 225s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 306 3.37 0.43 0.248 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 127 7.5 2.74 0.525 0.469 225s supply 20 16 178 11.2 3.34 0.334 0.210 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 6.37 7.31 225s supply 7.31 8.92 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.97 225s supply 0.97 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 130.7296 9.6847 13.50 2.0e-15 *** 225s price -0.6671 0.1009 -6.61 1.2e-07 *** 225s income 0.3782 0.0159 23.74 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.738 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 127.413 MSE: 7.495 Root MSE: 2.738 225s Multiple R-Squared: 0.525 Adjusted R-Squared: 0.469 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 87.4510 9.7547 8.96 1.4e-10 *** 225s price -0.1671 0.1009 -1.66 0.11 225s farmPrice 0.2710 0.0183 14.81 < 2e-16 *** 225s trend 0.3782 0.0159 23.74 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.34 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 178.456 MSE: 11.154 Root MSE: 3.34 225s Multiple R-Squared: 0.334 Adjusted R-Squared: 0.21 225s 225s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 365 4.27 0.319 0.127 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 153 8.97 3.00 0.431 0.364 225s supply 20 16 213 13.29 3.65 0.207 0.058 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.19 3.68 225s supply 3.68 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 7.63 8.77 225s supply 8.77 10.64 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.973 225s supply 0.973 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 136.2729 9.8523 13.83 8.9e-16 *** 225s price -0.7306 0.1027 -7.11 2.7e-08 *** 225s income 0.3865 0.0149 25.95 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.996 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 152.579 MSE: 8.975 Root MSE: 2.996 225s Multiple R-Squared: 0.431 Adjusted R-Squared: 0.364 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.0701 9.9030 9.40 4.2e-11 *** 225s price -0.2306 0.1027 -2.24 0.031 * 225s farmPrice 0.2777 0.0174 15.99 < 2e-16 *** 225s trend 0.3865 0.0149 25.95 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.646 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 212.723 MSE: 13.295 Root MSE: 3.646 225s Multiple R-Squared: 0.207 Adjusted R-Squared: 0.058 225s 225s [1] "***************************************************" 225s [1] "3SLS formula: Schmidt" 225s [1] "************* 3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 9.25 0.694 0.512 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 225s price 0.2401 0.0999 2.40 0.0288 * 225s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 225s trend 0.2529 0.0997 2.54 0.0219 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "******* 3SLS with different instruments (EViews-like) **********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 6.29 0.694 0.5 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.37 3.16 225s supply 3.16 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.37 3.16 225s supply 3.16 4.83 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 225s price -0.412 0.134 -3.08 0.0041 ** 225s income 0.362 0.052 6.95 6.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 225s price 0.2401 0.0894 2.69 0.0112 * 225s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 225s trend 0.2529 0.0891 2.84 0.0077 ** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 8.24 0.694 0.481 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.96 225s supply 3.96 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.96 225s supply 3.96 6.04 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 225s price -0.4116 0.1448 -2.84 0.0076 ** 225s income 0.3617 0.0564 6.41 2.9e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 225s price 0.2401 0.0999 2.40 0.02208 * 225s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 225s trend 0.2529 0.0997 2.54 0.01605 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "************* W3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 9.25 0.694 0.512 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 225s price 0.2401 0.0999 2.40 0.0288 * 225s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 225s trend 0.2529 0.0997 2.54 0.0219 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "******* 3SLS with different instruments and restriction ********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 175 2.68 0.673 0.665 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65 3.82 1.96 0.758 0.729 225s supply 20 16 110 6.90 2.63 0.588 0.511 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.82 4.87 225s supply 4.87 6.90 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.948 225s supply 0.948 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 95.0869 9.9882 9.52 4.0e-11 *** 225s price -0.2583 0.1296 -1.99 0.054 . 225s income 0.3244 0.0534 6.08 6.8e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.955 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.961 MSE: 3.821 Root MSE: 1.955 225s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.729 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 45.4891 12.9647 3.51 0.0013 ** 225s price 0.2929 0.1164 2.52 0.0167 * 225s farmPrice 0.2350 0.0490 4.80 3.1e-05 *** 225s trend 0.3244 0.0534 6.08 6.8e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.627 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.382 MSE: 6.899 Root MSE: 2.627 225s Multiple R-Squared: 0.588 Adjusted R-Squared: 0.511 225s 225s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 175 1.75 0.673 0.636 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65.2 3.83 1.96 0.757 0.728 225s supply 20 16 110.0 6.88 2.62 0.590 0.513 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.26 4.02 225s supply 4.02 5.50 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.95 225s supply 0.95 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 94.845 9.149 10.37 4.6e-12 *** 225s price -0.254 0.119 -2.14 0.039 * 225s income 0.323 0.049 6.58 1.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.958 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 65.171 MSE: 3.834 Root MSE: 1.958 225s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.728 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 45.7348 11.5558 3.96 0.00037 *** 225s price 0.2913 0.1036 2.81 0.00814 ** 225s farmPrice 0.2343 0.0438 5.35 6.0e-06 *** 225s trend 0.3226 0.0490 6.58 1.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.622 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.035 MSE: 6.877 Root MSE: 2.622 225s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 225s 225s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 175 1.76 0.674 0.635 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65.1 3.83 1.96 0.757 0.729 225s supply 20 16 109.9 6.87 2.62 0.590 0.513 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.24 3.60 225s supply 3.60 5.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.25 4.02 225s supply 4.02 5.50 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.949 225s supply 0.949 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 94.9533 9.1511 10.38 4.5e-12 *** 225s price -0.2555 0.1186 -2.15 0.038 * 225s income 0.3229 0.0491 6.58 1.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.957 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 65.09 MSE: 3.829 Root MSE: 1.957 225s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.729 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 45.7433 11.6043 3.94 0.00038 *** 225s price 0.2908 0.1039 2.80 0.00839 ** 225s farmPrice 0.2347 0.0440 5.34 6.2e-06 *** 225s trend 0.3229 0.0491 6.58 1.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.621 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 109.922 MSE: 6.87 Root MSE: 2.621 225s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 225s 225s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 175 2.68 0.673 0.665 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65 3.82 1.96 0.758 0.729 225s supply 20 16 110 6.90 2.63 0.588 0.511 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.82 4.87 225s supply 4.87 6.90 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.948 225s supply 0.948 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 95.0869 9.9882 9.52 4.0e-11 *** 225s price -0.2583 0.1296 -1.99 0.054 . 225s income 0.3244 0.0534 6.08 6.8e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.955 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.961 MSE: 3.821 Root MSE: 1.955 225s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.729 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 45.4891 12.9647 3.51 0.0013 ** 225s price 0.2929 0.1164 2.52 0.0167 * 225s farmPrice 0.2350 0.0490 4.80 3.1e-05 *** 225s trend 0.3244 0.0534 6.08 6.8e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.627 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.382 MSE: 6.899 Root MSE: 2.627 225s Multiple R-Squared: 0.588 Adjusted R-Squared: 0.511 225s 225s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 175 1.75 0.673 0.636 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65.2 3.83 1.96 0.757 0.728 225s supply 20 16 110.0 6.88 2.62 0.590 0.513 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.26 4.02 225s supply 4.02 5.50 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.95 225s supply 0.95 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 94.845 9.149 10.37 4.6e-12 *** 225s price -0.254 0.119 -2.14 0.039 * 225s income 0.323 0.049 6.58 1.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.958 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 65.171 MSE: 3.834 Root MSE: 1.958 225s Multiple R-Squared: 0.757 Adjusted R-Squared: 0.728 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 45.7348 11.5558 3.96 0.00037 *** 225s price 0.2913 0.1036 2.81 0.00814 ** 225s farmPrice 0.2343 0.0438 5.35 6.0e-06 *** 225s trend 0.3226 0.0490 6.58 1.5e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.622 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.035 MSE: 6.877 Root MSE: 2.622 225s Multiple R-Squared: 0.59 Adjusted R-Squared: 0.513 225s 225s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 175 2.7 0.673 0.664 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 64.9 3.82 1.95 0.758 0.730 225s supply 20 16 110.2 6.89 2.62 0.589 0.512 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.81 4.36 225s supply 4.36 6.34 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.82 4.86 225s supply 4.86 6.89 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.947 225s supply 0.947 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 95.2108 9.9899 9.53 3.9e-11 *** 225s price -0.2599 0.1296 -2.00 0.053 . 225s income 0.3248 0.0535 6.08 6.9e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.954 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.876 MSE: 3.816 Root MSE: 1.954 225s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 45.5042 13.0242 3.49 0.0013 ** 225s price 0.2923 0.1167 2.50 0.0172 * 225s farmPrice 0.2354 0.0492 4.78 3.3e-05 *** 225s trend 0.3248 0.0535 6.08 6.9e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.625 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.241 MSE: 6.89 Root MSE: 2.625 225s Multiple R-Squared: 0.589 Adjusted R-Squared: 0.512 225s 225s [1] "****** 3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 178 1.92 0.667 0.696 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.5 3.97 1.99 0.748 0.719 225s supply 20 16 110.9 6.93 2.63 0.586 0.509 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 5.06 225s supply 5.06 6.93 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.964 225s supply 0.964 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.3937 10.2477 9.11 9.1e-11 *** 225s price -0.2208 0.1165 -1.90 0.066 . 225s income 0.3033 0.0257 11.78 9.9e-14 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.993 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.513 MSE: 3.971 Root MSE: 1.993 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.0104 10.4895 4.67 4.3e-05 *** 225s price 0.2792 0.1165 2.40 0.022 * 225s farmPrice 0.2150 0.0247 8.70 2.8e-10 *** 225s trend 0.3033 0.0257 11.78 9.9e-14 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.633 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.934 MSE: 6.933 Root MSE: 2.633 225s Multiple R-Squared: 0.586 Adjusted R-Squared: 0.509 225s 225s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 178 1.3 0.668 0.659 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.6 3.98 1.99 0.748 0.718 225s supply 20 16 110.7 6.92 2.63 0.587 0.510 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.38 4.17 225s supply 4.17 5.53 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.965 225s supply 0.965 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.210 9.365 9.95 9.6e-12 *** 225s price -0.219 0.105 -2.09 0.044 * 225s income 0.304 0.023 13.19 3.8e-15 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.994 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.616 MSE: 3.977 Root MSE: 1.994 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 48.6930 9.6005 5.07 1.3e-05 *** 225s price 0.2806 0.1052 2.67 0.011 * 225s farmPrice 0.2168 0.0216 10.02 8.1e-12 *** 225s trend 0.3038 0.0230 13.19 3.8e-15 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.63 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.672 MSE: 6.917 Root MSE: 2.63 225s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.51 225s 225s [1] "**** W3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 179 1.92 0.666 0.698 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.7 3.98 2.00 0.747 0.718 225s supply 20 16 111.6 6.98 2.64 0.584 0.506 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.75 4.46 225s supply 4.46 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.98 5.09 225s supply 5.09 6.98 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.965 225s supply 0.965 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.180 10.378 8.98 1.3e-10 *** 225s price -0.218 0.118 -1.85 0.073 . 225s income 0.303 0.025 12.11 4.5e-14 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.996 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.719 MSE: 3.983 Root MSE: 1.996 225s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.718 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 48.8549 10.5929 4.61 5.1e-05 *** 225s price 0.2817 0.1182 2.38 0.023 * 225s farmPrice 0.2141 0.0239 8.94 1.5e-10 *** 225s trend 0.3030 0.0250 12.11 4.5e-14 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.641 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 111.614 MSE: 6.976 Root MSE: 2.641 225s Multiple R-Squared: 0.584 Adjusted R-Squared: 0.506 225s 225s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 178 1.92 0.667 0.696 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.5 3.97 1.99 0.748 0.719 225s supply 20 16 110.9 6.93 2.63 0.586 0.509 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 5.06 225s supply 5.06 6.93 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.964 225s supply 0.964 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.3937 10.2477 9.11 9.1e-11 *** 225s price -0.2208 0.1165 -1.90 0.066 . 225s income 0.3033 0.0257 11.78 9.9e-14 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.993 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.513 MSE: 3.971 Root MSE: 1.993 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.0104 10.4895 4.67 4.3e-05 *** 225s price 0.2792 0.1165 2.40 0.022 * 225s farmPrice 0.2150 0.0247 8.70 2.8e-10 *** 225s trend 0.3033 0.0257 11.78 9.9e-14 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.633 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.934 MSE: 6.933 Root MSE: 2.633 225s Multiple R-Squared: 0.586 Adjusted R-Squared: 0.509 225s 225s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 178 1.3 0.668 0.659 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.6 3.98 1.99 0.748 0.718 225s supply 20 16 110.7 6.92 2.63 0.587 0.510 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.38 4.17 225s supply 4.17 5.53 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.965 225s supply 0.965 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.210 9.365 9.95 9.6e-12 *** 225s price -0.219 0.105 -2.09 0.044 * 225s income 0.304 0.023 13.19 3.8e-15 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.994 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.616 MSE: 3.977 Root MSE: 1.994 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.718 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 48.6930 9.6005 5.07 1.3e-05 *** 225s price 0.2806 0.1052 2.67 0.011 * 225s farmPrice 0.2168 0.0216 10.02 8.1e-12 *** 225s trend 0.3038 0.0230 13.19 3.8e-15 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.63 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 110.672 MSE: 6.917 Root MSE: 2.63 225s Multiple R-Squared: 0.587 Adjusted R-Squared: 0.51 225s 225s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 179 1.3 0.666 0.661 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.8 3.99 2.00 0.747 0.717 225s supply 20 16 111.2 6.95 2.64 0.585 0.507 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.19 3.68 225s supply 3.68 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.39 4.19 225s supply 4.19 5.56 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.965 225s supply 0.965 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.0165 9.4718 9.82 1.4e-11 *** 225s price -0.2172 0.1066 -2.04 0.049 * 225s income 0.3036 0.0224 13.56 1.8e-15 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.997 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.8 MSE: 3.988 Root MSE: 1.997 225s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 48.5496 9.6886 5.01 1.6e-05 *** 225s price 0.2828 0.1066 2.65 0.012 * 225s farmPrice 0.2161 0.0210 10.30 3.9e-12 *** 225s trend 0.3036 0.0224 13.56 1.8e-15 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.637 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 111.249 MSE: 6.953 Root MSE: 2.637 225s Multiple R-Squared: 0.585 Adjusted R-Squared: 0.507 225s 225s [1] "***************************************************" 225s [1] "3SLS formula: GMM" 225s [1] "************* 3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 9.25 0.694 0.512 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 225s price 0.2401 0.0999 2.40 0.0288 * 225s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 225s trend 0.2529 0.0997 2.54 0.0219 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "******* 3SLS with different instruments (EViews-like) **********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 6.29 0.694 0.5 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.37 3.16 225s supply 3.16 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.37 3.16 225s supply 3.16 4.83 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 225s price -0.412 0.134 -3.08 0.0041 ** 225s income 0.362 0.052 6.95 6.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 225s price 0.2401 0.0894 2.69 0.0112 * 225s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 225s trend 0.2529 0.0891 2.84 0.0077 ** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 8.24 0.694 0.481 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.96 225s supply 3.96 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.96 225s supply 3.96 6.04 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 225s price -0.4116 0.1448 -2.84 0.0076 ** 225s income 0.3617 0.0564 6.41 2.9e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 12.0105 4.12 0.00024 *** 225s price 0.2401 0.0999 2.40 0.02208 * 225s farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 225s trend 0.2529 0.0997 2.54 0.01605 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "************* W3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 164 9.25 0.694 0.512 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 96.6 6.04 2.46 0.640 0.572 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.784 225s supply 0.784 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 225s price 0.2401 0.0999 2.40 0.0288 * 225s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 225s trend 0.2529 0.0997 2.54 0.0219 * 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.458 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 225s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 225s 225s [1] "******* 3SLS with different instruments and restriction ********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 166 2.78 0.691 0.636 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 63.4 3.73 1.93 0.764 0.736 225s supply 20 16 102.2 6.39 2.53 0.619 0.547 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.73 4.59 225s supply 4.59 6.39 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.94 225s supply 0.94 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 100.1363 8.6083 11.63 2.1e-13 *** 225s price -0.3244 0.1114 -2.91 0.0063 ** 225s income 0.3405 0.0509 6.69 1.1e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.931 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 63.395 MSE: 3.729 Root MSE: 1.931 225s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.7623 12.2354 4.07 0.00027 *** 225s price 0.2366 0.1018 2.33 0.02617 * 225s farmPrice 0.2473 0.0474 5.22 9.0e-06 *** 225s trend 0.3405 0.0509 6.69 1.1e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.527 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.181 MSE: 6.386 Root MSE: 2.527 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 225s 225s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 165 1.84 0.691 0.608 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 63.4 3.73 1.93 0.764 0.736 225s supply 20 16 102.1 6.38 2.53 0.619 0.548 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.17 3.79 225s supply 3.79 5.10 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.941 225s supply 0.941 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 99.9363 7.9106 12.63 2.1e-14 *** 225s price -0.3212 0.1019 -3.15 0.0034 ** 225s income 0.3393 0.0466 7.28 2.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.931 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 63.37 MSE: 3.728 Root MSE: 1.931 225s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.8516 10.9418 4.56 6.4e-05 *** 225s price 0.2364 0.0910 2.60 0.014 * 225s farmPrice 0.2467 0.0423 5.83 1.4e-06 *** 225s trend 0.3393 0.0466 7.28 2.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.526 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.07 MSE: 6.379 Root MSE: 2.526 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 225s 225s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 165 1.85 0.691 0.608 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 63.4 3.73 1.93 0.764 0.736 225s supply 20 16 102.1 6.38 2.53 0.619 0.548 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.24 3.60 225s supply 3.60 5.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.17 3.78 225s supply 3.78 5.10 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.941 225s supply 0.941 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 99.9706 7.9399 12.59 2.4e-14 *** 225s price -0.3217 0.1023 -3.15 0.0034 ** 225s income 0.3394 0.0467 7.26 2.1e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.931 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 63.372 MSE: 3.728 Root MSE: 1.931 225s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.8336 10.9955 4.53 6.9e-05 *** 225s price 0.2364 0.0915 2.59 0.014 * 225s farmPrice 0.2469 0.0425 5.80 1.6e-06 *** 225s trend 0.3394 0.0467 7.26 2.1e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.526 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.073 MSE: 6.38 Root MSE: 2.526 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 225s 225s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 166 2.78 0.691 0.636 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 63.4 3.73 1.93 0.764 0.736 225s supply 20 16 102.2 6.39 2.53 0.619 0.547 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.73 4.59 225s supply 4.59 6.39 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.94 225s supply 0.94 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 100.1363 8.6083 11.63 2.1e-13 *** 225s price -0.3244 0.1114 -2.91 0.0063 ** 225s income 0.3405 0.0509 6.69 1.1e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.931 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 63.395 MSE: 3.729 Root MSE: 1.931 225s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.7623 12.2354 4.07 0.00027 *** 225s price 0.2366 0.1018 2.33 0.02617 * 225s farmPrice 0.2473 0.0474 5.22 9.0e-06 *** 225s trend 0.3405 0.0509 6.69 1.1e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.527 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.181 MSE: 6.386 Root MSE: 2.527 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 225s 225s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 165 1.84 0.691 0.608 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 63.4 3.73 1.93 0.764 0.736 225s supply 20 16 102.1 6.38 2.53 0.619 0.548 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.17 3.79 225s supply 3.79 5.10 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.941 225s supply 0.941 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 99.9363 7.9106 12.63 2.1e-14 *** 225s price -0.3212 0.1019 -3.15 0.0034 ** 225s income 0.3393 0.0466 7.28 2.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.931 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 63.37 MSE: 3.728 Root MSE: 1.931 225s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.8516 10.9418 4.56 6.4e-05 *** 225s price 0.2364 0.0910 2.60 0.014 * 225s farmPrice 0.2467 0.0423 5.83 1.4e-06 *** 225s trend 0.3393 0.0466 7.28 2.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.526 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.07 MSE: 6.379 Root MSE: 2.526 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 225s 225s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 166 2.79 0.691 0.635 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 63.4 3.73 1.93 0.764 0.736 225s supply 20 16 102.2 6.39 2.53 0.619 0.547 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.81 4.36 225s supply 4.36 6.34 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.73 4.59 225s supply 4.59 6.39 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.94 225s supply 0.94 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 100.174 8.646 11.59 2.4e-13 *** 225s price -0.325 0.112 -2.91 0.0064 ** 225s income 0.341 0.051 6.67 1.2e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.931 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 63.398 MSE: 3.729 Root MSE: 1.931 225s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.7425 12.3029 4.04 0.00029 *** 225s price 0.2367 0.1023 2.31 0.02691 * 225s farmPrice 0.2474 0.0477 5.19 9.8e-06 *** 225s trend 0.3406 0.0510 6.67 1.2e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.527 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.183 MSE: 6.386 Root MSE: 2.527 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.547 225s 225s [1] "****** 3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 165 1.89 0.692 0.677 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 64.1 3.77 1.94 0.761 0.733 225s supply 20 16 101.2 6.32 2.52 0.623 0.552 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.77 4.68 225s supply 4.68 6.32 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.96 225s supply 0.96 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 98.8949 8.2696 11.96 6.4e-14 *** 225s price -0.2870 0.0909 -3.16 0.0033 ** 225s income 0.3148 0.0224 14.04 4.4e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.941 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.072 MSE: 3.769 Root MSE: 1.941 225s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 54.6693 8.4422 6.48 1.8e-07 *** 225s price 0.2130 0.0909 2.34 0.025 * 225s farmPrice 0.2237 0.0228 9.82 1.3e-11 *** 225s trend 0.3148 0.0224 14.04 4.4e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.515 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 101.181 MSE: 6.324 Root MSE: 2.515 225s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 225s 225s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 165 1.28 0.692 0.642 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 64.1 3.77 1.94 0.761 0.733 225s supply 20 16 101.1 6.32 2.51 0.623 0.552 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.21 3.86 225s supply 3.86 5.06 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.96 225s supply 0.96 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 98.6650 7.5755 13.02 5.6e-15 *** 225s price -0.2845 0.0822 -3.46 0.0014 ** 225s income 0.3146 0.0203 15.52 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.942 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.111 MSE: 3.771 Root MSE: 1.942 225s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 54.3281 7.7347 7.02 3.6e-08 *** 225s price 0.2155 0.0822 2.62 0.013 * 225s farmPrice 0.2247 0.0201 11.16 4.4e-13 *** 225s trend 0.3146 0.0203 15.52 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.514 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 101.149 MSE: 6.322 Root MSE: 2.514 225s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 225s 225s [1] "**** W3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 165 1.89 0.692 0.677 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 64.1 3.77 1.94 0.761 0.733 225s supply 20 16 101.3 6.33 2.52 0.622 0.551 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.75 4.46 225s supply 4.46 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.77 4.69 225s supply 4.69 6.33 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.96 225s supply 0.96 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 98.9360 8.2215 12.03 5.4e-14 *** 225s price -0.2872 0.0907 -3.17 0.0032 ** 225s income 0.3147 0.0215 14.64 2.2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.941 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.08 MSE: 3.769 Root MSE: 1.941 225s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 54.7520 8.3733 6.54 1.5e-07 *** 225s price 0.2128 0.0907 2.35 0.025 * 225s farmPrice 0.2231 0.0218 10.24 4.5e-12 *** 225s trend 0.3147 0.0215 14.64 2.2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.516 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 101.278 MSE: 6.33 Root MSE: 2.516 225s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 225s 225s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 165 1.89 0.692 0.677 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 64.1 3.77 1.94 0.761 0.733 225s supply 20 16 101.2 6.32 2.52 0.623 0.552 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.77 4.68 225s supply 4.68 6.32 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.96 225s supply 0.96 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 98.8949 8.2696 11.96 6.4e-14 *** 225s price -0.2870 0.0909 -3.16 0.0033 ** 225s income 0.3148 0.0224 14.04 4.4e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.941 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.072 MSE: 3.769 Root MSE: 1.941 225s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 54.6693 8.4422 6.48 1.8e-07 *** 225s price 0.2130 0.0909 2.34 0.025 * 225s farmPrice 0.2237 0.0228 9.82 1.3e-11 *** 225s trend 0.3148 0.0224 14.04 4.4e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.515 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 101.181 MSE: 6.324 Root MSE: 2.515 225s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 225s 225s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 165 1.28 0.692 0.642 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 64.1 3.77 1.94 0.761 0.733 225s supply 20 16 101.1 6.32 2.51 0.623 0.552 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.21 3.86 225s supply 3.86 5.06 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.96 225s supply 0.96 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 98.6650 7.5755 13.02 5.6e-15 *** 225s price -0.2845 0.0822 -3.46 0.0014 ** 225s income 0.3146 0.0203 15.52 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.942 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.111 MSE: 3.771 Root MSE: 1.942 225s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 54.3281 7.7347 7.02 3.6e-08 *** 225s price 0.2155 0.0822 2.62 0.013 * 225s farmPrice 0.2247 0.0201 11.16 4.4e-13 *** 225s trend 0.3146 0.0203 15.52 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.514 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 101.149 MSE: 6.322 Root MSE: 2.514 225s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 225s 225s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 165 1.28 0.692 0.643 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 64.1 3.77 1.94 0.761 0.733 225s supply 20 16 101.2 6.33 2.52 0.622 0.552 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.19 3.68 225s supply 3.68 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.21 3.87 225s supply 3.87 5.06 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.96 225s supply 0.96 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 98.6980 7.5376 13.09 4.9e-15 *** 225s price -0.2847 0.0820 -3.47 0.0014 ** 225s income 0.3145 0.0195 16.13 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.942 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 64.117 MSE: 3.772 Root MSE: 1.942 225s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 54.3972 7.6824 7.08 3.0e-08 *** 225s price 0.2153 0.0820 2.62 0.013 * 225s farmPrice 0.2242 0.0193 11.60 1.5e-13 *** 225s trend 0.3145 0.0195 16.13 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.515 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 101.231 MSE: 6.327 Root MSE: 2.515 225s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.552 225s 225s [1] "***************************************************" 225s [1] "3SLS formula: EViews" 225s [1] "************* 3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 174 2.12 0.675 0.659 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 106.6 6.66 2.58 0.602 0.528 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 4.93 225s supply 4.93 6.66 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.2953 11.5390 4.97 0.00014 *** 225s price 0.1373 0.0897 1.53 0.14529 225s farmPrice 0.2660 0.0470 5.66 3.6e-05 *** 225s trend 0.3970 0.0781 5.08 0.00011 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.582 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 225s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 225s 225s [1] "******* 3SLS with different instruments (EViews-like) **********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 173 1.51 0.677 0.612 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 105.7 6.61 2.57 0.606 0.532 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.37 3.16 225s supply 3.16 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.37 4.04 225s supply 4.04 5.29 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.957 225s supply 0.957 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 225s price -0.412 0.134 -3.08 0.0041 ** 225s income 0.362 0.052 6.95 6.0e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.0636 10.3208 5.53 3.9e-06 *** 225s price 0.1403 0.0802 1.75 0.089 . 225s farmPrice 0.2657 0.0421 6.32 3.8e-07 *** 225s trend 0.3927 0.0699 5.62 3.0e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.571 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 105.735 MSE: 6.608 Root MSE: 2.571 225s Multiple R-Squared: 0.606 Adjusted R-Squared: 0.532 225s 225s [1] "**** 3SLS with different instruments and methodResidCov = Theil ***" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 175 0.321 0.673 0.655 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 107.7 6.73 2.59 0.598 0.523 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.96 225s supply 3.96 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 5.14 225s supply 5.14 6.73 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.962 225s supply 0.962 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 225s price -0.4116 0.1448 -2.84 0.0076 ** 225s income 0.3617 0.0564 6.41 2.9e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.5567 11.5060 5.00 1.8e-05 *** 225s price 0.1338 0.0889 1.50 0.14 225s farmPrice 0.2664 0.0470 5.66 2.6e-06 *** 225s trend 0.4018 0.0765 5.26 8.7e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.594 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 107.679 MSE: 6.73 Root MSE: 2.594 225s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 225s 225s [1] "************* W3SLS with different instruments **************" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 174 2.12 0.675 0.659 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.4 3.97 1.99 0.748 0.719 225s supply 20 16 106.6 6.66 2.58 0.602 0.528 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.97 3.84 225s supply 3.84 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.97 4.93 225s supply 4.93 6.66 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.959 225s supply 0.959 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 225s price -0.4116 0.1448 -2.84 0.011 * 225s income 0.3617 0.0564 6.41 6.4e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.2953 11.5390 4.97 0.00014 *** 225s price 0.1373 0.0897 1.53 0.14529 225s farmPrice 0.2660 0.0470 5.66 3.6e-05 *** 225s trend 0.3970 0.0781 5.08 0.00011 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.582 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 106.628 MSE: 6.664 Root MSE: 2.582 225s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.528 225s 225s [1] "******* 3SLS with different instruments and restriction ********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 174 3.39 0.676 0.542 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 71.1 4.18 2.04 0.735 0.704 225s supply 20 16 102.6 6.41 2.53 0.617 0.546 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.18 4.84 225s supply 4.84 6.41 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.935 225s supply 0.935 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 109.4916 6.3475 17.25 < 2e-16 *** 225s price -0.4470 0.0812 -5.50 3.8e-06 *** 225s income 0.3703 0.0474 7.81 4.3e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.045 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 71.077 MSE: 4.181 Root MSE: 2.045 225s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.6795 11.2022 5.15 1.1e-05 *** 225s price 0.1324 0.0785 1.69 0.1 225s farmPrice 0.2700 0.0453 5.97 9.5e-07 *** 225s trend 0.3703 0.0474 7.81 4.3e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.532 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.574 MSE: 6.411 Root MSE: 2.532 225s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.546 225s 225s [1] "** 3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 173 2.29 0.678 0.515 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 70.5 4.15 2.04 0.737 0.706 225s supply 20 16 102.2 6.38 2.53 0.619 0.548 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.53 3.96 225s supply 3.96 5.11 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.934 225s supply 0.934 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 109.1085 5.8428 18.67 < 2e-16 *** 225s price -0.4422 0.0737 -6.00 8.6e-07 *** 225s income 0.3693 0.0432 8.54 5.6e-10 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.037 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 70.515 MSE: 4.148 Root MSE: 2.037 225s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.2679 10.0564 5.69 2.1e-06 *** 225s price 0.1375 0.0705 1.95 0.06 . 225s farmPrice 0.2691 0.0403 6.68 1.1e-07 *** 225s trend 0.3693 0.0432 8.54 5.6e-10 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.527 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.156 MSE: 6.385 Root MSE: 2.527 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 225s 225s [1] "** W3SLS with different instruments and restriction (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 173 2.29 0.678 0.515 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 70.5 4.15 2.04 0.737 0.706 225s supply 20 16 102.1 6.38 2.53 0.619 0.548 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.24 3.60 225s supply 3.60 5.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.52 3.96 225s supply 3.96 5.11 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.934 225s supply 0.934 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 109.0818 5.9083 18.46 < 2e-16 *** 225s price -0.4418 0.0746 -5.92 1.1e-06 *** 225s income 0.3692 0.0434 8.51 6.2e-10 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.036 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 70.475 MSE: 4.146 Root MSE: 2.036 225s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.2616 10.1094 5.66 2.4e-06 *** 225s price 0.1376 0.0711 1.94 0.061 . 225s farmPrice 0.2690 0.0405 6.64 1.3e-07 *** 225s trend 0.3692 0.0434 8.51 6.2e-10 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.527 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.135 MSE: 6.383 Root MSE: 2.527 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 225s 225s [1] "** 3SLS with different instruments and restriction via restrict.regMat *******" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 174 3.39 0.676 0.542 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 71.1 4.18 2.04 0.735 0.704 225s supply 20 16 102.6 6.41 2.53 0.617 0.546 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.35 225s supply 4.35 6.27 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.18 4.84 225s supply 4.84 6.41 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.935 225s supply 0.935 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 109.4916 6.3475 17.25 < 2e-16 *** 225s price -0.4470 0.0812 -5.50 3.8e-06 *** 225s income 0.3703 0.0474 7.81 4.3e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.045 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 71.077 MSE: 4.181 Root MSE: 2.045 225s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.6795 11.2022 5.15 1.1e-05 *** 225s price 0.1324 0.0785 1.69 0.1 225s farmPrice 0.2700 0.0453 5.97 9.5e-07 *** 225s trend 0.3703 0.0474 7.81 4.3e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.532 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.574 MSE: 6.411 Root MSE: 2.532 225s Multiple R-Squared: 0.617 Adjusted R-Squared: 0.546 225s 225s [1] "3SLS with different instruments with restriction via restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 173 2.29 0.678 0.515 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 70.5 4.15 2.04 0.737 0.706 225s supply 20 16 102.2 6.38 2.53 0.619 0.548 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.58 225s supply 3.58 5.02 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.53 3.96 225s supply 3.96 5.11 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.934 225s supply 0.934 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 109.1085 5.8428 18.67 < 2e-16 *** 225s price -0.4422 0.0737 -6.00 8.6e-07 *** 225s income 0.3693 0.0432 8.54 5.6e-10 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.037 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 70.515 MSE: 4.148 Root MSE: 2.037 225s Multiple R-Squared: 0.737 Adjusted R-Squared: 0.706 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.2679 10.0564 5.69 2.1e-06 *** 225s price 0.1375 0.0705 1.95 0.06 . 225s farmPrice 0.2691 0.0403 6.68 1.1e-07 *** 225s trend 0.3693 0.0432 8.54 5.6e-10 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.527 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.156 MSE: 6.385 Root MSE: 2.527 225s Multiple R-Squared: 0.619 Adjusted R-Squared: 0.548 225s 225s [1] "** W3SLS with different instr. and restr. via restrict.regMat ****" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 174 3.38 0.676 0.543 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 71 4.18 2.04 0.735 0.704 225s supply 20 16 103 6.41 2.53 0.618 0.546 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.81 4.36 225s supply 4.36 6.34 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 4.18 4.84 225s supply 4.84 6.41 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.935 225s supply 0.935 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 109.4522 6.4318 17.02 < 2e-16 *** 225s price -0.4465 0.0823 -5.42 4.8e-06 *** 225s income 0.3702 0.0476 7.78 4.8e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.044 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 71.017 MSE: 4.177 Root MSE: 2.044 225s Multiple R-Squared: 0.735 Adjusted R-Squared: 0.704 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 57.6669 11.2699 5.12 1.2e-05 *** 225s price 0.1326 0.0792 1.67 0.1 225s farmPrice 0.2699 0.0456 5.92 1.1e-06 *** 225s trend 0.3702 0.0476 7.78 4.8e-09 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.532 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 102.539 MSE: 6.409 Root MSE: 2.532 225s Multiple R-Squared: 0.618 Adjusted R-Squared: 0.546 225s 225s [1] "****** 3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 358 32.4 0.333 -0.013 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 141 8.32 2.88 0.472 0.410 225s supply 20 16 216 13.53 3.68 0.193 0.042 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.32 8.95 225s supply 8.95 13.53 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.844 225s supply 0.844 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 225s price -0.6034 0.0504 -12.0 6.2e-14 *** 225s income 0.5399 0.0182 29.7 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.884 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 225s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 14.7043 5.4316 2.71 0.01 * 225s price 0.3966 0.0504 7.87 3e-09 *** 225s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 225s trend 0.5399 0.0182 29.71 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.678 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 225s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 225s 225s [1] "** 3SLS with different instruments and 2 restrictions (EViews-like) *" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 359 21.9 0.331 -0.059 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 143 8.38 2.90 0.468 0.406 225s supply 20 16 216 13.52 3.68 0.193 0.042 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 7.13 7.43 225s supply 7.43 10.82 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.846 225s supply 0.846 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 107.9852 4.9704 21.7 < 2e-16 *** 225s price -0.5994 0.0458 -13.1 4.9e-15 *** 225s income 0.5420 0.0168 32.2 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.896 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 142.542 MSE: 8.385 Root MSE: 2.896 225s Multiple R-Squared: 0.468 Adjusted R-Squared: 0.406 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 14.4922 4.9950 2.90 0.0064 ** 225s price 0.4006 0.0458 8.75 2.5e-10 *** 225s farmPrice 0.4207 0.0184 22.92 < 2e-16 *** 225s trend 0.5420 0.0168 32.25 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.677 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 216.315 MSE: 13.52 Root MSE: 3.677 225s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 225s 225s [1] "**** W3SLS with different instruments and 2 restrictions *********" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 364 32.3 0.322 -0.022 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 143 8.43 2.90 0.466 0.403 225s supply 20 16 220 13.78 3.71 0.178 0.024 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.75 4.46 225s supply 4.46 6.04 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.43 9.15 225s supply 9.15 13.78 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.00 0.85 225s supply 0.85 1.00 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 107.9125 5.1136 21.1 < 2e-16 *** 225s price -0.5996 0.0479 -12.5 1.7e-14 *** 225s income 0.5430 0.0171 31.7 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.903 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 143.236 MSE: 8.426 Root MSE: 2.903 225s Multiple R-Squared: 0.466 Adjusted R-Squared: 0.403 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 13.9658 5.1591 2.71 0.01 * 225s price 0.4004 0.0479 8.36 7.3e-10 *** 225s farmPrice 0.4263 0.0193 22.08 < 2e-16 *** 225s trend 0.5430 0.0171 31.74 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.712 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 220.468 MSE: 13.779 Root MSE: 3.712 225s Multiple R-Squared: 0.178 Adjusted R-Squared: 0.024 225s 225s [1] " 3SLS with different instruments with 2 restrictions via R and restrict.regMat" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 358 32.4 0.333 -0.013 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 141 8.32 2.88 0.472 0.410 225s supply 20 16 216 13.53 3.68 0.193 0.042 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.79 4.45 225s supply 4.45 6.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.32 8.95 225s supply 8.95 13.53 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.844 225s supply 0.844 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 225s price -0.6034 0.0504 -12.0 6.2e-14 *** 225s income 0.5399 0.0182 29.7 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.884 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 225s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 14.7043 5.4316 2.71 0.01 * 225s price 0.3966 0.0504 7.87 3e-09 *** 225s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 225s trend 0.5399 0.0182 29.71 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.678 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 225s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 225s 225s [1] "3SLS with diff. instruments and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 359 21.9 0.331 -0.059 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 143 8.38 2.90 0.468 0.406 225s supply 20 16 216 13.52 3.68 0.193 0.042 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.22 3.67 225s supply 3.67 4.85 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 7.13 7.43 225s supply 7.43 10.82 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.846 225s supply 0.846 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 107.9852 4.9704 21.7 < 2e-16 *** 225s price -0.5994 0.0458 -13.1 4.9e-15 *** 225s income 0.5420 0.0168 32.2 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.896 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 142.542 MSE: 8.385 Root MSE: 2.896 225s Multiple R-Squared: 0.468 Adjusted R-Squared: 0.406 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 14.4922 4.9950 2.90 0.0064 ** 225s price 0.4006 0.0458 8.75 2.5e-10 *** 225s farmPrice 0.4207 0.0184 22.92 < 2e-16 *** 225s trend 0.5420 0.0168 32.25 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.677 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 216.315 MSE: 13.52 Root MSE: 3.677 225s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 225s 225s [1] "W3SLS with diff. instr. and 2 restr. via R and restrict.regMat (EViews-like)" 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 364 21.8 0.321 -0.069 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 144 8.49 2.91 0.462 0.399 225s supply 20 16 220 13.76 3.71 0.179 0.025 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.19 3.68 225s supply 3.68 4.83 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 7.21 7.59 225s supply 7.59 11.00 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.852 225s supply 0.852 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 107.3179 4.7598 22.6 < 2e-16 *** 225s price -0.5955 0.0438 -13.6 1.6e-15 *** 225s income 0.5449 0.0159 34.2 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.913 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 144.274 MSE: 8.487 Root MSE: 2.913 225s Multiple R-Squared: 0.462 Adjusted R-Squared: 0.399 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 13.7761 4.7784 2.88 0.0067 ** 225s price 0.4045 0.0438 9.23 6.6e-11 *** 225s farmPrice 0.4237 0.0174 24.30 < 2e-16 *** 225s trend 0.5449 0.0159 34.17 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.709 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 220.081 MSE: 13.755 Root MSE: 3.709 225s Multiple R-Squared: 0.179 Adjusted R-Squared: 0.025 225s 225s > 225s > 225s > ## **************** shorter summaries ********************** 225s > print( summary( fit3sls[[ 2 ]]$e1c, equations = FALSE ) ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 174 -0.718 0.675 0.922 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65.7 3.87 1.97 0.755 0.726 225s supply 20 16 108.7 6.79 2.61 0.594 0.518 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.87 4.50 225s supply 4.50 6.04 225s 225s warning: this covariance matrix is NOT positive semidefinit! 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.87 5.2 225s supply 5.20 6.8 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.981 225s supply 0.981 1.000 225s 225s 225s Coefficients: 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 225s demand_price -0.2436 0.0965 -2.52 0.02183 * 225s demand_income 0.3140 0.0469 6.69 3.8e-06 *** 225s supply_(Intercept) 52.2869 11.8853 4.40 0.00045 *** 225s supply_price 0.2282 0.0997 2.29 0.03595 * 225s supply_farmPrice 0.2272 0.0438 5.19 8.9e-05 *** 225s supply_trend 0.3648 0.0707 5.16 9.5e-05 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s > 225s > print( summary( fit3sls[[ 3 ]]$e2e ), residCov = FALSE ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 171 0.887 0.68 0.678 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.5 3.97 1.99 0.748 0.719 225s supply 20 16 104.0 6.50 2.55 0.612 0.539 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 94.2737 7.3905 12.76 1.6e-14 *** 225s price -0.2243 0.0888 -2.53 0.016 * 225s income 0.2979 0.0420 7.10 3.4e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.992 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.467 MSE: 3.969 Root MSE: 1.992 225s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 55.4521 10.3994 5.33 6.4e-06 *** 225s price 0.2207 0.0896 2.46 0.019 * 225s farmPrice 0.2095 0.0366 5.73 1.9e-06 *** 225s trend 0.2979 0.0420 7.10 3.4e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.55 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 104.013 MSE: 6.501 Root MSE: 2.55 225s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 225s 225s > 225s > print( summary( fit3sls[[ 4 ]]$e3, useDfSys = FALSE ), residCov = FALSE ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 173 1.27 0.678 0.722 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 67.8 3.99 2.00 0.747 0.717 225s supply 20 16 104.8 6.55 2.56 0.609 0.536 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 94.222 8.015 11.76 1.4e-09 *** 225s price -0.222 0.096 -2.31 0.034 * 225s income 0.296 0.045 6.57 4.8e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.997 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 67.796 MSE: 3.988 Root MSE: 1.997 225s Multiple R-Squared: 0.747 Adjusted R-Squared: 0.717 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 55.9604 11.5777 4.83 0.00018 *** 225s price 0.2193 0.1002 2.19 0.04374 * 225s farmPrice 0.2060 0.0403 5.11 0.00011 *** 225s trend 0.2956 0.0450 6.57 6.5e-06 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.559 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 104.753 MSE: 6.547 Root MSE: 2.559 225s Multiple R-Squared: 0.609 Adjusted R-Squared: 0.536 225s 225s > 225s > print( summary( fit3sls[[ 5 ]]$e4e, equations = FALSE ), 225s + equations = FALSE ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 439 21.3 0.18 -0.18 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 169 9.93 3.15 0.370 0.296 225s supply 20 16 271 16.91 4.11 -0.009 -0.198 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.30 3.73 225s supply 3.73 5.00 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 8.44 9.64 225s supply 9.64 13.53 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.902 225s supply 0.902 1.000 225s 225s 225s Coefficients: 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 93.2926 7.3154 12.75 1.0e-14 *** 225s demand_price -0.4781 0.0812 -5.89 1.1e-06 *** 225s demand_income 0.5683 0.0209 27.24 < 2e-16 *** 225s supply_(Intercept) 0.6559 7.5503 0.09 0.93 225s supply_price 0.5219 0.0812 6.43 2.1e-07 *** 225s supply_farmPrice 0.4355 0.0212 20.49 < 2e-16 *** 225s supply_trend 0.5683 0.0209 27.24 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s > 225s > print( summary( fit3sls[[ 1 ]]$e4wSym, residCov = FALSE ), 225s + equations = FALSE ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 172 1.74 0.68 0.697 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65.9 3.88 1.97 0.754 0.725 225s supply 20 16 105.7 6.60 2.57 0.606 0.532 225s 225s 225s Coefficients: 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 93.7870 7.9088 11.86 8.2e-14 *** 225s demand_price -0.2443 0.0892 -2.74 0.0096 ** 225s demand_income 0.3234 0.0229 14.14 4.4e-16 *** 225s supply_(Intercept) 49.8093 8.1522 6.11 5.5e-07 *** 225s supply_price 0.2557 0.0892 2.87 0.0069 ** 225s supply_farmPrice 0.2289 0.0237 9.67 2.0e-11 *** 225s supply_trend 0.3234 0.0229 14.14 4.4e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s > 225s > print( summary( fit3sls[[ 2 ]]$e5, residCov = FALSE ), residCov = TRUE ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 171 1.74 0.681 0.696 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65.8 3.87 1.97 0.755 0.726 225s supply 20 16 105.4 6.59 2.57 0.607 0.533 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.89 4.53 225s supply 4.53 6.25 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.87 4.87 225s supply 4.87 6.59 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.965 225s supply 0.965 1.000 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.9070 7.9234 11.85 8.3e-14 *** 225s price -0.2457 0.0891 -2.76 0.0092 ** 225s income 0.3236 0.0233 13.91 8.9e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 1.967 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 65.807 MSE: 3.871 Root MSE: 1.967 225s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.9049 8.1797 6.10 5.7e-07 *** 225s price 0.2543 0.0891 2.85 0.0072 ** 225s farmPrice 0.2293 0.0241 9.52 3.1e-11 *** 225s trend 0.3236 0.0233 13.91 8.9e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.566 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 105.389 MSE: 6.587 Root MSE: 2.566 225s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.533 225s 225s > 225s > print( summary( fit3slsi[[ 3 ]]$e3e, residCov = FALSE, 225s + equations = FALSE ) ) 225s 225s systemfit results 225s method: iterated 3SLS 225s 225s convergence achieved after 20 iterations 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 237 0.364 0.557 0.755 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 99.3 5.84 2.42 0.630 0.586 225s supply 20 16 138.1 8.63 2.94 0.485 0.388 225s 225s 225s Coefficients: 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 92.0353 8.9214 10.32 5.2e-12 *** 225s demand_price -0.1043 0.0958 -1.09 0.284 225s demand_income 0.1979 0.0299 6.61 1.4e-07 *** 225s supply_(Intercept) 68.2830 11.1530 6.12 6.0e-07 *** 225s supply_price 0.1851 0.1053 1.76 0.088 . 225s supply_farmPrice 0.1245 0.0251 4.96 1.9e-05 *** 225s supply_trend 0.1979 0.0299 6.61 1.4e-07 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s > 225s > print( summary( fit3slsi[[ 4 ]]$e1we ), equations = FALSE, residCov = FALSE ) 225s 225s systemfit results 225s method: iterated 3SLS 225s 225s convergence achieved after 6 iterations 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 33 177 0.667 0.67 0.782 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 65.7 3.87 1.97 0.755 0.726 225s supply 20 16 111.3 6.96 2.64 0.585 0.507 225s 225s 225s Coefficients: 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 225s demand_price -0.2436 0.0890 -2.74 0.01402 * 225s demand_income 0.3140 0.0433 7.25 1.3e-06 *** 225s supply_(Intercept) 52.5527 11.3956 4.61 0.00029 *** 225s supply_price 0.2271 0.0956 2.37 0.03043 * 225s supply_farmPrice 0.2245 0.0416 5.39 6.0e-05 *** 225s supply_trend 0.3756 0.0641 5.86 2.4e-05 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s > 225s > print( summary( fit3slsd[[ 5 ]]$e4, residCov = FALSE ) ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 35 358 32.4 0.333 -0.013 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 141 8.32 2.88 0.472 0.410 225s supply 20 16 216 13.53 3.68 0.193 0.042 225s 225s 225s 3SLS estimates for 'demand' (equation 1) 225s Model Formula: consump ~ price + income 225s Instruments: ~income + farmPrice 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 108.5837 5.3770 20.2 < 2e-16 *** 225s price -0.6034 0.0504 -12.0 6.2e-14 *** 225s income 0.5399 0.0182 29.7 < 2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 2.884 on 17 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 17 225s SSR: 141.436 MSE: 8.32 Root MSE: 2.884 225s Multiple R-Squared: 0.472 Adjusted R-Squared: 0.41 225s 225s 225s 3SLS estimates for 'supply' (equation 2) 225s Model Formula: consump ~ price + farmPrice + trend 225s Instruments: ~income + farmPrice + trend 225s 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 14.7043 5.4316 2.71 0.01 * 225s price 0.3966 0.0504 7.87 3e-09 *** 225s farmPrice 0.4228 0.0205 20.65 <2e-16 *** 225s trend 0.5399 0.0182 29.71 <2e-16 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s 225s Residual standard error: 3.678 on 16 degrees of freedom 225s Number of observations: 20 Degrees of Freedom: 16 225s SSR: 216.4 MSE: 13.525 Root MSE: 3.678 225s Multiple R-Squared: 0.193 Adjusted R-Squared: 0.042 225s 225s > 225s > print( summary( fit3slsd[[ 1 ]]$e2we, equations = FALSE ) ) 225s 225s systemfit results 225s method: 3SLS 225s 225s N DF SSR detRCov OLS-R2 McElroy-R2 225s system 40 34 199 1.77 0.629 0.65 225s 225s N DF SSR MSE RMSE R2 Adj R2 225s demand 20 17 72.4 4.26 2.06 0.730 0.698 225s supply 20 16 126.7 7.92 2.81 0.527 0.439 225s 225s The covariance matrix of the residuals used for estimation 225s demand supply 225s demand 3.24 3.60 225s supply 3.60 5.06 225s 225s The covariance matrix of the residuals 225s demand supply 225s demand 3.62 4.60 225s supply 4.60 6.34 225s 225s The correlations of the residuals 225s demand supply 225s demand 1.000 0.961 225s supply 0.961 1.000 225s 225s 225s Coefficients: 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 88.9298 5.9083 15.05 < 2e-16 *** 225s demand_price -0.1760 0.0746 -2.36 0.02415 * 225s demand_income 0.3032 0.0434 6.99 4.6e-08 *** 225s supply_(Intercept) 40.8325 10.1094 4.04 0.00029 *** 225s supply_price 0.3562 0.0711 5.01 1.7e-05 *** 225s supply_farmPrice 0.2200 0.0405 5.43 4.8e-06 *** 225s supply_trend 0.3032 0.0434 6.99 4.6e-08 *** 225s --- 225s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 225s > 225s > 225s > ## ****************** residuals ************************** 225s > print( residuals( fit3sls[[ 1 ]]$e1c ) ) 225s demand supply 225s 1 0.843 0.670 225s 2 -0.698 -0.142 225s 3 2.359 2.659 225s 4 1.490 1.618 225s 5 2.139 2.588 225s 6 1.277 1.485 225s 7 1.571 2.093 225s 8 -3.066 -4.163 225s 9 -1.125 -1.929 225s 10 2.492 3.207 225s 11 -0.108 -0.513 225s 12 -2.292 -2.375 225s 13 -1.598 -2.089 225s 14 -0.271 0.330 225s 15 1.958 3.086 225s 16 -3.430 -4.225 225s 17 -0.313 0.185 225s 18 -2.151 -3.680 225s 19 1.592 1.576 225s 20 -0.668 -0.382 225s > print( residuals( fit3sls[[ 1 ]]$e1c$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 225s 12 13 14 15 16 17 18 19 20 225s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 225s > 225s > print( residuals( fit3sls[[ 4 ]]$e1wc ) ) 225s demand supply 225s 1 0.843 0.670 225s 2 -0.698 -0.142 225s 3 2.359 2.659 225s 4 1.490 1.618 225s 5 2.139 2.588 225s 6 1.277 1.485 225s 7 1.571 2.093 225s 8 -3.066 -4.163 225s 9 -1.125 -1.929 225s 10 2.492 3.207 225s 11 -0.108 -0.513 225s 12 -2.292 -2.375 225s 13 -1.598 -2.089 225s 14 -0.271 0.330 225s 15 1.958 3.086 225s 16 -3.430 -4.225 225s 17 -0.313 0.185 225s 18 -2.151 -3.680 225s 19 1.592 1.576 225s 20 -0.668 -0.382 225s > print( residuals( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 225s 12 13 14 15 16 17 18 19 20 225s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 225s > 225s > print( residuals( fit3sls[[ 2 ]]$e2e ) ) 225s demand supply 225s 1 0.6744 0.0619 225s 2 -0.7785 -0.6344 225s 3 2.2797 2.2267 225s 4 1.4140 1.2428 225s 5 2.2144 2.4566 225s 6 1.3352 1.3851 225s 7 1.6419 2.0264 225s 8 -2.9923 -4.0603 225s 9 -1.0710 -1.8419 225s 10 2.5226 3.1787 225s 11 -0.3346 -0.8086 225s 12 -2.5999 -2.7819 225s 13 -1.8617 -2.3572 225s 14 -0.3584 0.2840 225s 15 2.1419 3.4511 225s 16 -3.2786 -3.7199 225s 17 -0.0706 0.7656 225s 18 -2.1179 -3.2218 225s 19 1.6924 2.0576 225s 20 -0.4528 0.2893 225s > print( residuals( fit3sls[[ 2 ]]$e2e$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 225s 0.0619 -0.6344 2.2267 1.2428 2.4566 1.3851 2.0264 -4.0603 -1.8419 3.1787 225s 11 12 13 14 15 16 17 18 19 20 225s -0.8086 -2.7819 -2.3572 0.2840 3.4511 -3.7199 0.7656 -3.2218 2.0576 0.2893 225s > 225s > print( residuals( fit3sls[[ 3 ]]$e3 ) ) 225s demand supply 225s 1 0.6499 0.045 225s 2 -0.7902 -0.639 225s 3 2.2682 2.223 225s 4 1.4031 1.239 225s 5 2.2253 2.490 225s 6 1.3437 1.414 225s 7 1.6522 2.051 225s 8 -2.9817 -4.013 225s 9 -1.0632 -1.808 225s 10 2.5270 3.179 225s 11 -0.3675 -0.872 225s 12 -2.6445 -2.878 225s 13 -1.8999 -2.437 225s 14 -0.3711 0.237 225s 15 2.1685 3.474 225s 16 -3.2566 -3.680 225s 17 -0.0355 0.809 225s 18 -2.1131 -3.213 225s 19 1.7070 2.060 225s 20 -0.4215 0.319 225s > print( residuals( fit3sls[[ 3 ]]$e3$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 225s 0.6499 -0.7902 2.2682 1.4031 2.2253 1.3437 1.6522 -2.9817 -1.0632 2.5270 225s 11 12 13 14 15 16 17 18 19 20 225s -0.3675 -2.6445 -1.8999 -0.3711 2.1685 -3.2566 -0.0355 -2.1131 1.7070 -0.4215 225s > 225s > print( residuals( fit3sls[[ 4 ]]$e4e ) ) 225s demand supply 225s 1 0.9543 0.278 225s 2 -0.6734 -0.586 225s 3 2.3881 2.272 225s 4 1.5091 1.252 225s 5 2.1028 2.356 225s 6 1.2414 1.271 225s 7 1.5161 1.894 225s 8 -3.1487 -4.421 225s 9 -1.1358 -1.958 225s 10 2.5334 3.368 225s 11 0.0936 -0.275 225s 12 -2.0762 -2.176 225s 13 -1.4415 -1.951 225s 14 -0.2039 0.559 225s 15 1.8691 3.353 225s 16 -3.5213 -4.003 225s 17 -0.3804 0.692 225s 18 -2.2018 -3.453 225s 19 1.4834 1.817 225s 20 -0.9080 -0.289 225s > print( residuals( fit3sls[[ 4 ]]$e4e$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s 0.278 -0.586 2.272 1.252 2.356 1.271 1.894 -4.421 -1.958 3.368 -0.275 225s 12 13 14 15 16 17 18 19 20 225s -2.176 -1.951 0.559 3.353 -4.003 0.692 -3.453 1.817 -0.289 225s > 225s > print( residuals( fit3sls[[ 5 ]]$e5 ) ) 225s demand supply 225s 1 3.391 2.137 225s 2 0.160 -0.366 225s 3 3.267 2.508 225s 4 2.250 1.132 225s 5 1.168 1.398 225s 6 0.434 0.165 225s 7 0.397 0.594 225s 8 -4.607 -7.911 225s 9 -1.631 -2.964 225s 10 2.800 5.323 225s 11 3.967 4.833 225s 12 2.518 3.479 225s 13 2.169 1.774 225s 14 1.169 3.182 225s 15 -0.415 2.626 225s 16 -5.608 -6.508 225s 17 -2.817 0.433 225s 18 -3.012 -5.580 225s 19 -0.454 -0.427 225s 20 -5.146 -5.829 225s > print( residuals( fit3sls[[ 5 ]]$e5$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s 3.391 0.160 3.267 2.250 1.168 0.434 0.397 -4.607 -1.631 2.800 3.967 225s 12 13 14 15 16 17 18 19 20 225s 2.518 2.169 1.169 -0.415 -5.608 -2.817 -3.012 -0.454 -5.146 225s > 225s > print( residuals( fit3slsi[[ 2 ]]$e3e ) ) 225s demand supply 225s 1 -0.376 -0.761 225s 2 -1.281 -1.123 225s 3 1.786 1.809 225s 4 0.942 0.878 225s 5 2.683 3.039 225s 6 1.699 1.899 225s 7 2.083 2.477 225s 8 -2.534 -3.021 225s 9 -0.736 -1.093 225s 10 2.713 3.153 225s 11 -1.748 -2.334 225s 12 -4.518 -5.058 225s 13 -3.502 -4.191 225s 14 -0.901 -0.705 225s 15 3.286 4.209 225s 16 -2.334 -2.514 225s 17 1.438 2.113 225s 18 -1.911 -2.680 225s 19 2.320 2.490 225s 20 0.889 1.412 225s > print( residuals( fit3slsi[[ 2 ]]$e3e$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s -0.376 -1.281 1.786 0.942 2.683 1.699 2.083 -2.534 -0.736 2.713 -1.748 225s 12 13 14 15 16 17 18 19 20 225s -4.518 -3.502 -0.901 3.286 -2.334 1.438 -1.911 2.320 0.889 225s > 225s > print( residuals( fit3slsi[[ 1 ]]$e2we ) ) 225s demand supply 225s 1 -0.376 -0.761 225s 2 -1.281 -1.123 225s 3 1.786 1.809 225s 4 0.942 0.878 225s 5 2.683 3.039 225s 6 1.699 1.899 225s 7 2.083 2.477 225s 8 -2.534 -3.021 225s 9 -0.736 -1.093 225s 10 2.713 3.153 225s 11 -1.748 -2.334 225s 12 -4.518 -5.058 225s 13 -3.502 -4.191 225s 14 -0.901 -0.705 225s 15 3.286 4.209 225s 16 -2.334 -2.514 225s 17 1.438 2.113 225s 18 -1.911 -2.680 225s 19 2.320 2.490 225s 20 0.889 1.412 225s > print( residuals( fit3slsi[[ 1 ]]$e2we$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s -0.376 -1.281 1.786 0.942 2.683 1.699 2.083 -2.534 -0.736 2.713 -1.748 225s 12 13 14 15 16 17 18 19 20 225s -4.518 -3.502 -0.901 3.286 -2.334 1.438 -1.911 2.320 0.889 225s > 225s > print( residuals( fit3slsd[[ 3 ]]$e4 ) ) 225s demand supply 225s 1 0.7282 0.088 225s 2 -0.7938 -0.850 225s 3 2.2722 2.054 225s 4 1.3947 1.007 225s 5 2.2092 2.526 225s 6 1.3211 1.378 225s 7 1.6076 1.935 225s 8 -3.0646 -4.397 225s 9 -1.0534 -1.692 225s 10 2.6003 3.674 225s 11 -0.1888 -0.319 225s 12 -2.4839 -2.564 225s 13 -1.8018 -2.397 225s 14 -0.3164 0.423 225s 15 2.1290 3.682 225s 16 -3.3141 -3.704 225s 17 -0.0169 1.445 225s 18 -2.1692 -3.473 225s 19 1.6008 1.716 225s 20 -0.6603 -0.530 225s > print( residuals( fit3slsd[[ 3 ]]$e4$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s 0.088 -0.850 2.054 1.007 2.526 1.378 1.935 -4.397 -1.692 3.674 -0.319 225s 12 13 14 15 16 17 18 19 20 225s -2.564 -2.397 0.423 3.682 -3.704 1.445 -3.473 1.716 -0.530 225s > 225s > print( residuals( fit3slsd[[ 5 ]]$e5we ) ) 225s demand supply 225s 1 3.290 2.057 225s 2 0.781 0.154 225s 3 3.754 2.921 225s 4 2.915 1.707 225s 5 0.906 1.148 225s 6 0.394 0.120 225s 7 0.632 0.775 225s 8 -3.766 -7.138 225s 9 -2.167 -3.402 225s 10 1.391 4.066 225s 11 2.631 3.690 225s 12 2.043 3.077 225s 13 2.405 2.007 225s 14 0.885 2.914 225s 15 -1.051 2.024 225s 16 -5.729 -6.584 225s 17 -4.810 -1.328 225s 18 -2.329 -4.924 225s 19 0.576 0.472 225s 20 -2.753 -3.755 225s > print( residuals( fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 225s 2.057 0.154 2.921 1.707 1.148 0.120 0.775 -7.138 -3.402 4.066 3.690 225s 12 13 14 15 16 17 18 19 20 225s 3.077 2.007 2.914 2.024 -6.584 -1.328 -4.924 0.472 -3.755 225s > 225s > 225s > ## *************** coefficients ********************* 225s > print( round( coef( fit3sls[[ 3 ]]$e1c ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 94.633 -0.244 0.314 52.287 225s supply_price supply_farmPrice supply_trend 225s 0.228 0.227 0.365 225s > print( round( coef( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ), digits = 6 ) ) 225s (Intercept) price farmPrice trend 225s 52.287 0.228 0.227 0.365 225s > 225s > print( round( coef( fit3slsi[[ 4 ]]$e2 ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 92.074 -0.106 0.200 68.855 225s supply_price supply_farmPrice supply_trend 225s 0.183 0.120 0.200 225s > print( round( coef( fit3slsi[[ 5 ]]$e2$eq[[ 1 ]] ), digits = 6 ) ) 225s (Intercept) price income 225s 92.074 -0.106 0.200 225s > 225s > print( round( coef( fit3sls[[ 2 ]]$e2w ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 94.182 -0.219 0.294 56.254 225s supply_price supply_farmPrice supply_trend 225s 0.218 0.204 0.294 225s > print( round( coef( fit3sls[[ 3 ]]$e2w$eq[[ 1 ]] ), digits = 6 ) ) 225s (Intercept) price income 225s 94.182 -0.219 0.294 225s > 225s > print( round( coef( fit3slsd[[ 5 ]]$e3e ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 109.109 -0.442 0.369 57.268 225s supply_price supply_farmPrice supply_trend 225s 0.137 0.269 0.369 225s > print( round( coef( fit3slsd[[ 5 ]]$e3e, modified.regMat = TRUE ), digits = 6 ) ) 225s C1 C2 C3 C4 C5 C6 225s 109.109 -0.442 0.369 57.268 0.137 0.269 225s > print( round( coef( fit3slsd[[ 1 ]]$e3e$eq[[ 2 ]] ), digits = 6 ) ) 225s (Intercept) price farmPrice trend 225s 40.818 0.357 0.219 0.303 225s > 225s > print( round( coef( fit3slsd[[ 4 ]]$e3w ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 100.174 -0.325 0.341 49.743 225s supply_price supply_farmPrice supply_trend 225s 0.237 0.247 0.341 225s > print( round( coef( fit3slsd[[ 4 ]]$e3w, modified.regMat = TRUE ), digits = 6 ) ) 225s C1 C2 C3 C4 C5 C6 225s 100.174 -0.325 0.341 49.743 0.237 0.247 225s > print( round( coef( fit3slsd[[ 5 ]]$e3w$eq[[ 2 ]] ), digits = 6 ) ) 225s (Intercept) price farmPrice trend 225s 57.667 0.133 0.270 0.370 225s > 225s > print( round( coef( fit3sls[[ 1 ]]$e4 ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 93.907 -0.246 0.324 49.905 225s supply_price supply_farmPrice supply_trend 225s 0.254 0.229 0.324 225s > print( round( coef( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ), digits = 6 ) ) 225s (Intercept) price income 225s 93.907 -0.246 0.324 225s > 225s > print( round( coef( fit3slsi[[ 2 ]]$e4we ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 91.390 -0.217 0.320 47.579 225s supply_price supply_farmPrice supply_trend 225s 0.283 0.224 0.320 225s > print( round( coef( fit3slsi[[ 1 ]]$e4we$eq[[ 1 ]] ), digits = 6 ) ) 225s (Intercept) price income 225s 91.390 -0.217 0.320 225s > 225s > print( round( coef( fit3slsi[[ 2 ]]$e5e ), digits = 6 ) ) 225s demand_(Intercept) demand_price demand_income supply_(Intercept) 225s 91.390 -0.217 0.320 47.579 225s supply_price supply_farmPrice supply_trend 225s 0.283 0.224 0.320 225s > print( round( coef( fit3slsi[[ 2 ]]$e5e, modified.regMat = TRUE ), digits = 6 ) ) 225s C1 C2 C3 C4 C5 C6 225s 91.390 -0.217 0.320 47.579 0.283 0.224 225s > print( round( coef( fit3slsi[[ 3 ]]$e5e$eq[[ 2 ]] ), digits = 6 ) ) 225s (Intercept) price farmPrice trend 225s 47.579 0.283 0.224 0.320 225s > 225s > 225s > ## *************** coefficients with stats ********************* 225s > print( round( coef( summary( fit3sls[[ 3 ]]$e1c, useDfSys = FALSE ) ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 94.633 7.9208 11.95 0.000000 225s demand_price -0.244 0.0965 -2.52 0.021832 225s demand_income 0.314 0.0469 6.69 0.000004 225s supply_(Intercept) 52.287 11.8853 4.40 0.000448 225s supply_price 0.228 0.0997 2.29 0.035951 225s supply_farmPrice 0.227 0.0438 5.19 0.000089 225s supply_trend 0.365 0.0707 5.16 0.000095 225s > print( round( coef( summary( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]], useDfSys = FALSE ) ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 52.287 11.8853 4.40 0.000448 225s price 0.228 0.0997 2.29 0.035951 225s farmPrice 0.227 0.0438 5.19 0.000089 225s trend 0.365 0.0707 5.16 0.000095 225s > 225s > print( round( coef( summary( fit3slsd[[ 2 ]]$e1w, useDfSys = FALSE ) ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 106.789 11.1435 9.58 0.000000 225s demand_price -0.412 0.1448 -2.84 0.011271 225s demand_income 0.362 0.0564 6.41 0.000006 225s supply_(Intercept) 57.295 11.7078 4.89 0.000162 225s supply_price 0.137 0.0979 1.40 0.179781 225s supply_farmPrice 0.266 0.0483 5.51 0.000048 225s supply_trend 0.397 0.0672 5.91 0.000022 225s > print( round( coef( summary( fit3slsd[[ 3 ]]$e1w$eq[[ 2 ]], useDfSys = FALSE ) ), 225s + digits = 3 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 49.532 12.011 4.12 0.001 225s price 0.240 0.100 2.40 0.029 225s farmPrice 0.256 0.047 5.41 0.000 225s trend 0.253 0.100 2.54 0.022 225s > 225s > print( round( coef( summary( fit3slsi[[ 4 ]]$e2 ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 92.074 9.6303 9.56 0.000000 225s demand_price -0.106 0.1023 -1.04 0.305469 225s demand_income 0.200 0.0297 6.73 0.000000 225s supply_(Intercept) 68.855 12.4839 5.52 0.000004 225s supply_price 0.183 0.1189 1.54 0.132354 225s supply_farmPrice 0.120 0.0260 4.63 0.000051 225s supply_trend 0.200 0.0297 6.73 0.000000 225s > print( round( coef( summary( fit3slsi[[ 5 ]]$e2$eq[[ 1 ]] ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 92.074 9.6303 9.56 0.000 225s price -0.106 0.1023 -1.04 0.305 225s income 0.200 0.0297 6.73 0.000 225s > 225s > print( round( coef( summary( fit3slsd[[ 5 ]]$e3e, useDfSys = FALSE ) ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 109.109 5.8428 18.67 0.000000 225s demand_price -0.442 0.0737 -6.00 0.000014 225s demand_income 0.369 0.0432 8.54 0.000000 225s supply_(Intercept) 57.268 10.0564 5.69 0.000033 225s supply_price 0.137 0.0705 1.95 0.069081 225s supply_farmPrice 0.269 0.0403 6.68 0.000005 225s supply_trend 0.369 0.0432 8.54 0.000000 225s > print( round( coef( summary( fit3slsd[[ 5 ]]$e3e, useDfSys = FALSE ), 225s + modified.regMat = TRUE ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s C1 109.109 5.8428 18.67 NA 225s C2 -0.442 0.0737 -6.00 NA 225s C3 0.369 0.0432 8.54 NA 225s C4 57.268 10.0564 5.69 NA 225s C5 0.137 0.0705 1.95 NA 225s C6 0.269 0.0403 6.68 NA 225s > print( round( coef( summary( fit3slsd[[ 1 ]]$e3e$eq[[ 2 ]], useDfSys = FALSE ) ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 40.818 10.0564 4.06 0.000912 225s price 0.357 0.0705 5.06 0.000116 225s farmPrice 0.219 0.0403 5.45 0.000053 225s trend 0.303 0.0432 7.00 0.000003 225s > 225s > print( round( coef( summary( fit3slsi[[ 4 ]]$e3w, useDfSys = FALSE ) ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 92.074 9.6303 9.56 0.000000 225s demand_price -0.106 0.1023 -1.04 0.312700 225s demand_income 0.200 0.0297 6.73 0.000004 225s supply_(Intercept) 68.855 12.4839 5.52 0.000047 225s supply_price 0.183 0.1189 1.54 0.142642 225s supply_farmPrice 0.120 0.0260 4.63 0.000278 225s supply_trend 0.200 0.0297 6.73 0.000005 225s > print( round( coef( summary( fit3slsi[[ 4 ]]$e3w, useDfSys = FALSE ), 225s + modified.regMat = TRUE ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s C1 92.074 9.6303 9.56 NA 225s C2 -0.106 0.1023 -1.04 NA 225s C3 0.200 0.0297 6.73 NA 225s C4 68.855 12.4839 5.52 NA 225s C5 0.183 0.1189 1.54 NA 225s C6 0.120 0.0260 4.63 NA 225s > print( round( coef( summary( fit3slsi[[ 5 ]]$e3w$eq[[ 2 ]], useDfSys = FALSE ) ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 68.855 12.4839 5.52 0.000047 225s price 0.183 0.1189 1.54 0.142642 225s farmPrice 0.120 0.0260 4.63 0.000278 225s trend 0.200 0.0297 6.73 0.000005 225s > 225s > print( round( coef( summary( fit3sls[[ 1 ]]$e4 ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 93.907 7.9234 11.85 0.000000 225s demand_price -0.246 0.0891 -2.76 0.009212 225s demand_income 0.324 0.0233 13.91 0.000000 225s supply_(Intercept) 49.905 8.1797 6.10 0.000001 225s supply_price 0.254 0.0891 2.85 0.007217 225s supply_farmPrice 0.229 0.0241 9.52 0.000000 225s supply_trend 0.324 0.0233 13.91 0.000000 225s > print( round( coef( summary( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 93.907 7.9234 11.85 0.00000 225s price -0.246 0.0891 -2.76 0.00921 225s income 0.324 0.0233 13.91 0.00000 225s > 225s > print( round( coef( summary( fit3slsi[[ 2 ]]$e5e ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 91.390 7.3161 12.49 0.00000 225s demand_price -0.217 0.0835 -2.60 0.01365 225s demand_income 0.320 0.0168 19.07 0.00000 225s supply_(Intercept) 47.579 7.4268 6.41 0.00000 225s supply_price 0.283 0.0835 3.39 0.00174 225s supply_farmPrice 0.224 0.0168 13.36 0.00000 225s supply_trend 0.320 0.0168 19.07 0.00000 225s > print( round( coef( summary( fit3slsi[[ 2 ]]$e5e ), modified.regMat = TRUE ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s C1 91.390 7.3161 12.49 0.00000 225s C2 -0.217 0.0835 -2.60 0.01365 225s C3 0.320 0.0168 19.07 0.00000 225s C4 47.579 7.4268 6.41 0.00000 225s C5 0.283 0.0835 3.39 0.00174 225s C6 0.224 0.0168 13.36 0.00000 225s > print( round( coef( summary( fit3slsi[[ 3 ]]$e5e$eq[[ 2 ]] ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 47.579 7.4268 6.41 0.00000 225s price 0.283 0.0835 3.39 0.00174 225s farmPrice 0.224 0.0168 13.36 0.00000 225s trend 0.320 0.0168 19.07 0.00000 225s > 225s > print( round( coef( summary( fit3sls[[ 2 ]]$e5we ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s demand_(Intercept) 94.083 7.3058 12.88 0.00000 225s demand_price -0.248 0.0812 -3.06 0.00424 225s demand_income 0.325 0.0205 15.81 0.00000 225s supply_(Intercept) 50.019 7.5314 6.64 0.00000 225s supply_price 0.252 0.0812 3.10 0.00383 225s supply_farmPrice 0.231 0.0209 11.05 0.00000 225s supply_trend 0.325 0.0205 15.81 0.00000 225s > print( round( coef( summary( fit3sls[[ 2 ]]$e5we ), modified.regMat = TRUE ), 225s + digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s C1 94.083 7.3058 12.88 0.00000 225s C2 -0.248 0.0812 -3.06 0.00424 225s C3 0.325 0.0205 15.81 0.00000 225s C4 50.019 7.5314 6.64 0.00000 225s C5 0.252 0.0812 3.10 0.00383 225s C6 0.231 0.0209 11.05 0.00000 225s > print( round( coef( summary( fit3sls[[ 3 ]]$e5we$eq[[ 2 ]] ) ), digits = 6 ) ) 225s Estimate Std. Error t value Pr(>|t|) 225s (Intercept) 50.019 7.5314 6.64 0.00000 225s price 0.252 0.0812 3.10 0.00383 225s farmPrice 0.231 0.0209 11.05 0.00000 225s trend 0.325 0.0205 15.81 0.00000 225s > 225s > 225s > ## *********** variance covariance matrix of the coefficients ******* 225s > print( round( vcov( fit3sls[[ 3 ]]$e1c ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 62.7397 -0.67342 0.04930 225s demand_price -0.6734 0.00931 -0.00264 225s demand_income 0.0493 -0.00264 0.00220 225s supply_(Intercept) 65.2708 -0.36561 -0.29198 225s supply_price -0.6979 0.00620 0.00079 225s supply_farmPrice 0.0423 -0.00227 0.00189 225s supply_trend 0.0638 -0.00342 0.00285 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 65.271 -0.69790 0.04230 225s demand_price -0.366 0.00620 -0.00227 225s demand_income -0.292 0.00079 0.00189 225s supply_(Intercept) 141.261 -1.08251 -0.29300 225s supply_price -1.083 0.00993 0.00080 225s supply_farmPrice -0.293 0.00080 0.00192 225s supply_trend -0.417 0.00110 0.00263 225s supply_trend 225s demand_(Intercept) 0.06383 225s demand_price -0.00342 225s demand_income 0.00285 225s supply_(Intercept) -0.41674 225s supply_price 0.00110 225s supply_farmPrice 0.00263 225s supply_trend 0.00500 225s > print( round( vcov( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 141.261 -1.08251 -0.29300 -0.41674 225s price -1.083 0.00993 0.00080 0.00110 225s farmPrice -0.293 0.00080 0.00192 0.00263 225s trend -0.417 0.00110 0.00263 0.00500 225s > 225s > print( round( vcov( fit3sls[[ 4 ]]$e2 ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 64.2351 -0.68447 0.04535 225s demand_price -0.6845 0.00921 -0.00243 225s demand_income 0.0454 -0.00243 0.00203 225s supply_(Intercept) 67.0281 -0.42600 -0.24804 225s supply_price -0.7080 0.00641 0.00069 225s supply_farmPrice 0.0366 -0.00196 0.00164 225s supply_trend 0.0454 -0.00243 0.00203 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 67.028 -0.70800 0.03661 225s demand_price -0.426 0.00641 -0.00196 225s demand_income -0.248 0.00069 0.00164 225s supply_(Intercept) 134.043 -1.07653 -0.24277 225s supply_price -1.077 0.01003 0.00068 225s supply_farmPrice -0.243 0.00068 0.00163 225s supply_trend -0.248 0.00069 0.00164 225s supply_trend 225s demand_(Intercept) 0.04535 225s demand_price -0.00243 225s demand_income 0.00203 225s supply_(Intercept) -0.24804 225s supply_price 0.00069 225s supply_farmPrice 0.00164 225s supply_trend 0.00203 225s > print( round( vcov( fit3sls[[ 5 ]]$e2$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 64.2351 -0.68447 0.04535 225s price -0.6845 0.00921 -0.00243 225s income 0.0454 -0.00243 0.00203 225s > 225s > print( round( vcov( fit3sls[[ 5 ]]$e3e ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 54.6190 -0.58283 0.03940 225s demand_price -0.5828 0.00789 -0.00211 225s demand_income 0.0394 -0.00211 0.00176 225s supply_(Intercept) 55.1360 -0.34396 -0.21065 225s supply_price -0.5835 0.00527 0.00058 225s supply_farmPrice 0.0310 -0.00166 0.00139 225s supply_trend 0.0394 -0.00211 0.00176 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 55.136 -0.58348 0.03102 225s demand_price -0.344 0.00527 -0.00166 225s demand_income -0.211 0.00058 0.00139 225s supply_(Intercept) 108.147 -0.86360 -0.19987 225s supply_price -0.864 0.00803 0.00056 225s supply_farmPrice -0.200 0.00056 0.00134 225s supply_trend -0.211 0.00058 0.00139 225s supply_trend 225s demand_(Intercept) 0.03940 225s demand_price -0.00211 225s demand_income 0.00176 225s supply_(Intercept) -0.21065 225s supply_price 0.00058 225s supply_farmPrice 0.00139 225s supply_trend 0.00176 225s > print( round( vcov( fit3sls[[ 5 ]]$e3e, modified.regMat = TRUE ), digits = 5 ) ) 225s C1 C2 C3 C4 C5 C6 225s C1 54.6190 -0.58283 0.03940 55.136 -0.58348 0.03102 225s C2 -0.5828 0.00789 -0.00211 -0.344 0.00527 -0.00166 225s C3 0.0394 -0.00211 0.00176 -0.211 0.00058 0.00139 225s C4 55.1360 -0.34396 -0.21065 108.147 -0.86360 -0.19987 225s C5 -0.5835 0.00527 0.00058 -0.864 0.00803 0.00056 225s C6 0.0310 -0.00166 0.00139 -0.200 0.00056 0.00134 225s > print( round( vcov( fit3sls[[ 1 ]]$e3e$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 108.147 -0.86360 -0.19987 -0.21065 225s price -0.864 0.00803 0.00056 0.00058 225s farmPrice -0.200 0.00056 0.00134 0.00139 225s trend -0.211 0.00058 0.00139 0.00176 225s > 225s > print( round( vcov( fit3sls[[ 1 ]]$e4 ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 62.7805 -0.68439 0.06014 225s demand_price -0.6844 0.00794 -0.00113 225s demand_income 0.0601 -0.00113 0.00054 225s supply_(Intercept) 63.2287 -0.69892 0.07078 225s supply_price -0.6844 0.00794 -0.00113 225s supply_farmPrice 0.0499 -0.00087 0.00038 225s supply_trend 0.0601 -0.00113 0.00054 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 63.2287 -0.68439 0.04986 225s demand_price -0.6989 0.00794 -0.00087 225s demand_income 0.0708 -0.00113 0.00038 225s supply_(Intercept) 66.9073 -0.69892 0.02657 225s supply_price -0.6989 0.00794 -0.00087 225s supply_farmPrice 0.0266 -0.00087 0.00058 225s supply_trend 0.0708 -0.00113 0.00038 225s supply_trend 225s demand_(Intercept) 0.06014 225s demand_price -0.00113 225s demand_income 0.00054 225s supply_(Intercept) 0.07078 225s supply_price -0.00113 225s supply_farmPrice 0.00038 225s supply_trend 0.00054 225s > print( round( vcov( fit3sls[[ 2 ]]$e4$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 62.7805 -0.68439 0.06014 225s price -0.6844 0.00794 -0.00113 225s income 0.0601 -0.00113 0.00054 225s > 225s > print( round( vcov( fit3sls[[ 3 ]]$e4wSym ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 62.5490 -0.68436 0.06248 225s demand_price -0.6844 0.00795 -0.00113 225s demand_income 0.0625 -0.00113 0.00052 225s supply_(Intercept) 62.9766 -0.69799 0.07241 225s supply_price -0.6844 0.00795 -0.00113 225s supply_farmPrice 0.0522 -0.00088 0.00037 225s supply_trend 0.0625 -0.00113 0.00052 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 62.9766 -0.68436 0.05220 225s demand_price -0.6980 0.00795 -0.00088 225s demand_income 0.0724 -0.00113 0.00037 225s supply_(Intercept) 66.4588 -0.69799 0.03007 225s supply_price -0.6980 0.00795 -0.00088 225s supply_farmPrice 0.0301 -0.00088 0.00056 225s supply_trend 0.0724 -0.00113 0.00037 225s supply_trend 225s demand_(Intercept) 0.06248 225s demand_price -0.00113 225s demand_income 0.00052 225s supply_(Intercept) 0.07241 225s supply_price -0.00113 225s supply_farmPrice 0.00037 225s supply_trend 0.00052 225s > print( round( vcov( fit3sls[[ 4 ]]$e4wSym$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 62.5490 -0.68436 0.06248 225s price -0.6844 0.00795 -0.00113 225s income 0.0625 -0.00113 0.00052 225s > 225s > print( round( vcov( fit3sls[[ 2 ]]$e5e ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 53.5147 -0.57537 0.04304 225s demand_price -0.5754 0.00659 -0.00085 225s demand_income 0.0430 -0.00085 0.00044 225s supply_(Intercept) 53.9493 -0.58881 0.05259 225s supply_price -0.5754 0.00659 -0.00085 225s supply_farmPrice 0.0345 -0.00063 0.00029 225s supply_trend 0.0430 -0.00085 0.00044 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 53.9493 -0.57537 0.03449 225s demand_price -0.5888 0.00659 -0.00063 225s demand_income 0.0526 -0.00085 0.00029 225s supply_(Intercept) 57.0063 -0.58881 0.01639 225s supply_price -0.5888 0.00659 -0.00063 225s supply_farmPrice 0.0164 -0.00063 0.00045 225s supply_trend 0.0526 -0.00085 0.00029 225s supply_trend 225s demand_(Intercept) 0.04304 225s demand_price -0.00085 225s demand_income 0.00044 225s supply_(Intercept) 0.05259 225s supply_price -0.00085 225s supply_farmPrice 0.00029 225s supply_trend 0.00044 225s > print( round( vcov( fit3sls[[ 2 ]]$e5e, modified.regMat = TRUE ), digits = 5 ) ) 225s C1 C2 C3 C4 C5 C6 225s C1 53.5147 -0.57537 0.04304 53.9493 -0.57537 0.03449 225s C2 -0.5754 0.00659 -0.00085 -0.5888 0.00659 -0.00063 225s C3 0.0430 -0.00085 0.00044 0.0526 -0.00085 0.00029 225s C4 53.9493 -0.58881 0.05259 57.0063 -0.58881 0.01639 225s C5 -0.5754 0.00659 -0.00085 -0.5888 0.00659 -0.00063 225s C6 0.0345 -0.00063 0.00029 0.0164 -0.00063 0.00045 225s > print( round( vcov( fit3sls[[ 3 ]]$e5e$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 57.0063 -0.58881 0.01639 0.05259 225s price -0.5888 0.00659 -0.00063 -0.00085 225s farmPrice 0.0164 -0.00063 0.00045 0.00029 225s trend 0.0526 -0.00085 0.00029 0.00044 225s > 225s > print( round( vcov( fit3slsi[[ 4 ]]$e1e ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 53.3287 -0.57241 0.04191 225s demand_price -0.5724 0.00791 -0.00225 225s demand_income 0.0419 -0.00225 0.00187 225s supply_(Intercept) 60.8329 -0.34075 -0.27213 225s supply_price -0.6504 0.00578 0.00074 225s supply_farmPrice 0.0394 -0.00211 0.00176 225s supply_trend 0.0595 -0.00319 0.00266 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 60.833 -0.65044 0.03942 225s demand_price -0.341 0.00578 -0.00211 225s demand_income -0.272 0.00074 0.00176 225s supply_(Intercept) 129.860 -0.99616 -0.26688 225s supply_price -0.996 0.00915 0.00073 225s supply_farmPrice -0.267 0.00073 0.00173 225s supply_trend -0.396 0.00107 0.00255 225s supply_trend 225s demand_(Intercept) 0.05949 225s demand_price -0.00319 225s demand_income 0.00266 225s supply_(Intercept) -0.39621 225s supply_price 0.00107 225s supply_farmPrice 0.00255 225s supply_trend 0.00411 225s > print( round( vcov( fit3slsi[[ 3 ]]$e1e$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 53.3287 -0.57241 0.04191 225s price -0.5724 0.00791 -0.00225 225s income 0.0419 -0.00225 0.00187 225s > 225s > print( round( vcov( fit3slsi[[ 5 ]]$e1we ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 53.3287 -0.57241 0.04191 225s demand_price -0.5724 0.00791 -0.00225 225s demand_income 0.0419 -0.00225 0.00187 225s supply_(Intercept) 60.8329 -0.34075 -0.27213 225s supply_price -0.6504 0.00578 0.00074 225s supply_farmPrice 0.0394 -0.00211 0.00176 225s supply_trend 0.0595 -0.00319 0.00266 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 60.833 -0.65044 0.03942 225s demand_price -0.341 0.00578 -0.00211 225s demand_income -0.272 0.00074 0.00176 225s supply_(Intercept) 129.860 -0.99616 -0.26688 225s supply_price -0.996 0.00915 0.00073 225s supply_farmPrice -0.267 0.00073 0.00173 225s supply_trend -0.396 0.00107 0.00255 225s supply_trend 225s demand_(Intercept) 0.05949 225s demand_price -0.00319 225s demand_income 0.00266 225s supply_(Intercept) -0.39621 225s supply_price 0.00107 225s supply_farmPrice 0.00255 225s supply_trend 0.00411 225s > print( round( vcov( fit3slsi[[ 1 ]]$e1we$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 129.860 -0.99616 -0.26688 -0.39621 225s price -0.996 0.00915 0.00073 0.00107 225s farmPrice -0.267 0.00073 0.00173 0.00255 225s trend -0.396 0.00107 0.00255 0.00411 225s > 225s > print( round( vcov( fit3slsi[[ 5 ]]$e2e ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 79.5917 -0.81281 0.02003 225s demand_price -0.8128 0.00917 -0.00107 225s demand_income 0.0200 -0.00107 0.00090 225s supply_(Intercept) 90.3437 -0.79178 -0.11134 225s supply_price -0.9184 0.00888 0.00031 225s supply_farmPrice 0.0165 -0.00088 0.00074 225s supply_trend 0.0200 -0.00107 0.00090 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 90.3437 -0.91836 0.01646 225s demand_price -0.7918 0.00888 -0.00088 225s demand_income -0.1113 0.00031 0.00074 225s supply_(Intercept) 124.3894 -1.13680 -0.09494 225s supply_price -1.1368 0.01108 0.00026 225s supply_farmPrice -0.0949 0.00026 0.00063 225s supply_trend -0.1113 0.00031 0.00074 225s supply_trend 225s demand_(Intercept) 0.02003 225s demand_price -0.00107 225s demand_income 0.00090 225s supply_(Intercept) -0.11134 225s supply_price 0.00031 225s supply_farmPrice 0.00074 225s supply_trend 0.00090 225s > print( round( vcov( fit3slsi[[ 4 ]]$e2e$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 124.3894 -1.13680 -0.09494 -0.11134 225s price -1.1368 0.01108 0.00026 0.00031 225s farmPrice -0.0949 0.00026 0.00063 0.00074 225s trend -0.1113 0.00031 0.00074 0.00090 225s > 225s > print( round( vcov( fit3slsi[[ 1 ]]$e3 ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 92.7431 -0.94355 0.01968 225s demand_price -0.9435 0.01046 -0.00105 225s demand_income 0.0197 -0.00105 0.00088 225s supply_(Intercept) 110.7701 -0.99345 -0.11331 225s supply_price -1.1222 0.01091 0.00031 225s supply_farmPrice 0.0168 -0.00090 0.00075 225s supply_trend 0.0197 -0.00105 0.00088 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 110.770 -1.12223 0.01680 225s demand_price -0.993 0.01091 -0.00090 225s demand_income -0.113 0.00031 0.00075 225s supply_(Intercept) 155.849 -1.44407 -0.10125 225s supply_price -1.444 0.01413 0.00028 225s supply_farmPrice -0.101 0.00028 0.00067 225s supply_trend -0.113 0.00031 0.00075 225s supply_trend 225s demand_(Intercept) 0.01968 225s demand_price -0.00105 225s demand_income 0.00088 225s supply_(Intercept) -0.11331 225s supply_price 0.00031 225s supply_farmPrice 0.00075 225s supply_trend 0.00088 225s > print( round( vcov( fit3slsi[[ 1 ]]$e3, modified.regMat = TRUE ), digits = 5 ) ) 225s C1 C2 C3 C4 C5 C6 225s C1 92.7431 -0.94355 0.01968 110.770 -1.12223 0.01680 225s C2 -0.9435 0.01046 -0.00105 -0.993 0.01091 -0.00090 225s C3 0.0197 -0.00105 0.00088 -0.113 0.00031 0.00075 225s C4 110.7701 -0.99345 -0.11331 155.849 -1.44407 -0.10125 225s C5 -1.1222 0.01091 0.00031 -1.444 0.01413 0.00028 225s C6 0.0168 -0.00090 0.00075 -0.101 0.00028 0.00067 225s > print( round( vcov( fit3slsi[[ 5 ]]$e3$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 92.7431 -0.94355 0.01968 225s price -0.9435 0.01046 -0.00105 225s income 0.0197 -0.00105 0.00088 225s > 225s > print( round( vcov( fit3slsi[[ 2 ]]$e4e ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 53.5249 -0.60193 0.07023 225s demand_price -0.6019 0.00697 -0.00098 225s demand_income 0.0702 -0.00098 0.00028 225s supply_(Intercept) 53.7695 -0.60749 0.07383 225s supply_price -0.6019 0.00697 -0.00098 225s supply_farmPrice 0.0611 -0.00082 0.00022 225s supply_trend 0.0702 -0.00098 0.00028 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 53.7695 -0.60193 0.06114 225s demand_price -0.6075 0.00697 -0.00082 225s demand_income 0.0738 -0.00098 0.00022 225s supply_(Intercept) 55.1575 -0.60749 0.05283 225s supply_price -0.6075 0.00697 -0.00082 225s supply_farmPrice 0.0528 -0.00082 0.00028 225s supply_trend 0.0738 -0.00098 0.00022 225s supply_trend 225s demand_(Intercept) 0.07023 225s demand_price -0.00098 225s demand_income 0.00028 225s supply_(Intercept) 0.07383 225s supply_price -0.00098 225s supply_farmPrice 0.00022 225s supply_trend 0.00028 225s > print( round( vcov( fit3slsi[[ 1 ]]$e4e$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 55.1575 -0.60749 0.05283 0.07383 225s price -0.6075 0.00697 -0.00082 -0.00098 225s farmPrice 0.0528 -0.00082 0.00028 0.00022 225s trend 0.0738 -0.00098 0.00022 0.00028 225s > 225s > print( round( vcov( fit3slsi[[ 3 ]]$e5 ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 62.6857 -0.71803 0.09573 225s demand_price -0.7180 0.00846 -0.00132 225s demand_income 0.0957 -0.00132 0.00037 225s supply_(Intercept) 62.7317 -0.72119 0.09909 225s supply_price -0.7180 0.00846 -0.00132 225s supply_farmPrice 0.0863 -0.00115 0.00030 225s supply_trend 0.0957 -0.00132 0.00037 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 62.7317 -0.71803 0.08635 225s demand_price -0.7212 0.00846 -0.00115 225s demand_income 0.0991 -0.00132 0.00030 225s supply_(Intercept) 64.1668 -0.72119 0.07539 225s supply_price -0.7212 0.00846 -0.00115 225s supply_farmPrice 0.0754 -0.00115 0.00038 225s supply_trend 0.0991 -0.00132 0.00030 225s supply_trend 225s demand_(Intercept) 0.09573 225s demand_price -0.00132 225s demand_income 0.00037 225s supply_(Intercept) 0.09909 225s supply_price -0.00132 225s supply_farmPrice 0.00030 225s supply_trend 0.00037 225s > print( round( vcov( fit3slsi[[ 3 ]]$e5, modified.regMat = TRUE ), digits = 5 ) ) 225s C1 C2 C3 C4 C5 C6 225s C1 62.6857 -0.71803 0.09573 62.7317 -0.71803 0.08635 225s C2 -0.7180 0.00846 -0.00132 -0.7212 0.00846 -0.00115 225s C3 0.0957 -0.00132 0.00037 0.0991 -0.00132 0.00030 225s C4 62.7317 -0.72119 0.09909 64.1668 -0.72119 0.07539 225s C5 -0.7180 0.00846 -0.00132 -0.7212 0.00846 -0.00115 225s C6 0.0863 -0.00115 0.00030 0.0754 -0.00115 0.00038 225s > print( round( vcov( fit3slsi[[ 2 ]]$e5$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 62.6857 -0.71803 0.09573 225s price -0.7180 0.00846 -0.00132 225s income 0.0957 -0.00132 0.00037 225s > 225s > print( round( vcov( fit3slsi[[ 5 ]]$e5w ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 107.334 -1.39936 0.34281 225s demand_price -1.399 0.01904 -0.00518 225s demand_income 0.343 -0.00518 0.00179 225s supply_(Intercept) 95.422 -1.22389 0.29205 225s supply_price -1.399 0.01904 -0.00518 225s supply_farmPrice 0.439 -0.00648 0.00214 225s supply_trend 0.343 -0.00518 0.00179 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 95.422 -1.39936 0.43918 225s demand_price -1.224 0.01904 -0.00648 225s demand_income 0.292 -0.00518 0.00214 225s supply_(Intercept) 92.381 -1.22389 0.30881 225s supply_price -1.224 0.01904 -0.00648 225s supply_farmPrice 0.309 -0.00648 0.00328 225s supply_trend 0.292 -0.00518 0.00214 225s supply_trend 225s demand_(Intercept) 0.34281 225s demand_price -0.00518 225s demand_income 0.00179 225s supply_(Intercept) 0.29205 225s supply_price -0.00518 225s supply_farmPrice 0.00214 225s supply_trend 0.00179 225s > print( round( vcov( fit3slsi[[ 5 ]]$e5w, modified.regMat = TRUE ), digits = 5 ) ) 225s C1 C2 C3 C4 C5 C6 225s C1 107.334 -1.39936 0.34281 95.422 -1.39936 0.43918 225s C2 -1.399 0.01904 -0.00518 -1.224 0.01904 -0.00648 225s C3 0.343 -0.00518 0.00179 0.292 -0.00518 0.00214 225s C4 95.422 -1.22389 0.29205 92.381 -1.22389 0.30881 225s C5 -1.399 0.01904 -0.00518 -1.224 0.01904 -0.00648 225s C6 0.439 -0.00648 0.00214 0.309 -0.00648 0.00328 225s > print( round( vcov( fit3slsi[[ 4 ]]$e5w$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 62.6858 -0.71803 0.09573 225s price -0.7180 0.00846 -0.00132 225s income 0.0957 -0.00132 0.00037 225s > 225s > print( round( vcov( fit3slsd[[ 5 ]]$e1c ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 124.179 -1.51767 0.28519 225s demand_price -1.518 0.02098 -0.00595 225s demand_income 0.285 -0.00595 0.00318 225s supply_(Intercept) 45.831 -0.16114 -0.30261 225s supply_price -0.564 0.00477 0.00089 225s supply_farmPrice 0.157 -0.00365 0.00213 225s supply_trend -0.416 0.00351 0.00066 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 45.831 -0.56422 0.15696 225s demand_price -0.161 0.00477 -0.00365 225s demand_income -0.303 0.00089 0.00213 225s supply_(Intercept) 132.389 -0.93831 -0.33973 225s supply_price -0.938 0.00791 0.00115 225s supply_farmPrice -0.340 0.00115 0.00221 225s supply_trend -0.515 0.00349 0.00108 225s supply_trend 225s demand_(Intercept) -0.41585 225s demand_price 0.00351 225s demand_income 0.00066 225s supply_(Intercept) -0.51541 225s supply_price 0.00349 225s supply_farmPrice 0.00108 225s supply_trend 0.00585 225s > print( round( vcov( fit3slsd[[ 2 ]]$e1c$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 136.580 -1.06234 -0.24479 -0.60682 225s price -0.994 0.00955 -0.00011 0.00471 225s farmPrice -0.334 0.00098 0.00234 0.00096 225s trend -0.438 0.00119 0.00284 0.00415 225s > 225s > print( round( vcov( fit3slsd[[ 1 ]]$e2 ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 40.2908 -0.42351 0.02315 225s demand_price -0.4235 0.00660 -0.00242 225s demand_income 0.0232 -0.00242 0.00225 225s supply_(Intercept) 23.1539 0.17811 -0.41781 225s supply_price -0.2648 0.00059 0.00211 225s supply_farmPrice 0.0342 -0.00220 0.00190 225s supply_trend 0.0232 -0.00242 0.00225 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 23.154 -0.26482 0.03423 225s demand_price 0.178 0.00059 -0.00220 225s demand_income -0.418 0.00211 0.00190 225s supply_(Intercept) 125.488 -0.81757 -0.40378 225s supply_price -0.818 0.00616 0.00186 225s supply_farmPrice -0.404 0.00186 0.00205 225s supply_trend -0.418 0.00211 0.00190 225s supply_trend 225s demand_(Intercept) 0.02315 225s demand_price -0.00242 225s demand_income 0.00225 225s supply_(Intercept) -0.41781 225s supply_price 0.00211 225s supply_farmPrice 0.00190 225s supply_trend 0.00225 225s > print( round( vcov( fit3slsd[[ 3 ]]$e2$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 99.763 -1.2027 0.21239 225s price -1.203 0.0168 -0.00490 225s income 0.212 -0.0049 0.00285 225s > 225s > print( round( vcov( fit3slsd[[ 5 ]]$e2we ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 34.9080 -0.36232 0.01530 225s demand_price -0.3623 0.00556 -0.00199 225s demand_income 0.0153 -0.00199 0.00188 225s supply_(Intercept) 20.3293 0.13409 -0.34409 225s supply_price -0.2272 0.00057 0.00174 225s supply_farmPrice 0.0249 -0.00176 0.00155 225s supply_trend 0.0153 -0.00199 0.00188 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 20.329 -0.22716 0.02494 225s demand_price 0.134 0.00057 -0.00176 225s demand_income -0.344 0.00174 0.00155 225s supply_(Intercept) 102.201 -0.66897 -0.32522 225s supply_price -0.669 0.00505 0.00150 225s supply_farmPrice -0.325 0.00150 0.00164 225s supply_trend -0.344 0.00174 0.00155 225s supply_trend 225s demand_(Intercept) 0.01530 225s demand_price -0.00199 225s demand_income 0.00188 225s supply_(Intercept) -0.34409 225s supply_price 0.00174 225s supply_farmPrice 0.00155 225s supply_trend 0.00188 225s > print( round( vcov( fit3slsd[[ 3 ]]$e2we$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 83.743 -1.0065 0.17519 225s price -1.006 0.0141 -0.00410 225s income 0.175 -0.0041 0.00241 225s > 225s > print( round( vcov( fit3slsd[[ 2 ]]$e3 ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 155.228 -2.21373 0.68055 225s demand_price -1.929 0.03005 -0.01103 225s demand_income 0.389 -0.00812 0.00434 225s supply_(Intercept) 120.424 -1.33693 0.13854 225s supply_price -1.546 0.02054 -0.00522 225s supply_farmPrice 0.314 -0.00655 0.00350 225s supply_trend 0.389 -0.00812 0.00434 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) -25.183 -0.42614 0.63002 225s demand_price 0.811 0.00271 -0.01000 225s demand_income -0.572 0.00159 0.00380 225s supply_(Intercept) 84.582 -0.95409 0.10043 225s supply_price -0.279 0.00796 -0.00478 225s supply_farmPrice -0.521 0.00147 0.00350 225s supply_trend -0.572 0.00159 0.00380 225s supply_trend 225s demand_(Intercept) 0.68055 225s demand_price -0.01103 225s demand_income 0.00434 225s supply_(Intercept) 0.13854 225s supply_price -0.00522 225s supply_farmPrice 0.00350 225s supply_trend 0.00434 225s > print( round( vcov( fit3slsd[[ 2 ]]$e3, modified.regMat = TRUE ), digits = 5 ) ) 225s C1 C2 C3 C4 C5 C6 225s C1 155.228 -2.21373 0.68055 -25.183 -0.42614 0.63002 225s C2 -1.929 0.03005 -0.01103 0.811 0.00271 -0.01000 225s C3 0.389 -0.00812 0.00434 -0.572 0.00159 0.00380 225s C4 120.424 -1.33693 0.13854 84.582 -0.95409 0.10043 225s C5 -1.546 0.02054 -0.00522 -0.279 0.00796 -0.00478 225s C6 0.314 -0.00655 0.00350 -0.521 0.00147 0.00350 225s > print( round( vcov( fit3slsd[[ 4 ]]$e3$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 149.704 -1.13641 -0.33425 -0.32676 225s price -1.136 0.01036 0.00094 0.00091 225s farmPrice -0.334 0.00094 0.00225 0.00216 225s trend -0.327 0.00091 0.00216 0.00259 225s > 225s > print( round( vcov( fit3slsd[[ 3 ]]$e4 ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 105.016 -1.17085 0.12591 225s demand_price -1.171 0.01356 -0.00191 225s demand_income 0.126 -0.00191 0.00066 225s supply_(Intercept) 106.127 -1.19320 0.13778 225s supply_price -1.171 0.01356 -0.00191 225s supply_farmPrice 0.102 -0.00148 0.00047 225s supply_trend 0.126 -0.00191 0.00066 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 106.1266 -1.17085 0.10227 225s demand_price -1.1932 0.01356 -0.00148 225s demand_income 0.1378 -0.00191 0.00047 225s supply_(Intercept) 110.0305 -1.19320 0.08453 225s supply_price -1.1932 0.01356 -0.00148 225s supply_farmPrice 0.0845 -0.00148 0.00061 225s supply_trend 0.1378 -0.00191 0.00047 225s supply_trend 225s demand_(Intercept) 0.12591 225s demand_price -0.00191 225s demand_income 0.00066 225s supply_(Intercept) 0.13778 225s supply_price -0.00191 225s supply_farmPrice 0.00047 225s supply_trend 0.00066 225s > print( round( vcov( fit3slsd[[ 5 ]]$e4$eq[[ 1 ]] ), digits = 5 ) ) 225s (Intercept) price income 225s (Intercept) 28.9118 -0.25481 -0.03319 225s price -0.2548 0.00254 0.00001 225s income -0.0332 0.00001 0.00033 225s > 225s > print( round( vcov( fit3slsd[[ 4 ]]$e5e ), digits = 5 ) ) 225s demand_(Intercept) demand_price demand_income 225s demand_(Intercept) 57.3878 -0.60414 0.03280 225s demand_price -0.6041 0.00675 -0.00073 225s demand_income 0.0328 -0.00073 0.00041 225s supply_(Intercept) 57.4828 -0.61352 0.04167 225s supply_price -0.6041 0.00675 -0.00073 225s supply_farmPrice 0.0288 -0.00056 0.00028 225s supply_trend 0.0328 -0.00073 0.00041 225s supply_(Intercept) supply_price supply_farmPrice 225s demand_(Intercept) 57.4828 -0.60414 0.02879 225s demand_price -0.6135 0.00675 -0.00056 225s demand_income 0.0417 -0.00073 0.00028 225s supply_(Intercept) 59.8263 -0.61352 0.01389 225s supply_price -0.6135 0.00675 -0.00056 225s supply_farmPrice 0.0139 -0.00056 0.00041 225s supply_trend 0.0417 -0.00073 0.00028 225s supply_trend 225s demand_(Intercept) 0.03280 225s demand_price -0.00073 225s demand_income 0.00041 225s supply_(Intercept) 0.04167 225s supply_price -0.00073 225s supply_farmPrice 0.00028 225s supply_trend 0.00041 225s > print( round( vcov( fit3slsd[[ 4 ]]$e5e, modified.regMat = TRUE ), digits = 5 ) ) 225s C1 C2 C3 C4 C5 C6 225s C1 57.3878 -0.60414 0.03280 57.4828 -0.60414 0.02879 225s C2 -0.6041 0.00675 -0.00073 -0.6135 0.00675 -0.00056 225s C3 0.0328 -0.00073 0.00041 0.0417 -0.00073 0.00028 225s C4 57.4828 -0.61352 0.04167 59.8263 -0.61352 0.01389 225s C5 -0.6041 0.00675 -0.00073 -0.6135 0.00675 -0.00056 225s C6 0.0288 -0.00056 0.00028 0.0139 -0.00056 0.00041 225s > print( round( vcov( fit3slsd[[ 1 ]]$e5e$eq[[ 2 ]] ), digits = 5 ) ) 225s (Intercept) price farmPrice trend 225s (Intercept) 24.9502 -0.21066 -0.03490 -0.02530 225s price -0.2107 0.00210 0.00000 0.00004 225s farmPrice -0.0349 0.00000 0.00034 0.00018 225s trend -0.0253 0.00004 0.00018 0.00028 225s > 225s > 225s > ## *********** confidence intervals of coefficients ************* 225s > print( confint( fit3sls[[ 1 ]]$e1c, useDfSys = TRUE ) ) 225s 2.5 % 97.5 % 225s demand_(Intercept) 78.518 110.748 225s demand_price -0.440 -0.047 225s demand_income 0.218 0.409 225s supply_(Intercept) 28.106 76.468 225s supply_price 0.025 0.431 225s supply_farmPrice 0.138 0.316 225s supply_trend 0.221 0.509 225s > print( confint( fit3sls[[ 1 ]]$e1c$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 225s 5 % 95 % 225s (Intercept) 81.228 108.038 225s price -0.407 -0.080 225s income 0.235 0.393 225s > 225s > print( confint( fit3sls[[ 2 ]]$e2e, level = 0.9, useDfSys = TRUE ) ) 225s 5 % 95 % 225s demand_(Intercept) 79.254 109.293 225s demand_price -0.405 -0.044 225s demand_income 0.213 0.383 225s supply_(Intercept) 34.318 76.586 225s supply_price 0.039 0.403 225s supply_farmPrice 0.135 0.284 225s supply_trend 0.213 0.383 225s > print( confint( fit3sls[[ 2 ]]$e2e$eq[[ 2 ]], level = 0.99, useDfSys = TRUE ) ) 225s 0.5 % 99.5 % 225s (Intercept) 27.079 83.826 225s price -0.024 0.465 225s farmPrice 0.110 0.309 225s trend 0.183 0.412 225s > 225s > print( confint( fit3sls[[ 3 ]]$e3, level = 0.99 ) ) 225s 0.5 % 99.5 % 225s demand_(Intercept) 77.934 110.509 225s demand_price -0.417 -0.026 225s demand_income 0.204 0.387 225s supply_(Intercept) 32.432 79.489 225s supply_price 0.016 0.423 225s supply_farmPrice 0.124 0.288 225s supply_trend 0.204 0.387 225s > print( confint( fit3sls[[ 3 ]]$e3$eq[[ 1 ]], level = 0.5 ) ) 225s 25 % 75 % 225s (Intercept) 88.757 99.686 225s price -0.287 -0.156 225s income 0.265 0.326 225s > 225s > print( confint( fit3sls[[ 5 ]]$e3we, level = 0.99 ) ) 225s 0.5 % 99.5 % 225s demand_(Intercept) 79.280 109.202 225s demand_price -0.402 -0.043 225s demand_income 0.212 0.381 225s supply_(Intercept) 34.570 76.815 225s supply_price 0.038 0.402 225s supply_farmPrice 0.134 0.282 225s supply_trend 0.212 0.381 225s > print( confint( fit3sls[[ 5 ]]$e3we$eq[[ 1 ]], level = 0.5 ) ) 225s 25 % 75 % 225s (Intercept) 89.222 99.260 225s price -0.283 -0.162 225s income 0.268 0.325 225s > 225s > print( confint( fit3sls[[ 4 ]]$e4e, level = 0.5, useDfSys = TRUE ) ) 225s 25 % 75 % 225s demand_(Intercept) 79.319 109.021 225s demand_price -0.414 -0.085 225s demand_income 0.282 0.367 225s supply_(Intercept) 34.758 65.413 225s supply_price 0.086 0.415 225s supply_farmPrice 0.188 0.274 225s supply_trend 0.282 0.367 225s > print( confint( fit3sls[[ 4 ]]$e4e$eq[[ 2 ]], level = 0.25, useDfSys = TRUE ) ) 225s 37.5 % 62.5 % 225s (Intercept) 47.661 52.510 225s price 0.224 0.277 225s farmPrice 0.224 0.238 225s trend 0.318 0.331 225s > 225s > print( confint( fit3sls[[ 5 ]]$e5, level = 0.25 ) ) 225s 37.5 % 62.5 % 225s demand_(Intercept) 75.213 107.384 225s demand_price -0.630 -0.268 225s demand_income 0.512 0.606 225s supply_(Intercept) -18.445 14.766 225s supply_price 0.370 0.732 225s supply_farmPrice 0.384 0.481 225s supply_trend 0.512 0.606 225s > print( confint( fit3sls[[ 5 ]]$e5$eq[[ 1 ]], level = 0.975 ) ) 225s 1.3 % 98.8 % 225s (Intercept) 72.742 109.855 225s price -0.658 -0.241 225s income 0.505 0.614 225s > 225s > print( confint( fit3slsi[[ 2 ]]$e3e, level = 0.975, useDfSys = TRUE ) ) 225s 1.3 % 98.8 % 225s demand_(Intercept) 73.905 110.166 225s demand_price -0.299 0.090 225s demand_income 0.137 0.259 225s supply_(Intercept) 45.617 90.949 225s supply_price -0.029 0.399 225s supply_farmPrice 0.073 0.175 225s supply_trend 0.137 0.259 225s > print( confint( fit3slsi[[ 2 ]]$e3e$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 225s 0.1 % 100 % 225s (Intercept) 59.912 124.159 225s price -0.449 0.241 225s income 0.090 0.306 225s > 225s > print( confint( fit3slsi[[ 1 ]]$e5w, level = 0.975, useDfSys = TRUE ) ) 225s 1.3 % 98.8 % 225s demand_(Intercept) 74.084 106.230 225s demand_price -0.387 -0.014 225s demand_income 0.277 0.355 225s supply_(Intercept) 30.219 62.743 225s supply_price 0.113 0.486 225s supply_farmPrice 0.179 0.259 225s supply_trend 0.277 0.355 225s > print( confint( fit3slsi[[ 1 ]]$e5w$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 225s 0.1 % 100 % 225s (Intercept) 61.724 118.590 225s price -0.531 0.130 225s income 0.247 0.385 225s > 225s > print( confint( fit3slsd[[ 3 ]]$e4, level = 0.999 ) ) 225s 0.1 % 100 % 225s demand_(Intercept) 72.590 114.198 225s demand_price -0.457 0.016 225s demand_income 0.251 0.356 225s supply_(Intercept) 27.716 70.305 225s supply_price 0.043 0.516 225s supply_farmPrice 0.165 0.265 225s supply_trend 0.251 0.356 225s > print( confint( fit3slsd[[ 3 ]]$e4$eq[[ 2 ]] ) ) 225s 2.5 % 97.5 % 225s (Intercept) 27.716 70.305 225s price 0.043 0.516 225s farmPrice 0.165 0.265 225s trend 0.251 0.356 225s > 225s > print( confint( fit3slsd[[ 2 ]]$e4w, level = 0.999 ) ) 225s 0.1 % 100 % 225s demand_(Intercept) 120.616 166.320 225s demand_price -1.063 -0.578 225s demand_income 0.371 0.439 225s supply_(Intercept) 77.414 123.333 225s supply_price -0.563 -0.078 225s supply_farmPrice 0.253 0.333 225s supply_trend 0.371 0.439 225s > print( confint( fit3slsd[[ 2 ]]$e4w$eq[[ 2 ]] ) ) 225s 2.5 % 97.5 % 225s (Intercept) 77.414 123.333 225s price -0.563 -0.078 225s farmPrice 0.253 0.333 225s trend 0.371 0.439 225s > 225s > 225s > ## *********** fitted values ************* 225s > print( fitted( fit3sls[[ 2 ]]$e1c ) ) 225s demand supply 225s 1 97.6 97.8 225s 2 99.9 99.3 225s 3 99.8 99.5 225s 4 100.0 99.9 225s 5 102.1 101.7 225s 6 102.0 101.8 225s 7 102.4 101.9 225s 8 103.0 104.1 225s 9 101.5 102.3 225s 10 100.3 99.6 225s 11 95.5 95.9 225s 12 94.7 94.8 225s 13 96.1 96.6 225s 14 99.0 98.4 225s 15 103.8 102.7 225s 16 103.7 104.4 225s 17 103.8 103.3 225s 18 102.1 103.6 225s 19 103.6 103.6 225s 20 106.9 106.6 225s > print( fitted( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 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 225s 14 15 16 17 18 19 20 225s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 225s > 225s > print( fitted( fit3sls[[ 1 ]]$e1wc ) ) 225s demand supply 225s 1 97.6 97.8 225s 2 99.9 99.3 225s 3 99.8 99.5 225s 4 100.0 99.9 225s 5 102.1 101.7 225s 6 102.0 101.8 225s 7 102.4 101.9 225s 8 103.0 104.1 225s 9 101.5 102.3 225s 10 100.3 99.6 225s 11 95.5 95.9 225s 12 94.7 94.8 225s 13 96.1 96.6 225s 14 99.0 98.4 225s 15 103.8 102.7 225s 16 103.7 104.4 225s 17 103.8 103.3 225s 18 102.1 103.6 225s 19 103.6 103.6 225s 20 106.9 106.6 225s > print( fitted( fit3sls[[ 1 ]]$e1wc$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 225s 14 15 16 17 18 19 20 225s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 225s > 225s > print( fitted( fit3sls[[ 3 ]]$e2e ) ) 225s demand supply 225s 1 97.8 98.4 225s 2 100.0 99.8 225s 3 99.9 99.9 225s 4 100.1 100.3 225s 5 102.0 101.8 225s 6 101.9 101.9 225s 7 102.4 102.0 225s 8 102.9 104.0 225s 9 101.4 102.2 225s 10 100.3 99.6 225s 11 95.8 96.2 225s 12 95.0 95.2 225s 13 96.4 96.9 225s 14 99.1 98.5 225s 15 103.7 102.3 225s 16 103.5 103.9 225s 17 103.6 102.8 225s 18 102.0 103.2 225s 19 103.5 103.2 225s 20 106.7 105.9 225s > print( fitted( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 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 225s 14 15 16 17 18 19 20 225s 98.5 102.3 103.9 102.8 103.2 103.2 105.9 225s > 225s > print( fitted( fit3sls[[ 4 ]]$e3 ) ) 225s demand supply 225s 1 97.8 98.4 225s 2 100.0 99.8 225s 3 99.9 99.9 225s 4 100.1 100.3 225s 5 102.0 101.7 225s 6 101.9 101.8 225s 7 102.3 101.9 225s 8 102.9 103.9 225s 9 101.4 102.2 225s 10 100.3 99.6 225s 11 95.8 96.3 225s 12 95.1 95.3 225s 13 96.4 97.0 225s 14 99.1 98.5 225s 15 103.6 102.3 225s 16 103.5 103.9 225s 17 103.6 102.7 225s 18 102.0 103.1 225s 19 103.5 103.2 225s 20 106.7 105.9 225s > print( fitted( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 97.8 100.0 99.9 100.1 102.0 101.9 102.3 102.9 101.4 100.3 95.8 95.1 96.4 225s 14 15 16 17 18 19 20 225s 99.1 103.6 103.5 103.6 102.0 103.5 106.7 225s > 225s > print( fitted( fit3sls[[ 5 ]]$e4e ) ) 225s demand supply 225s 1 95.0 96.3 225s 2 98.9 99.4 225s 3 98.8 99.5 225s 4 99.1 100.2 225s 5 103.2 102.9 225s 6 102.9 103.1 225s 7 103.6 103.4 225s 8 104.5 107.7 225s 9 102.1 103.4 225s 10 100.2 97.8 225s 11 91.5 90.8 225s 12 89.8 88.9 225s 13 92.2 92.6 225s 14 97.6 95.6 225s 15 106.4 103.4 225s 16 105.9 106.9 225s 17 106.7 103.6 225s 18 102.9 105.4 225s 19 105.6 105.5 225s 20 111.3 111.7 225s > print( fitted( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 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 225s 14 15 16 17 18 19 20 225s 95.6 103.4 106.9 103.6 105.4 105.5 111.7 225s > 225s > print( fitted( fit3sls[[ 1 ]]$e5 ) ) 225s demand supply 225s 1 97.5 98.2 225s 2 99.9 99.8 225s 3 99.8 99.9 225s 4 100.0 100.3 225s 5 102.1 101.9 225s 6 102.0 102.0 225s 7 102.5 102.1 225s 8 103.1 104.3 225s 9 101.5 102.3 225s 10 100.3 99.4 225s 11 95.3 95.7 225s 12 94.5 94.6 225s 13 96.0 96.5 225s 14 99.0 98.2 225s 15 103.9 102.4 225s 16 103.7 104.2 225s 17 103.9 102.7 225s 18 102.1 103.4 225s 19 103.7 103.4 225s 20 107.2 106.6 225s > print( fitted( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 97.5 99.9 99.8 100.0 102.1 102.0 102.5 103.1 101.5 100.3 95.3 94.5 96.0 225s 14 15 16 17 18 19 20 225s 99.0 103.9 103.7 103.9 102.1 103.7 107.2 225s > 225s > print( fitted( fit3slsi[[ 3 ]]$e3e ) ) 225s demand supply 225s 1 98.9 99.2 225s 2 100.5 100.3 225s 3 100.4 100.4 225s 4 100.6 100.6 225s 5 101.6 101.2 225s 6 101.5 101.3 225s 7 101.9 101.5 225s 8 102.4 102.9 225s 9 101.1 101.4 225s 10 100.1 99.7 225s 11 97.2 97.8 225s 12 96.9 97.5 225s 13 98.0 98.7 225s 14 99.7 99.5 225s 15 102.5 101.6 225s 16 102.6 102.7 225s 17 102.1 101.4 225s 18 101.8 102.6 225s 19 102.9 102.7 225s 20 105.3 104.8 225s > print( fitted( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 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 225s 14 15 16 17 18 19 20 225s 99.7 102.5 102.6 102.1 101.8 102.9 105.3 225s > 225s > print( fitted( fit3slsd[[ 4 ]]$e4 ) ) 225s demand supply 225s 1 97.6 98.3 225s 2 99.7 99.7 225s 3 99.7 99.8 225s 4 99.8 100.1 225s 5 102.2 101.9 225s 6 102.0 102.0 225s 7 102.4 102.0 225s 8 102.8 104.1 225s 9 101.6 102.4 225s 10 100.7 99.8 225s 11 95.8 96.1 225s 12 94.8 94.8 225s 13 96.0 96.5 225s 14 99.1 98.3 225s 15 104.1 102.5 225s 16 103.7 104.2 225s 17 104.4 103.2 225s 18 101.9 103.2 225s 19 103.4 103.2 225s 20 106.3 105.9 225s > print( fitted( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 98.3 99.7 99.8 100.1 101.9 102.0 102.0 104.1 102.4 99.8 96.1 94.8 96.5 225s 14 15 16 17 18 19 20 225s 98.3 102.5 104.2 103.2 103.2 103.2 105.9 225s > 225s > print( fitted( fit3slsd[[ 2 ]]$e3w ) ) 225s demand supply 225s 1 96.1 97.0 225s 2 97.6 97.2 225s 3 97.8 97.8 225s 4 97.7 97.7 225s 5 103.5 103.5 225s 6 102.7 102.8 225s 7 102.6 102.1 225s 8 101.8 103.4 225s 9 103.3 104.8 225s 10 103.9 103.4 225s 11 96.2 97.0 225s 12 92.5 92.4 225s 13 92.7 93.0 225s 14 98.8 97.6 225s 15 107.3 105.6 225s 16 105.6 106.4 225s 17 111.1 110.7 225s 18 100.9 102.3 225s 19 102.3 101.4 225s 20 103.7 101.8 225s > print( fitted( fit3slsd[[ 2 ]]$e3w$eq[[ 2 ]] ) ) 225s 1 2 3 4 5 6 7 8 9 10 11 12 13 225s 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 225s 14 15 16 17 18 19 20 225s 97.6 105.6 106.4 110.7 102.3 101.4 101.8 225s > 225s > 225s > ## *********** predicted values ************* 225s > predictData <- Kmenta 225s > predictData$consump <- NULL 225s > predictData$price <- Kmenta$price * 0.9 225s > predictData$income <- Kmenta$income * 1.1 225s > 225s > print( predict( fit3sls[[ 2 ]]$e1c, se.fit = TRUE, interval = "prediction", 225s + useDfSys = TRUE ) ) 225s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 225s 1 97.6 0.661 93.4 101.9 97.8 0.826 225s 2 99.9 0.600 95.7 104.1 99.3 0.825 225s 3 99.8 0.564 95.6 104.0 99.5 0.755 225s 4 100.0 0.605 95.8 104.2 99.9 0.783 225s 5 102.1 0.516 98.0 106.2 101.7 0.669 225s 6 102.0 0.474 97.9 106.1 101.8 0.620 225s 7 102.4 0.493 98.3 106.5 101.9 0.608 225s 8 103.0 0.615 98.8 107.2 104.1 0.889 225s 9 101.5 0.544 97.3 105.6 102.3 0.753 225s 10 100.3 0.822 96.0 104.7 99.6 1.022 225s 11 95.5 0.963 91.1 100.0 95.9 1.172 225s 12 94.7 1.006 90.2 99.2 94.8 1.289 225s 13 96.1 0.915 91.7 100.5 96.6 1.114 225s 14 99.0 0.518 94.9 103.2 98.4 0.751 225s 15 103.8 0.793 99.5 108.2 102.7 0.863 225s 16 103.7 0.636 99.5 107.9 104.4 0.902 225s 17 103.8 1.348 99.0 108.7 103.3 1.636 225s 18 102.1 0.549 97.9 106.2 103.6 0.807 225s 19 103.6 0.695 99.4 107.9 103.6 0.898 225s 20 106.9 1.306 102.1 111.7 106.6 1.613 225s supply.lwr supply.upr 225s 1 92.3 103 225s 2 93.8 105 225s 3 94.0 105 225s 4 94.3 105 225s 5 96.2 107 225s 6 96.3 107 225s 7 96.5 107 225s 8 98.5 110 225s 9 96.8 108 225s 10 93.9 105 225s 11 90.1 102 225s 12 88.9 101 225s 13 90.9 102 225s 14 92.9 104 225s 15 97.1 108 225s 16 98.8 110 225s 17 97.1 110 225s 18 98.1 109 225s 19 98.0 109 225s 20 100.4 113 225s > print( predict( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 225s + useDfSys = TRUE ) ) 225s fit se.fit lwr upr 225s 1 97.6 0.661 93.4 101.9 225s 2 99.9 0.600 95.7 104.1 225s 3 99.8 0.564 95.6 104.0 225s 4 100.0 0.605 95.8 104.2 225s 5 102.1 0.516 98.0 106.2 225s 6 102.0 0.474 97.9 106.1 225s 7 102.4 0.493 98.3 106.5 225s 8 103.0 0.615 98.8 107.2 225s 9 101.5 0.544 97.3 105.6 225s 10 100.3 0.822 96.0 104.7 225s 11 95.5 0.963 91.1 100.0 225s 12 94.7 1.006 90.2 99.2 225s 13 96.1 0.915 91.7 100.5 225s 14 99.0 0.518 94.9 103.2 225s 15 103.8 0.793 99.5 108.2 225s 16 103.7 0.636 99.5 107.9 225s 17 103.8 1.348 99.0 108.7 225s 18 102.1 0.549 97.9 106.2 225s 19 103.6 0.695 99.4 107.9 225s 20 106.9 1.306 102.1 111.7 225s > 225s > print( predict( fit3sls[[ 3 ]]$e2e, se.pred = TRUE, interval = "confidence", 225s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 225s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 225s 1 102.7 2.20 99.3 106 96.2 2.78 225s 2 105.2 2.21 101.8 109 97.5 2.68 225s 3 105.1 2.22 101.6 109 97.7 2.69 225s 4 105.4 2.21 101.9 109 98.0 2.67 225s 5 107.2 2.47 101.9 112 99.6 2.80 225s 6 107.1 2.43 102.1 112 99.7 2.76 225s 7 107.7 2.42 102.8 113 99.7 2.72 225s 8 108.5 2.38 103.7 113 101.6 2.66 225s 9 106.5 2.48 101.2 112 100.1 2.85 225s 10 105.0 2.59 99.1 111 97.6 3.04 225s 11 100.1 2.36 95.5 105 94.2 3.07 225s 12 99.5 2.19 96.3 103 93.0 3.00 225s 13 101.2 2.11 98.7 104 94.6 2.85 225s 14 104.0 2.29 100.0 108 96.3 2.84 225s 15 108.9 2.68 102.4 115 100.2 2.90 225s 16 108.8 2.57 103.0 115 101.8 2.81 225s 17 108.4 2.99 100.4 116 100.8 3.28 225s 18 107.5 2.34 103.1 112 100.9 2.66 225s 19 109.2 2.42 104.3 114 100.8 2.64 225s 20 113.0 2.63 106.8 119 103.4 2.62 225s supply.lwr supply.upr 225s 1 92.2 100.2 225s 2 94.6 100.5 225s 3 94.6 100.7 225s 4 95.1 100.8 225s 5 95.4 103.8 225s 6 95.8 103.5 225s 7 96.3 103.1 225s 8 98.9 104.4 225s 9 95.4 104.7 225s 10 91.6 103.6 225s 11 88.0 100.4 225s 12 87.3 98.7 225s 13 90.1 99.2 225s 14 91.8 100.8 225s 15 95.3 105.2 225s 16 97.5 106.0 225s 17 93.4 108.3 225s 18 98.1 103.6 225s 19 98.4 103.2 225s 20 101.2 105.6 225s > print( predict( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 225s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 225s fit se.pred lwr upr 225s 1 96.2 2.78 92.2 100.2 225s 2 97.5 2.68 94.6 100.5 225s 3 97.7 2.69 94.6 100.7 225s 4 98.0 2.67 95.1 100.8 225s 5 99.6 2.80 95.4 103.8 225s 6 99.7 2.76 95.8 103.5 225s 7 99.7 2.72 96.3 103.1 225s 8 101.6 2.66 98.9 104.4 225s 9 100.1 2.85 95.4 104.7 225s 10 97.6 3.04 91.6 103.6 225s 11 94.2 3.07 88.0 100.4 225s 12 93.0 3.00 87.3 98.7 225s 13 94.6 2.85 90.1 99.2 225s 14 96.3 2.84 91.8 100.8 225s 15 100.2 2.90 95.3 105.2 225s 16 101.8 2.81 97.5 106.0 225s 17 100.8 3.28 93.4 108.3 225s 18 100.9 2.66 98.1 103.6 225s 19 100.8 2.64 98.4 103.2 225s 20 103.4 2.62 101.2 105.6 225s > 225s > print( predict( fit3sls[[ 5 ]]$e2w, se.pred = TRUE, interval = "confidence", 225s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 225s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 225s 1 102.6 2.24 99.0 106 96.3 2.84 225s 2 105.1 2.24 101.5 109 97.6 2.72 225s 3 105.0 2.25 101.3 109 97.7 2.73 225s 4 105.3 2.24 101.6 109 98.0 2.71 225s 5 107.1 2.54 101.5 113 99.6 2.88 225s 6 107.0 2.49 101.7 112 99.6 2.82 225s 7 107.6 2.48 102.3 113 99.7 2.77 225s 8 108.3 2.44 103.3 113 101.6 2.70 225s 9 106.4 2.55 100.7 112 100.0 2.94 225s 10 104.9 2.67 98.5 111 97.6 3.17 225s 11 100.1 2.43 95.1 105 94.3 3.20 225s 12 99.5 2.23 96.0 103 93.2 3.11 225s 13 101.2 2.14 98.5 104 94.8 2.92 225s 14 104.0 2.33 99.6 108 96.4 2.92 225s 15 108.7 2.77 101.8 116 100.2 2.99 225s 16 108.7 2.65 102.5 115 101.7 2.88 225s 17 108.3 3.12 99.7 117 100.8 3.45 225s 18 107.4 2.39 102.7 112 100.9 2.70 225s 19 109.1 2.48 103.8 114 100.8 2.67 225s 20 112.9 2.71 106.3 119 103.4 2.65 225s supply.lwr supply.upr 225s 1 91.8 100.7 225s 2 94.3 100.8 225s 3 94.3 101.1 225s 4 94.8 101.1 225s 5 94.9 104.3 225s 6 95.4 103.9 225s 7 95.9 103.5 225s 8 98.5 104.7 225s 9 94.9 105.2 225s 10 90.9 104.4 225s 11 87.4 101.2 225s 12 86.9 99.5 225s 13 89.7 99.8 225s 14 91.4 101.4 225s 15 94.7 105.8 225s 16 97.0 106.5 225s 17 92.5 109.1 225s 18 97.8 103.9 225s 19 98.1 103.5 225s 20 101.0 105.9 225s > print( predict( fit3sls[[ 5 ]]$e2w$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 225s + level = 0.999, newdata = predictData, useDfSys = TRUE ) ) 225s fit se.pred lwr upr 225s 1 96.3 2.84 91.8 100.7 225s 2 97.6 2.72 94.3 100.8 225s 3 97.7 2.73 94.3 101.1 225s 4 98.0 2.71 94.8 101.1 225s 5 99.6 2.88 94.9 104.3 225s 6 99.6 2.82 95.4 103.9 225s 7 99.7 2.77 95.9 103.5 225s 8 101.6 2.70 98.5 104.7 225s 9 100.0 2.94 94.9 105.2 225s 10 97.6 3.17 90.9 104.4 225s 11 94.3 3.20 87.4 101.2 225s 12 93.2 3.11 86.9 99.5 225s 13 94.8 2.92 89.7 99.8 225s 14 96.4 2.92 91.4 101.4 225s 15 100.2 2.99 94.7 105.8 225s 16 101.7 2.88 97.0 106.5 225s 17 100.8 3.45 92.5 109.1 225s 18 100.9 2.70 97.8 103.9 225s 19 100.8 2.67 98.1 103.5 225s 20 103.4 2.65 101.0 105.9 225s > 225s > print( predict( fit3sls[[ 4 ]]$e3, se.pred = TRUE, interval = "prediction", 225s + level = 0.975 ) ) 225s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 225s 1 97.8 2.10 92.9 103 98.4 2.64 225s 2 100.0 2.09 95.1 105 99.8 2.66 225s 3 99.9 2.08 95.0 105 99.9 2.65 225s 4 100.1 2.09 95.2 105 100.3 2.66 225s 5 102.0 2.06 97.2 107 101.7 2.65 225s 6 101.9 2.05 97.1 107 101.8 2.63 225s 7 102.3 2.06 97.5 107 101.9 2.63 225s 8 102.9 2.09 98.0 108 103.9 2.71 225s 9 101.4 2.07 96.6 106 102.2 2.67 225s 10 100.3 2.16 95.2 105 99.6 2.76 225s 11 95.8 2.21 90.6 101 96.3 2.80 225s 12 95.1 2.22 89.9 100 95.3 2.84 225s 13 96.4 2.19 91.3 102 97.0 2.78 225s 14 99.1 2.06 94.3 104 98.5 2.67 225s 15 103.6 2.15 98.6 109 102.3 2.68 225s 16 103.5 2.09 98.6 108 103.9 2.68 225s 17 103.6 2.41 97.9 109 102.7 3.00 225s 18 102.0 2.07 97.2 107 103.1 2.66 225s 19 103.5 2.12 98.6 108 103.2 2.69 225s 20 106.7 2.39 101.1 112 105.9 2.98 225s supply.lwr supply.upr 225s 1 92.2 105 225s 2 93.6 106 225s 3 93.7 106 225s 4 94.0 107 225s 5 95.5 108 225s 6 95.7 108 225s 7 95.8 108 225s 8 97.6 110 225s 9 95.9 108 225s 10 93.2 106 225s 11 89.7 103 225s 12 88.6 102 225s 13 90.5 103 225s 14 92.3 105 225s 15 96.0 109 225s 16 97.6 110 225s 17 95.7 110 225s 18 96.9 109 225s 19 96.9 109 225s 20 98.9 113 225s > print( predict( fit3sls[[ 4 ]]$e3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 225s + level = 0.975 ) ) 225s fit se.pred lwr upr 225s 1 97.8 2.10 92.9 103 225s 2 100.0 2.09 95.1 105 225s 3 99.9 2.08 95.0 105 225s 4 100.1 2.09 95.2 105 225s 5 102.0 2.06 97.2 107 225s 6 101.9 2.05 97.1 107 225s 7 102.3 2.06 97.5 107 225s 8 102.9 2.09 98.0 108 225s 9 101.4 2.07 96.6 106 225s 10 100.3 2.16 95.2 105 225s 11 95.8 2.21 90.6 101 225s 12 95.1 2.22 89.9 100 225s 13 96.4 2.19 91.3 102 225s 14 99.1 2.06 94.3 104 225s 15 103.6 2.15 98.6 109 225s 16 103.5 2.09 98.6 108 225s 17 103.6 2.41 97.9 109 225s 18 102.0 2.07 97.2 107 225s 19 103.5 2.12 98.6 108 225s 20 106.7 2.39 101.1 112 225s > 225s > print( predict( fit3sls[[ 5 ]]$e4e, se.fit = TRUE, interval = "confidence", 225s + level = 0.25, useDfSys = TRUE ) ) 225s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 225s 1 95.0 0.465 94.8 95.1 96.3 0.536 225s 2 98.9 0.532 98.7 99.1 99.4 0.663 225s 3 98.8 0.497 98.6 99.0 99.5 0.613 225s 4 99.1 0.541 99.0 99.3 100.2 0.662 225s 5 103.2 0.450 103.0 103.3 102.9 0.593 225s 6 102.9 0.417 102.7 103.0 103.1 0.543 225s 7 103.6 0.420 103.5 103.8 103.4 0.524 225s 8 104.5 0.525 104.3 104.6 107.7 0.634 225s 9 102.1 0.494 101.9 102.2 103.4 0.660 225s 10 100.2 0.760 100.0 100.4 97.8 0.895 225s 11 91.5 0.660 91.3 91.7 90.8 0.736 225s 12 89.8 0.563 89.6 89.9 88.9 0.742 225s 13 92.2 0.597 92.0 92.4 92.6 0.806 225s 14 97.6 0.426 97.4 97.7 95.6 0.568 225s 15 106.4 0.619 106.2 106.6 103.4 0.721 225s 16 105.9 0.476 105.8 106.1 106.9 0.608 225s 17 106.7 1.159 106.3 107.1 103.6 1.414 225s 18 102.9 0.494 102.7 103.0 105.4 0.582 225s 19 105.6 0.574 105.4 105.8 105.5 0.676 225s 20 111.3 1.030 110.9 111.6 111.7 1.146 225s supply.lwr supply.upr 225s 1 96.1 96.4 225s 2 99.1 99.6 225s 3 99.3 99.7 225s 4 100.0 100.4 225s 5 102.7 103.1 225s 6 102.9 103.3 225s 7 103.2 103.5 225s 8 107.5 107.9 225s 9 103.2 103.7 225s 10 97.5 98.0 225s 11 90.5 91.0 225s 12 88.7 89.1 225s 13 92.4 92.9 225s 14 95.4 95.8 225s 15 103.1 103.6 225s 16 106.7 107.0 225s 17 103.1 104.0 225s 18 105.3 105.6 225s 19 105.3 105.8 225s 20 111.4 112.1 225s > print( predict( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 225s + level = 0.25, useDfSys = TRUE ) ) 225s fit se.fit lwr upr 225s 1 96.3 0.536 96.1 96.4 225s 2 99.4 0.663 99.1 99.6 225s 3 99.5 0.613 99.3 99.7 225s 4 100.2 0.662 100.0 100.4 225s 5 102.9 0.593 102.7 103.1 225s 6 103.1 0.543 102.9 103.3 225s 7 103.4 0.524 103.2 103.5 225s 8 107.7 0.634 107.5 107.9 225s 9 103.4 0.660 103.2 103.7 225s 10 97.8 0.895 97.5 98.0 225s 11 90.8 0.736 90.5 91.0 225s 12 88.9 0.742 88.7 89.1 225s 13 92.6 0.806 92.4 92.9 225s 14 95.6 0.568 95.4 95.8 225s 15 103.4 0.721 103.1 103.6 225s 16 106.9 0.608 106.7 107.0 225s 17 103.6 1.414 103.1 104.0 225s 18 105.4 0.582 105.3 105.6 225s 19 105.5 0.676 105.3 105.8 225s 20 111.7 1.146 111.4 112.1 225s > 225s > print( predict( fit3sls[[ 1 ]]$e5, se.fit = TRUE, se.pred = TRUE, 225s + interval = "prediction", level = 0.5, newdata = predictData ) ) 225s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 225s 1 102.8 0.957 2.19 101.3 104 95.7 225s 2 105.6 0.829 2.13 104.1 107 97.1 225s 3 105.5 0.869 2.15 104.0 107 97.3 225s 4 105.8 0.823 2.13 104.3 107 97.6 225s 5 107.8 1.308 2.36 106.2 109 99.4 225s 6 107.7 1.213 2.31 106.1 109 99.4 225s 7 108.3 1.145 2.28 106.7 110 99.5 225s 8 109.1 0.984 2.20 107.6 111 101.7 225s 9 107.0 1.372 2.40 105.3 109 99.8 225s 10 105.4 1.659 2.57 103.6 107 97.1 225s 11 100.1 1.365 2.39 98.4 102 93.3 225s 12 99.4 0.969 2.19 97.9 101 92.1 225s 13 101.3 0.752 2.11 99.8 103 93.9 225s 14 104.3 1.112 2.26 102.8 106 95.7 225s 15 109.6 1.580 2.52 107.9 111 100.0 225s 16 109.6 1.368 2.40 107.9 111 101.7 225s 17 109.1 2.136 2.90 107.1 111 100.5 225s 18 108.1 0.966 2.19 106.6 110 100.8 225s 19 109.9 0.980 2.20 108.4 111 100.7 225s 20 114.1 0.997 2.21 112.6 116 103.7 225s supply.se.fit supply.se.pred supply.lwr supply.upr 225s 1 0.959 2.74 93.8 97.5 225s 2 0.742 2.67 95.3 99.0 225s 3 0.791 2.69 95.4 99.1 225s 4 0.735 2.67 95.8 99.4 225s 5 1.280 2.87 97.4 101.3 225s 6 1.159 2.82 97.5 101.3 225s 7 1.031 2.77 97.6 101.4 225s 8 0.867 2.71 99.8 103.5 225s 9 1.416 2.93 97.8 101.8 225s 10 1.724 3.09 95.0 99.2 225s 11 1.457 2.95 91.3 95.4 225s 12 1.102 2.79 90.2 94.0 225s 13 0.894 2.72 92.1 95.8 225s 14 1.092 2.79 93.8 97.6 225s 15 1.516 2.98 98.0 102.0 225s 16 1.321 2.89 99.7 103.7 225s 17 2.297 3.44 98.2 102.9 225s 18 0.847 2.70 98.9 102.6 225s 19 0.743 2.67 98.9 102.6 225s 20 0.589 2.63 101.9 105.5 225s > print( predict( fit3sls[[ 1 ]]$e5$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 225s + interval = "prediction", level = 0.5, newdata = predictData ) ) 225s fit se.fit se.pred lwr upr 225s 1 102.8 0.957 2.19 101.3 104 225s 2 105.6 0.829 2.13 104.1 107 225s 3 105.5 0.869 2.15 104.0 107 225s 4 105.8 0.823 2.13 104.3 107 225s 5 107.8 1.308 2.36 106.2 109 225s 6 107.7 1.213 2.31 106.1 109 225s 7 108.3 1.145 2.28 106.7 110 225s 8 109.1 0.984 2.20 107.6 111 225s 9 107.0 1.372 2.40 105.3 109 225s 10 105.4 1.659 2.57 103.6 107 225s 11 100.1 1.365 2.39 98.4 102 225s 12 99.4 0.969 2.19 97.9 101 225s 13 101.3 0.752 2.11 99.8 103 225s 14 104.3 1.112 2.26 102.8 106 225s 15 109.6 1.580 2.52 107.9 111 225s 16 109.6 1.368 2.40 107.9 111 225s 17 109.1 2.136 2.90 107.1 111 225s 18 108.1 0.966 2.19 106.6 110 225s 19 109.9 0.980 2.20 108.4 111 225s 20 114.1 0.997 2.21 112.6 116 225s > 225s > print( predict( fit3slsi[[ 3 ]]$e3e, se.fit = TRUE, se.pred = TRUE, 225s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 225s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 225s 1 98.9 0.590 2.49 97.3 100.5 99.2 225s 2 100.5 0.643 2.50 98.7 102.2 100.3 225s 3 100.4 0.602 2.49 98.7 102.0 100.4 225s 4 100.6 0.653 2.50 98.8 102.3 100.6 225s 5 101.6 0.548 2.48 100.1 103.1 101.2 225s 6 101.5 0.512 2.47 100.1 102.9 101.3 225s 7 101.9 0.524 2.47 100.5 103.3 101.5 225s 8 102.4 0.667 2.51 100.6 104.3 102.9 225s 9 101.1 0.599 2.49 99.5 102.7 101.4 225s 10 100.1 0.928 2.59 97.6 102.6 99.7 225s 11 97.2 0.898 2.58 94.7 99.6 97.8 225s 12 96.9 0.767 2.54 94.8 99.0 97.5 225s 13 98.0 0.745 2.53 96.0 100.1 98.7 225s 14 99.7 0.536 2.48 98.2 101.1 99.5 225s 15 102.5 0.745 2.53 100.5 104.5 101.6 225s 16 102.6 0.589 2.49 101.0 104.2 102.7 225s 17 102.1 1.376 2.78 98.3 105.8 101.4 225s 18 101.8 0.615 2.49 100.2 103.5 102.6 225s 19 102.9 0.738 2.53 100.9 104.9 102.7 225s 20 105.3 1.357 2.77 101.6 109.0 104.8 225s supply.se.fit supply.se.pred supply.lwr supply.upr 225s 1 0.638 3.01 97.5 101.0 225s 2 0.752 3.03 98.3 102.4 225s 3 0.700 3.02 98.4 102.3 225s 4 0.761 3.03 98.6 102.7 225s 5 0.649 3.01 99.4 103.0 225s 6 0.610 3.00 99.7 103.0 225s 7 0.613 3.00 99.8 103.2 225s 8 0.829 3.05 100.7 105.2 225s 9 0.731 3.03 99.4 103.4 225s 10 1.092 3.13 96.7 102.6 225s 11 1.037 3.12 94.9 100.6 225s 12 0.902 3.07 95.0 99.9 225s 13 0.855 3.06 96.4 101.1 225s 14 0.670 3.01 97.6 101.3 225s 15 0.812 3.05 99.4 103.8 225s 16 0.707 3.02 100.8 104.7 225s 17 1.584 3.34 97.1 105.7 225s 18 0.740 3.03 100.6 104.6 225s 19 0.852 3.06 100.4 105.1 225s 20 1.564 3.33 100.6 109.1 225s > print( predict( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 225s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 225s fit se.fit se.pred lwr upr 225s 1 98.9 0.590 2.49 97.3 100.5 225s 2 100.5 0.643 2.50 98.7 102.2 225s 3 100.4 0.602 2.49 98.7 102.0 225s 4 100.6 0.653 2.50 98.8 102.3 225s 5 101.6 0.548 2.48 100.1 103.1 225s 6 101.5 0.512 2.47 100.1 102.9 225s 7 101.9 0.524 2.47 100.5 103.3 225s 8 102.4 0.667 2.51 100.6 104.3 225s 9 101.1 0.599 2.49 99.5 102.7 225s 10 100.1 0.928 2.59 97.6 102.6 225s 11 97.2 0.898 2.58 94.7 99.6 225s 12 96.9 0.767 2.54 94.8 99.0 225s 13 98.0 0.745 2.53 96.0 100.1 225s 14 99.7 0.536 2.48 98.2 101.1 225s 15 102.5 0.745 2.53 100.5 104.5 225s 16 102.6 0.589 2.49 101.0 104.2 225s 17 102.1 1.376 2.78 98.3 105.8 225s 18 101.8 0.615 2.49 100.2 103.5 225s 19 102.9 0.738 2.53 100.9 104.9 225s 20 105.3 1.357 2.77 101.6 109.0 225s > 225s > print( predict( fit3slsi[[ 1 ]]$e5w, se.fit = TRUE, se.pred = TRUE, 225s + interval = "prediction", level = 0.5, newdata = predictData ) ) 225s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 225s 1 102.4 0.986 2.25 100.9 104 95.3 225s 2 105.2 0.851 2.20 103.7 107 96.9 225s 3 105.1 0.896 2.22 103.6 107 97.0 225s 4 105.4 0.844 2.20 103.9 107 97.4 225s 5 107.1 1.351 2.44 105.5 109 98.7 225s 6 107.1 1.250 2.38 105.5 109 98.9 225s 7 107.8 1.173 2.34 106.2 109 99.0 225s 8 108.7 0.983 2.25 107.2 110 101.3 225s 9 106.3 1.420 2.48 104.6 108 99.1 225s 10 104.6 1.713 2.65 102.8 106 96.2 225s 11 99.4 1.372 2.45 97.8 101 92.8 225s 12 99.0 0.965 2.25 97.5 101 91.9 225s 13 101.0 0.768 2.17 99.5 102 93.8 225s 14 103.8 1.149 2.33 102.2 105 95.3 225s 15 108.8 1.631 2.60 107.0 111 99.2 225s 16 108.9 1.405 2.47 107.2 111 101.1 225s 17 108.0 2.211 3.00 106.0 110 99.4 225s 18 107.7 0.978 2.25 106.1 109 100.4 225s 19 109.5 0.964 2.25 108.0 111 100.5 225s 20 113.8 0.818 2.19 112.3 115 103.7 225s supply.se.fit supply.se.pred supply.lwr supply.upr 225s 1 0.987 2.85 93.3 97.2 225s 2 0.772 2.79 95.0 98.8 225s 3 0.824 2.80 95.1 98.9 225s 4 0.767 2.79 95.5 99.3 225s 5 1.341 3.00 96.7 100.8 225s 6 1.215 2.94 96.9 100.9 225s 7 1.084 2.89 97.1 101.0 225s 8 0.907 2.83 99.4 103.2 225s 9 1.483 3.06 97.0 101.2 225s 10 1.795 3.22 94.1 98.4 225s 11 1.455 3.05 90.7 94.8 225s 12 1.002 2.86 90.0 93.9 225s 13 0.805 2.80 91.9 95.7 225s 14 1.087 2.89 93.4 97.3 225s 15 1.585 3.11 97.1 101.4 225s 16 1.383 3.01 99.0 103.1 225s 17 2.399 3.60 96.9 101.8 225s 18 0.883 2.82 98.5 102.4 225s 19 0.770 2.79 98.6 102.4 225s 20 0.616 2.75 101.9 105.6 225s > print( predict( fit3slsi[[ 1 ]]$e5w$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 225s + interval = "prediction", level = 0.5, newdata = predictData ) ) 225s fit se.fit se.pred lwr upr 225s 1 102.4 0.986 2.25 100.9 104 225s 2 105.2 0.851 2.20 103.7 107 225s 3 105.1 0.896 2.22 103.6 107 225s 4 105.4 0.844 2.20 103.9 107 225s 5 107.1 1.351 2.44 105.5 109 225s 6 107.1 1.250 2.38 105.5 109 225s 7 107.8 1.173 2.34 106.2 109 225s 8 108.7 0.983 2.25 107.2 110 225s 9 106.3 1.420 2.48 104.6 108 225s 10 104.6 1.713 2.65 102.8 106 225s 11 99.4 1.372 2.45 97.8 101 225s 12 99.0 0.965 2.25 97.5 101 225s 13 101.0 0.768 2.17 99.5 102 225s 14 103.8 1.149 2.33 102.2 105 225s 15 108.8 1.631 2.60 107.0 111 225s 16 108.9 1.405 2.47 107.2 111 225s 17 108.0 2.211 3.00 106.0 110 225s 18 107.7 0.978 2.25 106.1 109 225s 19 109.5 0.964 2.25 108.0 111 225s 20 113.8 0.818 2.19 112.3 115 225s > 225s > print( predict( fit3slsd[[ 4 ]]$e4, se.fit = TRUE, interval = "prediction", 225s + level = 0.9, newdata = predictData ) ) 225s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 225s 1 103 0.972 99.6 107 96.1 0.980 225s 2 106 0.820 102.2 109 97.5 0.751 225s 3 106 0.863 102.1 109 97.6 0.801 225s 4 106 0.813 102.4 109 97.9 0.741 225s 5 108 1.305 104.2 112 99.8 1.287 225s 6 108 1.206 104.1 112 99.8 1.164 225s 7 109 1.132 104.7 112 99.9 1.035 225s 8 109 0.960 105.5 113 101.8 0.857 225s 9 107 1.377 103.4 111 100.3 1.422 225s 10 106 1.688 101.8 110 97.8 1.748 225s 11 101 1.415 96.8 105 94.1 1.490 225s 12 100 1.004 96.3 104 92.7 1.115 225s 13 102 0.766 98.1 105 94.4 0.891 225s 14 105 1.124 101.0 109 96.2 1.107 225s 15 110 1.575 105.8 114 100.5 1.523 225s 16 110 1.355 105.9 114 102.1 1.318 225s 17 110 2.158 105.0 115 101.3 2.305 225s 18 108 0.947 104.5 112 101.0 0.843 225s 19 110 0.953 106.3 114 100.9 0.735 225s 20 114 0.974 109.9 117 103.5 0.583 225s supply.lwr supply.upr 225s 1 91.6 100.7 225s 2 93.0 101.9 225s 3 93.2 102.1 225s 4 93.5 102.3 225s 5 95.0 104.6 225s 6 95.2 104.5 225s 7 95.3 104.5 225s 8 97.3 106.3 225s 9 95.4 105.2 225s 10 92.6 103.0 225s 11 89.2 99.0 225s 12 88.1 97.4 225s 13 89.8 98.9 225s 14 91.6 100.9 225s 15 95.5 105.5 225s 16 97.3 106.9 225s 17 95.6 107.1 225s 18 96.5 105.5 225s 19 96.5 105.3 225s 20 99.2 107.9 225s > print( predict( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 225s + level = 0.9, newdata = predictData ) ) 225s fit se.fit lwr upr 225s 1 96.1 0.980 91.6 100.7 225s 2 97.5 0.751 93.0 101.9 225s 3 97.6 0.801 93.2 102.1 225s 4 97.9 0.741 93.5 102.3 225s 5 99.8 1.287 95.0 104.6 225s 6 99.8 1.164 95.2 104.5 225s 7 99.9 1.035 95.3 104.5 225s 8 101.8 0.857 97.3 106.3 225s 9 100.3 1.422 95.4 105.2 225s 10 97.8 1.748 92.6 103.0 225s 11 94.1 1.490 89.2 99.0 225s 12 92.7 1.115 88.1 97.4 225s 13 94.4 0.891 89.8 98.9 225s 14 96.2 1.107 91.6 100.9 225s 15 100.5 1.523 95.5 105.5 225s 16 102.1 1.318 97.3 106.9 225s 17 101.3 2.305 95.6 107.1 225s 18 101.0 0.843 96.5 105.5 225s 19 100.9 0.735 96.5 105.3 225s 20 103.5 0.583 99.2 107.9 225s > 225s > print( predict( fit3slsd[[ 2 ]]$e3w, se.fit = TRUE, se.pred = TRUE, 225s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 226s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 226s 1 96.1 0.832 3.23 93.8 98.3 97.0 226s 2 97.6 0.849 3.24 95.3 99.9 97.2 226s 3 97.8 0.771 3.22 95.7 99.9 97.8 226s 4 97.7 0.857 3.24 95.3 100.0 97.7 226s 5 103.5 0.648 3.19 101.8 105.3 103.5 226s 6 102.7 0.519 3.16 101.3 104.1 102.8 226s 7 102.6 0.499 3.16 101.3 104.0 102.1 226s 8 101.8 0.627 3.18 100.1 103.5 103.4 226s 9 103.3 0.714 3.20 101.3 105.2 104.8 226s 10 103.9 1.172 3.33 100.7 107.1 103.4 226s 11 96.2 0.920 3.25 93.7 98.7 97.0 226s 12 92.5 1.261 3.37 89.1 95.9 92.4 226s 13 92.7 1.364 3.41 89.0 96.5 93.0 226s 14 98.8 0.528 3.17 97.3 100.2 97.6 226s 15 107.3 1.245 3.36 103.9 110.7 105.6 226s 16 105.6 0.856 3.24 103.2 107.9 106.4 226s 17 111.1 2.310 3.88 104.8 117.4 110.7 226s 18 100.9 0.592 3.18 99.2 102.5 102.3 226s 19 102.3 0.700 3.20 100.4 104.2 101.4 226s 20 103.7 1.350 3.40 100.0 107.4 101.8 226s supply.se.fit supply.se.pred supply.lwr supply.upr 226s 1 0.791 3.73 94.8 99.2 226s 2 0.857 3.74 94.8 99.5 226s 3 0.776 3.72 95.7 99.9 226s 4 0.825 3.73 95.5 100.0 226s 5 0.817 3.73 101.2 105.7 226s 6 0.713 3.71 100.9 104.8 226s 7 0.644 3.70 100.4 103.9 226s 8 0.858 3.74 101.0 105.7 226s 9 0.962 3.77 102.2 107.4 226s 10 1.040 3.79 100.6 106.3 226s 11 1.083 3.80 94.1 100.0 226s 12 1.633 3.99 88.0 96.9 226s 13 1.568 3.96 88.7 97.3 226s 14 0.871 3.74 95.2 100.0 226s 15 1.029 3.78 102.8 108.4 226s 16 1.056 3.79 103.6 109.3 226s 17 2.050 4.18 105.1 116.2 226s 18 0.687 3.71 100.4 104.2 226s 19 0.773 3.72 99.3 103.5 226s 20 1.300 3.87 98.3 105.4 226s > print( predict( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 226s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 226s fit se.fit se.pred lwr upr 226s 1 96.1 0.832 3.23 93.8 98.3 226s 2 97.6 0.849 3.24 95.3 99.9 226s 3 97.8 0.771 3.22 95.7 99.9 226s 4 97.7 0.857 3.24 95.3 100.0 226s 5 103.5 0.648 3.19 101.8 105.3 226s 6 102.7 0.519 3.16 101.3 104.1 226s 7 102.6 0.499 3.16 101.3 104.0 226s 8 101.8 0.627 3.18 100.1 103.5 226s 9 103.3 0.714 3.20 101.3 105.2 226s 10 103.9 1.172 3.33 100.7 107.1 226s 11 96.2 0.920 3.25 93.7 98.7 226s 12 92.5 1.261 3.37 89.1 95.9 226s 13 92.7 1.364 3.41 89.0 96.5 226s 14 98.8 0.528 3.17 97.3 100.2 226s 15 107.3 1.245 3.36 103.9 110.7 226s 16 105.6 0.856 3.24 103.2 107.9 226s 17 111.1 2.310 3.88 104.8 117.4 226s 18 100.9 0.592 3.18 99.2 102.5 226s 19 102.3 0.700 3.20 100.4 104.2 226s 20 103.7 1.350 3.40 100.0 107.4 226s > 226s > 226s > # predict just one observation 226s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 226s + trend = 25 ) 226s > 226s > print( predict( fit3sls[[ 3 ]]$e1c, newdata = smallData ) ) 226s demand.pred supply.pred 226s 1 110 118 226s > print( predict( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]], newdata = smallData ) ) 226s fit 226s 1 110 226s > 226s > print( predict( fit3sls[[ 4 ]]$e2e, se.fit = TRUE, level = 0.9, 226s + newdata = smallData ) ) 226s demand.pred demand.se.fit supply.pred supply.se.fit 226s 1 110 2.34 117 3.29 226s > print( predict( fit3sls[[ 5 ]]$e2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 226s + newdata = smallData ) ) 226s fit se.pred 226s 1 110 3.07 226s > 226s > print( predict( fit3sls[[ 1]]$e3, interval = "prediction", level = 0.975, 226s + newdata = smallData ) ) 226s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 226s 1 110 102 117 117 106 127 226s > print( predict( fit3sls[[ 1 ]]$e3$eq[[ 1 ]], interval = "confidence", level = 0.8, 226s + newdata = smallData ) ) 226s fit lwr upr 226s 1 110 106 113 226s > 226s > print( predict( fit3sls[[ 4]]$e3we, interval = "prediction", level = 0.975, 226s + newdata = smallData ) ) 226s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 226s 1 110 103 117 117 107 126 226s > print( predict( fit3sls[[ 4 ]]$e3we$eq[[ 1 ]], interval = "confidence", level = 0.8, 226s + newdata = smallData ) ) 226s fit lwr upr 226s 1 110 107 113 226s > 226s > print( predict( fit3sls[[ 2 ]]$e4e, se.fit = TRUE, interval = "confidence", 226s + level = 0.999, newdata = smallData ) ) 226s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 226s 1 110 2.14 103 118 119 2.25 226s supply.lwr supply.upr 226s 1 110 127 226s > print( predict( fit3sls[[ 2 ]]$e4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 226s + level = 0.75, newdata = smallData ) ) 226s fit se.pred lwr upr 226s 1 119 3.41 115 123 226s > 226s > print( predict( fit3sls[[ 3 ]]$e5, se.fit = TRUE, interval = "prediction", 226s + newdata = smallData ) ) 226s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 226s 1 111 2.3 104 117 119 2.44 226s supply.lwr supply.upr 226s 1 111 126 226s > print( predict( fit3sls[[ 3 ]]$e5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 226s + newdata = smallData ) ) 226s fit se.pred lwr upr 226s 1 111 3.02 106 115 226s > 226s > print( predict( fit3slsi[[ 4 ]]$e3e, se.fit = TRUE, se.pred = TRUE, 226s + interval = "prediction", level = 0.5, newdata = smallData ) ) 226s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 226s 1 108 2.75 3.66 106 111 112 226s supply.se.fit supply.se.pred supply.lwr supply.upr 226s 1 3.46 4.54 109 115 226s > print( predict( fit3slsd[[ 5 ]]$e4$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 226s + interval = "confidence", level = 0.25, newdata = smallData ) ) 226s fit se.fit se.pred lwr upr 226s 1 111 1.85 3.42 111 112 226s > 226s > print( predict( fit3slsd[[ 2 ]]$e2we, se.fit = TRUE, se.pred = TRUE, 226s + interval = "prediction", level = 0.5, newdata = smallData ) ) 226s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 226s 1 101 2.76 4.1 98.7 104 111 226s supply.se.fit supply.se.pred supply.lwr supply.upr 226s 1 2.79 4.47 108 114 226s > print( predict( fit3slsi[[ 3 ]]$e4we$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 226s + interval = "confidence", level = 0.25, newdata = smallData ) ) 226s fit se.fit se.pred lwr upr 226s 1 111 2.03 2.86 111 112 226s > 226s > 226s > ## ************ correlation of predicted values *************** 226s > print( correlation.systemfit( fit3sls[[ 1 ]]$e1c, 2, 1 ) ) 226s [,1] 226s [1,] 0.880 226s [2,] 0.881 226s [3,] 0.886 226s [4,] 0.901 226s [5,] 0.866 226s [6,] 0.881 226s [7,] 0.892 226s [8,] 0.887 226s [9,] 0.901 226s [10,] 0.924 226s [11,] 0.925 226s [12,] 0.916 226s [13,] 0.910 226s [14,] 0.885 226s [15,] 0.909 226s [16,] 0.921 226s [17,] 0.928 226s [18,] 0.845 226s [19,] 0.890 226s [20,] 0.920 226s > 226s > print( correlation.systemfit( fit3sls[[ 2 ]]$e2e, 1, 2 ) ) 226s [,1] 226s [1,] 0.935 226s [2,] 0.927 226s [3,] 0.923 226s [4,] 0.921 226s [5,] 0.876 226s [6,] 0.884 226s [7,] 0.894 226s [8,] 0.875 226s [9,] 0.890 226s [10,] 0.917 226s [11,] 0.911 226s [12,] 0.898 226s [13,] 0.892 226s [14,] 0.871 226s [15,] 0.905 226s [16,] 0.945 226s [17,] 0.926 226s [18,] 0.908 226s [19,] 0.915 226s [20,] 0.926 226s > 226s > print( correlation.systemfit( fit3sls[[ 5 ]]$e2w, 2, 1 ) ) 226s [,1] 226s [1,] 0.932 226s [2,] 0.928 226s [3,] 0.925 226s [4,] 0.923 226s [5,] 0.882 226s [6,] 0.890 226s [7,] 0.899 226s [8,] 0.880 226s [9,] 0.895 226s [10,] 0.921 226s [11,] 0.914 226s [12,] 0.900 226s [13,] 0.895 226s [14,] 0.876 226s [15,] 0.905 226s [16,] 0.947 226s [17,] 0.928 226s [18,] 0.915 226s [19,] 0.916 226s [20,] 0.928 226s > 226s > print( correlation.systemfit( fit3sls[[ 3 ]]$e3, 2, 1 ) ) 226s [,1] 226s [1,] 0.931 226s [2,] 0.925 226s [3,] 0.922 226s [4,] 0.920 226s [5,] 0.877 226s [6,] 0.884 226s [7,] 0.894 226s [8,] 0.875 226s [9,] 0.890 226s [10,] 0.917 226s [11,] 0.910 226s [12,] 0.896 226s [13,] 0.891 226s [14,] 0.871 226s [15,] 0.903 226s [16,] 0.944 226s [17,] 0.925 226s [18,] 0.911 226s [19,] 0.913 226s [20,] 0.925 226s > 226s > print( correlation.systemfit( fit3sls[[ 4 ]]$e4e, 1, 2 ) ) 226s [,1] 226s [1,] 0.924 226s [2,] 0.933 226s [3,] 0.933 226s [4,] 0.938 226s [5,] 0.862 226s [6,] 0.868 226s [7,] 0.874 226s [8,] 0.879 226s [9,] 0.883 226s [10,] 0.943 226s [11,] 0.830 226s [12,] 0.744 226s [13,] 0.826 226s [14,] 0.834 226s [15,] 0.952 226s [16,] 0.918 226s [17,] 0.954 226s [18,] 0.930 226s [19,] 0.890 226s [20,] 0.893 226s > 226s > print( correlation.systemfit( fit3sls[[ 5 ]]$e5, 2, 1 ) ) 226s [,1] 226s [1,] 0.922 226s [2,] 0.935 226s [3,] 0.934 226s [4,] 0.939 226s [5,] 0.863 226s [6,] 0.868 226s [7,] 0.874 226s [8,] 0.876 226s [9,] 0.884 226s [10,] 0.942 226s [11,] 0.824 226s [12,] 0.747 226s [13,] 0.830 226s [14,] 0.833 226s [15,] 0.952 226s [16,] 0.919 226s [17,] 0.955 226s [18,] 0.928 226s [19,] 0.886 226s [20,] 0.888 226s > 226s > print( correlation.systemfit( fit3slsi[[ 2 ]]$e3e, 1, 2 ) ) 226s [,1] 226s [1,] 0.982 226s [2,] 0.994 226s [3,] 0.993 226s [4,] 0.992 226s [5,] 0.990 226s [6,] 0.990 226s [7,] 0.991 226s [8,] 0.978 226s [9,] 0.984 226s [10,] 0.992 226s [11,] 0.991 226s [12,] 0.985 226s [13,] 0.986 226s [14,] 0.980 226s [15,] 0.976 226s [16,] 0.994 226s [17,] 0.992 226s [18,] 0.987 226s [19,] 0.990 226s [20,] 0.991 226s > 226s > print( correlation.systemfit( fit3slsi[[ 4 ]]$e5w, 1, 2 ) ) 226s [,1] 226s [1,] 0.962 226s [2,] 0.975 226s [3,] 0.974 226s [4,] 0.976 226s [5,] 0.946 226s [6,] 0.948 226s [7,] 0.951 226s [8,] 0.944 226s [9,] 0.952 226s [10,] 0.976 226s [11,] 0.912 226s [12,] 0.871 226s [13,] 0.926 226s [14,] 0.927 226s [15,] 0.979 226s [16,] 0.968 226s [17,] 0.981 226s [18,] 0.970 226s [19,] 0.947 226s [20,] 0.943 226s > 226s > print( correlation.systemfit( fit3slsd[[ 3 ]]$e4, 2, 1 ) ) 226s [,1] 226s [1,] 0.932 226s [2,] 0.954 226s [3,] 0.952 226s [4,] 0.957 226s [5,] 0.892 226s [6,] 0.887 226s [7,] 0.887 226s [8,] 0.905 226s [9,] 0.914 226s [10,] 0.963 226s [11,] 0.860 226s [12,] 0.779 226s [13,] 0.878 226s [14,] 0.852 226s [15,] 0.968 226s [16,] 0.938 226s [17,] 0.973 226s [18,] 0.946 226s [19,] 0.913 226s [20,] 0.921 226s > 226s > 226s > ## ************ Log-Likelihood values *************** 226s > print( logLik( fit3sls[[ 1 ]]$e1c ) ) 226s 'log Lik.' -53 (df=10) 226s > print( logLik( fit3sls[[ 1 ]]$e1c, residCovDiag = TRUE ) ) 226s 'log Lik.' -85.6 (df=10) 226s > 226s > print( logLik( fit3sls[[ 2 ]]$e2e ) ) 226s 'log Lik.' -55.6 (df=9) 226s > print( logLik( fit3sls[[ 2 ]]$e2e, residCovDiag = TRUE ) ) 226s 'log Lik.' -85.4 (df=9) 226s > 226s > print( logLik( fit3sls[[ 3 ]]$e3 ) ) 226s 'log Lik.' -55.3 (df=9) 226s > print( logLik( fit3sls[[ 3 ]]$e3, residCovDiag = TRUE ) ) 226s 'log Lik.' -85.5 (df=9) 226s > 226s > print( logLik( fit3sls[[ 4 ]]$e4e ) ) 226s 'log Lik.' -58.5 (df=8) 226s > print( logLik( fit3sls[[ 4 ]]$e4e, residCovDiag = TRUE ) ) 226s 'log Lik.' -85.2 (df=8) 226s > 226s > print( logLik( fit3sls[[ 2 ]]$e4wSym ) ) 226s 'log Lik.' -58.5 (df=8) 226s > print( logLik( fit3sls[[ 2 ]]$e4wSym, residCovDiag = TRUE ) ) 226s 'log Lik.' -85.3 (df=8) 226s > 226s > print( logLik( fit3sls[[ 5 ]]$e5 ) ) 226s 'log Lik.' -87.3 (df=8) 226s > print( logLik( fit3sls[[ 5 ]]$e5, residCovDiag = TRUE ) ) 226s 'log Lik.' -104 (df=8) 226s > 226s > print( logLik( fit3slsi[[ 2 ]]$e3e ) ) 226s 'log Lik.' -46.7 (df=9) 226s > print( logLik( fit3slsi[[ 2 ]]$e3e, residCovDiag = TRUE ) ) 226s 'log Lik.' -92.1 (df=9) 226s > 226s > print( logLik( fit3slsi[[ 1 ]]$e1we ) ) 226s 'log Lik.' -52.7 (df=10) 226s > print( logLik( fit3slsi[[ 1 ]]$e1we, residCovDiag = TRUE ) ) 226s 'log Lik.' -85.8 (df=10) 226s > 226s > print( logLik( fit3slsd[[ 3 ]]$e4 ) ) 226s 'log Lik.' -59.4 (df=8) 226s > print( logLik( fit3slsd[[ 3 ]]$e4, residCovDiag = TRUE ) ) 226s 'log Lik.' -86.1 (df=8) 226s > 226s > print( logLik( fit3slsd[[ 5 ]]$e2we ) ) 226s 'log Lik.' -65 (df=9) 226s > print( logLik( fit3slsd[[ 5 ]]$e2we, residCovDiag = TRUE ) ) 226s 'log Lik.' -85.7 (df=9) 226s > 226s > 226s > ## ************** F tests **************** 226s > # testing first restriction 226s > print( linearHypothesis( fit3sls[[ 1 ]]$e1, restrm ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 1.69 0.2 226s > linearHypothesis( fit3sls[[ 1 ]]$e1, restrict ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 1.69 0.2 226s > 226s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restrm ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 1.52 0.23 226s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 1.52 0.23 226s > 226s > print( linearHypothesis( fit3sls[[ 3 ]]$e1c, restrm ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[3]]$e1c 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 2.47 0.13 226s > linearHypothesis( fit3sls[[ 3 ]]$e1c, restrict ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[3]]$e1c 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 2.47 0.13 226s > 226s > print( linearHypothesis( fit3slsi[[ 4 ]]$e1, restrm ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[4]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 4.75 0.037 * 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 4 ]]$e1, restrict ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[4]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 4.75 0.037 * 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrm ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[5]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.18 0.68 226s > linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrict ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[5]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.18 0.68 226s > 226s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1w, restrm ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e1w 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.51 0.48 226s > linearHypothesis( fit3slsd[[ 2 ]]$e1w, restrict ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e1w 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.51 0.48 226s > 226s > # testing second restriction 226s > restrOnly2m <- matrix(0,1,7) 226s > restrOnly2q <- 0.5 226s > restrOnly2m[1,2] <- -1 226s > restrOnly2m[1,5] <- 1 226s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 226s > # first restriction not imposed 226s > print( linearHypothesis( fit3sls[[ 5 ]]$e1c, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[5]]$e1c 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.17 0.69 226s > linearHypothesis( fit3sls[[ 5 ]]$e1c, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[5]]$e1c 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.17 0.69 226s > 226s > print( linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[1]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.13 0.72 226s > linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[1]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.13 0.72 226s > 226s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1we, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[3]]$e1we 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.13 0.72 226s > linearHypothesis( fit3slsi[[ 3 ]]$e1we, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[3]]$e1we 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.13 0.72 226s > 226s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.25 0.62 226s > linearHypothesis( fit3slsd[[ 2 ]]$e1, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 34 226s 2 33 1 0.25 0.62 226s > 226s > # first restriction imposed 226s > print( linearHypothesis( fit3sls[[ 4 ]]$e2, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e2 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.81 0.38 226s > linearHypothesis( fit3sls[[ 4 ]]$e2, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e2 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.81 0.38 226s > 226s > print( linearHypothesis( fit3sls[[ 4 ]]$e3, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e3 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.81 0.38 226s > linearHypothesis( fit3sls[[ 4 ]]$e3, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e3 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.81 0.38 226s > 226s > print( linearHypothesis( fit3sls[[ 1 ]]$e2w, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e2w 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.9 0.35 226s > linearHypothesis( fit3sls[[ 1 ]]$e2w, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e2w 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.9 0.35 226s > 226s > print( linearHypothesis( fit3sls[[ 1 ]]$e3we, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e3we 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.75 0.39 226s > linearHypothesis( fit3sls[[ 1 ]]$e3we, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e3we 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.75 0.39 226s > 226s > print( linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e2e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 15.1 0.00044 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e2e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 15.1 0.00044 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e3e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 15.1 0.00044 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e3e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 15.1 0.00044 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsd[[ 1 ]]$e2, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e2 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.16 0.69 226s > linearHypothesis( fit3slsd[[ 1 ]]$e2, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e2 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.16 0.69 226s > 226s > print( linearHypothesis( fit3slsd[[ 1 ]]$e3, restrOnly2m, restrOnly2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e3 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.16 0.69 226s > linearHypothesis( fit3slsd[[ 1 ]]$e3, restrictOnly2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e3 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 34 1 0.16 0.69 226s > 226s > # testing both of the restrictions 226s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restr2m, restr2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 1 0.38 226s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 1 0.38 226s > 226s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1, restr2m, restr2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[3]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 5.59 0.0081 ** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 3 ]]$e1, restrict2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[3]]$e1 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 5.59 0.0081 ** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsd[[ 4 ]]$e1e, restr2m, restr2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[4]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 0.64 0.53 226s > linearHypothesis( fit3slsd[[ 4 ]]$e1e, restrict2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[4]]$e1e 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 0.64 0.53 226s > 226s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1w, restr2m, restr2q ) ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[5]]$e1w 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 0.45 0.64 226s > linearHypothesis( fit3slsd[[ 5 ]]$e1w, restrict2 ) 226s Linear hypothesis test (Theil's F test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[5]]$e1w 226s 226s Res.Df Df F Pr(>F) 226s 1 35 226s 2 33 2 0.45 0.64 226s > 226s > 226s > ## ************** Wald tests **************** 226s > # testing first restriction 226s > print( linearHypothesis( fit3sls[[ 1 ]]$e1, restrm, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 1.11 0.29 226s > linearHypothesis( fit3sls[[ 1 ]]$e1, restrict, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[1]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 1.11 0.29 226s > 226s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restrm, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 1.23 0.27 226s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 1.23 0.27 226s > 226s > print( linearHypothesis( fit3sls[[ 3 ]]$e1c, restrm, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[3]]$e1c 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 1.73 0.19 226s > linearHypothesis( fit3sls[[ 3 ]]$e1c, restrict, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[3]]$e1c 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 1.73 0.19 226s > 226s > print( linearHypothesis( fit3slsi[[ 4 ]]$e1, restrm, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[4]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 4.81 0.028 * 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 4 ]]$e1, restrict, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[4]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 4.81 0.028 * 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsi[[ 2 ]]$e1we, restrm, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[2]]$e1we 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 5.72 0.017 * 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 2 ]]$e1we, restrict, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[2]]$e1we 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 5.72 0.017 * 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrm, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[5]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.15 0.7 226s > linearHypothesis( fit3slsd[[ 5 ]]$e1e, restrict, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[5]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.15 0.7 226s > 226s > # testing second restriction 226s > # first restriction not imposed 226s > print( linearHypothesis( fit3sls[[ 5 ]]$e1c, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[5]]$e1c 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.12 0.73 226s > linearHypothesis( fit3sls[[ 5 ]]$e1c, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[5]]$e1c 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.12 0.73 226s > 226s > print( linearHypothesis( fit3sls[[ 3 ]]$e1wc, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[3]]$e1wc 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.12 0.73 226s > linearHypothesis( fit3sls[[ 3 ]]$e1wc, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[3]]$e1wc 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.12 0.73 226s > 226s > print( linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[1]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.16 0.69 226s > linearHypothesis( fit3slsi[[ 1 ]]$e1e, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[1]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.16 0.69 226s > 226s > print( linearHypothesis( fit3slsd[[ 2 ]]$e1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.17 0.68 226s > linearHypothesis( fit3slsd[[ 2 ]]$e1, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 34 226s 2 33 1 0.17 0.68 226s > 226s > # first restriction imposed 226s > print( linearHypothesis( fit3sls[[ 4 ]]$e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e2 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.55 0.46 226s > linearHypothesis( fit3sls[[ 4 ]]$e2, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e2 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.55 0.46 226s > 226s > print( linearHypothesis( fit3sls[[ 4 ]]$e3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e3 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.55 0.46 226s > linearHypothesis( fit3sls[[ 4 ]]$e3, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[4]]$e3 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.55 0.46 226s > 226s > print( linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e2e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 17.8 2.4e-05 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 5 ]]$e2e, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e2e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 17.8 2.4e-05 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e3e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 17.8 2.4e-05 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 5 ]]$e3e, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[5]]$e3e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 17.8 2.4e-05 *** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsd[[ 1 ]]$e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e2 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.13 0.72 226s > linearHypothesis( fit3slsd[[ 1 ]]$e2, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e2 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.13 0.72 226s > 226s > print( linearHypothesis( fit3slsd[[ 1 ]]$e3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e3 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.13 0.72 226s > linearHypothesis( fit3slsd[[ 1 ]]$e3, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[1]]$e3 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.13 0.72 226s > 226s > print( linearHypothesis( fit3slsd[[ 2 ]]$e2we, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e2we 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 1.52 0.22 226s > linearHypothesis( fit3slsd[[ 2 ]]$e2we, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[2]]$e2we 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 1.52 0.22 226s > 226s > print( linearHypothesis( fit3slsd[[ 3 ]]$e3w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[3]]$e3w 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.23 0.63 226s > linearHypothesis( fit3slsd[[ 3 ]]$e3w, restrictOnly2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[3]]$e3w 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 34 1 0.23 0.63 226s > 226s > # testing both of the restrictions 226s > print( linearHypothesis( fit3sls[[ 2 ]]$e1e, restr2m, restr2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 1.62 0.44 226s > linearHypothesis( fit3sls[[ 2 ]]$e1e, restrict2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[2]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 1.62 0.44 226s > 226s > print( linearHypothesis( fit3sls[[ 5 ]]$e1wc, restr2m, restr2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[5]]$e1wc 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 2.43 0.3 226s > linearHypothesis( fit3sls[[ 5 ]]$e1wc, restrict2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3sls[[5]]$e1wc 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 2.43 0.3 226s > 226s > print( linearHypothesis( fit3slsi[[ 3 ]]$e1, restr2m, restr2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[3]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 11.3 0.0035 ** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > linearHypothesis( fit3slsi[[ 3 ]]$e1, restrict2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsi[[3]]$e1 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 11.3 0.0035 ** 226s --- 226s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 226s > 226s > print( linearHypothesis( fit3slsd[[ 4 ]]$e1e, restr2m, restr2q, test = "Chisq" ) ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[4]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 1.55 0.46 226s > linearHypothesis( fit3slsd[[ 4 ]]$e1e, restrict2, test = "Chisq" ) 226s Linear hypothesis test (Chi^2 statistic of a Wald test) 226s 226s Hypothesis: 226s demand_income - supply_trend = 0 226s - demand_price + supply_price = 0.5 226s 226s Model 1: restricted model 226s Model 2: fit3slsd[[4]]$e1e 226s 226s Res.Df Df Chisq Pr(>Chisq) 226s 1 35 226s 2 33 2 1.55 0.46 226s > 226s > 226s > ## *********** model frame ************* 226s > print( mf <- model.frame( fit3sls[[ 3 ]]$e1c ) ) 226s consump price income farmPrice trend 226s 1 98.5 100.3 87.4 98.0 1 226s 2 99.2 104.3 97.6 99.1 2 226s 3 102.2 103.4 96.7 99.1 3 226s 4 101.5 104.5 98.2 98.1 4 226s 5 104.2 98.0 99.8 110.8 5 226s 6 103.2 99.5 100.5 108.2 6 226s 7 104.0 101.1 103.2 105.6 7 226s 8 99.9 104.8 107.8 109.8 8 226s 9 100.3 96.4 96.6 108.7 9 226s 10 102.8 91.2 88.9 100.6 10 226s 11 95.4 93.1 75.1 81.0 11 226s 12 92.4 98.8 76.9 68.6 12 226s 13 94.5 102.9 84.6 70.9 13 226s 14 98.8 98.8 90.6 81.4 14 226s 15 105.8 95.1 103.1 102.3 15 226s 16 100.2 98.5 105.1 105.0 16 226s 17 103.5 86.5 96.4 110.5 17 226s 18 99.9 104.0 104.4 92.5 18 226s 19 105.2 105.8 110.7 89.3 19 226s 20 106.2 113.5 127.1 93.0 20 226s > print( mf1 <- model.frame( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]] ) ) 226s consump price income 226s 1 98.5 100.3 87.4 226s 2 99.2 104.3 97.6 226s 3 102.2 103.4 96.7 226s 4 101.5 104.5 98.2 226s 5 104.2 98.0 99.8 226s 6 103.2 99.5 100.5 226s 7 104.0 101.1 103.2 226s 8 99.9 104.8 107.8 226s 9 100.3 96.4 96.6 226s 10 102.8 91.2 88.9 226s 11 95.4 93.1 75.1 226s 12 92.4 98.8 76.9 226s 13 94.5 102.9 84.6 226s 14 98.8 98.8 90.6 226s 15 105.8 95.1 103.1 226s 16 100.2 98.5 105.1 226s 17 103.5 86.5 96.4 226s 18 99.9 104.0 104.4 226s 19 105.2 105.8 110.7 226s 20 106.2 113.5 127.1 226s > print( attributes( mf1 )$terms ) 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s > print( mf2 <- model.frame( fit3sls[[ 3 ]]$e1c$eq[[ 2 ]] ) ) 226s consump price farmPrice trend 226s 1 98.5 100.3 98.0 1 226s 2 99.2 104.3 99.1 2 226s 3 102.2 103.4 99.1 3 226s 4 101.5 104.5 98.1 4 226s 5 104.2 98.0 110.8 5 226s 6 103.2 99.5 108.2 6 226s 7 104.0 101.1 105.6 7 226s 8 99.9 104.8 109.8 8 226s 9 100.3 96.4 108.7 9 226s 10 102.8 91.2 100.6 10 226s 11 95.4 93.1 81.0 11 226s 12 92.4 98.8 68.6 12 226s 13 94.5 102.9 70.9 13 226s 14 98.8 98.8 81.4 14 226s 15 105.8 95.1 102.3 15 226s 16 100.2 98.5 105.0 16 226s 17 103.5 86.5 110.5 17 226s 18 99.9 104.0 92.5 18 226s 19 105.2 105.8 89.3 19 226s 20 106.2 113.5 93.0 20 226s > print( attributes( mf2 )$terms ) 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s > 226s > print( all.equal( mf, model.frame( fit3sls[[ 3 ]]$e1wc ) ) ) 226s [1] TRUE 226s > print( all.equal( mf2, model.frame( fit3sls[[ 3 ]]$e1wc$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > print( all.equal( mf, model.frame( fit3sls[[ 4 ]]$e2e ) ) ) 226s [1] TRUE 226s > print( all.equal( mf2, model.frame( fit3sls[[ 4 ]]$e2e$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > print( all.equal( mf, model.frame( fit3sls[[ 5 ]]$e3 ) ) ) 226s [1] TRUE 226s > print( all.equal( mf1, model.frame( fit3sls[[ 5 ]]$e3$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > 226s > print( all.equal( mf, model.frame( fit3sls[[ 1 ]]$e4e ) ) ) 226s [1] TRUE 226s > print( all.equal( mf2, model.frame( fit3sls[[ 1 ]]$e4e$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > print( all.equal( mf, model.frame( fit3sls[[ 2 ]]$e5 ) ) ) 226s [1] TRUE 226s > print( all.equal( mf1, model.frame( fit3sls[[ 3 ]]$e5$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > 226s > print( all.equal( mf, model.frame( fit3slsi[[ 4 ]]$e3e ) ) ) 226s [1] TRUE 226s > print( all.equal( mf1, model.frame( fit3slsi[[ 4 ]]$e3e$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > 226s > print( all.equal( mf, model.frame( fit3slsd[[ 5 ]]$e4 ) ) ) 226s [1] TRUE 226s > print( all.equal( mf2, model.frame( fit3slsd[[ 5 ]]$e4$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > fit3sls[[ 3 ]]$e1c$eq[[ 1 ]]$modelInst 226s income farmPrice trend 226s 1 87.4 98.0 1 226s 2 97.6 99.1 2 226s 3 96.7 99.1 3 226s 4 98.2 98.1 4 226s 5 99.8 110.8 5 226s 6 100.5 108.2 6 226s 7 103.2 105.6 7 226s 8 107.8 109.8 8 226s 9 96.6 108.7 9 226s 10 88.9 100.6 10 226s 11 75.1 81.0 11 226s 12 76.9 68.6 12 226s 13 84.6 70.9 13 226s 14 90.6 81.4 14 226s 15 103.1 102.3 15 226s 16 105.1 105.0 16 226s 17 96.4 110.5 17 226s 18 104.4 92.5 18 226s 19 110.7 89.3 19 226s 20 127.1 93.0 20 226s > fit3sls[[ 3 ]]$e1c$eq[[ 2 ]]$modelInst 226s income farmPrice trend 226s 1 87.4 98.0 1 226s 2 97.6 99.1 2 226s 3 96.7 99.1 3 226s 4 98.2 98.1 4 226s 5 99.8 110.8 5 226s 6 100.5 108.2 6 226s 7 103.2 105.6 7 226s 8 107.8 109.8 8 226s 9 96.6 108.7 9 226s 10 88.9 100.6 10 226s 11 75.1 81.0 11 226s 12 76.9 68.6 12 226s 13 84.6 70.9 13 226s 14 90.6 81.4 14 226s 15 103.1 102.3 15 226s 16 105.1 105.0 16 226s 17 96.4 110.5 17 226s 18 104.4 92.5 18 226s 19 110.7 89.3 19 226s 20 127.1 93.0 20 226s > 226s > fit3sls[[ 1 ]]$e3$eq[[ 1 ]]$modelInst 226s income farmPrice trend 226s 1 87.4 98.0 1 226s 2 97.6 99.1 2 226s 3 96.7 99.1 3 226s 4 98.2 98.1 4 226s 5 99.8 110.8 5 226s 6 100.5 108.2 6 226s 7 103.2 105.6 7 226s 8 107.8 109.8 8 226s 9 96.6 108.7 9 226s 10 88.9 100.6 10 226s 11 75.1 81.0 11 226s 12 76.9 68.6 12 226s 13 84.6 70.9 13 226s 14 90.6 81.4 14 226s 15 103.1 102.3 15 226s 16 105.1 105.0 16 226s 17 96.4 110.5 17 226s 18 104.4 92.5 18 226s 19 110.7 89.3 19 226s 20 127.1 93.0 20 226s > fit3sls[[ 1 ]]$e3$eq[[ 2 ]]$modelInst 226s income farmPrice trend 226s 1 87.4 98.0 1 226s 2 97.6 99.1 2 226s 3 96.7 99.1 3 226s 4 98.2 98.1 4 226s 5 99.8 110.8 5 226s 6 100.5 108.2 6 226s 7 103.2 105.6 7 226s 8 107.8 109.8 8 226s 9 96.6 108.7 9 226s 10 88.9 100.6 10 226s 11 75.1 81.0 11 226s 12 76.9 68.6 12 226s 13 84.6 70.9 13 226s 14 90.6 81.4 14 226s 15 103.1 102.3 15 226s 16 105.1 105.0 16 226s 17 96.4 110.5 17 226s 18 104.4 92.5 18 226s 19 110.7 89.3 19 226s 20 127.1 93.0 20 226s > 226s > fit3slsd[[ 5 ]]$e4$eq[[ 1 ]]$modelInst 226s income farmPrice 226s 1 87.4 98.0 226s 2 97.6 99.1 226s 3 96.7 99.1 226s 4 98.2 98.1 226s 5 99.8 110.8 226s 6 100.5 108.2 226s 7 103.2 105.6 226s 8 107.8 109.8 226s 9 96.6 108.7 226s 10 88.9 100.6 226s 11 75.1 81.0 226s 12 76.9 68.6 226s 13 84.6 70.9 226s 14 90.6 81.4 226s 15 103.1 102.3 226s 16 105.1 105.0 226s 17 96.4 110.5 226s 18 104.4 92.5 226s 19 110.7 89.3 226s 20 127.1 93.0 226s > fit3slsd[[ 5 ]]$e4$eq[[ 2 ]]$modelInst 226s income farmPrice trend 226s 1 87.4 98.0 1 226s 2 97.6 99.1 2 226s 3 96.7 99.1 3 226s 4 98.2 98.1 4 226s 5 99.8 110.8 5 226s 6 100.5 108.2 6 226s 7 103.2 105.6 7 226s 8 107.8 109.8 8 226s 9 96.6 108.7 9 226s 10 88.9 100.6 10 226s 11 75.1 81.0 11 226s 12 76.9 68.6 12 226s 13 84.6 70.9 13 226s 14 90.6 81.4 14 226s 15 103.1 102.3 15 226s 16 105.1 105.0 16 226s 17 96.4 110.5 17 226s 18 104.4 92.5 18 226s 19 110.7 89.3 19 226s 20 127.1 93.0 20 226s > 226s > 226s > ## **************** model matrix ************************ 226s > # with x (returnModelMatrix) = TRUE 226s > print( !is.null( fit3sls[[ 4 ]]$e1c$eq[[ 1 ]]$x ) ) 226s [1] TRUE 226s > print( mm <- model.matrix( fit3sls[[ 4 ]]$e1c ) ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 1 100.3 87.4 0 226s demand_2 1 104.3 97.6 0 226s demand_3 1 103.4 96.7 0 226s demand_4 1 104.5 98.2 0 226s demand_5 1 98.0 99.8 0 226s demand_6 1 99.5 100.5 0 226s demand_7 1 101.1 103.2 0 226s demand_8 1 104.8 107.8 0 226s demand_9 1 96.4 96.6 0 226s demand_10 1 91.2 88.9 0 226s demand_11 1 93.1 75.1 0 226s demand_12 1 98.8 76.9 0 226s demand_13 1 102.9 84.6 0 226s demand_14 1 98.8 90.6 0 226s demand_15 1 95.1 103.1 0 226s demand_16 1 98.5 105.1 0 226s demand_17 1 86.5 96.4 0 226s demand_18 1 104.0 104.4 0 226s demand_19 1 105.8 110.7 0 226s demand_20 1 113.5 127.1 0 226s supply_1 0 0.0 0.0 1 226s supply_2 0 0.0 0.0 1 226s supply_3 0 0.0 0.0 1 226s supply_4 0 0.0 0.0 1 226s supply_5 0 0.0 0.0 1 226s supply_6 0 0.0 0.0 1 226s supply_7 0 0.0 0.0 1 226s supply_8 0 0.0 0.0 1 226s supply_9 0 0.0 0.0 1 226s supply_10 0 0.0 0.0 1 226s supply_11 0 0.0 0.0 1 226s supply_12 0 0.0 0.0 1 226s supply_13 0 0.0 0.0 1 226s supply_14 0 0.0 0.0 1 226s supply_15 0 0.0 0.0 1 226s supply_16 0 0.0 0.0 1 226s supply_17 0 0.0 0.0 1 226s supply_18 0 0.0 0.0 1 226s supply_19 0 0.0 0.0 1 226s supply_20 0 0.0 0.0 1 226s supply_price supply_farmPrice supply_trend 226s demand_1 0.0 0.0 0 226s demand_2 0.0 0.0 0 226s demand_3 0.0 0.0 0 226s demand_4 0.0 0.0 0 226s demand_5 0.0 0.0 0 226s demand_6 0.0 0.0 0 226s demand_7 0.0 0.0 0 226s demand_8 0.0 0.0 0 226s demand_9 0.0 0.0 0 226s demand_10 0.0 0.0 0 226s demand_11 0.0 0.0 0 226s demand_12 0.0 0.0 0 226s demand_13 0.0 0.0 0 226s demand_14 0.0 0.0 0 226s demand_15 0.0 0.0 0 226s demand_16 0.0 0.0 0 226s demand_17 0.0 0.0 0 226s demand_18 0.0 0.0 0 226s demand_19 0.0 0.0 0 226s demand_20 0.0 0.0 0 226s supply_1 100.3 98.0 1 226s supply_2 104.3 99.1 2 226s supply_3 103.4 99.1 3 226s supply_4 104.5 98.1 4 226s supply_5 98.0 110.8 5 226s supply_6 99.5 108.2 6 226s supply_7 101.1 105.6 7 226s supply_8 104.8 109.8 8 226s supply_9 96.4 108.7 9 226s supply_10 91.2 100.6 10 226s supply_11 93.1 81.0 11 226s supply_12 98.8 68.6 12 226s supply_13 102.9 70.9 13 226s supply_14 98.8 81.4 14 226s supply_15 95.1 102.3 15 226s supply_16 98.5 105.0 16 226s supply_17 86.5 110.5 17 226s supply_18 104.0 92.5 18 226s supply_19 105.8 89.3 19 226s supply_20 113.5 93.0 20 226s > print( mm1 <- model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 1 ]] ) ) 226s (Intercept) price income 226s 1 1 100.3 87.4 226s 2 1 104.3 97.6 226s 3 1 103.4 96.7 226s 4 1 104.5 98.2 226s 5 1 98.0 99.8 226s 6 1 99.5 100.5 226s 7 1 101.1 103.2 226s 8 1 104.8 107.8 226s 9 1 96.4 96.6 226s 10 1 91.2 88.9 226s 11 1 93.1 75.1 226s 12 1 98.8 76.9 226s 13 1 102.9 84.6 226s 14 1 98.8 90.6 226s 15 1 95.1 103.1 226s 16 1 98.5 105.1 226s 17 1 86.5 96.4 226s 18 1 104.0 104.4 226s 19 1 105.8 110.7 226s 20 1 113.5 127.1 226s attr(,"assign") 226s [1] 0 1 2 226s > print( mm2 <- model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]] ) ) 226s (Intercept) price farmPrice trend 226s 1 1 100.3 98.0 1 226s 2 1 104.3 99.1 2 226s 3 1 103.4 99.1 3 226s 4 1 104.5 98.1 4 226s 5 1 98.0 110.8 5 226s 6 1 99.5 108.2 6 226s 7 1 101.1 105.6 7 226s 8 1 104.8 109.8 8 226s 9 1 96.4 108.7 9 226s 10 1 91.2 100.6 10 226s 11 1 93.1 81.0 11 226s 12 1 98.8 68.6 12 226s 13 1 102.9 70.9 13 226s 14 1 98.8 81.4 14 226s 15 1 95.1 102.3 15 226s 16 1 98.5 105.0 16 226s 17 1 86.5 110.5 17 226s 18 1 104.0 92.5 18 226s 19 1 105.8 89.3 19 226s 20 1 113.5 93.0 20 226s attr(,"assign") 226s [1] 0 1 2 3 226s > 226s > # with x (returnModelMatrix) = FALSE 226s > print( all.equal( mm, model.matrix( fit3sls[[ 4 ]]$e1wc ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3sls[[ 4 ]]$e1wc$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > print( !is.null( fit3sls[[ 4 ]]$e1wc$eq[[ 1 ]]$x ) ) 226s [1] FALSE 226s > 226s > # with x (returnModelMatrix) = TRUE 226s > print( !is.null( fit3sls[[ 5 ]]$e2$eq[[ 1 ]]$x ) ) 226s [1] TRUE 226s > print( all.equal( mm, model.matrix( fit3sls[[ 5 ]]$e2 ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3sls[[ 5 ]]$e2$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3sls[[ 5 ]]$e2$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > # with x (returnModelMatrix) = FALSE 226s > print( all.equal( mm, model.matrix( fit3sls[[ 5 ]]$e2e ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3sls[[ 5 ]]$e2e$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3sls[[ 5 ]]$e2e$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > print( !is.null( fit3sls[[ 5 ]]$e1wc$e2e[[ 1 ]]$x ) ) 226s [1] FALSE 226s > 226s > # with x (returnModelMatrix) = TRUE 226s > print( !is.null( fit3sls[[ 1 ]]$e3e$eq[[ 1 ]]$x ) ) 226s [1] TRUE 226s > print( all.equal( mm, model.matrix( fit3sls[[ 1 ]]$e3e ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3sls[[ 1 ]]$e3e$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3sls[[ 1 ]]$e3e$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > # with x (returnModelMatrix) = FALSE 226s > print( all.equal( mm, model.matrix( fit3sls[[ 1 ]]$e3 ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3sls[[ 1 ]]$e3$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3sls[[ 1 ]]$e3$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > print( !is.null( fit3sls[[ 1 ]]$e3$eq[[ 1 ]]$x ) ) 226s [1] FALSE 226s > 226s > # with x (returnModelMatrix) = TRUE 226s > print( !is.null( fit3slsi[[ 2 ]]$e4$eq[[ 1 ]]$x ) ) 226s [1] TRUE 226s > print( all.equal( mm, model.matrix( fit3slsi[[ 2 ]]$e4 ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsi[[ 2 ]]$e4$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsi[[ 2 ]]$e4$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > # with x (returnModelMatrix) = FALSE 226s > print( all.equal( mm, model.matrix( fit3slsi[[ 2 ]]$e4we ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsi[[ 2 ]]$e4we$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsi[[ 2 ]]$e4we$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > print( !is.null( fit3slsi[[ 2 ]]$e1wc$e4we[[ 1 ]]$x ) ) 226s [1] FALSE 226s > 226s > # with x (returnModelMatrix) = TRUE 226s > print( !is.null( fit3slsi[[ 5 ]]$e5w$eq[[ 1 ]]$x ) ) 226s [1] TRUE 226s > print( all.equal( mm, model.matrix( fit3slsi[[ 5 ]]$e5w ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsi[[ 5 ]]$e5w$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsi[[ 5 ]]$e5w$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > # with x (returnModelMatrix) = FALSE 226s > print( all.equal( mm, model.matrix( fit3slsi[[ 5 ]]$e5 ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsi[[ 5 ]]$e5$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsi[[ 5 ]]$e5$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > print( !is.null( fit3slsi[[ 5 ]]$e5$eq[[ 1 ]]$x ) ) 226s [1] FALSE 226s > 226s > # with x (returnModelMatrix) = TRUE 226s > print( !is.null( fit3slsd[[ 3 ]]$e5e$eq[[ 1 ]]$x ) ) 226s [1] TRUE 226s > print( all.equal( mm, model.matrix( fit3slsd[[ 3 ]]$e5e ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsd[[ 3 ]]$e5e$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsd[[ 3 ]]$e5e$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > # with x (returnModelMatrix) = FALSE 226s > print( all.equal( mm, model.matrix( fit3slsd[[ 3 ]]$e5we ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsd[[ 3 ]]$e5we$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsd[[ 3 ]]$e5we$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > print( !is.null( fit3sls[[ 3 ]]$e5we$eq[[ 1 ]]$x ) ) 226s [1] FALSE 226s > 226s > # with x (returnModelMatrix) = TRUE 226s > print( !is.null( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]]$x ) ) 226s [1] TRUE 226s > print( all.equal( mm, model.matrix( fit3slsd[[ 2 ]]$e3w ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsd[[ 2 ]]$e3w$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsd[[ 2 ]]$e3w$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > 226s > # with x (returnModelMatrix) = FALSE 226s > print( all.equal( mm, model.matrix( fit3slsd[[ 2 ]]$e3 ) ) ) 226s [1] TRUE 226s > print( all.equal( mm1, model.matrix( fit3slsd[[ 2 ]]$e3$eq[[ 1 ]] ) ) ) 226s [1] TRUE 226s > print( all.equal( mm2, model.matrix( fit3slsd[[ 2 ]]$e3$eq[[ 2 ]] ) ) ) 226s [1] TRUE 226s > print( !is.null( fit3slsd[[ 2 ]]$e3$eq[[ 1 ]]$x ) ) 226s [1] FALSE 226s > 226s > # matrices of instrumental variables 226s > model.matrix( fit3sls[[ 1 ]]$e1c, which = "z" ) 226s demand_(Intercept) demand_income demand_farmPrice demand_trend 226s demand_1 1 87.4 98.0 1 226s demand_2 1 97.6 99.1 2 226s demand_3 1 96.7 99.1 3 226s demand_4 1 98.2 98.1 4 226s demand_5 1 99.8 110.8 5 226s demand_6 1 100.5 108.2 6 226s demand_7 1 103.2 105.6 7 226s demand_8 1 107.8 109.8 8 226s demand_9 1 96.6 108.7 9 226s demand_10 1 88.9 100.6 10 226s demand_11 1 75.1 81.0 11 226s demand_12 1 76.9 68.6 12 226s demand_13 1 84.6 70.9 13 226s demand_14 1 90.6 81.4 14 226s demand_15 1 103.1 102.3 15 226s demand_16 1 105.1 105.0 16 226s demand_17 1 96.4 110.5 17 226s demand_18 1 104.4 92.5 18 226s demand_19 1 110.7 89.3 19 226s demand_20 1 127.1 93.0 20 226s supply_1 0 0.0 0.0 0 226s supply_2 0 0.0 0.0 0 226s supply_3 0 0.0 0.0 0 226s supply_4 0 0.0 0.0 0 226s supply_5 0 0.0 0.0 0 226s supply_6 0 0.0 0.0 0 226s supply_7 0 0.0 0.0 0 226s supply_8 0 0.0 0.0 0 226s supply_9 0 0.0 0.0 0 226s supply_10 0 0.0 0.0 0 226s supply_11 0 0.0 0.0 0 226s supply_12 0 0.0 0.0 0 226s supply_13 0 0.0 0.0 0 226s supply_14 0 0.0 0.0 0 226s supply_15 0 0.0 0.0 0 226s supply_16 0 0.0 0.0 0 226s supply_17 0 0.0 0.0 0 226s supply_18 0 0.0 0.0 0 226s supply_19 0 0.0 0.0 0 226s supply_20 0 0.0 0.0 0 226s supply_(Intercept) supply_income supply_farmPrice supply_trend 226s demand_1 0 0.0 0.0 0 226s demand_2 0 0.0 0.0 0 226s demand_3 0 0.0 0.0 0 226s demand_4 0 0.0 0.0 0 226s demand_5 0 0.0 0.0 0 226s demand_6 0 0.0 0.0 0 226s demand_7 0 0.0 0.0 0 226s demand_8 0 0.0 0.0 0 226s demand_9 0 0.0 0.0 0 226s demand_10 0 0.0 0.0 0 226s demand_11 0 0.0 0.0 0 226s demand_12 0 0.0 0.0 0 226s demand_13 0 0.0 0.0 0 226s demand_14 0 0.0 0.0 0 226s demand_15 0 0.0 0.0 0 226s demand_16 0 0.0 0.0 0 226s demand_17 0 0.0 0.0 0 226s demand_18 0 0.0 0.0 0 226s demand_19 0 0.0 0.0 0 226s demand_20 0 0.0 0.0 0 226s supply_1 1 87.4 98.0 1 226s supply_2 1 97.6 99.1 2 226s supply_3 1 96.7 99.1 3 226s supply_4 1 98.2 98.1 4 226s supply_5 1 99.8 110.8 5 226s supply_6 1 100.5 108.2 6 226s supply_7 1 103.2 105.6 7 226s supply_8 1 107.8 109.8 8 226s supply_9 1 96.6 108.7 9 226s supply_10 1 88.9 100.6 10 226s supply_11 1 75.1 81.0 11 226s supply_12 1 76.9 68.6 12 226s supply_13 1 84.6 70.9 13 226s supply_14 1 90.6 81.4 14 226s supply_15 1 103.1 102.3 15 226s supply_16 1 105.1 105.0 16 226s supply_17 1 96.4 110.5 17 226s supply_18 1 104.4 92.5 18 226s supply_19 1 110.7 89.3 19 226s supply_20 1 127.1 93.0 20 226s > model.matrix( fit3sls[[ 3 ]]$e1c$eq[[ 1 ]], which = "z" ) 226s (Intercept) income farmPrice trend 226s 1 1 87.4 98.0 1 226s 2 1 97.6 99.1 2 226s 3 1 96.7 99.1 3 226s 4 1 98.2 98.1 4 226s 5 1 99.8 110.8 5 226s 6 1 100.5 108.2 6 226s 7 1 103.2 105.6 7 226s 8 1 107.8 109.8 8 226s 9 1 96.6 108.7 9 226s 10 1 88.9 100.6 10 226s 11 1 75.1 81.0 11 226s 12 1 76.9 68.6 12 226s 13 1 84.6 70.9 13 226s 14 1 90.6 81.4 14 226s 15 1 103.1 102.3 15 226s 16 1 105.1 105.0 16 226s 17 1 96.4 110.5 17 226s 18 1 104.4 92.5 18 226s 19 1 110.7 89.3 19 226s 20 1 127.1 93.0 20 226s attr(,"assign") 226s [1] 0 1 2 3 226s > model.matrix( fit3sls[[ 4 ]]$e1c$eq[[ 2 ]], which = "z" ) 226s (Intercept) income farmPrice trend 226s 1 1 87.4 98.0 1 226s 2 1 97.6 99.1 2 226s 3 1 96.7 99.1 3 226s 4 1 98.2 98.1 4 226s 5 1 99.8 110.8 5 226s 6 1 100.5 108.2 6 226s 7 1 103.2 105.6 7 226s 8 1 107.8 109.8 8 226s 9 1 96.6 108.7 9 226s 10 1 88.9 100.6 10 226s 11 1 75.1 81.0 11 226s 12 1 76.9 68.6 12 226s 13 1 84.6 70.9 13 226s 14 1 90.6 81.4 14 226s 15 1 103.1 102.3 15 226s 16 1 105.1 105.0 16 226s 17 1 96.4 110.5 17 226s 18 1 104.4 92.5 18 226s 19 1 110.7 89.3 19 226s 20 1 127.1 93.0 20 226s attr(,"assign") 226s [1] 0 1 2 3 226s > 226s > # matrices of fitted regressors 226s > model.matrix( fit3slsd[[ 1 ]]$e3w, which = "xHat" ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 1 95.2 87.4 0 226s demand_2 1 99.3 97.6 0 226s demand_3 1 99.0 96.7 0 226s demand_4 1 99.9 98.2 0 226s demand_5 1 97.0 99.8 0 226s demand_6 1 98.0 100.5 0 226s demand_7 1 99.9 103.2 0 226s demand_8 1 100.7 107.8 0 226s demand_9 1 96.2 96.6 0 226s demand_10 1 95.1 88.9 0 226s demand_11 1 94.7 75.1 0 226s demand_12 1 99.0 76.9 0 226s demand_13 1 101.7 84.6 0 226s demand_14 1 101.3 90.6 0 226s demand_15 1 100.8 103.1 0 226s demand_16 1 100.9 105.1 0 226s demand_17 1 95.6 96.4 0 226s demand_18 1 104.2 104.4 0 226s demand_19 1 107.8 110.7 0 226s demand_20 1 113.9 127.1 0 226s supply_1 0 0.0 0.0 1 226s supply_2 0 0.0 0.0 1 226s supply_3 0 0.0 0.0 1 226s supply_4 0 0.0 0.0 1 226s supply_5 0 0.0 0.0 1 226s supply_6 0 0.0 0.0 1 226s supply_7 0 0.0 0.0 1 226s supply_8 0 0.0 0.0 1 226s supply_9 0 0.0 0.0 1 226s supply_10 0 0.0 0.0 1 226s supply_11 0 0.0 0.0 1 226s supply_12 0 0.0 0.0 1 226s supply_13 0 0.0 0.0 1 226s supply_14 0 0.0 0.0 1 226s supply_15 0 0.0 0.0 1 226s supply_16 0 0.0 0.0 1 226s supply_17 0 0.0 0.0 1 226s supply_18 0 0.0 0.0 1 226s supply_19 0 0.0 0.0 1 226s supply_20 0 0.0 0.0 1 226s supply_price supply_farmPrice supply_trend 226s demand_1 0.0 0.0 0 226s demand_2 0.0 0.0 0 226s demand_3 0.0 0.0 0 226s demand_4 0.0 0.0 0 226s demand_5 0.0 0.0 0 226s demand_6 0.0 0.0 0 226s demand_7 0.0 0.0 0 226s demand_8 0.0 0.0 0 226s demand_9 0.0 0.0 0 226s demand_10 0.0 0.0 0 226s demand_11 0.0 0.0 0 226s demand_12 0.0 0.0 0 226s demand_13 0.0 0.0 0 226s demand_14 0.0 0.0 0 226s demand_15 0.0 0.0 0 226s demand_16 0.0 0.0 0 226s demand_17 0.0 0.0 0 226s demand_18 0.0 0.0 0 226s demand_19 0.0 0.0 0 226s demand_20 0.0 0.0 0 226s supply_1 99.6 98.0 1 226s supply_2 105.1 99.1 2 226s supply_3 103.8 99.1 3 226s supply_4 104.5 98.1 4 226s supply_5 98.7 110.8 5 226s supply_6 99.6 108.2 6 226s supply_7 102.0 105.6 7 226s supply_8 102.2 109.8 8 226s supply_9 94.6 108.7 9 226s supply_10 92.7 100.6 10 226s supply_11 92.4 81.0 11 226s supply_12 98.9 68.6 12 226s supply_13 102.2 70.9 13 226s supply_14 100.3 81.4 14 226s supply_15 97.6 102.3 15 226s supply_16 96.9 105.0 16 226s supply_17 87.7 110.5 17 226s supply_18 101.1 92.5 18 226s supply_19 106.1 89.3 19 226s supply_20 114.4 93.0 20 226s > model.matrix( fit3slsd[[ 3 ]]$e3w$eq[[ 1 ]], which = "xHat" ) 226s (Intercept) price income 226s 1 1 95.2 87.4 226s 2 1 99.3 97.6 226s 3 1 99.0 96.7 226s 4 1 99.9 98.2 226s 5 1 97.0 99.8 226s 6 1 98.0 100.5 226s 7 1 99.9 103.2 226s 8 1 100.7 107.8 226s 9 1 96.2 96.6 226s 10 1 95.1 88.9 226s 11 1 94.7 75.1 226s 12 1 99.0 76.9 226s 13 1 101.7 84.6 226s 14 1 101.3 90.6 226s 15 1 100.8 103.1 226s 16 1 100.9 105.1 226s 17 1 95.6 96.4 226s 18 1 104.2 104.4 226s 19 1 107.8 110.7 226s 20 1 113.9 127.1 226s > model.matrix( fit3slsd[[ 4 ]]$e3w$eq[[ 2 ]], which = "xHat" ) 226s (Intercept) price farmPrice trend 226s 1 1 99.6 98.0 1 226s 2 1 105.1 99.1 2 226s 3 1 103.8 99.1 3 226s 4 1 104.5 98.1 4 226s 5 1 98.7 110.8 5 226s 6 1 99.6 108.2 6 226s 7 1 102.0 105.6 7 226s 8 1 102.2 109.8 8 226s 9 1 94.6 108.7 9 226s 10 1 92.7 100.6 10 226s 11 1 92.4 81.0 11 226s 12 1 98.9 68.6 12 226s 13 1 102.2 70.9 13 226s 14 1 100.3 81.4 14 226s 15 1 97.6 102.3 15 226s 16 1 96.9 105.0 16 226s 17 1 87.7 110.5 17 226s 18 1 101.1 92.5 18 226s 19 1 106.1 89.3 19 226s 20 1 114.4 93.0 20 226s > 226s > 226s > ## **************** formulas ************************ 226s > formula( fit3sls[[ 2 ]]$e1c ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) 226s consump ~ price + income 226s > 226s > formula( fit3sls[[ 3 ]]$e2e ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) 226s consump ~ price + farmPrice + trend 226s > 226s > formula( fit3sls[[ 4 ]]$e3 ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) 226s consump ~ price + income 226s > 226s > formula( fit3sls[[ 5 ]]$e4e ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) 226s consump ~ price + farmPrice + trend 226s > 226s > formula( fit3sls[[ 1 ]]$e5 ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) 226s consump ~ price + income 226s > 226s > formula( fit3slsi[[ 3 ]]$e3e ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) 226s consump ~ price + income 226s > 226s > formula( fit3slsd[[ 4 ]]$e4 ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) 226s consump ~ price + farmPrice + trend 226s > 226s > formula( fit3slsd[[ 2 ]]$e1w ) 226s $demand 226s consump ~ price + income 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s 226s > formula( fit3slsd[[ 2 ]]$e1w$eq[[ 1 ]] ) 226s consump ~ price + income 226s > 226s > 226s > ## **************** model terms ******************* 226s > terms( fit3sls[[ 2 ]]$e1c ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3sls[[ 2 ]]$e1c$eq[[ 1 ]] ) 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s > 226s > terms( fit3sls[[ 3 ]]$e2e ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3sls[[ 3 ]]$e2e$eq[[ 2 ]] ) 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s > 226s > terms( fit3sls[[ 4 ]]$e3 ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3sls[[ 4 ]]$e3$eq[[ 1 ]] ) 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s > 226s > terms( fit3sls[[ 5 ]]$e4e ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3sls[[ 5 ]]$e4e$eq[[ 2 ]] ) 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s > 226s > terms( fit3sls[[ 1 ]]$e5 ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3sls[[ 1 ]]$e5$eq[[ 1 ]] ) 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s > 226s > terms( fit3sls[[ 2 ]]$e4wSym ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3sls[[ 2 ]]$e4wSym$eq[[ 1 ]] ) 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s > 226s > terms( fit3slsi[[ 3 ]]$e3e ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]] ) 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s > 226s > terms( fit3slsd[[ 4 ]]$e4 ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3slsd[[ 4 ]]$e4$eq[[ 2 ]] ) 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s > 226s > terms( fit3slsd[[ 5 ]]$e5we ) 226s $demand 226s consump ~ price + income 226s attr(,"variables") 226s list(consump, price, income) 226s attr(,"factors") 226s price income 226s consump 0 0 226s price 1 0 226s income 0 1 226s attr(,"term.labels") 226s [1] "price" "income" 226s attr(,"order") 226s [1] 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, income) 226s attr(,"dataClasses") 226s consump price income 226s "numeric" "numeric" "numeric" 226s 226s $supply 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s 226s > terms( fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]] ) 226s consump ~ price + farmPrice + trend 226s attr(,"variables") 226s list(consump, price, farmPrice, trend) 226s attr(,"factors") 226s price farmPrice trend 226s consump 0 0 0 226s price 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "price" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 1 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(consump, price, farmPrice, trend) 226s attr(,"dataClasses") 226s consump price farmPrice trend 226s "numeric" "numeric" "numeric" "numeric" 226s > 226s > 226s > ## **************** terms of instruments ******************* 226s > fit3sls[[ 2 ]]$e1c$eq[[ 1 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3sls[[ 3 ]]$e2e$eq[[ 2 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3sls[[ 4 ]]$e3$eq[[ 1 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3sls[[ 5 ]]$e4e$eq[[ 2 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3sls[[ 1 ]]$e5$eq[[ 1 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3sls[[ 2 ]]$e4wSym$eq[[ 1 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3slsi[[ 3 ]]$e3e$eq[[ 1 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3slsd[[ 4 ]]$e4$eq[[ 2 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > fit3slsd[[ 5 ]]$e5we$eq[[ 2 ]]$termsInst 226s ~income + farmPrice + trend 226s attr(,"variables") 226s list(income, farmPrice, trend) 226s attr(,"factors") 226s income farmPrice trend 226s income 1 0 0 226s farmPrice 0 1 0 226s trend 0 0 1 226s attr(,"term.labels") 226s [1] "income" "farmPrice" "trend" 226s attr(,"order") 226s [1] 1 1 1 226s attr(,"intercept") 226s [1] 1 226s attr(,"response") 226s [1] 0 226s attr(,".Environment") 226s 226s attr(,"predvars") 226s list(income, farmPrice, trend) 226s attr(,"dataClasses") 226s income farmPrice trend 226s "numeric" "numeric" "numeric" 226s > 226s > 226s > ## **************** estfun ************************ 226s > library( "sandwich" ) 226s > 226s > estfun( fit3sls[[ 1 ]]$e1 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 0.93243 92.895 81.494 -0.67273 226s demand_2 -0.67769 -71.238 -66.143 0.48894 226s demand_3 3.38220 351.019 327.058 -2.44019 226s demand_4 2.06995 216.373 203.269 -1.49343 226s demand_5 3.17940 313.652 317.304 -2.29388 226s demand_6 1.83161 182.517 184.077 -1.32147 226s demand_7 2.47947 252.837 255.881 -1.78889 226s demand_8 -5.09517 -520.901 -549.259 3.67607 226s demand_9 -2.17668 -205.928 -210.267 1.57043 226s demand_10 3.95122 366.354 351.263 -2.85073 226s demand_11 -0.37870 -34.993 -28.440 0.27322 226s demand_12 -3.13231 -309.838 -240.875 2.25990 226s demand_13 -2.46263 -251.590 -208.339 1.77674 226s demand_14 0.13711 13.748 12.422 -0.09892 226s demand_15 3.55301 346.849 366.315 -2.56343 226s demand_16 -5.27287 -510.898 -554.179 3.80428 226s demand_17 -0.02852 -2.502 -2.750 0.02058 226s demand_18 -3.97374 -401.582 -414.859 2.86698 226s demand_19 2.30169 244.124 254.797 -1.66062 226s demand_20 -0.61976 -70.898 -78.771 0.44714 226s supply_1 -0.79213 -78.918 -69.232 0.70287 226s supply_2 0.37122 39.022 36.231 -0.32939 226s supply_3 -2.54401 -264.028 -246.006 2.25734 226s supply_4 -1.58295 -165.467 -155.446 1.40458 226s supply_5 -2.40285 -237.044 -239.804 2.13208 226s supply_6 -1.41153 -140.656 -141.858 1.25247 226s supply_7 -1.86174 -189.846 -192.132 1.65195 226s supply_8 3.60208 368.256 388.304 -3.19618 226s supply_9 1.52187 143.979 147.013 -1.35038 226s supply_10 -2.85966 -265.145 -254.224 2.53741 226s supply_11 0.33741 31.177 25.339 -0.29938 226s supply_12 2.36613 234.051 181.956 -2.09950 226s supply_13 1.88385 192.460 159.374 -1.67157 226s supply_14 -0.00962 -0.965 -0.872 0.00854 226s supply_15 -2.52306 -246.304 -260.128 2.23875 226s supply_16 3.84942 372.977 404.574 -3.41564 226s supply_17 0.07279 6.384 7.017 -0.06459 226s supply_18 2.96969 300.114 310.035 -2.63504 226s supply_19 -1.54232 -163.584 -170.735 1.36853 226s supply_20 0.55542 63.538 70.594 -0.49283 226s supply_price supply_farmPrice supply_trend 226s demand_1 -67.022 -65.927 -0.673 226s demand_2 51.397 48.454 0.978 226s demand_3 -253.253 -241.823 -7.321 226s demand_4 -156.109 -146.505 -5.974 226s demand_5 -226.294 -254.162 -11.469 226s demand_6 -131.682 -142.983 -7.929 226s demand_7 -182.417 -188.907 -12.522 226s demand_8 375.820 403.632 29.409 226s demand_9 148.573 170.706 14.134 226s demand_10 -264.317 -286.783 -28.507 226s demand_11 25.247 22.131 3.005 226s demand_12 223.542 155.029 27.119 226s demand_13 181.517 125.971 23.098 226s demand_14 -9.919 -8.052 -1.385 226s demand_15 -250.245 -262.238 -38.451 226s demand_16 368.603 399.449 60.868 226s demand_17 1.805 2.274 0.350 226s demand_18 289.734 265.195 51.606 226s demand_19 -176.131 -148.294 -31.552 226s demand_20 51.151 41.584 8.943 226s supply_1 70.025 68.881 0.703 226s supply_2 -34.625 -32.642 -0.659 226s supply_3 234.276 223.702 6.772 226s supply_4 146.821 137.789 5.618 226s supply_5 210.332 236.235 10.660 226s supply_6 124.806 135.517 7.515 226s supply_7 168.453 174.446 11.564 226s supply_8 -326.759 -350.940 -25.569 226s supply_9 -127.755 -146.786 -12.153 226s supply_10 235.267 255.264 25.374 226s supply_11 -27.664 -24.250 -3.293 226s supply_12 -207.676 -144.026 -25.194 226s supply_13 -170.773 -118.514 -21.730 226s supply_14 0.856 0.695 0.120 226s supply_15 218.549 229.024 33.581 226s supply_16 -330.948 -358.642 -54.650 226s supply_17 -5.665 -7.137 -1.098 226s supply_18 -266.295 -243.742 -47.431 226s supply_19 145.150 122.209 26.002 226s supply_20 -56.378 -45.834 -9.857 226s > round( colSums( estfun( fit3sls[[ 1 ]]$e1 ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > estfun( fit3sls[[ 2 ]]$e1e ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 1.0970 109.29 95.88 -0.8158 226s demand_2 -0.7973 -83.81 -77.82 0.5929 226s demand_3 3.9791 412.96 384.77 -2.9592 226s demand_4 2.4352 254.56 239.14 -1.8110 226s demand_5 3.7405 369.00 373.30 -2.7817 226s demand_6 2.1548 214.73 216.56 -1.6025 226s demand_7 2.9170 297.45 301.04 -2.1693 226s demand_8 -5.9943 -612.82 -646.19 4.4579 226s demand_9 -2.5608 -242.27 -247.37 1.9044 226s demand_10 4.6485 431.00 413.25 -3.4570 226s demand_11 -0.4455 -41.17 -33.46 0.3313 226s demand_12 -3.6851 -364.52 -283.38 2.7405 226s demand_13 -2.8972 -295.99 -245.10 2.1546 226s demand_14 0.1613 16.17 14.61 -0.1200 226s demand_15 4.1800 408.06 430.96 -3.1086 226s demand_16 -6.2034 -601.06 -651.98 4.6134 226s demand_17 -0.0336 -2.94 -3.24 0.0250 226s demand_18 -4.6750 -472.45 -488.07 3.4767 226s demand_19 2.7079 287.21 299.76 -2.0138 226s demand_20 -0.7291 -83.41 -92.67 0.5422 226s supply_1 -0.9222 -91.88 -80.60 0.8435 226s supply_2 0.4880 51.30 47.63 -0.4463 226s supply_3 -3.0517 -316.72 -295.10 2.7912 226s supply_4 -1.8908 -197.65 -185.68 1.7294 226s supply_5 -2.8789 -284.00 -287.31 2.6331 226s supply_6 -1.6828 -167.69 -169.12 1.5391 226s supply_7 -2.2343 -227.83 -230.58 2.0435 226s supply_8 4.3919 449.01 473.45 -4.0170 226s supply_9 1.8611 176.08 179.79 -1.7022 226s supply_10 -3.4650 -321.27 -308.04 3.1691 226s supply_11 0.3885 35.90 29.18 -0.3554 226s supply_12 2.8352 280.45 218.03 -2.5932 226s supply_13 2.2501 229.88 190.36 -2.0580 226s supply_14 -0.0404 -4.05 -3.66 0.0369 226s supply_15 -3.0726 -299.95 -316.79 2.8103 226s supply_16 4.6536 450.90 489.09 -4.2563 226s supply_17 0.0715 6.27 6.89 -0.0654 226s supply_18 3.5683 360.61 372.53 -3.2636 226s supply_19 -1.9084 -202.41 -211.25 1.7454 226s supply_20 0.6388 73.07 81.19 -0.5842 226s supply_price supply_farmPrice supply_trend 226s demand_1 -81.28 -79.95 -0.816 226s demand_2 62.33 58.76 1.186 226s demand_3 -307.11 -293.25 -8.877 226s demand_4 -189.31 -177.66 -7.244 226s demand_5 -274.42 -308.22 -13.909 226s demand_6 -159.69 -173.39 -9.615 226s demand_7 -221.21 -229.08 -15.185 226s demand_8 455.75 489.48 35.663 226s demand_9 180.17 207.01 17.140 226s demand_10 -320.53 -347.78 -34.570 226s demand_11 30.62 26.84 3.645 226s demand_12 271.08 188.00 32.886 226s demand_13 220.12 152.76 28.010 226s demand_14 -12.03 -9.76 -1.679 226s demand_15 -303.47 -318.01 -46.629 226s demand_16 447.00 484.40 73.814 226s demand_17 2.19 2.76 0.424 226s demand_18 351.35 321.60 62.581 226s demand_19 -213.59 -179.83 -38.262 226s demand_20 62.03 50.43 10.845 226s supply_1 84.04 82.66 0.843 226s supply_2 -46.92 -44.23 -0.893 226s supply_3 289.68 276.60 8.373 226s supply_4 180.78 169.66 6.918 226s supply_5 259.76 291.74 13.165 226s supply_6 153.37 166.53 9.235 226s supply_7 208.38 215.80 14.305 226s supply_8 -410.67 -441.06 -32.136 226s supply_9 -161.04 -185.03 -15.320 226s supply_10 293.84 318.82 31.691 226s supply_11 -32.84 -28.78 -3.909 226s supply_12 -256.51 -177.89 -31.118 226s supply_13 -210.25 -145.91 -26.754 226s supply_14 3.70 3.00 0.517 226s supply_15 274.34 287.49 42.154 226s supply_16 -412.40 -446.91 -68.101 226s supply_17 -5.73 -7.23 -1.112 226s supply_18 -329.82 -301.88 -58.745 226s supply_19 185.13 155.87 33.163 226s supply_20 -66.83 -54.33 -11.684 226s > round( colSums( estfun( fit3sls[[ 2 ]]$e1e ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > estfun( fit3sls[[ 3 ]]$e1c ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 1.3280 132.31 116.07 -0.9904 226s demand_2 -0.9652 -101.46 -94.20 0.7198 226s demand_3 4.8171 499.94 465.81 -3.5924 226s demand_4 2.9481 308.17 289.50 -2.1986 226s demand_5 4.5282 446.72 451.92 -3.3770 226s demand_6 2.6087 259.95 262.17 -1.9455 226s demand_7 3.5314 360.10 364.44 -2.6336 226s demand_8 -7.2568 -741.89 -782.28 5.4119 226s demand_9 -3.1001 -293.29 -299.47 2.3120 226s demand_10 5.6275 521.78 500.28 -4.1968 226s demand_11 -0.5394 -49.84 -40.51 0.4022 226s demand_12 -4.4612 -441.28 -343.06 3.3270 226s demand_13 -3.5074 -358.33 -296.72 2.6157 226s demand_14 0.1953 19.58 17.69 -0.1456 226s demand_15 5.0603 494.00 521.72 -3.7739 226s demand_16 -7.5098 -727.64 -789.29 5.6006 226s demand_17 -0.0406 -3.56 -3.92 0.0303 226s demand_18 -5.6596 -571.95 -590.86 4.2207 226s demand_19 3.2782 347.69 362.89 -2.4448 226s demand_20 -0.8827 -100.98 -112.19 0.6583 226s supply_1 -1.2187 -121.42 -106.51 1.0461 226s supply_2 0.4947 52.00 48.29 -0.4247 226s supply_3 -3.7909 -393.44 -366.58 3.2542 226s supply_4 -2.3698 -247.71 -232.71 2.0343 226s supply_5 -3.5854 -353.70 -357.82 3.0777 226s supply_6 -2.1176 -211.02 -212.82 1.8178 226s supply_7 -2.7729 -282.76 -286.16 2.3803 226s supply_8 5.2704 538.82 568.15 -4.5242 226s supply_9 2.2191 209.94 214.37 -1.9049 226s supply_10 -4.2139 -390.71 -374.62 3.6173 226s supply_11 0.5250 48.51 39.42 -0.4506 226s supply_12 3.5301 349.19 271.47 -3.0303 226s supply_13 2.8205 288.15 238.61 -2.4212 226s supply_14 0.0251 2.52 2.28 -0.0216 226s supply_15 -3.6967 -360.87 -381.13 3.1733 226s supply_16 5.6869 551.02 597.70 -4.8817 226s supply_17 0.1301 11.41 12.54 -0.1117 226s supply_18 4.4171 446.39 461.15 -3.7917 226s supply_19 -2.2186 -235.31 -245.60 1.9044 226s supply_20 0.8653 98.99 109.98 -0.7428 226s supply_price supply_farmPrice supply_trend 226s demand_1 -98.67 -97.06 -0.990 226s demand_2 75.67 71.33 1.440 226s demand_3 -372.84 -356.01 -10.777 226s demand_4 -229.82 -215.68 -8.794 226s demand_5 -333.15 -374.17 -16.885 226s demand_6 -193.86 -210.50 -11.673 226s demand_7 -268.55 -278.11 -18.435 226s demand_8 553.28 594.22 43.295 226s demand_9 218.73 251.31 20.808 226s demand_10 -389.13 -422.20 -41.968 226s demand_11 37.17 32.58 4.425 226s demand_12 329.10 228.23 39.924 226s demand_13 267.23 185.45 34.004 226s demand_14 -14.60 -11.85 -2.039 226s demand_15 -368.41 -386.07 -56.608 226s demand_16 542.65 588.07 89.610 226s demand_17 2.66 3.35 0.515 226s demand_18 426.54 390.42 75.973 226s demand_19 -259.30 -218.32 -46.450 226s demand_20 75.30 61.22 13.166 226s supply_1 104.22 102.52 1.046 226s supply_2 -44.64 -42.09 -0.849 226s supply_3 337.73 322.49 9.763 226s supply_4 212.64 199.56 8.137 226s supply_5 303.62 341.01 15.389 226s supply_6 181.14 196.69 10.907 226s supply_7 242.72 251.36 16.662 226s supply_8 -462.53 -496.76 -36.194 226s supply_9 -180.22 -207.07 -17.144 226s supply_10 335.39 363.90 36.173 226s supply_11 -41.64 -36.50 -4.957 226s supply_12 -299.75 -207.88 -36.364 226s supply_13 -247.35 -171.66 -31.475 226s supply_14 -2.16 -1.75 -0.302 226s supply_15 309.78 324.63 47.599 226s supply_16 -473.00 -512.58 -78.108 226s supply_17 -9.80 -12.34 -1.899 226s supply_18 -383.19 -350.73 -68.251 226s supply_19 201.99 170.07 36.184 226s supply_20 -84.97 -69.08 -14.856 226s > round( colSums( estfun( fit3sls[[ 3 ]]$e1c ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > estfun( fit3sls[[ 4 ]]$e1wc ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 1.3280 132.31 116.07 -0.9904 226s demand_2 -0.9652 -101.46 -94.20 0.7198 226s demand_3 4.8171 499.94 465.81 -3.5924 226s demand_4 2.9481 308.17 289.50 -2.1986 226s demand_5 4.5282 446.72 451.92 -3.3770 226s demand_6 2.6087 259.95 262.17 -1.9455 226s demand_7 3.5314 360.10 364.44 -2.6336 226s demand_8 -7.2568 -741.89 -782.28 5.4119 226s demand_9 -3.1001 -293.29 -299.47 2.3120 226s demand_10 5.6275 521.78 500.28 -4.1968 226s demand_11 -0.5394 -49.84 -40.51 0.4022 226s demand_12 -4.4612 -441.28 -343.06 3.3270 226s demand_13 -3.5074 -358.33 -296.72 2.6157 226s demand_14 0.1953 19.58 17.69 -0.1456 226s demand_15 5.0603 494.00 521.72 -3.7739 226s demand_16 -7.5098 -727.64 -789.29 5.6006 226s demand_17 -0.0406 -3.56 -3.92 0.0303 226s demand_18 -5.6596 -571.95 -590.86 4.2207 226s demand_19 3.2782 347.69 362.89 -2.4448 226s demand_20 -0.8827 -100.98 -112.19 0.6583 226s supply_1 -1.2187 -121.42 -106.51 1.0461 226s supply_2 0.4947 52.00 48.29 -0.4247 226s supply_3 -3.7909 -393.44 -366.58 3.2542 226s supply_4 -2.3698 -247.71 -232.71 2.0343 226s supply_5 -3.5854 -353.70 -357.82 3.0777 226s supply_6 -2.1176 -211.02 -212.82 1.8178 226s supply_7 -2.7729 -282.76 -286.16 2.3803 226s supply_8 5.2704 538.82 568.15 -4.5242 226s supply_9 2.2191 209.94 214.37 -1.9049 226s supply_10 -4.2139 -390.71 -374.62 3.6173 226s supply_11 0.5250 48.51 39.42 -0.4506 226s supply_12 3.5301 349.19 271.47 -3.0303 226s supply_13 2.8205 288.15 238.61 -2.4212 226s supply_14 0.0251 2.52 2.28 -0.0216 226s supply_15 -3.6967 -360.87 -381.13 3.1733 226s supply_16 5.6869 551.02 597.70 -4.8817 226s supply_17 0.1301 11.41 12.54 -0.1117 226s supply_18 4.4171 446.39 461.15 -3.7917 226s supply_19 -2.2186 -235.31 -245.60 1.9044 226s supply_20 0.8653 98.99 109.98 -0.7428 226s supply_price supply_farmPrice supply_trend 226s demand_1 -98.67 -97.06 -0.990 226s demand_2 75.67 71.33 1.440 226s demand_3 -372.84 -356.01 -10.777 226s demand_4 -229.82 -215.68 -8.794 226s demand_5 -333.15 -374.17 -16.885 226s demand_6 -193.86 -210.50 -11.673 226s demand_7 -268.55 -278.11 -18.435 226s demand_8 553.28 594.22 43.295 226s demand_9 218.73 251.31 20.808 226s demand_10 -389.13 -422.20 -41.968 226s demand_11 37.17 32.58 4.425 226s demand_12 329.10 228.23 39.924 226s demand_13 267.23 185.45 34.004 226s demand_14 -14.60 -11.85 -2.039 226s demand_15 -368.41 -386.07 -56.608 226s demand_16 542.65 588.07 89.610 226s demand_17 2.66 3.35 0.515 226s demand_18 426.54 390.42 75.973 226s demand_19 -259.30 -218.32 -46.450 226s demand_20 75.30 61.22 13.166 226s supply_1 104.22 102.52 1.046 226s supply_2 -44.64 -42.09 -0.849 226s supply_3 337.73 322.49 9.763 226s supply_4 212.64 199.56 8.137 226s supply_5 303.62 341.01 15.389 226s supply_6 181.14 196.69 10.907 226s supply_7 242.72 251.36 16.662 226s supply_8 -462.53 -496.76 -36.194 226s supply_9 -180.22 -207.07 -17.144 226s supply_10 335.39 363.90 36.173 226s supply_11 -41.64 -36.50 -4.957 226s supply_12 -299.75 -207.88 -36.364 226s supply_13 -247.35 -171.66 -31.475 226s supply_14 -2.16 -1.75 -0.302 226s supply_15 309.78 324.63 47.599 226s supply_16 -473.00 -512.58 -78.108 226s supply_17 -9.80 -12.34 -1.899 226s supply_18 -383.19 -350.73 -68.251 226s supply_19 201.99 170.07 36.184 226s supply_20 -84.97 -69.08 -14.856 226s > 226s > round( colSums( estfun( fit3sls[[ 5 ]]$e1wc ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > round( colSums( estfun( fit3sls[[ 5 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > round( colSums( estfun( fit3sls[[ 4 ]]$e1wc ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > round( colSums( estfun( fit3sls[[ 4 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > round( colSums( estfun( fit3sls[[ 3 ]]$e1wc ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > round( colSums( estfun( fit3sls[[ 3 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > round( colSums( estfun( fit3sls[[ 2 ]]$e1wc ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > round( colSums( estfun( fit3sls[[ 2 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > round( colSums( estfun( fit3sls[[ 1 ]]$e1wc ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > round( colSums( estfun( fit3sls[[ 1 ]]$e1wc, residFit = FALSE ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > estfun( fit3slsd[[ 5 ]]$e1w ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 -0.471 -44.9 -41.2 0.299 226s demand_2 -1.315 -130.6 -128.3 0.835 226s demand_3 0.736 72.8 71.2 -0.467 226s demand_4 0.203 20.3 19.9 -0.129 226s demand_5 0.825 80.0 82.4 -0.524 226s demand_6 0.290 28.4 29.1 -0.184 226s demand_7 0.657 65.6 67.8 -0.417 226s demand_8 -2.887 -290.8 -311.2 1.833 226s demand_9 -1.172 -112.7 -113.2 0.744 226s demand_10 1.981 188.4 176.1 -1.258 226s demand_11 0.308 29.2 23.1 -0.196 226s demand_12 -0.922 -91.4 -70.9 0.586 226s demand_13 -0.639 -65.0 -54.1 0.406 226s demand_14 0.597 60.5 54.0 -0.379 226s demand_15 2.100 211.7 216.5 -1.333 226s demand_16 -1.984 -200.3 -208.6 1.260 226s demand_17 0.785 75.0 75.7 -0.499 226s demand_18 -1.136 -118.3 -118.6 0.721 226s demand_19 1.814 195.6 200.8 -1.152 226s demand_20 0.232 26.4 29.5 -0.147 226s supply_1 -0.434 -41.3 -37.9 0.449 226s supply_2 -0.126 -12.6 -12.3 0.131 226s supply_3 -1.272 -125.8 -123.0 1.316 226s supply_4 -0.902 -90.1 -88.6 0.933 226s supply_5 -0.805 -78.1 -80.4 0.833 226s supply_6 -0.457 -44.8 -46.0 0.473 226s supply_7 -0.758 -75.8 -78.3 0.784 226s supply_8 1.582 159.3 170.5 -1.636 226s supply_9 1.004 96.6 97.0 -1.039 226s supply_10 -0.856 -81.5 -76.1 0.886 226s supply_11 0.191 18.1 14.3 -0.197 226s supply_12 0.607 60.1 46.7 -0.628 226s supply_13 0.335 34.0 28.3 -0.346 226s supply_14 -0.201 -20.3 -18.2 0.208 226s supply_15 -0.801 -80.8 -82.6 0.829 226s supply_16 1.930 194.8 202.9 -1.997 226s supply_17 0.811 77.5 78.2 -0.839 226s supply_18 1.241 129.3 129.5 -1.283 226s supply_19 -0.858 -92.5 -95.0 0.888 226s supply_20 -0.229 -26.1 -29.1 0.237 226s supply_price supply_farmPrice supply_trend 226s demand_1 29.8 29.3 0.299 226s demand_2 87.8 82.7 1.670 226s demand_3 -48.5 -46.3 -1.402 226s demand_4 -13.5 -12.7 -0.516 226s demand_5 -51.7 -58.1 -2.620 226s demand_6 -18.3 -19.9 -1.105 226s demand_7 -42.5 -44.0 -2.919 226s demand_8 187.4 201.3 14.667 226s demand_9 70.4 80.9 6.698 226s demand_10 -116.6 -126.5 -12.579 226s demand_11 -18.1 -15.8 -2.152 226s demand_12 57.9 40.2 7.029 226s demand_13 41.5 28.8 5.278 226s demand_14 -38.0 -30.8 -5.304 226s demand_15 -130.2 -136.4 -20.000 226s demand_16 122.1 132.3 20.164 226s demand_17 -43.7 -55.1 -8.477 226s demand_18 72.9 66.7 12.986 226s demand_19 -122.2 -102.9 -21.890 226s demand_20 -16.9 -13.7 -2.947 226s supply_1 44.7 44.0 0.449 226s supply_2 13.7 13.0 0.262 226s supply_3 136.5 130.4 3.947 226s supply_4 97.5 91.5 3.731 226s supply_5 82.2 92.3 4.165 226s supply_6 47.1 51.2 2.839 226s supply_7 80.0 82.8 5.491 226s supply_8 -167.3 -179.7 -13.089 226s supply_9 -98.3 -112.9 -9.349 226s supply_10 82.1 89.1 8.857 226s supply_11 -18.2 -16.0 -2.169 226s supply_12 -62.1 -43.1 -7.532 226s supply_13 -35.4 -24.5 -4.499 226s supply_14 20.8 16.9 2.907 226s supply_15 80.9 84.8 12.430 226s supply_16 -193.5 -209.7 -31.948 226s supply_17 -73.6 -92.7 -14.264 226s supply_18 -129.7 -118.7 -23.101 226s supply_19 94.1 79.3 16.863 226s supply_20 27.1 22.1 4.744 226s > estfun( fit3slsd[[ 5 ]]$e1w, residFit = FALSE ) 226s Warning message: 226s In estfun.systemfit(fit3slsd[[5]]$e1w) : 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s demand_1 0.89947 85.649 78.613 -0.57123 226s demand_2 0.00817 0.811 0.797 -0.00519 226s demand_3 1.94109 192.071 187.703 -1.23275 226s demand_4 1.44439 144.277 141.839 -0.91731 226s demand_5 1.10477 107.119 110.256 -0.70162 226s demand_6 0.67950 66.596 68.290 -0.43154 226s demand_7 0.96428 96.352 99.513 -0.61239 226s demand_8 -1.80100 -181.402 -194.148 1.14378 226s demand_9 -1.09741 -105.536 -106.009 0.69694 226s demand_10 0.93145 88.611 82.806 -0.59155 226s demand_11 -0.13250 -12.551 -9.951 0.08415 226s demand_12 -0.98743 -97.798 -75.933 0.62710 226s demand_13 -0.32371 -32.932 -27.386 0.20558 226s demand_14 -0.09978 -10.112 -9.040 0.06337 226s demand_15 0.56754 57.219 58.513 -0.36043 226s demand_16 -2.64753 -267.185 -278.255 1.68140 226s demand_17 -1.65258 -157.934 -159.308 1.04952 226s demand_18 -1.17988 -122.919 -123.179 0.74932 226s demand_19 1.26015 135.883 139.499 -0.80030 226s demand_20 0.12101 13.783 15.380 -0.07685 226s supply_1 -0.39424 -37.540 -34.456 0.40779 226s supply_2 -0.17503 -17.388 -17.083 0.18104 226s supply_3 -1.29167 -127.811 -124.905 1.33607 226s supply_4 -0.90312 -90.210 -88.686 0.93416 226s supply_5 -0.84242 -81.682 -84.074 0.87137 226s supply_6 -0.46834 -45.901 -47.069 0.48444 226s supply_7 -0.80988 -80.925 -83.580 0.83772 226s supply_8 1.72577 173.825 186.038 -1.78508 226s supply_9 1.10899 106.650 107.128 -1.14710 226s supply_10 -0.94120 -89.538 -83.673 0.97355 226s supply_11 0.22943 21.733 17.231 -0.23732 226s supply_12 0.60019 59.445 46.155 -0.62082 226s supply_13 0.37695 38.348 31.890 -0.38990 226s supply_14 -0.28729 -29.116 -26.029 0.29717 226s supply_15 -0.94355 -95.128 -97.280 0.97597 226s supply_16 2.01917 203.771 212.215 -2.08856 226s supply_17 0.74286 70.994 71.612 -0.76839 226s supply_18 1.40908 146.797 147.108 -1.45750 226s supply_19 -0.87479 -94.329 -96.840 0.90486 226s supply_20 -0.28090 -31.995 -35.702 0.29055 226s supply_price supply_farmPrice supply_trend 226s demand_1 -56.911 -55.981 -0.5712 226s demand_2 -0.545 -0.514 -0.0104 226s demand_3 -127.940 -122.166 -3.6983 226s demand_4 -95.886 -89.988 -3.6692 226s demand_5 -69.215 -77.739 -3.5081 226s demand_6 -43.002 -46.692 -2.5892 226s demand_7 -62.447 -64.669 -4.2868 226s demand_8 116.934 125.587 9.1502 226s demand_9 65.935 75.758 6.2725 226s demand_10 -54.848 -59.510 -5.9155 226s demand_11 7.776 6.816 0.9257 226s demand_12 62.030 43.019 7.5252 226s demand_13 21.003 14.576 2.6726 226s demand_14 6.354 5.158 0.8871 226s demand_15 -35.186 -36.872 -5.4065 226s demand_16 162.914 176.547 26.9023 226s demand_17 92.041 115.972 17.8418 226s demand_18 75.726 69.312 13.4878 226s demand_19 -84.882 -71.467 -15.2057 226s demand_20 -8.791 -7.147 -1.5370 226s supply_1 40.627 39.963 0.4078 226s supply_2 19.031 17.941 0.3621 226s supply_3 138.662 132.404 4.0082 226s supply_4 97.648 91.641 3.7366 226s supply_5 85.962 96.548 4.3569 226s supply_6 48.274 52.416 2.9066 226s supply_7 85.424 88.463 5.8640 226s supply_8 -182.496 -196.002 -14.2806 226s supply_9 -108.523 -124.690 -10.3239 226s supply_10 90.266 97.939 9.7355 226s supply_11 -21.929 -19.223 -2.6105 226s supply_12 -61.410 -42.588 -7.4498 226s supply_13 -39.834 -27.644 -5.0687 226s supply_14 29.799 24.189 4.1603 226s supply_15 95.276 99.842 14.6396 226s supply_16 -202.365 -219.299 -33.4170 226s supply_17 -67.387 -84.908 -13.0627 226s supply_18 -147.294 -134.819 -26.2351 226s supply_19 95.972 80.804 17.1923 226s supply_20 33.238 27.021 5.8111 226s > 226s > round( colSums( estfun( fit3slsd[[ 5 ]]$e1w ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0.0 0.0 0.0 0.0 226s supply_price supply_farmPrice supply_trend 226s 38.6 0.0 -52.4 226s Warning message: 226s > In estfun.systemfit(fit3slsd[[5]]$e1w) : 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 226s round( colSums( estfun( fit3slsd[[ 5 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > round( colSums( estfun( fit3slsd[[ 4 ]]$e1w ) ), digits = 7 ) 226s Warning message: 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0.00 0.00 0.00 0.00 226s supply_price supply_farmPrice supply_trend 226s 9.67 0.00 -13.12 226s > round( colSums( estfun( fit3slsd[[ 4 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 226s In estfun.systemfit(fit3slsd[[4]]$e1w) : 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0.0 0.0 0.0 0.0 226s supply_price supply_farmPrice supply_trend 226s -28.9 0.0 39.3 226s Warning message: 226s In estfun.systemfit(fit3slsd[[4]]$e1w, residFit = FALSE) : 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 226s > 226s > round( colSums( estfun( fit3slsd[[ 3 ]]$e1w ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0.00 0.00 0.00 0.00 226s supply_price supply_farmPrice supply_trend 226s 9.67 0.00 -13.12 226s Warning message: 226s In estfun.systemfit(fit3slsd[[3]]$e1w) : 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function i> round( colSums( estfun( fit3slsd[[ 3 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 226s s returned 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0.0 0.0 0.0 0.0 226s supply_price supply_farmPrice supply_trend 226s -28.9 0.0 39.3 226s Warning message: 226s In estfun.systemfit(fit3slsd[[3]]$e1w, residFit = FALSE) :> 226s > round( colSums( estfun( fit3slsd[[ 2 ]]$e1w ) ), digits = 7 ) 226s 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0.0 0.0 0.0 0.0 226s supply_price supply_farmPrice supply_trend 226s 38.6 0.0 -52.4 226s > round( colSums( estfun( fit3slsd[[ 2 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 226s Warning message: 226s In estfun.systemfit(fit3slsd[[2]]$e1w) : 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > 226s > round( colSums( estfun( fit3slsd[[ 1 ]]$e1w ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0 0 0 0 226s supply_price supply_farmPrice supply_trend 226s 0 0 0 226s > round( colSums( estfun( fit3slsd[[ 1 ]]$e1w, residFit = FALSE ) ), digits = 7 ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s 0.0 0.0 0.0 0.0 226s supply_price supply_farmPrice supply_trend 226s -38.6 0.0 52.4 226s Warning message: 226s In estfun.systemfit(fit3slsd[[1]]$e1w, residFit = FALSE) : 226s > 226s > 226s > ## **************** bread ************************ 226s > bread( fit3sls[[ 1 ]]$e1 ) 226s the columns of the returned estimating function do not all sum up to zero, which indicates that the wrong estimating function is returned 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 2509.59 -26.9369 1.9721 2525.8 226s [2,] -26.94 0.3724 -0.1057 -14.1 226s [3,] 1.97 -0.1057 0.0881 -11.3 226s [4,] 2525.80 -14.1479 -11.2987 5658.1 226s [5,] -27.01 0.2401 0.0307 -43.3 226s [6,] 1.64 -0.0877 0.0732 -11.8 226s [7,] 2.47 -0.1324 0.1104 -16.4 226s supply_price supply_farmPrice supply_trend 226s [1,] -27.0066 1.6369 2.4699 226s [2,] 0.2401 -0.0877 -0.1324 226s [3,] 0.0307 0.0732 0.1104 226s [4,] -43.3336 -11.7989 -16.3581 226s [5,] 0.3974 0.0325 0.0428 226s [6,] 0.0325 0.0774 0.1019 226s [7,] 0.0428 0.1019 0.2125 226s > 226s > bread( fit3sls[[ 2 ]]$e1e ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 2133.15 -22.8963 1.6763 2082.83 226s [2,] -22.90 0.3165 -0.0898 -11.67 226s [3,] 1.68 -0.0898 0.0749 -9.32 226s [4,] 2082.83 -11.6667 -9.3172 4526.47 226s [5,] -22.27 0.1980 0.0253 -34.67 226s [6,] 1.35 -0.0723 0.0603 -9.44 226s [7,] 2.04 -0.1091 0.0910 -13.09 226s supply_price supply_farmPrice supply_trend 226s [1,] -22.2702 1.3498 2.0367 226s [2,] 0.1980 -0.0723 -0.1091 226s [3,] 0.0253 0.0603 0.0910 226s [4,] -34.6668 -9.4391 -13.0865 226s [5,] 0.3179 0.0260 0.0342 226s [6,] 0.0260 0.0619 0.0815 226s [7,] 0.0342 0.0815 0.1700 226s > 226s > bread( fit3sls[[ 3 ]]$e1c ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 2509.59 -26.9369 1.9721 2610.8 226s [2,] -26.94 0.3724 -0.1057 -14.6 226s [3,] 1.97 -0.1057 0.0881 -11.7 226s [4,] 2610.83 -14.6243 -11.6791 5650.4 226s [5,] -27.92 0.2482 0.0317 -43.3 226s [6,] 1.69 -0.0907 0.0756 -11.7 226s [7,] 2.55 -0.1368 0.1141 -16.7 226s supply_price supply_farmPrice supply_trend 226s [1,] -27.9159 1.6920 2.5531 226s [2,] 0.2482 -0.0907 -0.1368 226s [3,] 0.0317 0.0756 0.1141 226s [4,] -43.3005 -11.7199 -16.6696 226s [5,] 0.3972 0.0321 0.0441 226s [6,] 0.0321 0.0766 0.1051 226s [7,] 0.0441 0.1051 0.1999 226s > 226s > bread( fit3sls[[ 4 ]]$e1wc ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 2509.59 -26.9369 1.9721 2610.8 226s [2,] -26.94 0.3724 -0.1057 -14.6 226s [3,] 1.97 -0.1057 0.0881 -11.7 226s [4,] 2610.83 -14.6243 -11.6791 5650.4 226s [5,] -27.92 0.2482 0.0317 -43.3 226s [6,] 1.69 -0.0907 0.0756 -11.7 226s [7,] 2.55 -0.1368 0.1141 -16.7 226s supply_price supply_farmPrice supply_trend 226s [1,] -27.9159 1.6920 2.5531 226s [2,] 0.2482 -0.0907 -0.1368 226s [3,] 0.0317 0.0756 0.1141 226s [4,] -43.3005 -11.7199 -16.6696 226s [5,] 0.3972 0.0321 0.0441 226s [6,] 0.0321 0.0766 0.1051 226s [7,] 0.0441 0.1051 0.1999 226s > 226s > bread( fit3slsd[[ 5 ]]$e1w ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 4967.14 -60.707 11.4076 1773.52 226s [2,] -60.71 0.839 -0.2382 -6.24 226s [3,] 11.41 -0.238 0.1273 -11.71 226s [4,] 1773.52 -6.236 -11.7103 5325.96 226s [5,] -21.83 0.185 0.0346 -37.94 226s [6,] 6.07 -0.141 0.0826 -13.55 226s [7,] -16.09 0.136 0.0255 -20.05 226s supply_price supply_farmPrice supply_trend 226s [1,] -21.8336 6.0740 -16.0922 226s [2,] 0.1845 -0.1413 0.1360 226s [3,] 0.0346 0.0826 0.0255 226s [4,] -37.9350 -13.5483 -20.0519 226s [5,] 0.3216 0.0453 0.1323 226s [6,] 0.0453 0.0885 0.0440 226s [7,] 0.1323 0.0440 0.2443 226s > 226s > bread( fit3slsd[[ 4 ]]$e1w ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 4967.14 -60.707 11.4076 1773.52 226s [2,] -60.71 0.839 -0.2382 -6.24 226s [3,] 11.41 -0.238 0.1273 -11.71 226s [4,] 1773.52 -6.236 -11.7103 5325.96 226s [5,] -21.83 0.185 0.0346 -37.94 226s [6,] 6.07 -0.141 0.0826 -13.55 226s [7,] -16.09 0.136 0.0255 -20.05 226s supply_price supply_farmPrice supply_trend 226s [1,] -21.8336 6.0740 -16.0922 226s [2,] 0.1845 -0.1413 0.1360 226s [3,] 0.0346 0.0826 0.0255 226s [4,] -37.9350 -13.5483 -20.0519 226s [5,] 0.3216 0.0453 0.1323 226s [6,] 0.0453 0.0885 0.0440 226s [7,] 0.1323 0.0440 0.2443 226s > 226s > bread( fit3slsd[[ 3 ]]$e1w ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 4967.14 -60.707 11.4076 1773.52 226s [2,] -60.71 0.839 -0.2382 -6.24 226s [3,] 11.41 -0.238 0.1273 -11.71 226s [4,] 1773.52 -6.236 -11.7103 5325.96 226s [5,] -21.83 0.185 0.0346 -37.94 226s [6,] 6.07 -0.141 0.0826 -13.55 226s [7,] -16.09 0.136 0.0255 -20.05 226s supply_price supply_farmPrice supply_trend 226s [1,] -21.8336 6.0740 -16.0922 226s [2,] 0.1845 -0.1413 0.1360 226s [3,] 0.0346 0.0826 0.0255 226s [4,] -37.9350 -13.5483 -20.0519 226s [5,] 0.3216 0.0453 0.1323 226s [6,] 0.0453 0.0885 0.0440 226s [7,] 0.1323 0.0440 0.2443 226s > 226s > bread( fit3slsd[[ 2 ]]$e1w ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 4967.14 -60.707 11.4076 1773.52 226s [2,] -60.71 0.839 -0.2382 -6.24 226s [3,] 11.41 -0.238 0.1273 -11.71 226s [4,] 1773.52 -6.236 -11.7103 5325.96 226s [5,] -21.83 0.185 0.0346 -37.94 226s [6,] 6.07 -0.141 0.0826 -13.55 226s [7,] -16.09 0.136 0.0255 -20.05 226s supply_price supply_farmPrice supply_trend 226s [1,] -21.8336 6.0740 -16.0922 226s [2,] 0.1845 -0.1413 0.1360 226s [3,] 0.0346 0.0826 0.0255 226s [4,] -37.9350 -13.5483 -20.0519 226s [5,] 0.3216 0.0453 0.1323 226s [6,] 0.0453 0.0885 0.0440 226s [7,] 0.1323 0.0440 0.2443 226s > 226s > bread( fit3slsd[[ 1 ]]$e1w ) 226s demand_(Intercept) demand_price demand_income supply_(Intercept) 226s [1,] 4967.14 -60.707 11.4076 1773.52 226s [2,] -60.71 0.839 -0.2382 -6.24 226s [3,] 11.41 -0.238 0.1273 -11.71 226s [4,] 1773.52 -6.236 -11.7103 5325.96 226s [5,] -21.83 0.185 0.0346 -37.94 226s [6,] 6.07 -0.141 0.0826 -13.55 226s [7,] -16.09 0.136 0.0255 -20.05 226s supply_price supply_farmPrice supply_trend 226s [1,] -21.8336 6.0740 -16.0922 226s [2,] 0.1845 -0.1413 0.1360 226s [3,] 0.0346 0.0826 0.0255 226s [4,] -37.9350 -13.5483 -20.0519 226s [5,] 0.3216 0.0453 0.1323 226s [6,] 0.0453 0.0885 0.0440 226s [7,] 0.1323 0.0440 0.2443 226s > 226s BEGIN TEST test_hausman.R 226s 226s R version 4.3.2 (2023-10-31) -- "Eye Holes" 226s Copyright (C) 2023 The R Foundation for Statistical Computing 226s Platform: aarch64-unknown-linux-gnu (64-bit) 226s 226s R is free software and comes with ABSOLUTELY NO WARRANTY. 226s You are welcome to redistribute it under certain conditions. 226s Type 'license()' or 'licence()' for distribution details. 226s 226s R is a collaborative project with many contributors. 226s Type 'contributors()' for more information and 226s 'citation()' on how to cite R or R packages in publications. 226s 226s Type 'demo()' for some demos, 'help()' for on-line help, or 226s 'help.start()' for an HTML browser interface to help. 226s Type 'q()' to quit R. 226s 226s > library( "systemfit" ) 226s Loading required package: Matrix 227s Loading required package: car 227s Loading required package: carData 227s Loading required package: lmtest 227s Loading required package: zoo 227s 227s Attaching package: ‘zoo’ 227s 227s The following objects are masked from ‘package:base’: 227s 227s as.Date, as.Date.numeric 227s 227s 227s Please cite the 'systemfit' package as: 227s 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/. 227s 227s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 227s https://r-forge.r-project.org/projects/systemfit/ 227s > options( digits = 5 ) 227s > 227s > data( "Kmenta" ) 227s > useMatrix <- FALSE 227s > 227s > eqDemand <- consump ~ price + income 227s > eqSupply <- consump ~ price + farmPrice + trend 227s > inst <- ~ income + farmPrice + trend 227s > eqSystem <- list( demand = eqDemand, supply = eqSupply ) 227s > restrm <- matrix(0,1,7) # restriction matrix "R" 227s > restrm[1,3] <- 1 227s > restrm[1,7] <- -1 227s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 227s > restr2m[1,3] <- 1 227s > restr2m[1,7] <- -1 227s > restr2m[2,2] <- -1 227s > restr2m[2,5] <- 1 227s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 227s > tc <- matrix(0,7,6) 227s > tc[1,1] <- 1 227s > tc[2,2] <- 1 227s > tc[3,3] <- 1 227s > tc[4,4] <- 1 227s > tc[5,5] <- 1 227s > tc[6,6] <- 1 227s > tc[7,3] <- 1 227s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 227s > restr3m[1,2] <- -1 227s > restr3m[1,5] <- 1 227s > restr3q <- c( 0.5 ) # restriction vector "q" 2 227s > 227s > 227s > ## ******************* unrestricted estimation ***************** 227s > ## ******************** default estimation ********************* 227s > fit2sls1 <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 227s + useMatrix = useMatrix ) 227s > fit3sls1 <- systemfit( eqSystem, "3SLS", data = Kmenta, inst = inst, 227s + useMatrix = useMatrix ) 227s > print( hausman.systemfit( fit2sls1, fit3sls1 ) ) 227s 227s Hausman specification test for consistency of the 3SLS estimation 227s 227s data: Kmenta 227s Hausman = 2.54, df = 7, p-value = 0.92 227s 227s > 227s > ## ************** 2SLS estimation with singleEqSigma = FALSE ***************** 227s > fit2sls1s <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 227s + singleEqSigma = FALSE, useMatrix = useMatrix ) 227s > print( hausman.systemfit( fit2sls1s, fit3sls1 ) ) 227s 227s Hausman specification test for consistency of the 3SLS estimation 227s 227s data: Kmenta 227s Hausman = 3.28, df = 7, p-value = 0.86 227s 227s > 227s > ## ******************* estimations with methodResidCov = 0 ***************** 227s > fit2sls1r <- systemfit( eqSystem, "2SLS", data = Kmenta, inst = inst, 227s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > fit3sls1r <- systemfit( eqSystem, "3SLS", data = Kmenta, inst = inst, 227s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > print( hausman.systemfit( fit2sls1r, fit3sls1r ) ) 227s 227s Hausman specification test for consistency of the 3SLS estimation 227s 227s data: Kmenta 227s Hausman = 2.98, df = 7, p-value = 0.89 227s 227s > 227s > 227s > ## ********************* estimation with restriction ******************** 227s > ## *********************** default estimation *********************** 227s > fit2sls2 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 227s + inst = inst, useMatrix = useMatrix ) 227s > fit3sls2 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restrm, 227s + inst = inst, useMatrix = useMatrix ) 227s > # print( hausman.systemfit( fit2sls2, fit3sls2 ) ) 227s > 227s > ## ************* 2SLS estimation with singleEqSigma = TRUE ***************** 227s > fit2sls2s <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 227s + inst = inst, singleEqSigma = TRUE, useMatrix = useMatrix ) 227s > # print( hausman.systemfit( fit2sls2s, fit3sls2 ) ) 227s > 227s > ## ********************* estimations with methodResidCov = 0 ************** 227s > fit2sls2r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restrm, 227s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > fit3sls2r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restrm, 227s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > # print( hausman.systemfit( fit2sls2r, fit3sls2r ) ) 227s > 227s > 227s > ## ****************** estimation with restriction via restrict.regMat ****************** 227s > ## ********************** default estimation ******************** 227s > fit2sls3 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.regMat = tc, 227s + inst = inst, useMatrix = useMatrix ) 227s > fit3sls3 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.regMat = tc, 227s + inst = inst, useMatrix = useMatrix ) 227s > print( hausman.systemfit( fit2sls3, fit3sls3 ) ) 227s 227s Hausman specification test for consistency of the 3SLS estimation 227s 227s data: Kmenta 227s Hausman = -0.281, df = 6, p-value = 1 227s 227s > 227s > ## ******************* estimations with methodResidCov = 0 ******* 227s > fit2sls3r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.regMat = tc, 227s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > fit3sls3r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.regMat = tc, 227s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > print( hausman.systemfit( fit2sls3r, fit3sls3r ) ) 227s 227s Hausman specification test for consistency of the 3SLS estimation 227s 227s data: Kmenta 227s Hausman = -0.0132, df = 6, p-value = 1 227s 227s > 227s > 227s > ## ***************** estimations with 2 restrictions ******************* 227s > ## *********************** default estimations ************** 227s > fit2sls4 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr2m, 227s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 227s > fit3sls4 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr2m, 227s + restrict.rhs = restr2q, inst = inst, useMatrix = useMatrix ) 227s > # print( hausman.systemfit( fit2sls4, fit3sls4 ) ) 227s > 227s > ## ***************** estimations with methodResidCov = 0 ************** 227s > fit2sls4r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr2m, 227s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 227s + useMatrix = useMatrix ) 227s > fit3sls4r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr2m, 227s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 227s + useMatrix = useMatrix ) 227s > # print( hausman.systemfit( fit2sls4r, fit3sls4r ) ) 227s > 227s > 227s > ## *********** estimations with 2 restrictions via R and restrict.regMat *************** 227s > ## ***************** default estimations ******************* 227s > fit2sls5 <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr3m, 227s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 227s + useMatrix = useMatrix ) 227s > fit3sls5 <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr3m, 227s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 227s + useMatrix = useMatrix ) 227s > # print( hausman.systemfit( fit2sls5, fit3sls5 ) ) 227s > 227s > ## ************* estimations with methodResidCov = 0 ********* 227s > fit2sls5r <- systemfit( eqSystem, "2SLS", data = Kmenta, restrict.matrix = restr3m, 227s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 227s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > fit3sls5r <- systemfit( eqSystem, "3SLS", data = Kmenta, restrict.matrix = restr3m, 227s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 227s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 227s > # print( hausman.systemfit( fit2sls5r, fit3sls5r ) ) 227s > 227s BEGIN TEST test_ols.R 227s 227s R version 4.3.2 (2023-10-31) -- "Eye Holes" 227s Copyright (C) 2023 The R Foundation for Statistical Computing 227s Platform: aarch64-unknown-linux-gnu (64-bit) 227s 227s R is free software and comes with ABSOLUTELY NO WARRANTY. 227s You are welcome to redistribute it under certain conditions. 227s Type 'license()' or 'licence()' for distribution details. 227s 227s R is a collaborative project with many contributors. 227s Type 'contributors()' for more information and 227s 'citation()' on how to cite R or R packages in publications. 227s 227s Type 'demo()' for some demos, 'help()' for on-line help, or 227s 'help.start()' for an HTML browser interface to help. 227s Type 'q()' to quit R. 227s 228s Loading required package: Matrix 228s > library( systemfit ) 228s Loading required package: car 228s Loading required package: carData 228s Loading required package: lmtest 228s Loading required package: zoo 228s 228s Attaching package: ‘zoo’ 228s 228s The following objects are masked from ‘package:base’: 228s 228s as.Date, as.Date.numeric 228s 228s 228s Please cite the 'systemfit' package as: 228s 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/. 228s 228s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 228s https://r-forge.r-project.org/projects/systemfit/ 228s > options( digits = 3 ) 228s > 228s > data( "Kmenta" ) 229s > useMatrix <- FALSE 229s > 229s > demand <- consump ~ price + income 229s > supply <- consump ~ price + farmPrice + trend 229s > system <- list( demand = demand, supply = supply ) 229s > restrm <- matrix(0,1,7) # restriction matrix "R" 229s > restrm[1,3] <- 1 229s > restrm[1,7] <- -1 229s > restrict <- "demand_income - supply_trend = 0" 229s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 229s > restr2m[1,3] <- 1 229s > restr2m[1,7] <- -1 229s > restr2m[2,2] <- -1 229s > restr2m[2,5] <- 1 229s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 229s > restrict2 <- c( "demand_income - supply_trend = 0", 229s + "- demand_price + supply_price = 0.5" ) 229s > tc <- matrix(0,7,6) 229s > tc[1,1] <- 1 229s > tc[2,2] <- 1 229s > tc[3,3] <- 1 229s > tc[4,4] <- 1 229s > tc[5,5] <- 1 229s > tc[6,6] <- 1 229s > tc[7,3] <- 1 229s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 229s > restr3m[1,2] <- -1 229s > restr3m[1,5] <- 1 229s > restr3q <- c( 0.5 ) # restriction vector "q" 2 229s > restrict3 <- "- C2 + C5 = 0.5" 229s > 229s > # It is not possible to estimate OLS with systemfit 229s > # exactly as EViews does, because EViews uses 229s > # methodResidCov == "geomean" for the coefficient covariance matrix and 229s > # methodResidCov == "noDfCor" for the residual covariance matrix, while 229s > # systemfit uses always the same formulas for both calculations. 229s > 229s > ## ******* single-equation OLS estimations ********************* 229s > lmDemand <- lm( demand, data = Kmenta ) 229s > lmSupply <- lm( supply, data = Kmenta ) 229s > 229s > ## *************** OLS estimation ************************ 229s > ## ********** OLS estimation (default) ******************** 229s > fitols1 <- systemfit( system, "OLS", data = Kmenta, useMatrix = useMatrix ) 229s > print( summary( fitols1 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 4.43 0.709 0.558 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.73 4.14 229s supply 4.14 5.78 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 229s price -0.3163 0.0907 -3.49 0.0028 ** 229s income 0.3346 0.0454 7.37 1.1e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 229s price 0.1604 0.0949 1.69 0.11039 229s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 229s trend 0.2483 0.0975 2.55 0.02157 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > nobs( fitols1 ) 229s [1] 40 229s > all.equal( coef( fitols1 ), c( coef( lmDemand ), coef( lmSupply ) ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > all.equal( coef( summary( fitols1 ) ), 229s + rbind( coef( summary( lmDemand ) ), coef( summary( lmSupply ) ) ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > all.equal( vcov( fitols1 ), 229s + as.matrix( bdiag( vcov( lmDemand ), vcov( lmSupply ) ) ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > 229s > ## ********** OLS estimation (no singleEqSigma=F) ****************** 229s > fitols1s <- systemfit( system, "OLS", data = Kmenta, 229s + singleEqSigma = FALSE, useMatrix = useMatrix ) 229s > print( summary( fitols1s ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 4.43 0.709 0.558 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.73 4.14 229s supply 4.14 5.78 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 8.4671 11.80 1.3e-09 *** 229s price -0.3163 0.1021 -3.10 0.0065 ** 229s income 0.3346 0.0511 6.54 5.0e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 10.3587 5.63 3.8e-05 *** 229s price 0.1604 0.0857 1.87 0.080 . 229s farmPrice 0.2481 0.0417 5.94 2.1e-05 *** 229s trend 0.2483 0.0881 2.82 0.012 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > all.equal( coef( fitols1s ), c( coef( lmDemand ), coef( lmSupply ) ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > 229s > ## **************** OLS (useDfSys=T) *********************** 229s > print( summary( fitols1, useDfSys = TRUE ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 4.43 0.709 0.558 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.73 4.14 229s supply 4.14 5.78 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 229s price -0.3163 0.0907 -3.49 0.0014 ** 229s income 0.3346 0.0454 7.37 1.8e-08 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 229s price 0.1604 0.0949 1.69 0.100 229s farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 229s trend 0.2483 0.0975 2.55 0.016 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > 229s > ## **************** OLS (methodResidCov="noDfCor") *********************** 229s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 229s + methodResidCov = "noDfCor", x = TRUE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols1r ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 3.02 0.709 0.537 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.17 3.41 229s supply 3.41 4.63 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 6.9325 14.41 5.8e-11 *** 229s price -0.3163 0.0836 -3.78 0.0015 ** 229s income 0.3346 0.0419 7.99 3.7e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 10.2527 5.68 3.4e-05 *** 229s price 0.1604 0.0849 1.89 0.077 . 229s farmPrice 0.2481 0.0413 6.01 1.8e-05 *** 229s trend 0.2483 0.0872 2.85 0.012 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > all.equal( coef( fitols1r ), c( coef( lmDemand ), coef( lmSupply ) ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > 229s > ## ******** OLS (methodResidCov="noDfCor", singleEqSigma=F) *********** 229s > fitols1rs <- systemfit( system, "OLS", data = Kmenta, 229s + methodResidCov = "noDfCor", singleEqSigma = FALSE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols1rs ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 3.02 0.709 0.537 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.17 3.41 229s supply 3.41 4.63 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 7.6907 12.99 3.0e-10 *** 229s price -0.3163 0.0927 -3.41 0.0033 ** 229s income 0.3346 0.0465 7.20 1.5e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 9.4088 6.19 1.3e-05 *** 229s price 0.1604 0.0779 2.06 0.0561 . 229s farmPrice 0.2481 0.0379 6.55 6.7e-06 *** 229s trend 0.2483 0.0800 3.10 0.0068 ** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > all.equal( coef( fitols1rs ), c( coef( lmDemand ), coef( lmSupply ) ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > 229s > ## **************** OLS (methodResidCov="Theil" ) *********************** 229s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 229s + methodResidCov = "Theil", x = TRUE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols1r ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 3.26 0.709 0.503 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.73 4.28 229s supply 4.28 5.78 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 229s price -0.3163 0.0907 -3.49 0.0028 ** 229s income 0.3346 0.0454 7.37 1.1e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 229s price 0.1604 0.0949 1.69 0.11039 229s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 229s trend 0.2483 0.0975 2.55 0.02157 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > all.equal( coef( fitols1r ), c( coef( lmDemand ), coef( lmSupply ) ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > 229s > ## **************** OLS (methodResidCov="max") *********************** 229s > fitols1r <- systemfit( system, "OLS", data = Kmenta, 229s + methodResidCov = "max", x = TRUE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols1r ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 3.37 0.709 0.509 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.73 4.26 229s supply 4.26 5.78 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 229s price -0.3163 0.0907 -3.49 0.0028 ** 229s income 0.3346 0.0454 7.37 1.1e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 229s price 0.1604 0.0949 1.69 0.11039 229s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 229s trend 0.2483 0.0975 2.55 0.02157 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > 229s > ## ******** OLS (methodResidCov="max", singleEqSigma=F) *********** 229s > fitols1rs <- systemfit( system, "OLS", data = Kmenta, 229s + methodResidCov = "max", singleEqSigma = FALSE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols1rs ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 3.37 0.709 0.509 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.73 4.26 229s supply 4.26 5.78 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.8954 8.4671 11.80 1.3e-09 *** 229s price -0.3163 0.1021 -3.10 0.0065 ** 229s income 0.3346 0.0511 6.54 5.0e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.93 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 229s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.2754 10.3587 5.63 3.8e-05 *** 229s price 0.1604 0.0857 1.87 0.080 . 229s farmPrice 0.2481 0.0417 5.94 2.1e-05 *** 229s trend 0.2483 0.0881 2.82 0.012 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.405 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 229s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 229s 229s > 229s > 229s > ## ********* OLS with cross-equation restriction ************ 229s > ## ****** OLS with cross-equation restriction (default) ********* 229s > fitols2 <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.matrix = restrm, useMatrix = useMatrix ) 229s > print( summary( fitols2 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 2.5 0.703 0.608 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.78 4.47 229s supply 4.47 5.94 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 8.4225 11.82 1.4e-13 *** 229s price -0.2917 0.0975 -2.99 0.0051 ** 229s income 0.3129 0.0441 7.10 3.3e-08 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 10.0721 5.60 2.9e-06 *** 229s price 0.1639 0.0853 1.92 0.063 . 229s farmPrice 0.2571 0.0402 6.39 2.7e-07 *** 229s trend 0.3129 0.0441 7.10 3.3e-08 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > # the same with symbolically specified restrictions 229s > fitols2Sym <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.matrix = restrict, useMatrix = useMatrix ) 229s > all.equal( fitols2, fitols2Sym ) 229s [1] "Component “call”: target, current do not match when deparsed" 229s > 229s > ## ****** OLS with cross-equation restriction (singleEqSigma=T) ******* 229s > fitols2s <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.matrix = restrm, singleEqSigma = TRUE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols2s ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 2.5 0.703 0.608 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.78 4.47 229s supply 4.47 5.94 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 7.5640 13.16 6.7e-15 *** 229s price -0.2917 0.0887 -3.29 0.0023 ** 229s income 0.3129 0.0415 7.54 9.4e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 11.3165 4.98 1.8e-05 *** 229s price 0.1639 0.0960 1.71 0.097 . 229s farmPrice 0.2571 0.0451 5.69 2.1e-06 *** 229s trend 0.3129 0.0415 7.54 9.4e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## ****** OLS with cross-equation restriction (useDfSys=F) ******* 229s > print( summary( fitols2, useDfSys = FALSE ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 2.5 0.703 0.608 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.78 4.47 229s supply 4.47 5.94 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 8.4225 11.82 1.3e-09 *** 229s price -0.2917 0.0975 -2.99 0.0082 ** 229s income 0.3129 0.0441 7.10 1.8e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 10.0721 5.60 4.0e-05 *** 229s price 0.1639 0.0853 1.92 0.073 . 229s farmPrice 0.2571 0.0402 6.39 8.9e-06 *** 229s trend 0.3129 0.0441 7.10 2.5e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## ****** OLS with cross-equation restriction (methodResidCov="noDfCor") ******* 229s > fitols2r <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.matrix = restrm, methodResidCov = "noDfCor", 229s + useMatrix = useMatrix ) 229s > print( summary( fitols2r ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 1.7 0.703 0.577 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.21 3.68 229s supply 3.68 4.75 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 229s price -0.2917 0.0899 -3.25 0.0026 ** 229s income 0.3129 0.0406 7.70 5.9e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 229s price 0.1639 0.0786 2.08 0.045 * 229s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 229s trend 0.3129 0.0406 7.70 5.9e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## ** OLS with cross-equation restriction (methodResidCov="noDfCor",singleEqSigma=T) *** 229s > fitols2rs <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.matrix = restrm, methodResidCov = "noDfCor", 229s + x = TRUE, useMatrix = useMatrix ) 229s > print( summary( fitols2rs ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 1.7 0.703 0.577 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.21 3.68 229s supply 3.68 4.75 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 229s price -0.2917 0.0899 -3.25 0.0026 ** 229s income 0.3129 0.0406 7.70 5.9e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 229s price 0.1639 0.0786 2.08 0.045 * 229s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 229s trend 0.3129 0.0406 7.70 5.9e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## *** OLS with cross-equation restriction via restrict.regMat *** 229s > ## *** OLS with cross-equation restriction via restrict.regMat (default) *** 229s > fitols3 <- systemfit( system, "OLS", data = Kmenta, restrict.regMat = tc, 229s + x = TRUE, useMatrix = useMatrix ) 229s > print( summary( fitols3 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 2.5 0.703 0.608 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.78 4.47 229s supply 4.47 5.94 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 8.4225 11.82 1.4e-13 *** 229s price -0.2917 0.0975 -2.99 0.0051 ** 229s income 0.3129 0.0441 7.10 3.3e-08 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 10.0721 5.60 2.9e-06 *** 229s price 0.1639 0.0853 1.92 0.063 . 229s farmPrice 0.2571 0.0402 6.39 2.7e-07 *** 229s trend 0.3129 0.0441 7.10 3.3e-08 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## *** OLS with cross-equation restriction via restrict.regMat (singleEqSigma=T) *** 229s > fitols3s <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.regMat = tc, singleEqSigma = TRUE, useMatrix = useMatrix ) 229s > print( summary( fitols3s ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 2.5 0.703 0.608 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.78 4.47 229s supply 4.47 5.94 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 7.5640 13.16 6.7e-15 *** 229s price -0.2917 0.0887 -3.29 0.0023 ** 229s income 0.3129 0.0415 7.54 9.4e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 11.3165 4.98 1.8e-05 *** 229s price 0.1639 0.0960 1.71 0.097 . 229s farmPrice 0.2571 0.0451 5.69 2.1e-06 *** 229s trend 0.3129 0.0415 7.54 9.4e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## *** OLS with cross-equation restriction via restrict.regMat (useDfSys=F) *** 229s > print( summary( fitols3, useDfSys = FALSE ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 2.5 0.703 0.608 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.78 4.47 229s supply 4.47 5.94 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 8.4225 11.82 1.3e-09 *** 229s price -0.2917 0.0975 -2.99 0.0082 ** 229s income 0.3129 0.0441 7.10 1.8e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 10.0721 5.60 4.0e-05 *** 229s price 0.1639 0.0853 1.92 0.073 . 229s farmPrice 0.2571 0.0402 6.39 8.9e-06 *** 229s trend 0.3129 0.0441 7.10 2.5e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## *** OLS with cross-equation restriction via restrict.regMat (methodResidCov="noDfCor") *** 229s > fitols3r <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.regMat = tc, methodResidCov = "noDfCor", 229s + useMatrix = useMatrix ) 229s > print( summary( fitols3r ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 1.7 0.703 0.577 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.21 3.68 229s supply 3.68 4.75 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 229s price -0.2917 0.0899 -3.25 0.0026 ** 229s income 0.3129 0.0406 7.70 5.9e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 229s price 0.1639 0.0786 2.08 0.045 * 229s farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 229s trend 0.3129 0.0406 7.70 5.9e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## OLS with cross-equation restriction via restrict.regMat (methodResidCov="noDfCor",singleEqSigma=T) 229s > fitols3rs <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.regMat = tc, methodResidCov = "noDfCor", singleEqSigma = TRUE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols3rs ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 1.7 0.703 0.577 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.21 3.68 229s supply 3.68 4.75 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 6.9734 14.28 6.7e-16 *** 229s price -0.2917 0.0816 -3.57 0.0011 ** 229s income 0.3129 0.0381 8.22 1.4e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 10.1248 5.57 3.1e-06 *** 229s price 0.1639 0.0859 1.91 0.065 . 229s farmPrice 0.2571 0.0404 6.36 2.9e-07 *** 229s trend 0.3129 0.0381 8.22 1.4e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > ## ********* OLS with 2 cross-equation restrictions *********** 229s > ## ********* OLS with 2 cross-equation restrictions (default) *********** 229s > fitols4 <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 229s + restrict.rhs = restr2q, useMatrix = useMatrix ) 229s > print( summary( fitols4 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 2.69 0.702 0.605 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.76 4.46 229s supply 4.46 5.99 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 6.1599 16.47 < 2e-16 *** 229s price -0.3168 0.0629 -5.04 1.4e-05 *** 229s income 0.3189 0.0399 8.00 2.0e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.5515 7.17 2.3e-08 *** 229s price 0.1832 0.0629 2.91 0.0062 ** 229s farmPrice 0.2595 0.0391 6.64 1.1e-07 *** 229s trend 0.3189 0.0399 8.00 2.0e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > # the same with symbolically specified restrictions 229s > fitols4Sym <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.matrix = restrict2, useMatrix = useMatrix ) 229s > all.equal( fitols4, fitols4Sym ) 229s [1] "Component “call”: target, current do not match when deparsed" 229s > 229s > ## ****** OLS with 2 cross-equation restrictions (singleEqSigma=T) ******* 229s > fitols4s <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 229s + restrict.rhs = restr2q, singleEqSigma = TRUE, x = TRUE, 229s + useMatrix = useMatrix ) 229s > print( summary( fitols4s ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 2.69 0.702 0.605 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.76 4.46 229s supply 4.46 5.99 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 6.0474 16.78 < 2e-16 *** 229s price -0.3168 0.0648 -4.89 2.3e-05 *** 229s income 0.3189 0.0385 8.29 9.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.9687 6.80 7.0e-08 *** 229s price 0.1832 0.0648 2.83 0.0077 ** 229s farmPrice 0.2595 0.0446 5.82 1.3e-06 *** 229s trend 0.3189 0.0385 8.29 9.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > 229s > ## ****** OLS with 2 cross-equation restrictions (useDfSys=F) ******* 229s > print( summary( fitols4, useDfSys = FALSE ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 2.69 0.702 0.605 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.76 4.46 229s supply 4.46 5.99 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 6.1599 16.47 6.9e-12 *** 229s price -0.3168 0.0629 -5.04 1e-04 *** 229s income 0.3189 0.0399 8.00 3.6e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.5515 7.17 2.2e-06 *** 229s price 0.1832 0.0629 2.91 0.01 * 229s farmPrice 0.2595 0.0391 6.64 5.6e-06 *** 229s trend 0.3189 0.0399 8.00 5.5e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > 229s > ## ****** OLS with 2 cross-equation restrictions (methodResidCov="noDfCor") ******* 229s > fitols4r <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 229s + restrict.rhs = restr2q, methodResidCov = "noDfCor", 229s + useMatrix = useMatrix ) 229s > print( summary( fitols4r ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 1.83 0.702 0.575 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.20 3.67 229s supply 3.67 4.79 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 229s price -0.3168 0.0589 -5.38 5.0e-06 *** 229s income 0.3189 0.0373 8.55 4.3e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 229s price 0.1832 0.0589 3.11 0.0037 ** 229s farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 229s trend 0.3189 0.0373 8.55 4.3e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > 229s > ## OLS with 2 cross-equation restrictions (methodResidCov="noDfCor", singleEqSigma=T) * 229s > fitols4rs <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr2m, 229s + restrict.rhs = restr2q, methodResidCov = "noDfCor", 229s + singleEqSigma = TRUE, useMatrix = useMatrix ) 229s > print( summary( fitols4rs ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 1.83 0.702 0.575 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.20 3.67 229s supply 3.67 4.79 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 229s price -0.3168 0.0589 -5.38 5.0e-06 *** 229s income 0.3189 0.0352 9.05 1.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 229s price 0.1832 0.0589 3.11 0.0037 ** 229s farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 229s trend 0.3189 0.0352 9.05 1.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > 229s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat **** 229s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (default) **** 229s > fitols5 <- systemfit( system, "OLS", data = Kmenta, restrict.matrix = restr3m, 229s + restrict.rhs = restr3q, restrict.regMat = tc, methodResidCov = "noDfCor", 229s + useMatrix = useMatrix ) 229s > print( summary( fitols5 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 1.83 0.702 0.575 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.20 3.67 229s supply 3.67 4.79 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 229s price -0.3168 0.0589 -5.38 5.0e-06 *** 229s income 0.3189 0.0373 8.55 4.3e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 229s price 0.1832 0.0589 3.11 0.0037 ** 229s farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 229s trend 0.3189 0.0373 8.55 4.3e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > # the same with symbolically specified restrictions 229s > fitols5Sym <- systemfit( system, "OLS", data = Kmenta, 229s + restrict.matrix = restrict3, restrict.regMat = tc, 229s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 229s > all.equal( fitols5, fitols5Sym ) 229s [1] "Component “call”: target, current do not match when deparsed" 229s > 229s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (singleEqSigma=T) **** 229s > fitols5s <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 229s + restrict.rhs = restr3q, restrict.regMat = tc, singleEqSigma = T, 229s + x = TRUE, useMatrix = useMatrix ) 229s > print( summary( fitols5s ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 2.69 0.702 0.605 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.76 4.46 229s supply 4.46 5.99 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 6.0474 16.78 < 2e-16 *** 229s price -0.3168 0.0648 -4.89 2.3e-05 *** 229s income 0.3189 0.0385 8.29 9.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.9687 6.80 7.0e-08 *** 229s price 0.1832 0.0648 2.83 0.0077 ** 229s farmPrice 0.2595 0.0446 5.82 1.3e-06 *** 229s trend 0.3189 0.0385 8.29 9.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > 229s > ## ***** OLS with 2 cross-equation restrictions via R and restrict.regMat (useDfSys=F) **** 229s > fitols5o <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 229s + restrict.rhs = restr3q, restrict.regMat = tc, useMatrix = useMatrix ) 229s > print( summary( fitols5o, useDfSys = FALSE ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 2.69 0.702 0.605 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.76 4.46 229s supply 4.46 5.99 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 6.1599 16.47 6.9e-12 *** 229s price -0.3168 0.0629 -5.04 1e-04 *** 229s income 0.3189 0.0399 8.00 3.6e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.5515 7.17 2.2e-06 *** 229s price 0.1832 0.0629 2.91 0.01 * 229s farmPrice 0.2595 0.0391 6.64 5.6e-06 *** 229s trend 0.3189 0.0399 8.00 5.5e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > 229s > ## OLS with 2 cross-equation restr. via R and restrict.regMat (methodResidCov="noDfCor",singleEqSigma=T) 229s > fitols5rs <- systemfit( system, "OLS", data = Kmenta,restrict.matrix = restr3m, 229s + restrict.rhs = restr3q, restrict.regMat = tc, methodResidCov = "noDfCor", 229s + singleEqSigma = TRUE, useMatrix = useMatrix ) 229s > print( summary( fitols5rs ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 1.83 0.702 0.575 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.20 3.67 229s supply 3.67 4.79 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.938 229s supply 0.938 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 229s price -0.3168 0.0589 -5.38 5.0e-06 *** 229s income 0.3189 0.0352 9.05 1.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.94 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.003 MSE: 3.765 Root MSE: 1.94 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 229s price 0.1832 0.0589 3.11 0.0037 ** 229s farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 229s trend 0.3189 0.0352 9.05 1.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.447 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.813 MSE: 5.988 Root MSE: 2.447 229s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 229s 229s > 229s > 229s > ## *********** estimations with a single regressor ************ 229s > fitolsS1 <- systemfit( 229s + list( consump ~ price - 1, consump ~ price + trend ), "OLS", 229s + data = Kmenta, useMatrix = useMatrix ) 229s > print( summary( fitolsS1 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 36 1121 484 -1.09 -1.05 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s eq1 20 19 861 45.3 6.73 -2.213 -2.213 229s eq2 20 17 259 15.3 3.91 0.032 -0.082 229s 229s The covariance matrix of the residuals 229s eq1 eq2 229s eq1 45.3 14.4 229s eq2 14.4 15.3 229s 229s The correlations of the residuals 229s eq1 eq2 229s eq1 1.000 0.549 229s eq2 0.549 1.000 229s 229s 229s OLS estimates for 'eq1' (equation 1) 229s Model Formula: consump ~ price - 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s price 1.006 0.015 66.9 <2e-16 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 6.733 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 229s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 229s 229s 229s OLS estimates for 'eq2' (equation 2) 229s Model Formula: consump ~ price + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 93.6767 15.2367 6.15 1.1e-05 *** 229s price 0.0622 0.1513 0.41 0.69 229s trend 0.0953 0.1515 0.63 0.54 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 3.907 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 259.497 MSE: 15.265 Root MSE: 3.907 229s Multiple R-Squared: 0.032 Adjusted R-Squared: -0.082 229s 229s > fitolsS2 <- systemfit( 229s + list( consump ~ price - 1, consump ~ trend - 1 ), "OLS", 229s + data = Kmenta, useMatrix = useMatrix ) 229s > print( summary( fitolsS2 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 38 47370 110957 -87.3 -5.28 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s eq1 20 19 861 45.3 6.73 -2.21 -2.21 229s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 229s 229s The covariance matrix of the residuals 229s eq1 eq2 229s eq1 45.34 -5.15 229s eq2 -5.15 2447.84 229s 229s The correlations of the residuals 229s eq1 eq2 229s eq1 1.0000 -0.0439 229s eq2 -0.0439 1.0000 229s 229s 229s OLS estimates for 'eq1' (equation 1) 229s Model Formula: consump ~ price - 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s price 1.006 0.015 66.9 <2e-16 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 6.733 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 229s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 229s 229s 229s OLS estimates for 'eq2' (equation 2) 229s Model Formula: consump ~ trend - 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s trend 7.405 0.924 8.02 1.6e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 49.476 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 229s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 229s 229s > fitolsS3 <- systemfit( 229s + list( consump ~ trend - 1, price ~ trend - 1 ), "OLS", 229s + data = Kmenta, useMatrix = useMatrix ) 229s > print( summary( fitolsS3 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 38 93537 108970 -99 -0.977 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s eq1 20 19 46509 2448 49.5 -172.5 -172.5 229s eq2 20 19 47028 2475 49.8 -69.5 -69.5 229s 229s The covariance matrix of the residuals 229s eq1 eq2 229s eq1 2448 2439 229s eq2 2439 2475 229s 229s The correlations of the residuals 229s eq1 eq2 229s eq1 1.000 0.988 229s eq2 0.988 1.000 229s 229s 229s OLS estimates for 'eq1' (equation 1) 229s Model Formula: consump ~ trend - 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s trend 7.405 0.924 8.02 1.6e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 49.476 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 229s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 229s 229s 229s OLS estimates for 'eq2' (equation 2) 229s Model Formula: price ~ trend - 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s trend 7.318 0.929 7.88 2.1e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 49.751 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 229s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 229s 229s > fitolsS4 <- systemfit( 229s + list( consump ~ trend - 1, price ~ trend - 1 ), "OLS", 229s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 229s + useMatrix = useMatrix ) 229s > print( summary( fitolsS4 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 39 93548 111736 -99 -1.03 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s eq1 20 19 46514 2448 49.5 -172.5 -172.5 229s eq2 20 19 47033 2475 49.8 -69.5 -69.5 229s 229s The covariance matrix of the residuals 229s eq1 eq2 229s eq1 2448 2439 229s eq2 2439 2475 229s 229s The correlations of the residuals 229s eq1 eq2 229s eq1 1.000 0.988 229s eq2 0.988 1.000 229s 229s 229s OLS estimates for 'eq1' (equation 1) 229s Model Formula: consump ~ trend - 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s trend 7.362 0.646 11.4 5.7e-14 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 49.478 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 46514.283 MSE: 2448.12 Root MSE: 49.478 229s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 229s 229s 229s OLS estimates for 'eq2' (equation 2) 229s Model Formula: price ~ trend - 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s trend 7.362 0.646 11.4 5.7e-14 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 49.754 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 47033.469 MSE: 2475.446 Root MSE: 49.754 229s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 229s 229s > fitolsS5 <- systemfit( 229s + list( consump ~ 1, farmPrice ~ 1 ), "OLS", 229s + data = Kmenta, useMatrix = useMatrix ) 229s > print( summary( fitolsS5 ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 38 3337 1224 0 0 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s eq1 20 19 268 14.1 3.76 0 0 229s eq2 20 19 3069 161.5 12.71 0 0 229s 229s The covariance matrix of the residuals 229s eq1 eq2 229s eq1 14.1 32.5 229s eq2 32.5 161.5 229s 229s The correlations of the residuals 229s eq1 eq2 229s eq1 1.000 0.681 229s eq2 0.681 1.000 229s 229s 229s OLS estimates for 'eq1' (equation 1) 229s Model Formula: consump ~ 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 100.90 0.84 120 <2e-16 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 3.756 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 229s Multiple R-Squared: 0 Adjusted R-Squared: 0 229s 229s 229s OLS estimates for 'eq2' (equation 2) 229s Model Formula: farmPrice ~ 1 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 96.62 2.84 34 <2e-16 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 12.709 on 19 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 19 229s SSR: 3068.757 MSE: 161.514 Root MSE: 12.709 229s Multiple R-Squared: 0 Adjusted R-Squared: 0 229s 229s > 229s > 229s > ## **************** shorter summaries ********************** 229s > print( summary( fitols1, useDfSys = TRUE, equations = FALSE ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 33 156 4.43 0.709 0.558 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 63.3 3.73 1.93 0.764 0.736 229s supply 20 16 92.6 5.78 2.40 0.655 0.590 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.73 4.14 229s supply 4.14 5.78 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.891 229s supply 0.891 1.000 229s 229s 229s Coefficients: 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 229s demand_price -0.3163 0.0907 -3.49 0.0014 ** 229s demand_income 0.3346 0.0454 7.37 1.8e-08 *** 229s supply_(Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 229s supply_price 0.1604 0.0949 1.69 0.1004 229s supply_farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 229s supply_trend 0.2483 0.0975 2.55 0.0157 * 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s > 229s > print( summary( fitols2r ), residCov = FALSE, equations = FALSE ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 1.7 0.703 0.577 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s 229s Coefficients: 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 99.5563 7.7652 12.82 1.4e-14 *** 229s demand_price -0.2917 0.0899 -3.25 0.0026 ** 229s demand_income 0.3129 0.0406 7.70 5.9e-09 *** 229s supply_(Intercept) 56.3795 9.2860 6.07 7.0e-07 *** 229s supply_price 0.1639 0.0786 2.08 0.0447 * 229s supply_farmPrice 0.2571 0.0371 6.93 5.4e-08 *** 229s supply_trend 0.3129 0.0406 7.70 5.9e-09 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s > 229s > print( summary( fitols3s, useDfSys = FALSE ), residCov = TRUE ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 34 159 2.5 0.703 0.608 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.2 3.78 1.94 0.761 0.732 229s supply 20 16 95.1 5.94 2.44 0.645 0.579 229s 229s The covariance matrix of the residuals 229s demand supply 229s demand 3.78 4.47 229s supply 4.47 5.94 229s 229s The correlations of the residuals 229s demand supply 229s demand 1.000 0.943 229s supply 0.943 1.000 229s 229s 229s OLS estimates for 'demand' (equation 1) 229s Model Formula: consump ~ price + income 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.5563 7.5640 13.16 2.4e-10 *** 229s price -0.2917 0.0887 -3.29 0.0043 ** 229s income 0.3129 0.0415 7.54 8.1e-07 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 1.943 on 17 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 17 229s SSR: 64.186 MSE: 3.776 Root MSE: 1.943 229s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.732 229s 229s 229s OLS estimates for 'supply' (equation 2) 229s Model Formula: consump ~ price + farmPrice + trend 229s 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.3795 11.3165 4.98 0.00014 *** 229s price 0.1639 0.0960 1.71 0.10724 229s farmPrice 0.2571 0.0451 5.69 3.3e-05 *** 229s trend 0.3129 0.0415 7.54 1.2e-06 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s 229s Residual standard error: 2.438 on 16 degrees of freedom 229s Number of observations: 20 Degrees of Freedom: 16 229s SSR: 95.088 MSE: 5.943 Root MSE: 2.438 229s Multiple R-Squared: 0.645 Adjusted R-Squared: 0.579 229s 229s > 229s > print( summary( fitols4rs, residCov = FALSE, equations = FALSE ) ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 1.83 0.702 0.575 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s 229s Coefficients: 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 101.4817 5.5234 18.37 < 2e-16 *** 229s demand_price -0.3168 0.0589 -5.38 5.0e-06 *** 229s demand_income 0.3189 0.0352 9.05 1.1e-10 *** 229s supply_(Intercept) 54.1494 7.2089 7.51 8.5e-09 *** 229s supply_price 0.1832 0.0589 3.11 0.0037 ** 229s supply_farmPrice 0.2595 0.0399 6.51 1.7e-07 *** 229s supply_trend 0.3189 0.0352 9.05 1.1e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s > 229s > print( summary( fitols5, equations = FALSE ), residCov = FALSE ) 229s 229s systemfit results 229s method: OLS 229s 229s N DF SSR detRCov OLS-R2 McElroy-R2 229s system 40 35 160 1.83 0.702 0.575 229s 229s N DF SSR MSE RMSE R2 Adj R2 229s demand 20 17 64.0 3.77 1.94 0.761 0.733 229s supply 20 16 95.8 5.99 2.45 0.643 0.576 229s 229s 229s Coefficients: 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 101.4817 5.7621 17.61 < 2e-16 *** 229s demand_price -0.3168 0.0589 -5.38 5.0e-06 *** 229s demand_income 0.3189 0.0373 8.55 4.3e-10 *** 229s supply_(Intercept) 54.1494 7.0638 7.67 5.4e-09 *** 229s supply_price 0.1832 0.0589 3.11 0.0037 ** 229s supply_farmPrice 0.2595 0.0365 7.10 2.8e-08 *** 229s supply_trend 0.3189 0.0373 8.55 4.3e-10 *** 229s --- 229s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 229s > 229s > 229s > ## ****************** residuals ************************** 229s > print( residuals( fitols1 ) ) 229s demand supply 229s 1 1.074 -0.444 229s 2 -0.390 -0.896 229s 3 2.625 1.965 229s 4 1.802 1.134 229s 5 1.946 1.514 229s 6 1.175 0.680 229s 7 1.530 1.569 229s 8 -2.933 -4.407 229s 9 -1.365 -2.599 229s 10 2.031 2.469 229s 11 -0.149 -0.598 229s 12 -1.954 -1.697 229s 13 -1.121 -1.064 229s 14 -0.220 0.970 229s 15 1.487 3.159 229s 16 -3.701 -3.866 229s 17 -1.273 -0.265 229s 18 -2.002 -2.449 229s 19 1.738 3.110 229s 20 -0.299 1.714 229s > print( residuals( fitols1$eq[[ 2 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 229s -0.444 -0.896 1.965 1.134 1.514 0.680 1.569 -4.407 -2.599 2.469 -0.598 229s 12 13 14 15 16 17 18 19 20 229s -1.697 -1.064 0.970 3.159 -3.866 -0.265 -2.449 3.110 1.714 229s > 229s > print( residuals( fitols2r ) ) 229s demand supply 229s 1 0.8465 0.156 229s 2 -0.4933 -0.384 229s 3 2.5225 2.415 229s 4 1.7066 1.525 229s 5 2.0445 1.750 229s 6 1.2529 0.870 229s 7 1.6277 1.711 229s 8 -2.8261 -4.380 229s 9 -1.2979 -2.597 229s 10 2.0592 2.497 229s 11 -0.4663 -0.466 229s 12 -2.3732 -1.540 229s 13 -1.4734 -1.006 229s 14 -0.3398 0.885 229s 15 1.7283 2.835 229s 16 -3.4975 -4.290 229s 17 -0.9651 -0.760 229s 18 -1.9512 -2.911 229s 19 1.8829 2.606 229s 20 0.0129 1.085 229s > print( residuals( fitols2r$eq[[ 1 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 229s 0.8465 -0.4933 2.5225 1.7066 2.0445 1.2529 1.6277 -2.8261 -1.2979 2.0592 229s 11 12 13 14 15 16 17 18 19 20 229s -0.4663 -2.3732 -1.4734 -0.3398 1.7283 -3.4975 -0.9651 -1.9512 1.8829 0.0129 229s > 229s > print( residuals( fitols3s ) ) 229s demand supply 229s 1 0.8465 0.156 229s 2 -0.4933 -0.384 229s 3 2.5225 2.415 229s 4 1.7066 1.525 229s 5 2.0445 1.750 229s 6 1.2529 0.870 229s 7 1.6277 1.711 229s 8 -2.8261 -4.380 229s 9 -1.2979 -2.597 229s 10 2.0592 2.497 229s 11 -0.4663 -0.466 229s 12 -2.3732 -1.540 229s 13 -1.4734 -1.006 229s 14 -0.3398 0.885 229s 15 1.7283 2.835 229s 16 -3.4975 -4.290 229s 17 -0.9651 -0.760 229s 18 -1.9512 -2.911 229s 19 1.8829 2.606 229s 20 0.0129 1.085 229s > print( residuals( fitols3s$eq[[ 2 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 229s 0.156 -0.384 2.415 1.525 1.750 0.870 1.711 -4.380 -2.597 2.497 -0.466 229s 12 13 14 15 16 17 18 19 20 229s -1.540 -1.006 0.885 2.835 -4.290 -0.760 -2.911 2.606 1.085 229s > 229s > print( residuals( fitols4rs ) ) 229s demand supply 229s 1 0.915 0.204 229s 2 -0.387 -0.421 229s 3 2.613 2.388 229s 4 1.815 1.474 229s 5 1.980 1.787 229s 6 1.221 0.879 229s 7 1.620 1.690 229s 8 -2.769 -4.489 229s 9 -1.382 -2.549 229s 10 1.890 2.660 229s 11 -0.506 -0.297 229s 12 -2.280 -1.456 229s 13 -1.323 -1.013 229s 14 -0.330 0.925 229s 15 1.572 2.889 229s 16 -3.582 -4.313 229s 17 -1.298 -0.573 229s 18 -1.892 -3.023 229s 19 1.948 2.462 229s 20 0.174 0.777 229s > print( residuals( fitols4rs$eq[[ 1 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 229s 0.915 -0.387 2.613 1.815 1.980 1.221 1.620 -2.769 -1.382 1.890 -0.506 229s 12 13 14 15 16 17 18 19 20 229s -2.280 -1.323 -0.330 1.572 -3.582 -1.298 -1.892 1.948 0.174 229s > 229s > print( residuals( fitols5 ) ) 229s demand supply 229s 1 0.915 0.204 229s 2 -0.387 -0.421 229s 3 2.613 2.388 229s 4 1.815 1.474 229s 5 1.980 1.787 229s 6 1.221 0.879 229s 7 1.620 1.690 229s 8 -2.769 -4.489 229s 9 -1.382 -2.549 229s 10 1.890 2.660 229s 11 -0.506 -0.297 229s 12 -2.280 -1.456 229s 13 -1.323 -1.013 229s 14 -0.330 0.925 229s 15 1.572 2.889 229s 16 -3.582 -4.313 229s 17 -1.298 -0.573 229s 18 -1.892 -3.023 229s 19 1.948 2.462 229s 20 0.174 0.777 229s > print( residuals( fitols5$eq[[ 2 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 229s 0.204 -0.421 2.388 1.474 1.787 0.879 1.690 -4.489 -2.549 2.660 -0.297 229s 12 13 14 15 16 17 18 19 20 229s -1.456 -1.013 0.925 2.889 -4.313 -0.573 -3.023 2.462 0.777 229s > 229s > 229s > ## *************** coefficients ********************* 229s > print( round( coef( fitols1rs ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 99.895 -0.316 0.335 58.275 229s supply_price supply_farmPrice supply_trend 229s 0.160 0.248 0.248 229s > print( round( coef( fitols1rs$eq[[ 2 ]] ), digits = 6 ) ) 229s (Intercept) price farmPrice trend 229s 58.275 0.160 0.248 0.248 229s > 229s > print( round( coef( fitols2s ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 99.556 -0.292 0.313 56.380 229s supply_price supply_farmPrice supply_trend 229s 0.164 0.257 0.313 229s > print( round( coef( fitols2s$eq[[ 1 ]] ), digits = 6 ) ) 229s (Intercept) price income 229s 99.556 -0.292 0.313 229s > 229s > print( round( coef( fitols3 ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 99.556 -0.292 0.313 56.380 229s supply_price supply_farmPrice supply_trend 229s 0.164 0.257 0.313 229s > print( round( coef( fitols3, modified.regMat = TRUE ), digits = 6 ) ) 229s C1 C2 C3 C4 C5 C6 229s 99.556 -0.292 0.313 56.380 0.164 0.257 229s > print( round( coef( fitols3$eq[[ 2 ]] ), digits = 6 ) ) 229s (Intercept) price farmPrice trend 229s 56.380 0.164 0.257 0.313 229s > 229s > print( round( coef( fitols4r ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 101.482 -0.317 0.319 54.149 229s supply_price supply_farmPrice supply_trend 229s 0.183 0.260 0.319 229s > print( round( coef( fitols4r$eq[[ 1 ]] ), digits = 6 ) ) 229s (Intercept) price income 229s 101.482 -0.317 0.319 229s > 229s > print( round( coef( fitols5 ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 101.482 -0.317 0.319 54.149 229s supply_price supply_farmPrice supply_trend 229s 0.183 0.260 0.319 229s > print( round( coef( fitols5, modified.regMat = TRUE ), digits = 6 ) ) 229s C1 C2 C3 C4 C5 C6 229s 101.482 -0.317 0.319 54.149 0.183 0.260 229s > print( round( coef( fitols5$eq[[ 2 ]] ), digits = 6 ) ) 229s (Intercept) price farmPrice trend 229s 54.149 0.183 0.260 0.319 229s > 229s > 229s > ## *************** coefficients with stats ********************* 229s > print( round( coef( summary( fitols1rs, useDfSys = FALSE ) ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 99.895 8.4671 11.80 0.000000 229s demand_price -0.316 0.1021 -3.10 0.006536 229s demand_income 0.335 0.0511 6.54 0.000005 229s supply_(Intercept) 58.275 10.3587 5.63 0.000038 229s supply_price 0.160 0.0857 1.87 0.079851 229s supply_farmPrice 0.248 0.0417 5.94 0.000021 229s supply_trend 0.248 0.0881 2.82 0.012382 229s > print( round( coef( summary( fitols1rs$eq[[ 2 ]], useDfSys = FALSE ) ), 229s + digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 58.275 10.3587 5.63 0.000038 229s price 0.160 0.0857 1.87 0.079851 229s farmPrice 0.248 0.0417 5.94 0.000021 229s trend 0.248 0.0881 2.82 0.012382 229s > 229s > print( round( coef( summary( fitols2s ) ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 99.556 7.5640 13.16 0.000000 229s demand_price -0.292 0.0887 -3.29 0.002340 229s demand_income 0.313 0.0415 7.54 0.000000 229s supply_(Intercept) 56.380 11.3165 4.98 0.000018 229s supply_price 0.164 0.0960 1.71 0.097028 229s supply_farmPrice 0.257 0.0451 5.69 0.000002 229s supply_trend 0.313 0.0415 7.54 0.000000 229s > print( round( coef( summary( fitols2s$eq[[ 1 ]] ) ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 99.556 7.5640 13.16 0.00000 229s price -0.292 0.0887 -3.29 0.00234 229s income 0.313 0.0415 7.54 0.00000 229s > 229s > print( round( coef( summary( fitols3, useDfSys = FALSE ) ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 99.556 8.4225 11.82 0.000000 229s demand_price -0.292 0.0975 -2.99 0.008189 229s demand_income 0.313 0.0441 7.10 0.000002 229s supply_(Intercept) 56.380 10.0721 5.60 0.000040 229s supply_price 0.164 0.0853 1.92 0.072611 229s supply_farmPrice 0.257 0.0402 6.39 0.000009 229s supply_trend 0.313 0.0441 7.10 0.000003 229s > print( round( coef( summary( fitols3, useDfSys = FALSE ), modified.regMat = TRUE ), 229s + digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s C1 99.556 8.4225 11.82 NA 229s C2 -0.292 0.0975 -2.99 NA 229s C3 0.313 0.0441 7.10 NA 229s C4 56.380 10.0721 5.60 NA 229s C5 0.164 0.0853 1.92 NA 229s C6 0.257 0.0402 6.39 NA 229s > print( round( coef( summary( fitols3$eq[[ 2 ]], useDfSys = FALSE ) ), 229s + digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 56.380 10.0721 5.60 0.000040 229s price 0.164 0.0853 1.92 0.072611 229s farmPrice 0.257 0.0402 6.39 0.000009 229s trend 0.313 0.0441 7.10 0.000003 229s > 229s > print( round( coef( summary( fitols4r, useDfSys = FALSE ) ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 101.482 5.7621 17.61 0.0e+00 229s demand_price -0.317 0.0589 -5.38 5.0e-05 229s demand_income 0.319 0.0373 8.55 0.0e+00 229s supply_(Intercept) 54.149 7.0638 7.67 1.0e-06 229s supply_price 0.183 0.0589 3.11 6.7e-03 229s supply_farmPrice 0.260 0.0365 7.10 3.0e-06 229s supply_trend 0.319 0.0373 8.55 0.0e+00 229s > print( round( coef( summary( fitols4r$eq[[ 1 ]], useDfSys = FALSE ) ), 229s + digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 101.482 5.7621 17.61 0e+00 229s price -0.317 0.0589 -5.38 5e-05 229s income 0.319 0.0373 8.55 0e+00 229s > 229s > print( round( coef( summary( fitols5 ) ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s demand_(Intercept) 101.482 5.7621 17.61 0.000000 229s demand_price -0.317 0.0589 -5.38 0.000005 229s demand_income 0.319 0.0373 8.55 0.000000 229s supply_(Intercept) 54.149 7.0638 7.67 0.000000 229s supply_price 0.183 0.0589 3.11 0.003680 229s supply_farmPrice 0.260 0.0365 7.10 0.000000 229s supply_trend 0.319 0.0373 8.55 0.000000 229s > print( round( coef( summary( fitols5 ), modified.regMat = TRUE ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s C1 101.482 5.7621 17.61 0.000000 229s C2 -0.317 0.0589 -5.38 0.000005 229s C3 0.319 0.0373 8.55 0.000000 229s C4 54.149 7.0638 7.67 0.000000 229s C5 0.183 0.0589 3.11 0.003680 229s C6 0.260 0.0365 7.10 0.000000 229s > print( round( coef( summary( fitols5$eq[[ 2 ]] ) ), digits = 6 ) ) 229s Estimate Std. Error t value Pr(>|t|) 229s (Intercept) 54.149 7.0638 7.67 0.00000 229s price 0.183 0.0589 3.11 0.00368 229s farmPrice 0.260 0.0365 7.10 0.00000 229s trend 0.319 0.0373 8.55 0.00000 229s > 229s > 229s > ## *********** variance covariance matrix of the coefficients ******* 229s > print( round( vcov( fitols1rs ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 71.6926 -0.75420 0.04078 229s demand_price -0.7542 0.01043 -0.00296 229s demand_income 0.0408 -0.00296 0.00262 229s supply_(Intercept) 0.0000 0.00000 0.00000 229s supply_price 0.0000 0.00000 0.00000 229s supply_farmPrice 0.0000 0.00000 0.00000 229s supply_trend 0.0000 0.00000 0.00000 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) 0.000 0.000000 0.000000 229s demand_price 0.000 0.000000 0.000000 229s demand_income 0.000 0.000000 0.000000 229s supply_(Intercept) 107.303 -0.806417 -0.248549 229s supply_price -0.806 0.007352 0.000689 229s supply_farmPrice -0.249 0.000689 0.001742 229s supply_trend -0.228 0.000426 0.001074 229s supply_trend 229s demand_(Intercept) 0.000000 229s demand_price 0.000000 229s demand_income 0.000000 229s supply_(Intercept) -0.227988 229s supply_price 0.000426 229s supply_farmPrice 0.001074 229s supply_trend 0.007766 229s > print( round( vcov( fitols1rs$eq[[ 2 ]] ), digits = 6 ) ) 229s (Intercept) price farmPrice trend 229s (Intercept) 107.303 -0.806417 -0.248549 -0.227988 229s price -0.806 0.007352 0.000689 0.000426 229s farmPrice -0.249 0.000689 0.001742 0.001074 229s trend -0.228 0.000426 0.001074 0.007766 229s > 229s > print( round( vcov( fitols2s ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 57.21413 -0.596328 0.026850 229s demand_price -0.59633 0.007862 -0.001948 229s demand_income 0.02685 -0.001948 0.001722 229s supply_(Intercept) -0.78825 0.057190 -0.050565 229s supply_price 0.00147 -0.000107 0.000095 229s supply_farmPrice 0.00371 -0.000269 0.000238 229s supply_trend 0.02685 -0.001948 0.001722 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) -0.7883 0.001474 0.003714 229s demand_price 0.0572 -0.000107 -0.000269 229s demand_income -0.0506 0.000095 0.000238 229s supply_(Intercept) 128.0635 -1.001596 -0.280017 229s supply_price -1.0016 0.009225 0.000806 229s supply_farmPrice -0.2800 0.000806 0.002038 229s supply_trend -0.0506 0.000095 0.000238 229s supply_trend 229s demand_(Intercept) 0.026850 229s demand_price -0.001948 229s demand_income 0.001722 229s supply_(Intercept) -0.050565 229s supply_price 0.000095 229s supply_farmPrice 0.000238 229s supply_trend 0.001722 229s > print( round( vcov( fitols2s$eq[[ 1 ]] ), digits = 6 ) ) 229s (Intercept) price income 229s (Intercept) 57.2141 -0.59633 0.02685 229s price -0.5963 0.00786 -0.00195 229s income 0.0268 -0.00195 0.00172 229s > 229s > print( round( vcov( fitols3 ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 70.93892 -0.736413 0.030252 229s demand_price -0.73641 0.009503 -0.002195 229s demand_income 0.03025 -0.002195 0.001941 229s supply_(Intercept) -0.88813 0.064436 -0.056972 229s supply_price 0.00166 -0.000120 0.000107 229s supply_farmPrice 0.00419 -0.000304 0.000268 229s supply_trend 0.03025 -0.002195 0.001941 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) -0.8881 0.001661 0.004185 229s demand_price 0.0644 -0.000120 -0.000304 229s demand_income -0.0570 0.000107 0.000268 229s supply_(Intercept) 101.4478 -0.790443 -0.223090 229s supply_price -0.7904 0.007274 0.000640 229s supply_farmPrice -0.2231 0.000640 0.001617 229s supply_trend -0.0570 0.000107 0.000268 229s supply_trend 229s demand_(Intercept) 0.030252 229s demand_price -0.002195 229s demand_income 0.001941 229s supply_(Intercept) -0.056972 229s supply_price 0.000107 229s supply_farmPrice 0.000268 229s supply_trend 0.001941 229s > print( round( vcov( fitols3, modified.regMat = TRUE ), digits = 6 ) ) 229s C1 C2 C3 C4 C5 C6 229s C1 70.93892 -0.736413 0.030252 -0.8881 0.001661 0.004185 229s C2 -0.73641 0.009503 -0.002195 0.0644 -0.000120 -0.000304 229s C3 0.03025 -0.002195 0.001941 -0.0570 0.000107 0.000268 229s C4 -0.88813 0.064436 -0.056972 101.4478 -0.790443 -0.223090 229s C5 0.00166 -0.000120 0.000107 -0.7904 0.007274 0.000640 229s C6 0.00419 -0.000304 0.000268 -0.2231 0.000640 0.001617 229s > print( round( vcov( fitols3$eq[[ 2 ]] ), digits = 6 ) ) 229s (Intercept) price farmPrice trend 229s (Intercept) 101.448 -0.790443 -0.223090 -0.056972 229s price -0.790 0.007274 0.000640 0.000107 229s farmPrice -0.223 0.000640 0.001617 0.000268 229s trend -0.057 0.000107 0.000268 0.001941 229s > 229s > print( round( vcov( fitols4r ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 33.2016 -0.272100 -0.059329 229s demand_price -0.2721 0.003464 -0.000762 229s demand_income -0.0593 -0.000762 0.001390 229s supply_(Intercept) 30.8652 -0.357363 0.050012 229s supply_price -0.2721 0.003464 -0.000762 229s supply_farmPrice -0.0313 0.000196 0.000120 229s supply_trend -0.0593 -0.000762 0.001390 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) 30.865 -0.272100 -0.031328 229s demand_price -0.357 0.003464 0.000196 229s demand_income 0.050 -0.000762 0.000120 229s supply_(Intercept) 49.897 -0.357363 -0.149852 229s supply_price -0.357 0.003464 0.000196 229s supply_farmPrice -0.150 0.000196 0.001335 229s supply_trend 0.050 -0.000762 0.000120 229s supply_trend 229s demand_(Intercept) -0.059329 229s demand_price -0.000762 229s demand_income 0.001390 229s supply_(Intercept) 0.050012 229s supply_price -0.000762 229s supply_farmPrice 0.000120 229s supply_trend 0.001390 229s > print( round( vcov( fitols4r$eq[[ 1 ]] ), digits = 6 ) ) 229s (Intercept) price income 229s (Intercept) 33.2016 -0.272100 -0.059329 229s price -0.2721 0.003464 -0.000762 229s income -0.0593 -0.000762 0.001390 229s > 229s > print( round( vcov( fitols5 ), digits = 6 ) ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 33.2016 -0.272100 -0.059329 229s demand_price -0.2721 0.003464 -0.000762 229s demand_income -0.0593 -0.000762 0.001390 229s supply_(Intercept) 30.8652 -0.357363 0.050012 229s supply_price -0.2721 0.003464 -0.000762 229s supply_farmPrice -0.0313 0.000196 0.000120 229s supply_trend -0.0593 -0.000762 0.001390 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) 30.865 -0.272100 -0.031328 229s demand_price -0.357 0.003464 0.000196 229s demand_income 0.050 -0.000762 0.000120 229s supply_(Intercept) 49.897 -0.357363 -0.149852 229s supply_price -0.357 0.003464 0.000196 229s supply_farmPrice -0.150 0.000196 0.001335 229s supply_trend 0.050 -0.000762 0.000120 229s supply_trend 229s demand_(Intercept) -0.059329 229s demand_price -0.000762 229s demand_income 0.001390 229s supply_(Intercept) 0.050012 229s supply_price -0.000762 229s supply_farmPrice 0.000120 229s supply_trend 0.001390 229s > print( round( vcov( fitols5, modified.regMat = TRUE ), digits = 6 ) ) 229s C1 C2 C3 C4 C5 C6 229s C1 33.2016 -0.272100 -0.059329 30.865 -0.272100 -0.031328 229s C2 -0.2721 0.003464 -0.000762 -0.357 0.003464 0.000196 229s C3 -0.0593 -0.000762 0.001390 0.050 -0.000762 0.000120 229s C4 30.8652 -0.357363 0.050012 49.897 -0.357363 -0.149852 229s C5 -0.2721 0.003464 -0.000762 -0.357 0.003464 0.000196 229s C6 -0.0313 0.000196 0.000120 -0.150 0.000196 0.001335 229s > print( round( vcov( fitols5$eq[[ 2 ]] ), digits = 6 ) ) 229s (Intercept) price farmPrice trend 229s (Intercept) 49.897 -0.357363 -0.149852 0.050012 229s price -0.357 0.003464 0.000196 -0.000762 229s farmPrice -0.150 0.000196 0.001335 0.000120 229s trend 0.050 -0.000762 0.000120 0.001390 229s > 229s > 229s > ## *********** confidence intervals of coefficients ************* 229s > print( confint( fitols1, useDfSys = TRUE ) ) 229s 2.5 % 97.5 % 229s demand_(Intercept) 84.597 115.194 229s demand_price -0.501 -0.132 229s demand_income 0.242 0.427 229s supply_(Intercept) 34.954 81.597 229s supply_price -0.033 0.353 229s supply_farmPrice 0.154 0.342 229s supply_trend 0.050 0.447 229s > print( confint( fitols1$eq[[ 2 ]], level = 0.9, useDfSys = TRUE ) ) 229s 5 % 95 % 229s (Intercept) 38.876 77.675 229s price 0.000 0.321 229s farmPrice 0.170 0.326 229s trend 0.083 0.413 229s > 229s > print( confint( fitols2r, level = 0.9 ) ) 229s 5 % 95 % 229s demand_(Intercept) 83.776 115.337 229s demand_price -0.474 -0.109 229s demand_income 0.230 0.395 229s supply_(Intercept) 37.508 75.251 229s supply_price 0.004 0.324 229s supply_farmPrice 0.182 0.332 229s supply_trend 0.230 0.395 229s > print( confint( fitols2r$eq[[ 1 ]], level = 0.99 ) ) 229s 0.5 % 99.5 % 229s (Intercept) 78.370 120.743 229s price -0.537 -0.046 229s income 0.202 0.424 229s > 229s > print( confint( fitols3s, level = 0.99 ) ) 229s 0.5 % 99.5 % 229s demand_(Intercept) 84.184 114.928 229s demand_price -0.472 -0.112 229s demand_income 0.229 0.397 229s supply_(Intercept) 33.382 79.377 229s supply_price -0.031 0.359 229s supply_farmPrice 0.165 0.349 229s supply_trend 0.229 0.397 229s > print( confint( fitols3s$eq[[ 2 ]], level = 0.5 ) ) 229s 25 % 75 % 229s (Intercept) 48.664 64.095 229s price 0.098 0.229 229s farmPrice 0.226 0.288 229s trend 0.285 0.341 229s > 229s > print( confint( fitols4rs, level = 0.5 ) ) 229s 25 % 75 % 229s demand_(Intercept) 90.269 112.695 229s demand_price -0.436 -0.197 229s demand_income 0.247 0.390 229s supply_(Intercept) 39.515 68.784 229s supply_price 0.064 0.303 229s supply_farmPrice 0.179 0.340 229s supply_trend 0.247 0.390 229s > print( confint( fitols4rs$eq[[ 1 ]], level = 0.25 ) ) 229s 37.5 % 62.5 % 229s (Intercept) 99.708 103.256 229s price -0.336 -0.298 229s income 0.308 0.330 229s > 229s > print( confint( fitols5, level = 0.25 ) ) 229s 37.5 % 62.5 % 229s demand_(Intercept) 89.784 113.179 229s demand_price -0.436 -0.197 229s demand_income 0.243 0.395 229s supply_(Intercept) 39.809 68.490 229s supply_price 0.064 0.303 229s supply_farmPrice 0.185 0.334 229s supply_trend 0.243 0.395 229s > print( confint( fitols5$eq[[ 2 ]], level = 0.999 ) ) 229s 0.1 % 100 % 229s (Intercept) 28.782 79.517 229s price -0.028 0.395 229s farmPrice 0.128 0.391 229s trend 0.185 0.453 229s > 229s > print( confint( fitols3, level = 0.999, useDfSys = FALSE ) ) 229s 0.1 % 100 % 229s demand_(Intercept) 81.786 117.326 229s demand_price -0.497 -0.086 229s demand_income 0.220 0.406 229s supply_(Intercept) 35.028 77.731 229s supply_price -0.017 0.345 229s supply_farmPrice 0.172 0.342 229s supply_trend 0.219 0.406 229s > print( confint( fitols3$eq[[ 1 ]], useDfSys = FALSE ) ) 229s 2.5 % 97.5 % 229s (Intercept) 81.786 117.326 229s price -0.497 -0.086 229s income 0.220 0.406 229s > 229s > 229s > ## *********** fitted values ************* 229s > print( fitted( fitols1 ) ) 229s demand supply 229s 1 97.4 98.9 229s 2 99.6 100.1 229s 3 99.5 100.2 229s 4 99.7 100.4 229s 5 102.3 102.7 229s 6 102.1 102.6 229s 7 102.5 102.4 229s 8 102.8 104.3 229s 9 101.7 102.9 229s 10 100.8 100.4 229s 11 95.6 96.0 229s 12 94.4 94.1 229s 13 95.7 95.6 229s 14 99.0 97.8 229s 15 104.3 102.6 229s 16 103.9 104.1 229s 17 104.8 103.8 229s 18 101.9 102.4 229s 19 103.5 102.1 229s 20 106.5 104.5 229s > print( fitted( fitols1$eq[[ 2 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 12 13 229s 98.9 100.1 100.2 100.4 102.7 102.6 102.4 104.3 102.9 100.4 96.0 94.1 95.6 229s 14 15 16 17 18 19 20 229s 97.8 102.6 104.1 103.8 102.4 102.1 104.5 229s > 229s > print( fitted( fitols2r ) ) 229s demand supply 229s 1 97.6 98.3 229s 2 99.7 99.6 229s 3 99.6 99.7 229s 4 99.8 100.0 229s 5 102.2 102.5 229s 6 102.0 102.4 229s 7 102.4 102.3 229s 8 102.7 104.3 229s 9 101.6 102.9 229s 10 100.8 100.3 229s 11 95.9 95.9 229s 12 94.8 94.0 229s 13 96.0 95.5 229s 14 99.1 97.9 229s 15 104.1 103.0 229s 16 103.7 104.5 229s 17 104.5 104.3 229s 18 101.9 102.8 229s 19 103.3 102.6 229s 20 106.2 105.1 229s > print( fitted( fitols2r$eq[[ 1 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 12 13 229s 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 229s 14 15 16 17 18 19 20 229s 99.1 104.1 103.7 104.5 101.9 103.3 106.2 229s > 229s > print( fitted( fitols3s ) ) 229s demand supply 229s 1 97.6 98.3 229s 2 99.7 99.6 229s 3 99.6 99.7 229s 4 99.8 100.0 229s 5 102.2 102.5 229s 6 102.0 102.4 229s 7 102.4 102.3 229s 8 102.7 104.3 229s 9 101.6 102.9 229s 10 100.8 100.3 229s 11 95.9 95.9 229s 12 94.8 94.0 229s 13 96.0 95.5 229s 14 99.1 97.9 229s 15 104.1 103.0 229s 16 103.7 104.5 229s 17 104.5 104.3 229s 18 101.9 102.8 229s 19 103.3 102.6 229s 20 106.2 105.1 229s > print( fitted( fitols3s$eq[[ 2 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 12 13 229s 98.3 99.6 99.7 100.0 102.5 102.4 102.3 104.3 102.9 100.3 95.9 94.0 95.5 229s 14 15 16 17 18 19 20 229s 97.9 103.0 104.5 104.3 102.8 102.6 105.1 229s > 229s > print( fitted( fitols4rs ) ) 229s demand supply 229s 1 97.6 98.3 229s 2 99.6 99.6 229s 3 99.5 99.8 229s 4 99.7 100.0 229s 5 102.3 102.5 229s 6 102.0 102.4 229s 7 102.4 102.3 229s 8 102.7 104.4 229s 9 101.7 102.9 229s 10 100.9 100.2 229s 11 95.9 95.7 229s 12 94.7 93.9 229s 13 95.9 95.5 229s 14 99.1 97.8 229s 15 104.2 102.9 229s 16 103.8 104.5 229s 17 104.8 104.1 229s 18 101.8 103.0 229s 19 103.3 102.8 229s 20 106.1 105.5 229s > print( fitted( fitols4rs$eq[[ 1 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 12 13 229s 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 229s 14 15 16 17 18 19 20 229s 99.1 104.2 103.8 104.8 101.8 103.3 106.1 229s > 229s > print( fitted( fitols5 ) ) 229s demand supply 229s 1 97.6 98.3 229s 2 99.6 99.6 229s 3 99.5 99.8 229s 4 99.7 100.0 229s 5 102.3 102.5 229s 6 102.0 102.4 229s 7 102.4 102.3 229s 8 102.7 104.4 229s 9 101.7 102.9 229s 10 100.9 100.2 229s 11 95.9 95.7 229s 12 94.7 93.9 229s 13 95.9 95.5 229s 14 99.1 97.8 229s 15 104.2 102.9 229s 16 103.8 104.5 229s 17 104.8 104.1 229s 18 101.8 103.0 229s 19 103.3 102.8 229s 20 106.1 105.5 229s > print( fitted( fitols5$eq[[ 2 ]] ) ) 229s 1 2 3 4 5 6 7 8 9 10 11 12 13 229s 98.3 99.6 99.8 100.0 102.5 102.4 102.3 104.4 102.9 100.2 95.7 93.9 95.5 229s 14 15 16 17 18 19 20 229s 97.8 102.9 104.5 104.1 103.0 102.8 105.5 229s > 229s > 229s > ## *********** predicted values ************* 229s > predictData <- Kmenta 229s > predictData$consump <- NULL 229s > predictData$price <- Kmenta$price * 0.9 229s > predictData$income <- Kmenta$income * 1.1 229s > 229s > print( predict( fitols1, se.fit = TRUE, interval = "prediction", 229s + useDfSys = TRUE ) ) 229s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 229s 1 97.4 0.643 93.3 101.5 98.9 1.056 229s 2 99.6 0.577 95.5 103.7 100.1 1.037 229s 3 99.5 0.545 95.5 103.6 100.2 0.939 229s 4 99.7 0.582 95.6 103.8 100.4 0.912 229s 5 102.3 0.502 98.2 106.4 102.7 0.895 229s 6 102.1 0.463 98.0 106.1 102.6 0.791 229s 7 102.5 0.484 98.4 106.5 102.4 0.719 229s 8 102.8 0.601 98.7 106.9 104.3 0.963 229s 9 101.7 0.527 97.6 105.8 102.9 0.788 229s 10 100.8 0.788 96.5 105.0 100.4 0.981 229s 11 95.6 0.946 91.2 100.0 96.0 1.185 229s 12 94.4 0.980 90.0 98.8 94.1 1.394 229s 13 95.7 0.880 91.3 100.0 95.6 1.244 229s 14 99.0 0.508 94.9 103.0 97.8 0.896 229s 15 104.3 0.758 100.1 108.5 102.6 0.874 229s 16 103.9 0.616 99.8 108.0 104.1 0.916 229s 17 104.8 1.273 100.1 109.5 103.8 1.605 229s 18 101.9 0.536 97.9 106.0 102.4 0.962 229s 19 103.5 0.680 99.3 107.6 102.1 1.098 229s 20 106.5 1.274 101.8 111.2 104.5 1.664 229s supply.lwr supply.upr 229s 1 93.6 104.3 229s 2 94.8 105.4 229s 3 94.9 105.5 229s 4 95.1 105.6 229s 5 97.5 107.9 229s 6 97.4 107.7 229s 7 97.3 107.5 229s 8 99.0 109.6 229s 9 97.8 108.1 229s 10 95.1 105.6 229s 11 90.6 101.5 229s 12 88.5 99.8 229s 13 90.1 101.1 229s 14 92.6 103.0 229s 15 97.4 107.8 229s 16 98.9 109.3 229s 17 97.9 109.7 229s 18 97.1 107.6 229s 19 96.7 107.5 229s 20 98.6 110.5 229s > print( predict( fitols1$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 229s + useDfSys = TRUE ) ) 229s fit se.fit lwr upr 229s 1 98.9 1.056 93.6 104.3 229s 2 100.1 1.037 94.8 105.4 229s 3 100.2 0.939 94.9 105.5 229s 4 100.4 0.912 95.1 105.6 229s 5 102.7 0.895 97.5 107.9 229s 6 102.6 0.791 97.4 107.7 229s 7 102.4 0.719 97.3 107.5 229s 8 104.3 0.963 99.0 109.6 229s 9 102.9 0.788 97.8 108.1 229s 10 100.4 0.981 95.1 105.6 229s 11 96.0 1.185 90.6 101.5 229s 12 94.1 1.394 88.5 99.8 229s 13 95.6 1.244 90.1 101.1 229s 14 97.8 0.896 92.6 103.0 229s 15 102.6 0.874 97.4 107.8 229s 16 104.1 0.916 98.9 109.3 229s 17 103.8 1.605 97.9 109.7 229s 18 102.4 0.962 97.1 107.6 229s 19 102.1 1.098 96.7 107.5 229s 20 104.5 1.664 98.6 110.5 229s > 229s > print( predict( fitols2r, se.pred = TRUE, interval = "confidence", 229s + level = 0.999, newdata = predictData ) ) 229s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 229s 1 103 2.17 99.9 107 96.7 2.62 229s 2 106 2.16 102.4 109 97.9 2.55 229s 3 106 2.17 102.2 109 98.1 2.55 229s 4 106 2.16 102.5 109 98.3 2.54 229s 5 108 2.43 102.9 113 100.9 2.67 229s 6 108 2.38 103.1 113 100.7 2.63 229s 7 109 2.37 103.7 113 100.6 2.59 229s 8 109 2.33 104.5 114 102.6 2.55 229s 9 107 2.44 102.2 113 101.4 2.69 229s 10 106 2.57 100.2 112 98.8 2.84 229s 11 101 2.36 96.1 106 94.4 2.89 229s 12 100 2.17 96.6 104 92.3 2.88 229s 13 102 2.08 99.0 104 93.9 2.75 229s 14 105 2.25 100.7 109 96.3 2.72 229s 15 110 2.63 103.7 116 101.4 2.72 229s 16 110 2.52 104.1 116 102.9 2.65 229s 17 110 2.96 102.0 118 102.9 3.03 229s 18 108 2.28 103.9 112 101.1 2.55 229s 19 110 2.36 105.1 115 100.9 2.55 229s 20 114 2.57 107.4 120 103.3 2.51 229s supply.lwr supply.upr 229s 1 93.2 100.2 229s 2 95.2 100.5 229s 3 95.3 100.8 229s 4 95.8 100.8 229s 5 97.0 104.8 229s 6 97.2 104.3 229s 7 97.5 103.7 229s 8 99.9 105.2 229s 9 97.3 105.5 229s 10 93.6 104.1 229s 11 88.8 100.0 229s 12 86.8 97.9 229s 13 89.3 98.5 229s 14 91.9 100.6 229s 15 97.0 105.8 229s 16 99.2 106.6 229s 17 96.4 109.4 229s 18 98.4 103.9 229s 19 98.2 103.5 229s 20 101.1 105.5 229s > print( predict( fitols2r$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 229s + level = 0.999, newdata = predictData ) ) 229s fit se.pred lwr upr 229s 1 103 2.17 99.9 107 229s 2 106 2.16 102.4 109 229s 3 106 2.17 102.2 109 229s 4 106 2.16 102.5 109 229s 5 108 2.43 102.9 113 229s 6 108 2.38 103.1 113 229s 7 109 2.37 103.7 113 229s 8 109 2.33 104.5 114 229s 9 107 2.44 102.2 113 229s 10 106 2.57 100.2 112 229s 11 101 2.36 96.1 106 229s 12 100 2.17 96.6 104 229s 13 102 2.08 99.0 104 229s 14 105 2.25 100.7 109 229s 15 110 2.63 103.7 116 229s 16 110 2.52 104.1 116 229s 17 110 2.96 102.0 118 229s 18 108 2.28 103.9 112 229s 19 110 2.36 105.1 115 229s 20 114 2.57 107.4 120 229s > 229s > print( predict( fitols3s, se.fit = TRUE, se.pred = TRUE, 229s + interval = "prediction", level = 0.5, newdata = predictData ) ) 229s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 229s 1 103 0.940 2.16 101.8 105 96.7 229s 2 106 0.944 2.16 104.3 107 97.9 229s 3 106 0.969 2.17 104.2 107 98.1 229s 4 106 0.949 2.16 104.4 107 98.3 229s 5 108 1.452 2.43 106.5 110 100.9 229s 6 108 1.372 2.38 106.4 110 100.7 229s 7 109 1.356 2.37 106.9 110 100.6 229s 8 109 1.296 2.34 107.6 111 102.6 229s 9 107 1.464 2.43 105.8 109 101.4 229s 10 106 1.652 2.55 104.5 108 98.8 229s 11 101 1.305 2.34 99.4 103 94.4 229s 12 100 0.941 2.16 98.6 102 92.3 229s 13 102 0.725 2.07 100.2 103 93.9 229s 14 105 1.124 2.24 103.3 106 96.3 229s 15 110 1.774 2.63 108.3 112 101.4 229s 16 110 1.606 2.52 108.2 112 102.9 229s 17 110 2.216 2.95 108.0 112 102.9 229s 18 108 1.208 2.29 106.6 110 101.1 229s 19 110 1.356 2.37 108.3 112 100.9 229s 20 114 1.718 2.59 111.7 115 103.3 229s supply.se.fit supply.se.pred supply.lwr supply.upr 229s 1 1.149 2.69 94.8 98.5 229s 2 0.873 2.59 96.1 99.6 229s 3 0.907 2.60 96.3 99.8 229s 4 0.831 2.58 96.5 100.0 229s 5 1.324 2.77 99.0 102.8 229s 6 1.188 2.71 98.9 102.6 229s 7 1.049 2.65 98.8 102.4 229s 8 0.911 2.60 100.8 104.3 229s 9 1.396 2.81 99.5 103.3 229s 10 1.782 3.02 96.8 100.9 229s 11 1.906 3.09 92.3 96.5 229s 12 1.875 3.08 90.2 94.4 229s 13 1.560 2.89 91.9 95.8 229s 14 1.475 2.85 94.3 98.2 229s 15 1.477 2.85 99.5 103.3 229s 16 1.245 2.74 101.0 104.8 229s 17 2.195 3.28 100.6 105.1 229s 18 0.909 2.60 99.4 102.9 229s 19 0.875 2.59 99.1 102.6 229s 20 0.704 2.54 101.6 105.0 229s > print( predict( fitols3s$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 229s + interval = "prediction", level = 0.5, newdata = predictData ) ) 229s fit se.fit se.pred lwr upr 229s 1 96.7 1.149 2.69 94.8 98.5 229s 2 97.9 0.873 2.59 96.1 99.6 229s 3 98.1 0.907 2.60 96.3 99.8 229s 4 98.3 0.831 2.58 96.5 100.0 229s 5 100.9 1.324 2.77 99.0 102.8 229s 6 100.7 1.188 2.71 98.9 102.6 229s 7 100.6 1.049 2.65 98.8 102.4 229s 8 102.6 0.911 2.60 100.8 104.3 229s 9 101.4 1.396 2.81 99.5 103.3 229s 10 98.8 1.782 3.02 96.8 100.9 229s 11 94.4 1.906 3.09 92.3 96.5 229s 12 92.3 1.875 3.08 90.2 94.4 229s 13 93.9 1.560 2.89 91.9 95.8 229s 14 96.3 1.475 2.85 94.3 98.2 229s 15 101.4 1.477 2.85 99.5 103.3 229s 16 102.9 1.245 2.74 101.0 104.8 229s 17 102.9 2.195 3.28 100.6 105.1 229s 18 101.1 0.909 2.60 99.4 102.9 229s 19 100.9 0.875 2.59 99.1 102.6 229s 20 103.3 0.704 2.54 101.6 105.0 229s > 229s > print( predict( fitols4rs, se.fit = TRUE, se.pred = TRUE, 229s + interval = "confidence", level = 0.99 ) ) 229s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 229s 1 97.6 0.541 2.01 96.1 99.0 98.3 229s 2 99.6 0.471 2.00 98.3 100.9 99.6 229s 3 99.5 0.454 1.99 98.3 100.8 99.8 229s 4 99.7 0.475 2.00 98.4 101.0 100.0 229s 5 102.3 0.434 1.99 101.1 103.4 102.5 229s 6 102.0 0.418 1.98 100.9 103.2 102.4 229s 7 102.4 0.440 1.99 101.2 103.6 102.3 229s 8 102.7 0.537 2.01 101.2 104.1 104.4 229s 9 101.7 0.447 1.99 100.5 102.9 102.9 229s 10 100.9 0.628 2.04 99.2 102.6 100.2 229s 11 95.9 0.833 2.11 93.7 98.2 95.7 229s 12 94.7 0.807 2.10 92.5 96.9 93.9 229s 13 95.9 0.677 2.06 94.0 97.7 95.5 229s 14 99.1 0.459 1.99 97.8 100.3 97.8 229s 15 104.2 0.572 2.02 102.7 105.8 102.9 229s 16 103.8 0.509 2.01 102.4 105.2 104.5 229s 17 104.8 0.877 2.13 102.4 107.2 104.1 229s 18 101.8 0.478 2.00 100.5 103.1 103.0 229s 19 103.3 0.604 2.03 101.6 104.9 102.8 229s 20 106.1 1.102 2.23 103.1 109.1 105.5 229s supply.se.fit supply.se.pred supply.lwr supply.upr 229s 1 0.598 2.52 96.7 99.9 229s 2 0.679 2.54 97.8 101.5 229s 3 0.634 2.53 98.0 101.5 229s 4 0.643 2.53 98.3 101.8 229s 5 0.753 2.56 100.4 104.5 229s 6 0.680 2.54 100.5 104.2 229s 7 0.625 2.53 100.6 104.0 229s 8 0.799 2.57 102.2 106.6 229s 9 0.700 2.55 101.0 104.8 229s 10 0.716 2.55 98.2 102.1 229s 11 0.916 2.61 93.2 98.2 229s 12 1.226 2.74 90.5 97.2 229s 13 1.130 2.70 92.5 98.6 229s 14 0.796 2.57 95.7 100.0 229s 15 0.656 2.53 101.1 104.7 229s 16 0.644 2.53 102.8 106.3 229s 17 1.150 2.70 101.0 107.2 229s 18 0.575 2.51 101.4 104.5 229s 19 0.649 2.53 101.0 104.5 229s 20 0.875 2.60 103.1 107.8 229s > print( predict( fitols4rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 229s + interval = "confidence", level = 0.99 ) ) 229s fit se.fit se.pred lwr upr 229s 1 97.6 0.541 2.01 96.1 99.0 229s 2 99.6 0.471 2.00 98.3 100.9 229s 3 99.5 0.454 1.99 98.3 100.8 229s 4 99.7 0.475 2.00 98.4 101.0 229s 5 102.3 0.434 1.99 101.1 103.4 229s 6 102.0 0.418 1.98 100.9 103.2 229s 7 102.4 0.440 1.99 101.2 103.6 229s 8 102.7 0.537 2.01 101.2 104.1 229s 9 101.7 0.447 1.99 100.5 102.9 229s 10 100.9 0.628 2.04 99.2 102.6 229s 11 95.9 0.833 2.11 93.7 98.2 229s 12 94.7 0.807 2.10 92.5 96.9 229s 13 95.9 0.677 2.06 94.0 97.7 229s 14 99.1 0.459 1.99 97.8 100.3 229s 15 104.2 0.572 2.02 102.7 105.8 229s 16 103.8 0.509 2.01 102.4 105.2 229s 17 104.8 0.877 2.13 102.4 107.2 229s 18 101.8 0.478 2.00 100.5 103.1 229s 19 103.3 0.604 2.03 101.6 104.9 229s 20 106.1 1.102 2.23 103.1 109.1 229s > 229s > print( predict( fitols5, se.fit = TRUE, interval = "prediction", 229s + level = 0.9, newdata = predictData ) ) 229s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 229s 1 104 0.714 100.0 107 96.4 0.712 229s 2 106 0.748 102.5 110 97.7 0.591 229s 3 106 0.753 102.4 109 97.9 0.602 229s 4 106 0.756 102.6 110 98.1 0.565 229s 5 109 1.055 104.8 112 100.7 0.900 229s 6 108 1.013 104.7 112 100.5 0.811 229s 7 109 1.029 105.2 113 100.5 0.722 229s 8 109 1.055 105.7 113 102.5 0.703 229s 9 108 1.042 104.1 112 101.1 0.952 229s 10 107 1.148 102.8 110 98.5 1.136 229s 11 101 1.026 97.6 105 94.0 1.245 229s 12 100 0.800 96.7 104 92.1 1.347 229s 13 102 0.606 98.4 105 93.7 1.170 229s 14 105 0.820 101.5 109 96.0 1.034 229s 15 111 1.272 106.6 114 101.2 1.031 229s 16 110 1.191 106.4 114 102.7 0.925 229s 17 111 1.513 106.5 115 102.5 1.529 229s 18 108 0.963 104.8 112 101.0 0.720 229s 19 110 1.129 106.4 114 100.8 0.717 229s 20 114 1.601 109.5 118 103.4 0.562 229s supply.lwr supply.upr 229s 1 92.1 100.7 229s 2 93.4 102.0 229s 3 93.6 102.1 229s 4 93.9 102.4 229s 5 96.3 105.1 229s 6 96.2 104.9 229s 7 96.1 104.8 229s 8 98.2 106.8 229s 9 96.7 105.6 229s 10 93.9 103.0 229s 11 89.4 98.7 229s 12 87.4 96.8 229s 13 89.1 98.2 229s 14 91.5 100.5 229s 15 96.7 105.7 229s 16 98.3 107.2 229s 17 97.6 107.4 229s 18 96.7 105.4 229s 19 96.5 105.1 229s 20 99.1 107.6 229s > print( predict( fitols5$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 229s + level = 0.9, newdata = predictData ) ) 229s fit se.fit lwr upr 229s 1 96.4 0.712 92.1 100.7 229s 2 97.7 0.591 93.4 102.0 229s 3 97.9 0.602 93.6 102.1 229s 4 98.1 0.565 93.9 102.4 229s 5 100.7 0.900 96.3 105.1 229s 6 100.5 0.811 96.2 104.9 229s 7 100.5 0.722 96.1 104.8 229s 8 102.5 0.703 98.2 106.8 229s 9 101.1 0.952 96.7 105.6 229s 10 98.5 1.136 93.9 103.0 229s 11 94.0 1.245 89.4 98.7 229s 12 92.1 1.347 87.4 96.8 229s 13 93.7 1.170 89.1 98.2 229s 14 96.0 1.034 91.5 100.5 229s 15 101.2 1.031 96.7 105.7 229s 16 102.7 0.925 98.3 107.2 229s 17 102.5 1.529 97.6 107.4 229s 18 101.0 0.720 96.7 105.4 229s 19 100.8 0.717 96.5 105.1 229s 20 103.4 0.562 99.1 107.6 229s > 229s > # predict just one observation 229s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 229s + trend = 25 ) 229s > 229s > print( predict( fitols1, newdata = smallData ) ) 229s demand.pred supply.pred 229s 1 109 115 229s > print( predict( fitols1$eq[[ 1 ]], newdata = smallData ) ) 229s fit 229s 1 109 229s > 229s > print( predict( fitols2r, se.fit = TRUE, level = 0.9, 229s + newdata = smallData ) ) 229s demand.pred demand.se.fit supply.pred supply.se.fit 229s 1 109 2.48 116 2.8 229s > print( predict( fitols2r$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 229s + newdata = smallData ) ) 229s fit se.pred 229s 1 109 3.15 229s > 229s > print( predict( fitols3s, interval = "prediction", level = 0.975, 229s + newdata = smallData ) ) 229s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 229s 1 109 101 116 116 107 126 229s > print( predict( fitols3s$eq[[ 1 ]], interval = "confidence", level = 0.8, 229s + newdata = smallData ) ) 229s fit lwr upr 229s 1 109 105 112 229s > 229s > print( predict( fitols4rs, se.fit = TRUE, interval = "confidence", 229s + level = 0.999, newdata = smallData ) ) 229s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 229s 1 108 2.02 101 115 117 2.02 229s supply.lwr supply.upr 229s 1 110 124 229s > print( predict( fitols4rs$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 229s + level = 0.75, newdata = smallData ) ) 229s fit se.pred lwr upr 229s 1 117 3.18 113 121 229s > 229s > print( predict( fitols5, se.fit = TRUE, interval = "prediction", 229s + newdata = smallData ) ) 229s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 229s 1 108 2.18 102 114 117 2.01 229s supply.lwr supply.upr 229s 1 111 124 229s > print( predict( fitols5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 229s + newdata = smallData ) ) 229s fit se.pred lwr upr 229s 1 108 2.92 104 113 229s > 229s > print( predict( fitols5rs, se.fit = TRUE, se.pred = TRUE, 229s + interval = "prediction", level = 0.5, newdata = smallData ) ) 229s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 229s 1 108 2.02 2.8 106 110 117 229s supply.se.fit supply.se.pred supply.lwr supply.upr 229s 1 2.02 3.18 115 119 229s > print( predict( fitols5rs$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 229s + interval = "confidence", level = 0.25, newdata = smallData ) ) 229s fit se.fit se.pred lwr upr 229s 1 108 2.02 2.8 107 109 229s > 229s > 229s > ## ************ correlation of predicted values *************** 229s > print( correlation.systemfit( fitols1, 1, 2 ) ) 229s [,1] 229s [1,] 0 229s [2,] 0 229s [3,] 0 229s [4,] 0 229s [5,] 0 229s [6,] 0 229s [7,] 0 229s [8,] 0 229s [9,] 0 229s [10,] 0 229s [11,] 0 229s [12,] 0 229s [13,] 0 229s [14,] 0 229s [15,] 0 229s [16,] 0 229s [17,] 0 229s [18,] 0 229s [19,] 0 229s [20,] 0 229s > 229s > print( correlation.systemfit( fitols2r, 2, 1 ) ) 229s [,1] 229s [1,] 0.443122 229s [2,] 0.160426 229s [3,] 0.161091 229s [4,] 0.118312 229s [5,] -0.077411 229s [6,] -0.059235 229s [7,] -0.057777 229s [8,] -0.006908 229s [9,] -0.000372 229s [10,] -0.001410 229s [11,] 0.055233 229s [12,] 0.074936 229s [13,] 0.028274 229s [14,] -0.032082 229s [15,] 0.196029 229s [16,] 0.279921 229s [17,] 0.115570 229s [18,] 0.080620 229s [19,] 0.171681 229s [20,] 0.150544 229s > 229s > print( correlation.systemfit( fitols3s, 1, 2 ) ) 229s [,1] 229s [1,] 0.405901 229s [2,] 0.145364 229s [3,] 0.145375 229s [4,] 0.105835 229s [5,] -0.067958 229s [6,] -0.052026 229s [7,] -0.050543 229s [8,] -0.006031 229s [9,] -0.000326 229s [10,] -0.001237 229s [11,] 0.047534 229s [12,] 0.063493 229s [13,] 0.024060 229s [14,] -0.027910 229s [15,] 0.171580 229s [16,] 0.248212 229s [17,] 0.101409 229s [18,] 0.073084 229s [19,] 0.153950 229s [20,] 0.132944 229s > 229s > print( correlation.systemfit( fitols4rs, 2, 1 ) ) 229s [,1] 229s [1,] 0.38162 229s [2,] 0.29173 229s [3,] 0.25421 229s [4,] 0.28598 229s [5,] -0.02775 229s [6,] -0.04974 229s [7,] -0.05850 229s [8,] 0.09388 229s [9,] 0.09469 229s [10,] 0.43814 229s [11,] 0.10559 229s [12,] 0.00876 229s [13,] 0.04090 229s [14,] -0.03984 229s [15,] 0.40767 229s [16,] 0.24571 229s [17,] 0.64160 229s [18,] 0.24037 229s [19,] 0.34075 229s [20,] 0.54270 229s > 229s > print( correlation.systemfit( fitols5, 1, 2 ) ) 229s [,1] 229s [1,] 0.4051 229s [2,] 0.2729 229s [3,] 0.2415 229s [4,] 0.2693 229s [5,] -0.0301 229s [6,] -0.0527 229s [7,] -0.0624 229s [8,] 0.0971 229s [9,] 0.0945 229s [10,] 0.4365 229s [11,] 0.1258 229s [12,] 0.0210 229s [13,] 0.0436 229s [14,] -0.0405 229s [15,] 0.4102 229s [16,] 0.2610 229s [17,] 0.6400 229s [18,] 0.2661 229s [19,] 0.3796 229s [20,] 0.5742 229s > 229s > 229s > ## ************ Log-Likelihood values *************** 229s > print( logLik( fitols1 ) ) 229s 'log Lik.' -67.8 (df=8) 229s > print( logLik( fitols1, residCovDiag = TRUE ) ) 229s 'log Lik.' -83.6 (df=8) 229s > all.equal( logLik( fitols1, residCovDiag = TRUE ), 229s + logLik( lmDemand ) + logLik( lmSupply ), 229s + check.attributes = FALSE ) 229s [1] TRUE 229s > 229s > print( logLik( fitols2r ) ) 229s 'log Lik.' -62 (df=7) 229s > print( logLik( fitols2r, residCovDiag = TRUE ) ) 229s 'log Lik.' -84 (df=7) 229s > 229s > print( logLik( fitols3s ) ) 229s 'log Lik.' -62 (df=7) 229s > print( logLik( fitols3s, residCovDiag = TRUE ) ) 229s 'log Lik.' -84 (df=7) 229s > 229s > print( logLik( fitols4rs ) ) 229s 'log Lik.' -62.8 (df=6) 229s > print( logLik( fitols4rs, residCovDiag = TRUE ) ) 229s 'log Lik.' -84.1 (df=6) 229s > 229s > print( logLik( fitols5 ) ) 229s 'log Lik.' -62.8 (df=6) 229s > print( logLik( fitols5, residCovDiag = TRUE ) ) 229s 'log Lik.' -84.1 (df=6) 229s > 229s > 229s > ## ************** F tests **************** 229s > # testing first restriction 229s > print( linearHypothesis( fitols1, restrm ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.14 0.71 229s > linearHypothesis( fitols1, restrict ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.14 0.71 229s > 229s > print( linearHypothesis( fitols1s, restrm ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1s 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.15 0.7 229s > linearHypothesis( fitols1s, restrict ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1s 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.15 0.7 229s > 229s > print( linearHypothesis( fitols1, restrm ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.14 0.71 229s > linearHypothesis( fitols1, restrict ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.14 0.71 229s > 229s > print( linearHypothesis( fitols1r, restrm ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1r 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.14 0.71 229s > linearHypothesis( fitols1r, restrict ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1r 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.14 0.71 229s > 229s > # testing second restriction 229s > restrOnly2m <- matrix(0,1,7) 229s > restrOnly2q <- 0.5 229s > restrOnly2m[1,2] <- -1 229s > restrOnly2m[1,5] <- 1 229s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 229s > # first restriction not imposed 229s > print( linearHypothesis( fitols1, restrOnly2m, restrOnly2q ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.01 0.94 229s > linearHypothesis( fitols1, restrictOnly2 ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 34 229s 2 33 1 0.01 0.94 229s > 229s > # first restriction imposed 229s > print( linearHypothesis( fitols2, restrOnly2m, restrOnly2q ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols2 229s 229s Res.Df Df F Pr(>F) 229s 1 35 229s 2 34 1 0.02 0.88 229s > linearHypothesis( fitols2, restrictOnly2 ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols2 229s 229s Res.Df Df F Pr(>F) 229s 1 35 229s 2 34 1 0.02 0.88 229s > 229s > print( linearHypothesis( fitols3, restrOnly2m, restrOnly2q ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols3 229s 229s Res.Df Df F Pr(>F) 229s 1 35 229s 2 34 1 0.02 0.88 229s > linearHypothesis( fitols3, restrictOnly2 ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols3 229s 229s Res.Df Df F Pr(>F) 229s 1 35 229s 2 34 1 0.02 0.88 229s > 229s > # testing both of the restrictions 229s > print( linearHypothesis( fitols1, restr2m, restr2q ) ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 35 229s 2 33 2 0.08 0.93 229s > linearHypothesis( fitols1, restrict2 ) 229s Linear hypothesis test (Theil's F test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df F Pr(>F) 229s 1 35 229s 2 33 2 0.08 0.93 229s > 229s > 229s > ## ************** Wald tests **************** 229s > # testing first restriction 229s > print( linearHypothesis( fitols1, restrm, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.64 0.42 229s > linearHypothesis( fitols1, restrict, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.64 0.42 229s > 229s > print( linearHypothesis( fitols1s, restrm, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1s 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.72 0.4 229s > linearHypothesis( fitols1s, restrict, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1s 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.72 0.4 229s > 229s > print( linearHypothesis( fitols1, restrm, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.64 0.42 229s > linearHypothesis( fitols1, restrict, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.64 0.42 229s > 229s > print( linearHypothesis( fitols1r, restrm, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1r 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.64 0.42 229s > linearHypothesis( fitols1r, restrict, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s 229s Model 1: restricted model 229s Model 2: fitols1r 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.64 0.42 229s > 229s > # testing second restriction 229s > # first restriction not imposed 229s > print( linearHypothesis( fitols1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.03 0.86 229s > linearHypothesis( fitols1, restrictOnly2, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 34 229s 2 33 1 0.03 0.86 229s > # first restriction imposed 229s > print( linearHypothesis( fitols2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols2 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 35 229s 2 34 1 0.12 0.73 229s > linearHypothesis( fitols2, restrictOnly2, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols2 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 35 229s 2 34 1 0.12 0.73 229s > 229s > print( linearHypothesis( fitols3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols3 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 35 229s 2 34 1 0.12 0.73 229s > linearHypothesis( fitols3, restrictOnly2, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols3 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 35 229s 2 34 1 0.12 0.73 229s > 229s > # testing both of the restrictions 229s > print( linearHypothesis( fitols1, restr2m, restr2q, test = "Chisq" ) ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 35 229s 2 33 2 0.72 0.7 229s > linearHypothesis( fitols1, restrict2, test = "Chisq" ) 229s Linear hypothesis test (Chi^2 statistic of a Wald test) 229s 229s Hypothesis: 229s demand_income - supply_trend = 0 229s - demand_price + supply_price = 0.5 229s 229s Model 1: restricted model 229s Model 2: fitols1 229s 229s Res.Df Df Chisq Pr(>Chisq) 229s 1 35 229s 2 33 2 0.72 0.7 229s > 229s > 229s > ## ****************** model frame ************************** 229s > print( mf <- model.frame( fitols1 ) ) 229s consump price income farmPrice trend 229s 1 98.5 100.3 87.4 98.0 1 229s 2 99.2 104.3 97.6 99.1 2 229s 3 102.2 103.4 96.7 99.1 3 229s 4 101.5 104.5 98.2 98.1 4 229s 5 104.2 98.0 99.8 110.8 5 229s 6 103.2 99.5 100.5 108.2 6 229s 7 104.0 101.1 103.2 105.6 7 229s 8 99.9 104.8 107.8 109.8 8 229s 9 100.3 96.4 96.6 108.7 9 229s 10 102.8 91.2 88.9 100.6 10 229s 11 95.4 93.1 75.1 81.0 11 229s 12 92.4 98.8 76.9 68.6 12 229s 13 94.5 102.9 84.6 70.9 13 229s 14 98.8 98.8 90.6 81.4 14 229s 15 105.8 95.1 103.1 102.3 15 229s 16 100.2 98.5 105.1 105.0 16 229s 17 103.5 86.5 96.4 110.5 17 229s 18 99.9 104.0 104.4 92.5 18 229s 19 105.2 105.8 110.7 89.3 19 229s 20 106.2 113.5 127.1 93.0 20 229s > print( mf1 <- model.frame( fitols1$eq[[ 1 ]] ) ) 229s consump price income 229s 1 98.5 100.3 87.4 229s 2 99.2 104.3 97.6 229s 3 102.2 103.4 96.7 229s 4 101.5 104.5 98.2 229s 5 104.2 98.0 99.8 229s 6 103.2 99.5 100.5 229s 7 104.0 101.1 103.2 229s 8 99.9 104.8 107.8 229s 9 100.3 96.4 96.6 229s 10 102.8 91.2 88.9 229s 11 95.4 93.1 75.1 229s 12 92.4 98.8 76.9 229s 13 94.5 102.9 84.6 229s 14 98.8 98.8 90.6 229s 15 105.8 95.1 103.1 229s 16 100.2 98.5 105.1 229s 17 103.5 86.5 96.4 229s 18 99.9 104.0 104.4 229s 19 105.2 105.8 110.7 229s 20 106.2 113.5 127.1 229s > print( attributes( mf1 )$terms ) 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s > print( mf2 <- model.frame( fitols1$eq[[ 2 ]] ) ) 229s consump price farmPrice trend 229s 1 98.5 100.3 98.0 1 229s 2 99.2 104.3 99.1 2 229s 3 102.2 103.4 99.1 3 229s 4 101.5 104.5 98.1 4 229s 5 104.2 98.0 110.8 5 229s 6 103.2 99.5 108.2 6 229s 7 104.0 101.1 105.6 7 229s 8 99.9 104.8 109.8 8 229s 9 100.3 96.4 108.7 9 229s 10 102.8 91.2 100.6 10 229s 11 95.4 93.1 81.0 11 229s 12 92.4 98.8 68.6 12 229s 13 94.5 102.9 70.9 13 229s 14 98.8 98.8 81.4 14 229s 15 105.8 95.1 102.3 15 229s 16 100.2 98.5 105.0 16 229s 17 103.5 86.5 110.5 17 229s 18 99.9 104.0 92.5 18 229s 19 105.2 105.8 89.3 19 229s 20 106.2 113.5 93.0 20 229s > print( attributes( mf2 )$terms ) 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s > 229s > print( all.equal( mf, model.frame( fitols2r ) ) ) 229s [1] TRUE 229s > print( all.equal( mf1, model.frame( fitols2r$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > 229s > print( all.equal( mf, model.frame( fitols3s ) ) ) 229s [1] TRUE 229s > print( all.equal( mf2, model.frame( fitols3s$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > 229s > print( all.equal( mf, model.frame( fitols4rs ) ) ) 229s [1] TRUE 229s > print( all.equal( mf1, model.frame( fitols4rs$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > 229s > print( all.equal( mf, model.frame( fitols5 ) ) ) 229s [1] TRUE 229s > print( all.equal( mf2, model.frame( fitols5$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > 229s > 229s > ## **************** model matrix ************************ 229s > # with x (returnModelMatrix) = TRUE 229s > print( !is.null( fitols1r$eq[[ 1 ]]$x ) ) 229s [1] TRUE 229s > print( mm <- model.matrix( fitols1r ) ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s demand_1 1 100.3 87.4 0 229s demand_2 1 104.3 97.6 0 229s demand_3 1 103.4 96.7 0 229s demand_4 1 104.5 98.2 0 229s demand_5 1 98.0 99.8 0 229s demand_6 1 99.5 100.5 0 229s demand_7 1 101.1 103.2 0 229s demand_8 1 104.8 107.8 0 229s demand_9 1 96.4 96.6 0 229s demand_10 1 91.2 88.9 0 229s demand_11 1 93.1 75.1 0 229s demand_12 1 98.8 76.9 0 229s demand_13 1 102.9 84.6 0 229s demand_14 1 98.8 90.6 0 229s demand_15 1 95.1 103.1 0 229s demand_16 1 98.5 105.1 0 229s demand_17 1 86.5 96.4 0 229s demand_18 1 104.0 104.4 0 229s demand_19 1 105.8 110.7 0 229s demand_20 1 113.5 127.1 0 229s supply_1 0 0.0 0.0 1 229s supply_2 0 0.0 0.0 1 229s supply_3 0 0.0 0.0 1 229s supply_4 0 0.0 0.0 1 229s supply_5 0 0.0 0.0 1 229s supply_6 0 0.0 0.0 1 229s supply_7 0 0.0 0.0 1 229s supply_8 0 0.0 0.0 1 229s supply_9 0 0.0 0.0 1 229s supply_10 0 0.0 0.0 1 229s supply_11 0 0.0 0.0 1 229s supply_12 0 0.0 0.0 1 229s supply_13 0 0.0 0.0 1 229s supply_14 0 0.0 0.0 1 229s supply_15 0 0.0 0.0 1 229s supply_16 0 0.0 0.0 1 229s supply_17 0 0.0 0.0 1 229s supply_18 0 0.0 0.0 1 229s supply_19 0 0.0 0.0 1 229s supply_20 0 0.0 0.0 1 229s supply_price supply_farmPrice supply_trend 229s demand_1 0.0 0.0 0 229s demand_2 0.0 0.0 0 229s demand_3 0.0 0.0 0 229s demand_4 0.0 0.0 0 229s demand_5 0.0 0.0 0 229s demand_6 0.0 0.0 0 229s demand_7 0.0 0.0 0 229s demand_8 0.0 0.0 0 229s demand_9 0.0 0.0 0 229s demand_10 0.0 0.0 0 229s demand_11 0.0 0.0 0 229s demand_12 0.0 0.0 0 229s demand_13 0.0 0.0 0 229s demand_14 0.0 0.0 0 229s demand_15 0.0 0.0 0 229s demand_16 0.0 0.0 0 229s demand_17 0.0 0.0 0 229s demand_18 0.0 0.0 0 229s demand_19 0.0 0.0 0 229s demand_20 0.0 0.0 0 229s supply_1 100.3 98.0 1 229s supply_2 104.3 99.1 2 229s supply_3 103.4 99.1 3 229s supply_4 104.5 98.1 4 229s supply_5 98.0 110.8 5 229s supply_6 99.5 108.2 6 229s supply_7 101.1 105.6 7 229s supply_8 104.8 109.8 8 229s supply_9 96.4 108.7 9 229s supply_10 91.2 100.6 10 229s supply_11 93.1 81.0 11 229s supply_12 98.8 68.6 12 229s supply_13 102.9 70.9 13 229s supply_14 98.8 81.4 14 229s supply_15 95.1 102.3 15 229s supply_16 98.5 105.0 16 229s supply_17 86.5 110.5 17 229s supply_18 104.0 92.5 18 229s supply_19 105.8 89.3 19 229s supply_20 113.5 93.0 20 229s > print( mm1 <- model.matrix( fitols1r$eq[[ 1 ]] ) ) 229s (Intercept) price income 229s 1 1 100.3 87.4 229s 2 1 104.3 97.6 229s 3 1 103.4 96.7 229s 4 1 104.5 98.2 229s 5 1 98.0 99.8 229s 6 1 99.5 100.5 229s 7 1 101.1 103.2 229s 8 1 104.8 107.8 229s 9 1 96.4 96.6 229s 10 1 91.2 88.9 229s 11 1 93.1 75.1 229s 12 1 98.8 76.9 229s 13 1 102.9 84.6 229s 14 1 98.8 90.6 229s 15 1 95.1 103.1 229s 16 1 98.5 105.1 229s 17 1 86.5 96.4 229s 18 1 104.0 104.4 229s 19 1 105.8 110.7 229s 20 1 113.5 127.1 229s attr(,"assign") 229s [1] 0 1 2 229s > print( mm2 <- model.matrix( fitols1r$eq[[ 2 ]] ) ) 229s (Intercept) price farmPrice trend 229s 1 1 100.3 98.0 1 229s 2 1 104.3 99.1 2 229s 3 1 103.4 99.1 3 229s 4 1 104.5 98.1 4 229s 5 1 98.0 110.8 5 229s 6 1 99.5 108.2 6 229s 7 1 101.1 105.6 7 229s 8 1 104.8 109.8 8 229s 9 1 96.4 108.7 9 229s 10 1 91.2 100.6 10 229s 11 1 93.1 81.0 11 229s 12 1 98.8 68.6 12 229s 13 1 102.9 70.9 13 229s 14 1 98.8 81.4 14 229s 15 1 95.1 102.3 15 229s 16 1 98.5 105.0 16 229s 17 1 86.5 110.5 17 229s 18 1 104.0 92.5 18 229s 19 1 105.8 89.3 19 229s 20 1 113.5 93.0 20 229s attr(,"assign") 229s [1] 0 1 2 3 229s > 229s > # with x (returnModelMatrix) = FALSE 229s > print( all.equal( mm, model.matrix( fitols1rs ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols1rs$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols1rs$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > print( !is.null( fitols1rs$eq[[ 1 ]]$x ) ) 229s [1] FALSE 229s > 229s > # with x (returnModelMatrix) = TRUE 229s > print( !is.null( fitols2rs$eq[[ 1 ]]$x ) ) 229s [1] TRUE 229s > print( all.equal( mm, model.matrix( fitols2rs ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols2rs$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols2rs$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > 229s > # with x (returnModelMatrix) = FALSE 229s > print( all.equal( mm, model.matrix( fitols2 ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols2$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols2$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > print( !is.null( fitols2$eq[[ 1 ]]$x ) ) 229s [1] FALSE 229s > 229s > # with x (returnModelMatrix) = TRUE 229s > print( !is.null( fitols3$eq[[ 1 ]]$x ) ) 229s [1] TRUE 229s > print( all.equal( mm, model.matrix( fitols3 ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols3$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols3$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > 229s > # with x (returnModelMatrix) = FALSE 229s > print( all.equal( mm, model.matrix( fitols3r ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols3r$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols3r$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > print( !is.null( fitols3r$eq[[ 1 ]]$x ) ) 229s [1] FALSE 229s > 229s > # with x (returnModelMatrix) = TRUE 229s > print( !is.null( fitols4s$eq[[ 1 ]]$x ) ) 229s [1] TRUE 229s > print( all.equal( mm, model.matrix( fitols4s ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols4s$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols4s$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > 229s > # with x (returnModelMatrix) = FALSE 229s > print( all.equal( mm, model.matrix( fitols4Sym ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols4Sym$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols4Sym$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > print( !is.null( fitols4Sym$eq[[ 1 ]]$x ) ) 229s [1] FALSE 229s > 229s > # with x (returnModelMatrix) = TRUE 229s > print( !is.null( fitols5s$eq[[ 1 ]]$x ) ) 229s [1] TRUE 229s > print( all.equal( mm, model.matrix( fitols5s ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols5s$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols5s$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > 229s > # with x (returnModelMatrix) = FALSE 229s > print( all.equal( mm, model.matrix( fitols5 ) ) ) 229s [1] TRUE 229s > print( all.equal( mm1, model.matrix( fitols5$eq[[ 1 ]] ) ) ) 229s [1] TRUE 229s > print( all.equal( mm2, model.matrix( fitols5$eq[[ 2 ]] ) ) ) 229s [1] TRUE 229s > print( !is.null( fitols5$eq[[ 1 ]]$x ) ) 229s [1] FALSE 229s > 229s > try( model.matrix( fitols1, which = "z" ) ) 229s > Error in model.matrix.systemfit.equation(object$eq[[i]], which = which) : 229s argument 'which' can only be set to "xHat" or "z" if instruments were used 229s 229s > 229s > ## **************** formulas ************************ 229s > formula( fitols1 ) 229s $demand 229s consump ~ price + income 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s 229s > formula( fitols1$eq[[ 2 ]] ) 229s consump ~ price + farmPrice + trend 229s > 229s > formula( fitols2r ) 229s $demand 229s consump ~ price + income 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s 229s > formula( fitols2r$eq[[ 1 ]] ) 229s consump ~ price + income 229s > 229s > formula( fitols3s ) 229s $demand 229s consump ~ price + income 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s 229s > formula( fitols3s$eq[[ 2 ]] ) 229s consump ~ price + farmPrice + trend 229s > 229s > formula( fitols4rs ) 229s $demand 229s consump ~ price + income 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s 229s > formula( fitols4rs$eq[[ 1 ]] ) 229s consump ~ price + income 229s > 229s > formula( fitols5 ) 229s $demand 229s consump ~ price + income 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s 229s > formula( fitols5$eq[[ 2 ]] ) 229s consump ~ price + farmPrice + trend 229s > 229s > 229s > ## **************** model terms ******************* 229s > terms( fitols1 ) 229s $demand 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s 229s > terms( fitols1$eq[[ 2 ]] ) 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s > 229s > terms( fitols2r ) 229s $demand 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s 229s > terms( fitols2r$eq[[ 1 ]] ) 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s > 229s > terms( fitols3s ) 229s $demand 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s 229s > terms( fitols3s$eq[[ 2 ]] ) 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s > 229s > terms( fitols4rs ) 229s $demand 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s 229s > terms( fitols4rs$eq[[ 1 ]] ) 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s > 229s > terms( fitols5 ) 229s $demand 229s consump ~ price + income 229s attr(,"variables") 229s list(consump, price, income) 229s attr(,"factors") 229s price income 229s consump 0 0 229s price 1 0 229s income 0 1 229s attr(,"term.labels") 229s [1] "price" "income" 229s attr(,"order") 229s [1] 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, income) 229s attr(,"dataClasses") 229s consump price income 229s "numeric" "numeric" "numeric" 229s 229s $supply 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s 229s > terms( fitols5$eq[[ 2 ]] ) 229s consump ~ price + farmPrice + trend 229s attr(,"variables") 229s list(consump, price, farmPrice, trend) 229s attr(,"factors") 229s price farmPrice trend 229s consump 0 0 0 229s price 1 0 0 229s farmPrice 0 1 0 229s trend 0 0 1 229s attr(,"term.labels") 229s [1] "price" "farmPrice" "trend" 229s attr(,"order") 229s [1] 1 1 1 229s attr(,"intercept") 229s [1] 1 229s attr(,"response") 229s [1] 1 229s attr(,".Environment") 229s 229s attr(,"predvars") 229s list(consump, price, farmPrice, trend) 229s attr(,"dataClasses") 229s consump price farmPrice trend 229s "numeric" "numeric" "numeric" "numeric" 229s > 229s > 229s > ## **************** estfun ************************ 229s > library( "sandwich" ) 229s > 229s > estfun( fitols1 ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s demand_1 1.074 107.8 93.9 0.000 229s demand_2 -0.390 -40.7 -38.1 0.000 229s demand_3 2.625 271.5 253.8 0.000 229s demand_4 1.802 188.4 177.0 0.000 229s demand_5 1.946 190.7 194.2 0.000 229s demand_6 1.175 116.8 118.0 0.000 229s demand_7 1.530 154.7 157.9 0.000 229s demand_8 -2.933 -307.2 -316.1 0.000 229s demand_9 -1.365 -131.7 -131.9 0.000 229s demand_10 2.031 185.3 180.5 0.000 229s demand_11 -0.149 -13.9 -11.2 0.000 229s demand_12 -1.954 -193.1 -150.3 0.000 229s demand_13 -1.121 -115.4 -94.8 0.000 229s demand_14 -0.220 -21.7 -19.9 0.000 229s demand_15 1.487 141.4 153.3 0.000 229s demand_16 -3.701 -364.3 -388.9 0.000 229s demand_17 -1.273 -110.1 -122.7 0.000 229s demand_18 -2.002 -208.3 -209.0 0.000 229s demand_19 1.738 183.8 192.4 0.000 229s demand_20 -0.299 -33.9 -38.0 0.000 229s supply_1 0.000 0.0 0.0 -0.444 229s supply_2 0.000 0.0 0.0 -0.896 229s supply_3 0.000 0.0 0.0 1.965 229s supply_4 0.000 0.0 0.0 1.134 229s supply_5 0.000 0.0 0.0 1.514 229s supply_6 0.000 0.0 0.0 0.680 229s supply_7 0.000 0.0 0.0 1.569 229s supply_8 0.000 0.0 0.0 -4.407 229s supply_9 0.000 0.0 0.0 -2.599 229s supply_10 0.000 0.0 0.0 2.469 229s supply_11 0.000 0.0 0.0 -0.598 229s supply_12 0.000 0.0 0.0 -1.697 229s supply_13 0.000 0.0 0.0 -1.064 229s supply_14 0.000 0.0 0.0 0.970 229s supply_15 0.000 0.0 0.0 3.159 229s supply_16 0.000 0.0 0.0 -3.866 229s supply_17 0.000 0.0 0.0 -0.265 229s supply_18 0.000 0.0 0.0 -2.449 229s supply_19 0.000 0.0 0.0 3.110 229s supply_20 0.000 0.0 0.0 1.714 229s supply_price supply_farmPrice supply_trend 229s demand_1 0.0 0.0 0.000 229s demand_2 0.0 0.0 0.000 229s demand_3 0.0 0.0 0.000 229s demand_4 0.0 0.0 0.000 229s demand_5 0.0 0.0 0.000 229s demand_6 0.0 0.0 0.000 229s demand_7 0.0 0.0 0.000 229s demand_8 0.0 0.0 0.000 229s demand_9 0.0 0.0 0.000 229s demand_10 0.0 0.0 0.000 229s demand_11 0.0 0.0 0.000 229s demand_12 0.0 0.0 0.000 229s demand_13 0.0 0.0 0.000 229s demand_14 0.0 0.0 0.000 229s demand_15 0.0 0.0 0.000 229s demand_16 0.0 0.0 0.000 229s demand_17 0.0 0.0 0.000 229s demand_18 0.0 0.0 0.000 229s demand_19 0.0 0.0 0.000 229s demand_20 0.0 0.0 0.000 229s supply_1 -44.6 -43.5 -0.444 229s supply_2 -93.4 -88.7 -1.791 229s supply_3 203.3 194.7 5.895 229s supply_4 118.5 111.3 4.537 229s supply_5 148.4 167.7 7.569 229s supply_6 67.7 73.6 4.082 229s supply_7 158.6 165.7 10.983 229s supply_8 -461.7 -483.9 -35.259 229s supply_9 -250.7 -282.5 -23.391 229s supply_10 225.3 248.4 24.694 229s supply_11 -55.7 -48.5 -6.581 229s supply_12 -167.7 -116.4 -20.369 229s supply_13 -109.5 -75.4 -13.832 229s supply_14 95.8 79.0 13.582 229s supply_15 300.5 323.2 47.386 229s supply_16 -380.6 -405.9 -61.848 229s supply_17 -22.9 -29.2 -4.500 229s supply_18 -254.7 -226.5 -44.080 229s supply_19 328.9 277.7 59.084 229s supply_20 194.5 159.4 34.282 229s > round( colSums( estfun( fitols1 ) ), digits = 7 ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 0 0 0 0 229s supply_price supply_farmPrice supply_trend 229s 0 0 0 229s > 229s > estfun( fitols1s ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s demand_1 1.074 107.8 93.9 0.000 229s demand_2 -0.390 -40.7 -38.1 0.000 229s demand_3 2.625 271.5 253.8 0.000 229s demand_4 1.802 188.4 177.0 0.000 229s demand_5 1.946 190.7 194.2 0.000 229s demand_6 1.175 116.8 118.0 0.000 229s demand_7 1.530 154.7 157.9 0.000 229s demand_8 -2.933 -307.2 -316.1 0.000 229s demand_9 -1.365 -131.7 -131.9 0.000 229s demand_10 2.031 185.3 180.5 0.000 229s demand_11 -0.149 -13.9 -11.2 0.000 229s demand_12 -1.954 -193.1 -150.3 0.000 229s demand_13 -1.121 -115.4 -94.8 0.000 229s demand_14 -0.220 -21.7 -19.9 0.000 229s demand_15 1.487 141.4 153.3 0.000 229s demand_16 -3.701 -364.3 -388.9 0.000 229s demand_17 -1.273 -110.1 -122.7 0.000 229s demand_18 -2.002 -208.3 -209.0 0.000 229s demand_19 1.738 183.8 192.4 0.000 229s demand_20 -0.299 -33.9 -38.0 0.000 229s supply_1 0.000 0.0 0.0 -0.444 229s supply_2 0.000 0.0 0.0 -0.896 229s supply_3 0.000 0.0 0.0 1.965 229s supply_4 0.000 0.0 0.0 1.134 229s supply_5 0.000 0.0 0.0 1.514 229s supply_6 0.000 0.0 0.0 0.680 229s supply_7 0.000 0.0 0.0 1.569 229s supply_8 0.000 0.0 0.0 -4.407 229s supply_9 0.000 0.0 0.0 -2.599 229s supply_10 0.000 0.0 0.0 2.469 229s supply_11 0.000 0.0 0.0 -0.598 229s supply_12 0.000 0.0 0.0 -1.697 229s supply_13 0.000 0.0 0.0 -1.064 229s supply_14 0.000 0.0 0.0 0.970 229s supply_15 0.000 0.0 0.0 3.159 229s supply_16 0.000 0.0 0.0 -3.866 229s supply_17 0.000 0.0 0.0 -0.265 229s supply_18 0.000 0.0 0.0 -2.449 229s supply_19 0.000 0.0 0.0 3.110 229s supply_20 0.000 0.0 0.0 1.714 229s supply_price supply_farmPrice supply_trend 229s demand_1 0.0 0.0 0.000 229s demand_2 0.0 0.0 0.000 229s demand_3 0.0 0.0 0.000 229s demand_4 0.0 0.0 0.000 229s demand_5 0.0 0.0 0.000 229s demand_6 0.0 0.0 0.000 229s demand_7 0.0 0.0 0.000 229s demand_8 0.0 0.0 0.000 229s demand_9 0.0 0.0 0.000 229s demand_10 0.0 0.0 0.000 229s demand_11 0.0 0.0 0.000 229s demand_12 0.0 0.0 0.000 229s demand_13 0.0 0.0 0.000 229s demand_14 0.0 0.0 0.000 229s demand_15 0.0 0.0 0.000 229s demand_16 0.0 0.0 0.000 229s demand_17 0.0 0.0 0.000 229s demand_18 0.0 0.0 0.000 229s demand_19 0.0 0.0 0.000 229s demand_20 0.0 0.0 0.000 229s supply_1 -44.6 -43.5 -0.444 229s supply_2 -93.4 -88.7 -1.791 229s supply_3 203.3 194.7 5.895 229s supply_4 118.5 111.3 4.537 229s supply_5 148.4 167.7 7.569 229s supply_6 67.7 73.6 4.082 229s supply_7 158.6 165.7 10.983 229s supply_8 -461.7 -483.9 -35.259 229s supply_9 -250.7 -282.5 -23.391 229s supply_10 225.3 248.4 24.694 229s supply_11 -55.7 -48.5 -6.581 229s supply_12 -167.7 -116.4 -20.369 229s supply_13 -109.5 -75.4 -13.832 229s supply_14 95.8 79.0 13.582 229s supply_15 300.5 323.2 47.386 229s supply_16 -380.6 -405.9 -61.848 229s supply_17 -22.9 -29.2 -4.500 229s supply_18 -254.7 -226.5 -44.080 229s supply_19 328.9 277.7 59.084 229s supply_20 194.5 159.4 34.282 229s > round( colSums( estfun( fitols1s ) ), digits = 7 ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 0 0 0 0 229s supply_price supply_farmPrice supply_trend 229s 0 0 0 229s > 229s > estfun( fitols1r ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s demand_1 1.074 107.8 93.9 0.000 229s demand_2 -0.390 -40.7 -38.1 0.000 229s demand_3 2.625 271.5 253.8 0.000 229s demand_4 1.802 188.4 177.0 0.000 229s demand_5 1.946 190.7 194.2 0.000 229s demand_6 1.175 116.8 118.0 0.000 229s demand_7 1.530 154.7 157.9 0.000 229s demand_8 -2.933 -307.2 -316.1 0.000 229s demand_9 -1.365 -131.7 -131.9 0.000 229s demand_10 2.031 185.3 180.5 0.000 229s demand_11 -0.149 -13.9 -11.2 0.000 229s demand_12 -1.954 -193.1 -150.3 0.000 229s demand_13 -1.121 -115.4 -94.8 0.000 229s demand_14 -0.220 -21.7 -19.9 0.000 229s demand_15 1.487 141.4 153.3 0.000 229s demand_16 -3.701 -364.3 -388.9 0.000 229s demand_17 -1.273 -110.1 -122.7 0.000 229s demand_18 -2.002 -208.3 -209.0 0.000 229s demand_19 1.738 183.8 192.4 0.000 229s demand_20 -0.299 -33.9 -38.0 0.000 229s supply_1 0.000 0.0 0.0 -0.444 229s supply_2 0.000 0.0 0.0 -0.896 229s supply_3 0.000 0.0 0.0 1.965 229s supply_4 0.000 0.0 0.0 1.134 229s supply_5 0.000 0.0 0.0 1.514 229s supply_6 0.000 0.0 0.0 0.680 229s supply_7 0.000 0.0 0.0 1.569 229s supply_8 0.000 0.0 0.0 -4.407 229s supply_9 0.000 0.0 0.0 -2.599 229s supply_10 0.000 0.0 0.0 2.469 229s supply_11 0.000 0.0 0.0 -0.598 229s supply_12 0.000 0.0 0.0 -1.697 229s supply_13 0.000 0.0 0.0 -1.064 229s supply_14 0.000 0.0 0.0 0.970 229s supply_15 0.000 0.0 0.0 3.159 229s supply_16 0.000 0.0 0.0 -3.866 229s supply_17 0.000 0.0 0.0 -0.265 229s supply_18 0.000 0.0 0.0 -2.449 229s supply_19 0.000 0.0 0.0 3.110 229s supply_20 0.000 0.0 0.0 1.714 229s supply_price supply_farmPrice supply_trend 229s demand_1 0.0 0.0 0.000 229s demand_2 0.0 0.0 0.000 229s demand_3 0.0 0.0 0.000 229s demand_4 0.0 0.0 0.000 229s demand_5 0.0 0.0 0.000 229s demand_6 0.0 0.0 0.000 229s demand_7 0.0 0.0 0.000 229s demand_8 0.0 0.0 0.000 229s demand_9 0.0 0.0 0.000 229s demand_10 0.0 0.0 0.000 229s demand_11 0.0 0.0 0.000 229s demand_12 0.0 0.0 0.000 229s demand_13 0.0 0.0 0.000 229s demand_14 0.0 0.0 0.000 229s demand_15 0.0 0.0 0.000 229s demand_16 0.0 0.0 0.000 229s demand_17 0.0 0.0 0.000 229s demand_18 0.0 0.0 0.000 229s demand_19 0.0 0.0 0.000 229s demand_20 0.0 0.0 0.000 229s supply_1 -44.6 -43.5 -0.444 229s supply_2 -93.4 -88.7 -1.791 229s supply_3 203.3 194.7 5.895 229s supply_4 118.5 111.3 4.537 229s supply_5 148.4 167.7 7.569 229s supply_6 67.7 73.6 4.082 229s supply_7 158.6 165.7 10.983 229s supply_8 -461.7 -483.9 -35.259 229s supply_9 -250.7 -282.5 -23.391 229s supply_10 225.3 248.4 24.694 229s supply_11 -55.7 -48.5 -6.581 229s supply_12 -167.7 -116.4 -20.369 229s supply_13 -109.5 -75.4 -13.832 229s supply_14 95.8 79.0 13.582 229s supply_15 300.5 323.2 47.386 229s supply_16 -380.6 -405.9 -61.848 229s supply_17 -22.9 -29.2 -4.500 229s supply_18 -254.7 -226.5 -44.080 229s supply_19 328.9 277.7 59.084 229s supply_20 194.5 159.4 34.282 229s > round( colSums( estfun( fitols1r ) ), digits = 7 ) 229s demand_(Intercept) demand_price demand_income supply_(Intercept) 229s 0 0 0 0 229s supply_price supply_farmPrice supply_trend 229s 0 0 0 229s > 229s > try( estfun( fitols2 ) ) 229s > 229s > Error in estfun.systemfit(fitols2) : 229s returning the estimation function for models with restrictions has not yet been implemented. 229s try( estfun( fitols2Sym ) ) 229s Error in estfun.systemfit(fitols2Sym) : 229s returning the estimation function for models with restrictions has not yet been implemented. 229s > 229s > try( estfun( fitols3s ) ) 229s Error in estfun.systemfit(fitols3s) : 229s returning the estimation function for models with restrictions has not yet been implemented. 229s > 229s > try( estfun( fitols4r ) ) 229s Error in estfun.systemfit(fitols4r) : 229s returning the estimation function for models with restrictions has not yet been implemented. 229s > 229s > try( estfun( fitols4Sym ) ) 229s Error in estfun.systemfit(fitols4Sym) : 229s returning the estimation function for models with restrictions has not yet been implemented. 229s > 229s > try( estfun( fitols5 ) ) 229s > 229s > try( estfun( fitols5Sym ) ) 229s Error in estfun.systemfit(fitols5) : 229s returning the estimation function for models with restrictions has not yet been implemented. 229s Error in estfun.systemfit(fitols5Sym) : 229s returning the estimation function for models with restrictions has not yet been implemented. 229s > 229s > 229s > ## **************** bread ************************ 229s > bread( fitols1 ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 607.086 -6.3865 0.3453 229s demand_price -6.386 0.0883 -0.0251 229s demand_income 0.345 -0.0251 0.0222 229s supply_(Intercept) 0.000 0.0000 0.0000 229s supply_price 0.000 0.0000 0.0000 229s supply_farmPrice 0.000 0.0000 0.0000 229s supply_trend 0.000 0.0000 0.0000 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) 0.00 0.00000 0.00000 229s demand_price 0.00 0.00000 0.00000 229s demand_income 0.00 0.00000 0.00000 229s supply_(Intercept) 908.63 -6.82866 -2.10469 229s supply_price -6.83 0.06226 0.00584 229s supply_farmPrice -2.10 0.00584 0.01475 229s supply_trend -1.93 0.00361 0.00910 229s supply_trend 229s demand_(Intercept) 0.00000 229s demand_price 0.00000 229s demand_income 0.00000 229s supply_(Intercept) -1.93058 229s supply_price 0.00361 229s supply_farmPrice 0.00910 229s supply_trend 0.06576 229s > 229s > bread( fitols1s ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 607.086 -6.3865 0.3453 229s demand_price -6.386 0.0883 -0.0251 229s demand_income 0.345 -0.0251 0.0222 229s supply_(Intercept) 0.000 0.0000 0.0000 229s supply_price 0.000 0.0000 0.0000 229s supply_farmPrice 0.000 0.0000 0.0000 229s supply_trend 0.000 0.0000 0.0000 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) 0.00 0.00000 0.00000 229s demand_price 0.00 0.00000 0.00000 229s demand_income 0.00 0.00000 0.00000 229s supply_(Intercept) 908.63 -6.82866 -2.10469 229s supply_price -6.83 0.06226 0.00584 229s supply_farmPrice -2.10 0.00584 0.01475 229s supply_trend -1.93 0.00361 0.00910 229s supply_trend 229s demand_(Intercept) 0.00000 229s demand_price 0.00000 229s demand_income 0.00000 229s supply_(Intercept) -1.93058 229s supply_price 0.00361 229s supply_farmPrice 0.00910 229s supply_trend 0.06576 229s > 229s > bread( fitols1r ) 229s demand_(Intercept) demand_price demand_income 229s demand_(Intercept) 607.086 -6.3865 0.3453 229s demand_price -6.386 0.0883 -0.0251 229s demand_income 0.345 -0.0251 0.0222 229s supply_(Intercept) 0.000 0.0000 0.0000 229s supply_price 0.000 0.0000 0.0000 229s supply_farmPrice 0.000 0.0000 0.0000 229s supply_trend 0.000 0.0000 0.0000 229s supply_(Intercept) supply_price supply_farmPrice 229s demand_(Intercept) 0.00 0.00000 0.00000 229s demand_price 0.00 0.00000 0.00000 229s demand_income 0.00 0.00000 0.00000 229s supply_(Intercept) 908.63 -6.82866 -2.10469 229s supply_price -6.83 0.06226 0.00584 229s supply_farmPrice -2.10 0.00584 0.01475 229s supply_trend -1.93 0.00361 0.00910 229s supply_trend 229s demand_(Intercept) 0.00000 229s demand_price 0.00000 229s demand_income 0.00000 229s supply_(Intercept) -1.93058 229s supply_price 0.00361 229s supply_farmPrice 0.00910 229s supply_trend 0.06576 229s > 229s > try( bread( fitols2 ) ) 229s > 229s Error in bread.systemfit(fitols2) : 229s returning the 'bread' for models with restrictions has not yet been implemented. 229s BEGIN TEST test_panel.R 229s 229s R version 4.3.2 (2023-10-31) -- "Eye Holes" 229s Copyright (C) 2023 The R Foundation for Statistical Computing 229s Platform: aarch64-unknown-linux-gnu (64-bit) 229s 229s R is free software and comes with ABSOLUTELY NO WARRANTY. 229s You are welcome to redistribute it under certain conditions. 229s Type 'license()' or 'licence()' for distribution details. 229s 229s R is a collaborative project with many contributors. 229s Type 'contributors()' for more information and 229s 'citation()' on how to cite R or R packages in publications. 229s 229s Type 'demo()' for some demos, 'help()' for on-line help, or 229s 'help.start()' for an HTML browser interface to help. 229s Type 'q()' to quit R. 229s 229s > library( systemfit ) 230s Loading required package: Matrix 230s Loading required package: car 230s Loading required package: carData 230s Loading required package: lmtest 230s Loading required package: zoo 230s 230s Attaching package: ‘zoo’ 230s 230s The following objects are masked from ‘package:base’: 230s 230s as.Date, as.Date.numeric 230s 230s 230s Please cite the 'systemfit' package as: 230s 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/. 230s 230s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 230s https://r-forge.r-project.org/projects/systemfit/ 230s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 230s + library( plm ) 230s + options( digits = 3 ) 230s + useMatrix <- FALSE 230s + } 231s > 231s > ## Repeating the OLS and SUR estimations in Theil (1971, pp. 295, 300) 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + data( "GrunfeldGreene" ) 231s + GrunfeldTheil <- subset( GrunfeldGreene, 231s + firm %in% c( "General Electric", "Westinghouse" ) ) 231s + GrunfeldTheil <- pdata.frame( GrunfeldTheil, c( "firm", "year" ) ) 231s + formulaGrunfeld <- invest ~ value + capital 231s + } 231s > 231s > # OLS 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + theilOls <- systemfit( formulaGrunfeld, "OLS", 231s + data = GrunfeldTheil, useMatrix = useMatrix ) 231s + print( theilOls ) 231s + print( summary( theilOls ) ) 231s + print( summary( theilOls, useDfSys = TRUE, residCov = FALSE, 231s + equations = FALSE ) ) 231s + print( summary( theilOls, equations = FALSE ) ) 231s + print( coef( theilOls ) ) 231s + print( coef( summary(theilOls ) ) ) 231s + print( vcov( theilOls ) ) 231s + print( residuals( theilOls ) ) 231s + print( confint( theilOls ) ) 231s + print( fitted(theilOls ) ) 231s + print( logLik( theilOls ) ) 231s + print( logLik( theilOls, residCovDiag = TRUE ) ) 231s + print( nobs( theilOls ) ) 231s + print( model.frame( theilOls ) ) 231s + print( model.matrix( theilOls ) ) 231s + print( formula( theilOls ) ) 231s + print( formula( theilOls$eq[[ 1 ]] ) ) 231s + print( terms( theilOls ) ) 231s + print( terms( theilOls$eq[[ 1 ]] ) ) 231s + } 231s 231s systemfit results 231s method: OLS 231s 231s Coefficients: 231s General.Electric_(Intercept) General.Electric_value 231s -9.9563 0.0266 231s General.Electric_capital Westinghouse_(Intercept) 231s 0.1517 -0.5094 231s Westinghouse_value Westinghouse_capital 231s 0.0529 0.0924 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 40 34 14990 38001 0.711 0.618 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s General.Electric 20 17 13217 777 27.9 0.705 0.671 231s Westinghouse 20 17 1773 104 10.2 0.744 0.714 231s 231s The covariance matrix of the residuals 231s General.Electric Westinghouse 231s General.Electric 777 208 231s Westinghouse 208 104 231s 231s The correlations of the residuals 231s General.Electric Westinghouse 231s General.Electric 1.000 0.729 231s Westinghouse 0.729 1.000 231s 231s 231s OLS estimates for 'General.Electric' (equation 1) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -9.9563 31.3742 -0.32 0.75 231s value 0.0266 0.0156 1.71 0.11 231s capital 0.1517 0.0257 5.90 1.7e-05 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 27.883 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 231s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 231s 231s 231s OLS estimates for 'Westinghouse' (equation 2) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -0.5094 8.0153 -0.06 0.9501 231s value 0.0529 0.0157 3.37 0.0037 ** 231s capital 0.0924 0.0561 1.65 0.1179 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 10.213 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 231s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 231s 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 40 34 14990 38001 0.711 0.618 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s General.Electric 20 17 13217 777 27.9 0.705 0.671 231s Westinghouse 20 17 1773 104 10.2 0.744 0.714 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.7529 231s General.Electric_value 0.0266 0.0156 1.71 0.0972 . 231s General.Electric_capital 0.1517 0.0257 5.90 1.2e-06 *** 231s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.9497 231s Westinghouse_value 0.0529 0.0157 3.37 0.0019 ** 231s Westinghouse_capital 0.0924 0.0561 1.65 0.1087 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 40 34 14990 38001 0.711 0.618 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s General.Electric 20 17 13217 777 27.9 0.705 0.671 231s Westinghouse 20 17 1773 104 10.2 0.744 0.714 231s 231s The covariance matrix of the residuals 231s General.Electric Westinghouse 231s General.Electric 777 208 231s Westinghouse 208 104 231s 231s The correlations of the residuals 231s General.Electric Westinghouse 231s General.Electric 1.000 0.729 231s Westinghouse 0.729 1.000 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.7548 231s General.Electric_value 0.0266 0.0156 1.71 0.1063 231s General.Electric_capital 0.1517 0.0257 5.90 1.7e-05 *** 231s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.9501 231s Westinghouse_value 0.0529 0.0157 3.37 0.0037 ** 231s Westinghouse_capital 0.0924 0.0561 1.65 0.1179 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s General.Electric_(Intercept) General.Electric_value 231s -9.9563 0.0266 231s General.Electric_capital Westinghouse_(Intercept) 231s 0.1517 -0.5094 231s Westinghouse_value Westinghouse_capital 231s 0.0529 0.0924 231s Estimate Std. Error t value Pr(>|t|) 231s General.Electric_(Intercept) -9.9563 31.3742 -0.3173 7.55e-01 231s General.Electric_value 0.0266 0.0156 1.7057 1.06e-01 231s General.Electric_capital 0.1517 0.0257 5.9015 1.74e-05 231s Westinghouse_(Intercept) -0.5094 8.0153 -0.0636 9.50e-01 231s Westinghouse_value 0.0529 0.0157 3.3677 3.65e-03 231s Westinghouse_capital 0.0924 0.0561 1.6472 1.18e-01 231s General.Electric_(Intercept) 231s General.Electric_(Intercept) 984.344 231s General.Electric_value -0.451 231s General.Electric_capital -0.173 231s Westinghouse_(Intercept) 0.000 231s Westinghouse_value 0.000 231s Westinghouse_capital 0.000 231s General.Electric_value General.Electric_capital 231s General.Electric_(Intercept) -4.51e-01 -1.73e-01 231s General.Electric_value 2.42e-04 -4.73e-05 231s General.Electric_capital -4.73e-05 6.61e-04 231s Westinghouse_(Intercept) 0.00e+00 0.00e+00 231s Westinghouse_value 0.00e+00 0.00e+00 231s Westinghouse_capital 0.00e+00 0.00e+00 231s Westinghouse_(Intercept) Westinghouse_value 231s General.Electric_(Intercept) 0.000 0.000000 231s General.Electric_value 0.000 0.000000 231s General.Electric_capital 0.000 0.000000 231s Westinghouse_(Intercept) 64.245 -0.109545 231s Westinghouse_value -0.110 0.000247 231s Westinghouse_capital 0.169 -0.000653 231s Westinghouse_capital 231s General.Electric_(Intercept) 0.000000 231s General.Electric_value 0.000000 231s General.Electric_capital 0.000000 231s Westinghouse_(Intercept) 0.168911 231s Westinghouse_value -0.000653 231s Westinghouse_capital 0.003147 231s General.Electric Westinghouse 231s X1935 -2.860 3.144 231s X1936 -14.402 -0.958 231s X1937 -5.175 -3.684 231s X1938 -23.295 -7.915 231s X1939 -28.031 -10.322 231s X1940 -0.562 -6.613 231s X1941 40.750 17.265 231s X1942 16.036 8.547 231s X1943 -23.719 -2.916 231s X1944 -26.780 -3.257 231s X1945 1.768 -7.753 231s X1946 58.737 5.796 231s X1947 43.936 15.050 231s X1948 31.227 2.969 231s X1949 -23.552 -11.433 231s X1950 -37.511 -13.481 231s X1951 -4.983 4.619 231s X1952 1.893 13.138 231s X1953 5.087 11.308 231s X1954 -8.563 -13.505 231s 2.5 % 97.5 % 231s General.Electric_(Intercept) -76.150 56.238 231s General.Electric_value -0.006 0.059 231s General.Electric_capital 0.097 0.206 231s Westinghouse_(Intercept) -17.420 16.401 231s Westinghouse_value 0.020 0.086 231s Westinghouse_capital -0.026 0.211 231s General.Electric Westinghouse 231s X1935 36.0 9.79 231s X1936 59.4 26.86 231s X1937 82.4 38.73 231s X1938 67.9 30.81 231s X1939 76.1 29.16 231s X1940 75.0 35.18 231s X1941 72.3 31.25 231s X1942 75.9 34.79 231s X1943 85.0 39.94 231s X1944 83.6 41.07 231s X1945 91.8 47.02 231s X1946 101.2 47.66 231s X1947 103.3 40.51 231s X1948 115.1 46.59 231s X1949 121.9 43.47 231s X1950 131.0 45.72 231s X1951 140.2 49.76 231s X1952 155.4 58.64 231s X1953 174.4 78.77 231s X1954 198.2 82.11 231s 'log Lik.' -159 (df=7) 231s 'log Lik.' -167 (df=7) 231s [1] 40 231s General.Electric_invest General.Electric_value General.Electric_capital 231s X1935 33.1 1171 97.8 231s X1936 45.0 2016 104.4 231s X1937 77.2 2803 118.0 231s X1938 44.6 2040 156.2 231s X1939 48.1 2256 172.6 231s X1940 74.4 2132 186.6 231s X1941 113.0 1834 220.9 231s X1942 91.9 1588 287.8 231s X1943 61.3 1749 319.9 231s X1944 56.8 1687 321.3 231s X1945 93.6 2008 319.6 231s X1946 159.9 2208 346.0 231s X1947 147.2 1657 456.4 231s X1948 146.3 1604 543.4 231s X1949 98.3 1432 618.3 231s X1950 93.5 1610 647.4 231s X1951 135.2 1819 671.3 231s X1952 157.3 2080 726.1 231s X1953 179.5 2372 800.3 231s X1954 189.6 2760 888.9 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s X1935 12.9 192 1.8 231s X1936 25.9 516 0.8 231s X1937 35.0 729 7.4 231s X1938 22.9 560 18.1 231s X1939 18.8 520 23.5 231s X1940 28.6 628 26.5 231s X1941 48.5 537 36.2 231s X1942 43.3 561 60.8 231s X1943 37.0 617 84.4 231s X1944 37.8 627 91.2 231s X1945 39.3 737 92.4 231s X1946 53.5 760 86.0 231s X1947 55.6 581 111.1 231s X1948 49.6 662 130.6 231s X1949 32.0 584 141.8 231s X1950 32.2 635 136.7 231s X1951 54.4 724 129.7 231s X1952 71.8 864 145.5 231s X1953 90.1 1194 174.8 231s X1954 68.6 1189 213.5 231s General.Electric_(Intercept) General.Electric_value 231s General.Electric_X1935 1 1171 231s General.Electric_X1936 1 2016 231s General.Electric_X1937 1 2803 231s General.Electric_X1938 1 2040 231s General.Electric_X1939 1 2256 231s General.Electric_X1940 1 2132 231s General.Electric_X1941 1 1834 231s General.Electric_X1942 1 1588 231s General.Electric_X1943 1 1749 231s General.Electric_X1944 1 1687 231s General.Electric_X1945 1 2008 231s General.Electric_X1946 1 2208 231s General.Electric_X1947 1 1657 231s General.Electric_X1948 1 1604 231s General.Electric_X1949 1 1432 231s General.Electric_X1950 1 1610 231s General.Electric_X1951 1 1819 231s General.Electric_X1952 1 2080 231s General.Electric_X1953 1 2372 231s General.Electric_X1954 1 2760 231s Westinghouse_X1935 0 0 231s Westinghouse_X1936 0 0 231s Westinghouse_X1937 0 0 231s Westinghouse_X1938 0 0 231s Westinghouse_X1939 0 0 231s Westinghouse_X1940 0 0 231s Westinghouse_X1941 0 0 231s Westinghouse_X1942 0 0 231s Westinghouse_X1943 0 0 231s Westinghouse_X1944 0 0 231s Westinghouse_X1945 0 0 231s Westinghouse_X1946 0 0 231s Westinghouse_X1947 0 0 231s Westinghouse_X1948 0 0 231s Westinghouse_X1949 0 0 231s Westinghouse_X1950 0 0 231s Westinghouse_X1951 0 0 231s Westinghouse_X1952 0 0 231s Westinghouse_X1953 0 0 231s Westinghouse_X1954 0 0 231s General.Electric_capital Westinghouse_(Intercept) 231s General.Electric_X1935 97.8 0 231s General.Electric_X1936 104.4 0 231s General.Electric_X1937 118.0 0 231s General.Electric_X1938 156.2 0 231s General.Electric_X1939 172.6 0 231s General.Electric_X1940 186.6 0 231s General.Electric_X1941 220.9 0 231s General.Electric_X1942 287.8 0 231s General.Electric_X1943 319.9 0 231s General.Electric_X1944 321.3 0 231s General.Electric_X1945 319.6 0 231s General.Electric_X1946 346.0 0 231s General.Electric_X1947 456.4 0 231s General.Electric_X1948 543.4 0 231s General.Electric_X1949 618.3 0 231s General.Electric_X1950 647.4 0 231s General.Electric_X1951 671.3 0 231s General.Electric_X1952 726.1 0 231s General.Electric_X1953 800.3 0 231s General.Electric_X1954 888.9 0 231s Westinghouse_X1935 0.0 1 231s Westinghouse_X1936 0.0 1 231s Westinghouse_X1937 0.0 1 231s Westinghouse_X1938 0.0 1 231s Westinghouse_X1939 0.0 1 231s Westinghouse_X1940 0.0 1 231s Westinghouse_X1941 0.0 1 231s Westinghouse_X1942 0.0 1 231s Westinghouse_X1943 0.0 1 231s Westinghouse_X1944 0.0 1 231s Westinghouse_X1945 0.0 1 231s Westinghouse_X1946 0.0 1 231s Westinghouse_X1947 0.0 1 231s Westinghouse_X1948 0.0 1 231s Westinghouse_X1949 0.0 1 231s Westinghouse_X1950 0.0 1 231s Westinghouse_X1951 0.0 1 231s Westinghouse_X1952 0.0 1 231s Westinghouse_X1953 0.0 1 231s Westinghouse_X1954 0.0 1 231s Westinghouse_value Westinghouse_capital 231s General.Electric_X1935 0 0.0 231s General.Electric_X1936 0 0.0 231s General.Electric_X1937 0 0.0 231s General.Electric_X1938 0 0.0 231s General.Electric_X1939 0 0.0 231s General.Electric_X1940 0 0.0 231s General.Electric_X1941 0 0.0 231s General.Electric_X1942 0 0.0 231s General.Electric_X1943 0 0.0 231s General.Electric_X1944 0 0.0 231s General.Electric_X1945 0 0.0 231s General.Electric_X1946 0 0.0 231s General.Electric_X1947 0 0.0 231s General.Electric_X1948 0 0.0 231s General.Electric_X1949 0 0.0 231s General.Electric_X1950 0 0.0 231s General.Electric_X1951 0 0.0 231s General.Electric_X1952 0 0.0 231s General.Electric_X1953 0 0.0 231s General.Electric_X1954 0 0.0 231s Westinghouse_X1935 192 1.8 231s Westinghouse_X1936 516 0.8 231s Westinghouse_X1937 729 7.4 231s Westinghouse_X1938 560 18.1 231s Westinghouse_X1939 520 23.5 231s Westinghouse_X1940 628 26.5 231s Westinghouse_X1941 537 36.2 231s Westinghouse_X1942 561 60.8 231s Westinghouse_X1943 617 84.4 231s Westinghouse_X1944 627 91.2 231s Westinghouse_X1945 737 92.4 231s Westinghouse_X1946 760 86.0 231s Westinghouse_X1947 581 111.1 231s Westinghouse_X1948 662 130.6 231s Westinghouse_X1949 584 141.8 231s Westinghouse_X1950 635 136.7 231s Westinghouse_X1951 724 129.7 231s Westinghouse_X1952 864 145.5 231s Westinghouse_X1953 1194 174.8 231s Westinghouse_X1954 1189 213.5 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s attr(,"variables") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"factors") 231s Westinghouse_value Westinghouse_capital 231s Westinghouse_invest 0 0 231s Westinghouse_value 1 0 231s Westinghouse_capital 0 1 231s attr(,"term.labels") 231s [1] "Westinghouse_value" "Westinghouse_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"dataClasses") 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s "numeric" "numeric" "numeric" 231s 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s > 231s > # SUR 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + theilSur <- systemfit( formulaGrunfeld, "SUR", 231s + data = GrunfeldTheil, methodResidCov = "noDfCor", useMatrix = useMatrix ) 231s + print( theilSur ) 231s + print( summary( theilSur ) ) 231s + print( summary( theilSur, useDfSys = TRUE, equations = FALSE ) ) 231s + print( summary( theilSur, residCov = FALSE, equations = FALSE ) ) 231s + print( coef( theilSur ) ) 231s + print( coef( summary( theilSur ) ) ) 231s + print( vcov( theilSur ) ) 231s + print( residuals( theilSur ) ) 231s + print( confint( theilSur ) ) 231s + print( fitted( theilSur ) ) 231s + print( logLik( theilSur ) ) 231s + print( logLik( theilSur, residCovDiag = TRUE ) ) 231s + print( nobs( theilSur ) ) 231s + print( model.frame( theilSur ) ) 231s + print( model.matrix( theilSur ) ) 231s + print( formula( theilSur ) ) 231s + print( formula( theilSur$eq[[ 2 ]] ) ) 231s + print( terms( theilSur ) ) 231s + print( terms( theilSur$eq[[ 2 ]] ) ) 231s + } 231s 231s systemfit results 231s method: SUR 231s 231s Coefficients: 231s General.Electric_(Intercept) General.Electric_value 231s -27.7193 0.0383 231s General.Electric_capital Westinghouse_(Intercept) 231s 0.1390 -1.2520 231s Westinghouse_value Westinghouse_capital 231s 0.0576 0.0640 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 40 34 15590 25750 0.699 0.615 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s General.Electric 20 17 13788 811 28.5 0.693 0.656 231s Westinghouse 20 17 1801 106 10.3 0.740 0.710 231s 231s The covariance matrix of the residuals used for estimation 231s General.Electric Westinghouse 231s General.Electric 661 176.4 231s Westinghouse 176 88.7 231s 231s The covariance matrix of the residuals 231s General.Electric Westinghouse 231s General.Electric 689 190.6 231s Westinghouse 191 90.1 231s 231s The correlations of the residuals 231s General.Electric Westinghouse 231s General.Electric 1.000 0.765 231s Westinghouse 0.765 1.000 231s 231s 231s SUR estimates for 'General.Electric' (equation 1) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -27.7193 27.0328 -1.03 0.32 231s value 0.0383 0.0133 2.88 0.01 * 231s capital 0.1390 0.0230 6.04 1.3e-05 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 28.479 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 13788.376 MSE: 811.081 Root MSE: 28.479 231s Multiple R-Squared: 0.693 Adjusted R-Squared: 0.656 231s 231s 231s SUR estimates for 'Westinghouse' (equation 2) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -1.2520 6.9563 -0.18 0.85930 231s value 0.0576 0.0134 4.30 0.00049 *** 231s capital 0.0640 0.0489 1.31 0.20818 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 10.294 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 1801.301 MSE: 105.959 Root MSE: 10.294 231s Multiple R-Squared: 0.74 Adjusted R-Squared: 0.71 231s 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 40 34 15590 25750 0.699 0.615 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s General.Electric 20 17 13788 811 28.5 0.693 0.656 231s Westinghouse 20 17 1801 106 10.3 0.740 0.710 231s 231s The covariance matrix of the residuals used for estimation 231s General.Electric Westinghouse 231s General.Electric 661 176.4 231s Westinghouse 176 88.7 231s 231s The covariance matrix of the residuals 231s General.Electric Westinghouse 231s General.Electric 689 190.6 231s Westinghouse 191 90.1 231s 231s The correlations of the residuals 231s General.Electric Westinghouse 231s General.Electric 1.000 0.765 231s Westinghouse 0.765 1.000 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s General.Electric_(Intercept) -27.7193 27.0328 -1.03 0.31242 231s General.Electric_value 0.0383 0.0133 2.88 0.00679 ** 231s General.Electric_capital 0.1390 0.0230 6.04 7.7e-07 *** 231s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 0.85824 231s Westinghouse_value 0.0576 0.0134 4.30 0.00014 *** 231s Westinghouse_capital 0.0640 0.0489 1.31 0.19954 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 40 34 15590 25750 0.699 0.615 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s General.Electric 20 17 13788 811 28.5 0.693 0.656 231s Westinghouse 20 17 1801 106 10.3 0.740 0.710 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s General.Electric_(Intercept) -27.7193 27.0328 -1.03 0.31955 231s General.Electric_value 0.0383 0.0133 2.88 0.01034 * 231s General.Electric_capital 0.1390 0.0230 6.04 1.3e-05 *** 231s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 0.85930 231s Westinghouse_value 0.0576 0.0134 4.30 0.00049 *** 231s Westinghouse_capital 0.0640 0.0489 1.31 0.20818 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s General.Electric_(Intercept) General.Electric_value 231s -27.7193 0.0383 231s General.Electric_capital Westinghouse_(Intercept) 231s 0.1390 -1.2520 231s Westinghouse_value Westinghouse_capital 231s 0.0576 0.0640 231s Estimate Std. Error t value Pr(>|t|) 231s General.Electric_(Intercept) -27.7193 27.0328 -1.03 3.20e-01 231s General.Electric_value 0.0383 0.0133 2.88 1.03e-02 231s General.Electric_capital 0.1390 0.0230 6.04 1.34e-05 231s Westinghouse_(Intercept) -1.2520 6.9563 -0.18 8.59e-01 231s Westinghouse_value 0.0576 0.0134 4.30 4.88e-04 231s Westinghouse_capital 0.0640 0.0489 1.31 2.08e-01 231s General.Electric_(Intercept) 231s General.Electric_(Intercept) 730.774 231s General.Electric_value -0.329 231s General.Electric_capital -0.146 231s Westinghouse_(Intercept) 126.963 231s Westinghouse_value -0.226 231s Westinghouse_capital 0.393 231s General.Electric_value General.Electric_capital 231s General.Electric_(Intercept) -0.329266 -1.46e-01 231s General.Electric_value 0.000177 -3.40e-05 231s General.Electric_capital -0.000034 5.31e-04 231s Westinghouse_(Intercept) -0.052688 -3.96e-02 231s Westinghouse_value 0.000120 -1.69e-05 231s Westinghouse_capital -0.000325 5.95e-04 231s Westinghouse_(Intercept) Westinghouse_value 231s General.Electric_(Intercept) 126.9626 -2.26e-01 231s General.Electric_value -0.0527 1.20e-04 231s General.Electric_capital -0.0396 -1.69e-05 231s Westinghouse_(Intercept) 48.3908 -8.00e-02 231s Westinghouse_value -0.0800 1.80e-04 231s Westinghouse_capital 0.1136 -4.75e-04 231s Westinghouse_capital 231s General.Electric_(Intercept) 0.392515 231s General.Electric_value -0.000325 231s General.Electric_capital 0.000595 231s Westinghouse_(Intercept) 0.113618 231s Westinghouse_value -0.000475 231s Westinghouse_capital 0.002391 231s General.Electric Westinghouse 231s X1935 2.3756 3.03 231s X1936 -19.0218 -2.64 231s X1937 -18.8820 -6.18 231s X1938 -27.5395 -9.31 231s X1939 -34.6138 -11.37 231s X1940 -5.5099 -8.09 231s X1941 39.7415 16.49 231s X1942 18.7681 8.36 231s X1943 -22.4783 -2.70 231s X1944 -24.7900 -2.89 231s X1945 -0.0321 -7.87 231s X1946 54.9123 5.38 231s X1947 47.9946 16.20 231s X1948 37.0021 4.29 231s X1949 -14.7994 -9.42 231s X1950 -30.4914 -11.86 231s X1951 -0.1173 5.62 231s X1952 4.3913 13.93 231s X1953 5.0921 11.37 231s X1954 -12.0024 -12.32 231s 2.5 % 97.5 % 231s General.Electric_(Intercept) -84.754 29.315 231s General.Electric_value 0.010 0.066 231s General.Electric_capital 0.090 0.188 231s Westinghouse_(Intercept) -15.929 13.425 231s Westinghouse_value 0.029 0.086 231s Westinghouse_capital -0.039 0.167 231s General.Electric Westinghouse 231s X1935 30.7 9.9 231s X1936 64.0 28.5 231s X1937 96.1 41.2 231s X1938 72.1 32.2 231s X1939 82.7 30.2 231s X1940 79.9 36.7 231s X1941 73.3 32.0 231s X1942 73.1 35.0 231s X1943 83.8 39.7 231s X1944 81.6 40.7 231s X1945 93.6 47.1 231s X1946 105.0 48.1 231s X1947 99.2 39.4 231s X1948 109.3 45.3 231s X1949 113.1 41.5 231s X1950 124.0 44.1 231s X1951 135.3 48.8 231s X1952 152.9 57.9 231s X1953 174.4 78.7 231s X1954 201.6 80.9 231s 'log Lik.' -158 (df=9) 231s 'log Lik.' -167 (df=9) 231s [1] 40 231s General.Electric_invest General.Electric_value General.Electric_capital 231s X1935 33.1 1171 97.8 231s X1936 45.0 2016 104.4 231s X1937 77.2 2803 118.0 231s X1938 44.6 2040 156.2 231s X1939 48.1 2256 172.6 231s X1940 74.4 2132 186.6 231s X1941 113.0 1834 220.9 231s X1942 91.9 1588 287.8 231s X1943 61.3 1749 319.9 231s X1944 56.8 1687 321.3 231s X1945 93.6 2008 319.6 231s X1946 159.9 2208 346.0 231s X1947 147.2 1657 456.4 231s X1948 146.3 1604 543.4 231s X1949 98.3 1432 618.3 231s X1950 93.5 1610 647.4 231s X1951 135.2 1819 671.3 231s X1952 157.3 2080 726.1 231s X1953 179.5 2372 800.3 231s X1954 189.6 2760 888.9 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s X1935 12.9 192 1.8 231s X1936 25.9 516 0.8 231s X1937 35.0 729 7.4 231s X1938 22.9 560 18.1 231s X1939 18.8 520 23.5 231s X1940 28.6 628 26.5 231s X1941 48.5 537 36.2 231s X1942 43.3 561 60.8 231s X1943 37.0 617 84.4 231s X1944 37.8 627 91.2 231s X1945 39.3 737 92.4 231s X1946 53.5 760 86.0 231s X1947 55.6 581 111.1 231s X1948 49.6 662 130.6 231s X1949 32.0 584 141.8 231s X1950 32.2 635 136.7 231s X1951 54.4 724 129.7 231s X1952 71.8 864 145.5 231s X1953 90.1 1194 174.8 231s X1954 68.6 1189 213.5 231s General.Electric_(Intercept) General.Electric_value 231s General.Electric_X1935 1 1171 231s General.Electric_X1936 1 2016 231s General.Electric_X1937 1 2803 231s General.Electric_X1938 1 2040 231s General.Electric_X1939 1 2256 231s General.Electric_X1940 1 2132 231s General.Electric_X1941 1 1834 231s General.Electric_X1942 1 1588 231s General.Electric_X1943 1 1749 231s General.Electric_X1944 1 1687 231s General.Electric_X1945 1 2008 231s General.Electric_X1946 1 2208 231s General.Electric_X1947 1 1657 231s General.Electric_X1948 1 1604 231s General.Electric_X1949 1 1432 231s General.Electric_X1950 1 1610 231s General.Electric_X1951 1 1819 231s General.Electric_X1952 1 2080 231s General.Electric_X1953 1 2372 231s General.Electric_X1954 1 2760 231s Westinghouse_X1935 0 0 231s Westinghouse_X1936 0 0 231s Westinghouse_X1937 0 0 231s Westinghouse_X1938 0 0 231s Westinghouse_X1939 0 0 231s Westinghouse_X1940 0 0 231s Westinghouse_X1941 0 0 231s Westinghouse_X1942 0 0 231s Westinghouse_X1943 0 0 231s Westinghouse_X1944 0 0 231s Westinghouse_X1945 0 0 231s Westinghouse_X1946 0 0 231s Westinghouse_X1947 0 0 231s Westinghouse_X1948 0 0 231s Westinghouse_X1949 0 0 231s Westinghouse_X1950 0 0 231s Westinghouse_X1951 0 0 231s Westinghouse_X1952 0 0 231s Westinghouse_X1953 0 0 231s Westinghouse_X1954 0 0 231s General.Electric_capital Westinghouse_(Intercept) 231s General.Electric_X1935 97.8 0 231s General.Electric_X1936 104.4 0 231s General.Electric_X1937 118.0 0 231s General.Electric_X1938 156.2 0 231s General.Electric_X1939 172.6 0 231s General.Electric_X1940 186.6 0 231s General.Electric_X1941 220.9 0 231s General.Electric_X1942 287.8 0 231s General.Electric_X1943 319.9 0 231s General.Electric_X1944 321.3 0 231s General.Electric_X1945 319.6 0 231s General.Electric_X1946 346.0 0 231s General.Electric_X1947 456.4 0 231s General.Electric_X1948 543.4 0 231s General.Electric_X1949 618.3 0 231s General.Electric_X1950 647.4 0 231s General.Electric_X1951 671.3 0 231s General.Electric_X1952 726.1 0 231s General.Electric_X1953 800.3 0 231s General.Electric_X1954 888.9 0 231s Westinghouse_X1935 0.0 1 231s Westinghouse_X1936 0.0 1 231s Westinghouse_X1937 0.0 1 231s Westinghouse_X1938 0.0 1 231s Westinghouse_X1939 0.0 1 231s Westinghouse_X1940 0.0 1 231s Westinghouse_X1941 0.0 1 231s Westinghouse_X1942 0.0 1 231s Westinghouse_X1943 0.0 1 231s Westinghouse_X1944 0.0 1 231s Westinghouse_X1945 0.0 1 231s Westinghouse_X1946 0.0 1 231s Westinghouse_X1947 0.0 1 231s Westinghouse_X1948 0.0 1 231s Westinghouse_X1949 0.0 1 231s Westinghouse_X1950 0.0 1 231s Westinghouse_X1951 0.0 1 231s Westinghouse_X1952 0.0 1 231s Westinghouse_X1953 0.0 1 231s Westinghouse_X1954 0.0 1 231s Westinghouse_value Westinghouse_capital 231s General.Electric_X1935 0 0.0 231s General.Electric_X1936 0 0.0 231s General.Electric_X1937 0 0.0 231s General.Electric_X1938 0 0.0 231s General.Electric_X1939 0 0.0 231s General.Electric_X1940 0 0.0 231s General.Electric_X1941 0 0.0 231s General.Electric_X1942 0 0.0 231s General.Electric_X1943 0 0.0 231s General.Electric_X1944 0 0.0 231s General.Electric_X1945 0 0.0 231s General.Electric_X1946 0 0.0 231s General.Electric_X1947 0 0.0 231s General.Electric_X1948 0 0.0 231s General.Electric_X1949 0 0.0 231s General.Electric_X1950 0 0.0 231s General.Electric_X1951 0 0.0 231s General.Electric_X1952 0 0.0 231s General.Electric_X1953 0 0.0 231s General.Electric_X1954 0 0.0 231s Westinghouse_X1935 192 1.8 231s Westinghouse_X1936 516 0.8 231s Westinghouse_X1937 729 7.4 231s Westinghouse_X1938 560 18.1 231s Westinghouse_X1939 520 23.5 231s Westinghouse_X1940 628 26.5 231s Westinghouse_X1941 537 36.2 231s Westinghouse_X1942 561 60.8 231s Westinghouse_X1943 617 84.4 231s Westinghouse_X1944 627 91.2 231s Westinghouse_X1945 737 92.4 231s Westinghouse_X1946 760 86.0 231s Westinghouse_X1947 581 111.1 231s Westinghouse_X1948 662 130.6 231s Westinghouse_X1949 584 141.8 231s Westinghouse_X1950 635 136.7 231s Westinghouse_X1951 724 129.7 231s Westinghouse_X1952 864 145.5 231s Westinghouse_X1953 1194 174.8 231s Westinghouse_X1954 1189 213.5 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s attr(,"variables") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"factors") 231s Westinghouse_value Westinghouse_capital 231s Westinghouse_invest 0 0 231s Westinghouse_value 1 0 231s Westinghouse_capital 0 1 231s attr(,"term.labels") 231s [1] "Westinghouse_value" "Westinghouse_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"dataClasses") 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s "numeric" "numeric" "numeric" 231s 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s attr(,"variables") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"factors") 231s Westinghouse_value Westinghouse_capital 231s Westinghouse_invest 0 0 231s Westinghouse_value 1 0 231s Westinghouse_capital 0 1 231s attr(,"term.labels") 231s [1] "Westinghouse_value" "Westinghouse_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"dataClasses") 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s "numeric" "numeric" "numeric" 231s > 231s > ## Repeating the OLS and SUR estimations in Greene (2003, pp. 351) 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + GrunfeldGreene <- pdata.frame( GrunfeldGreene, c( "firm", "year" ) ) 231s + formulaGrunfeld <- invest ~ value + capital 231s + } 231s > 231s > # OLS 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greeneOls <- systemfit( formulaGrunfeld, "OLS", 231s + data = GrunfeldGreene, useMatrix = useMatrix ) 231s + print( greeneOls ) 231s + print( summary( greeneOls ) ) 231s + print( summary( greeneOls, useDfSys = TRUE, equations = FALSE ) ) 231s + print( summary( greeneOls, residCov = FALSE ) ) 231s + print( sapply( greeneOls$eq, function(x){return(summary(x)$ssr/20)} ) ) # sigma^2 231s + print( coef( greeneOls ) ) 231s + print( coef( summary( greeneOls ) ) ) 231s + print( vcov( greeneOls ) ) 231s + print( residuals( greeneOls ) ) 231s + print( confint(greeneOls ) ) 231s + print( fitted( greeneOls ) ) 231s + print( logLik( greeneOls ) ) 231s + print( logLik( greeneOls, residCovDiag = TRUE ) ) 231s + print( nobs( greeneOls ) ) 231s + print( model.frame( greeneOls ) ) 231s + print( model.matrix( greeneOls ) ) 231s + print( formula( greeneOls ) ) 231s + print( formula( greeneOls$eq[[ 2 ]] ) ) 231s + print( terms( greeneOls ) ) 231s + print( terms( greeneOls$eq[[ 2 ]] ) ) 231s + } 231s 231s systemfit results 231s method: OLS 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_value 231s -6.1900 0.0779 231s Chrysler_capital General.Electric_(Intercept) 231s 0.3157 -9.9563 231s General.Electric_value General.Electric_capital 231s 0.0266 0.1517 231s General.Motors_(Intercept) General.Motors_value 231s -149.7825 0.1193 231s General.Motors_capital US.Steel_(Intercept) 231s 0.3714 -30.3685 231s US.Steel_value US.Steel_capital 231s 0.1566 0.4239 231s Westinghouse_(Intercept) Westinghouse_value 231s -0.5094 0.0529 231s Westinghouse_capital 231s 0.0924 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 85 339121 2.09e+14 0.848 0.862 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 2997 176 13.3 0.914 0.903 231s General.Electric 20 17 13217 777 27.9 0.705 0.671 231s General.Motors 20 17 143206 8424 91.8 0.921 0.912 231s US.Steel 20 17 177928 10466 102.3 0.440 0.374 231s Westinghouse 20 17 1773 104 10.2 0.744 0.714 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 176.3 -25.1 -333 492 15.7 231s General.Electric -25.1 777.4 715 1065 207.6 231s General.Motors -332.7 714.7 8424 -2614 148.4 231s US.Steel 491.9 1064.6 -2614 10466 642.6 231s Westinghouse 15.7 207.6 148 643 104.3 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 231s General.Electric -0.0679 1.0000 0.279 0.373 0.729 231s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 231s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 231s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 231s 231s 231s OLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -6.1900 13.5065 -0.46 0.6525 231s value 0.0779 0.0200 3.90 0.0011 ** 231s capital 0.3157 0.0288 10.96 4e-09 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 13.279 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 231s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 231s 231s 231s OLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -9.9563 31.3742 -0.32 0.75 231s value 0.0266 0.0156 1.71 0.11 231s capital 0.1517 0.0257 5.90 1.7e-05 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 27.883 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 231s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 231s 231s 231s OLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -149.7825 105.8421 -1.42 0.17508 231s value 0.1193 0.0258 4.62 0.00025 *** 231s capital 0.3714 0.0371 10.02 1.5e-08 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 91.782 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 231s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 231s 231s 231s OLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -30.3685 157.0477 -0.19 0.849 231s value 0.1566 0.0789 1.98 0.064 . 231s capital 0.4239 0.1552 2.73 0.014 * 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 102.305 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 231s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 231s 231s 231s OLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -0.5094 8.0153 -0.06 0.9501 231s value 0.0529 0.0157 3.37 0.0037 ** 231s capital 0.0924 0.0561 1.65 0.1179 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 10.213 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 231s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 231s 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 85 339121 2.09e+14 0.848 0.862 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 2997 176 13.3 0.914 0.903 231s General.Electric 20 17 13217 777 27.9 0.705 0.671 231s General.Motors 20 17 143206 8424 91.8 0.921 0.912 231s US.Steel 20 17 177928 10466 102.3 0.440 0.374 231s Westinghouse 20 17 1773 104 10.2 0.744 0.714 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 176.3 -25.1 -333 492 15.7 231s General.Electric -25.1 777.4 715 1065 207.6 231s General.Motors -332.7 714.7 8424 -2614 148.4 231s US.Steel 491.9 1064.6 -2614 10466 642.6 231s Westinghouse 15.7 207.6 148 643 104.3 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 231s General.Electric -0.0679 1.0000 0.279 0.373 0.729 231s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 231s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 231s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) -6.1900 13.5065 -0.46 0.64791 231s Chrysler_value 0.0779 0.0200 3.90 0.00019 *** 231s Chrysler_capital 0.3157 0.0288 10.96 < 2e-16 *** 231s General.Electric_(Intercept) -9.9563 31.3742 -0.32 0.75176 231s General.Electric_value 0.0266 0.0156 1.71 0.09171 . 231s General.Electric_capital 0.1517 0.0257 5.90 7.2e-08 *** 231s General.Motors_(Intercept) -149.7825 105.8421 -1.42 0.16068 231s General.Motors_value 0.1193 0.0258 4.62 1.4e-05 *** 231s General.Motors_capital 0.3714 0.0371 10.02 4.4e-16 *** 231s US.Steel_(Intercept) -30.3685 157.0477 -0.19 0.84713 231s US.Steel_value 0.1566 0.0789 1.98 0.05039 . 231s US.Steel_capital 0.4239 0.1552 2.73 0.00768 ** 231s Westinghouse_(Intercept) -0.5094 8.0153 -0.06 0.94948 231s Westinghouse_value 0.0529 0.0157 3.37 0.00114 ** 231s Westinghouse_capital 0.0924 0.0561 1.65 0.10321 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 85 339121 2.09e+14 0.848 0.862 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 2997 176 13.3 0.914 0.903 231s General.Electric 20 17 13217 777 27.9 0.705 0.671 231s General.Motors 20 17 143206 8424 91.8 0.921 0.912 231s US.Steel 20 17 177928 10466 102.3 0.440 0.374 231s Westinghouse 20 17 1773 104 10.2 0.744 0.714 231s 231s 231s OLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -6.1900 13.5065 -0.46 0.6525 231s value 0.0779 0.0200 3.90 0.0011 ** 231s capital 0.3157 0.0288 10.96 4e-09 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 13.279 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 231s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 231s 231s 231s OLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -9.9563 31.3742 -0.32 0.75 231s value 0.0266 0.0156 1.71 0.11 231s capital 0.1517 0.0257 5.90 1.7e-05 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 27.883 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 231s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 231s 231s 231s OLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -149.7825 105.8421 -1.42 0.17508 231s value 0.1193 0.0258 4.62 0.00025 *** 231s capital 0.3714 0.0371 10.02 1.5e-08 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 91.782 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 231s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 231s 231s 231s OLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -30.3685 157.0477 -0.19 0.849 231s value 0.1566 0.0789 1.98 0.064 . 231s capital 0.4239 0.1552 2.73 0.014 * 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 102.305 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 231s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 231s 231s 231s OLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -0.5094 8.0153 -0.06 0.9501 231s value 0.0529 0.0157 3.37 0.0037 ** 231s capital 0.0924 0.0561 1.65 0.1179 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 10.213 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 231s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 231s 231s [1] 149.9 660.8 7160.3 8896.4 88.7 231s Chrysler_(Intercept) Chrysler_value 231s -6.1900 0.0779 231s Chrysler_capital General.Electric_(Intercept) 231s 0.3157 -9.9563 231s General.Electric_value General.Electric_capital 231s 0.0266 0.1517 231s General.Motors_(Intercept) General.Motors_value 231s -149.7825 0.1193 231s General.Motors_capital US.Steel_(Intercept) 231s 0.3714 -30.3685 231s US.Steel_value US.Steel_capital 231s 0.1566 0.4239 231s Westinghouse_(Intercept) Westinghouse_value 231s -0.5094 0.0529 231s Westinghouse_capital 231s 0.0924 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) -6.1900 13.5065 -0.4583 6.53e-01 231s Chrysler_value 0.0779 0.0200 3.9026 1.15e-03 231s Chrysler_capital 0.3157 0.0288 10.9574 3.99e-09 231s General.Electric_(Intercept) -9.9563 31.3742 -0.3173 7.55e-01 231s General.Electric_value 0.0266 0.0156 1.7057 1.06e-01 231s General.Electric_capital 0.1517 0.0257 5.9015 1.74e-05 231s General.Motors_(Intercept) -149.7825 105.8421 -1.4151 1.75e-01 231s General.Motors_value 0.1193 0.0258 4.6172 2.46e-04 231s General.Motors_capital 0.3714 0.0371 10.0193 1.51e-08 231s US.Steel_(Intercept) -30.3685 157.0477 -0.1934 8.49e-01 231s US.Steel_value 0.1566 0.0789 1.9848 6.35e-02 231s US.Steel_capital 0.4239 0.1552 2.7308 1.42e-02 231s Westinghouse_(Intercept) -0.5094 8.0153 -0.0636 9.50e-01 231s Westinghouse_value 0.0529 0.0157 3.3677 3.65e-03 231s Westinghouse_capital 0.0924 0.0561 1.6472 1.18e-01 231s Chrysler_(Intercept) Chrysler_value 231s Chrysler_(Intercept) 182.4250 -0.254690 231s Chrysler_value -0.2547 0.000399 231s Chrysler_capital 0.0243 -0.000180 231s General.Electric_(Intercept) 0.0000 0.000000 231s General.Electric_value 0.0000 0.000000 231s General.Electric_capital 0.0000 0.000000 231s General.Motors_(Intercept) 0.0000 0.000000 231s General.Motors_value 0.0000 0.000000 231s General.Motors_capital 0.0000 0.000000 231s US.Steel_(Intercept) 0.0000 0.000000 231s US.Steel_value 0.0000 0.000000 231s US.Steel_capital 0.0000 0.000000 231s Westinghouse_(Intercept) 0.0000 0.000000 231s Westinghouse_value 0.0000 0.000000 231s Westinghouse_capital 0.0000 0.000000 231s Chrysler_capital General.Electric_(Intercept) 231s Chrysler_(Intercept) 0.02429 0.000 231s Chrysler_value -0.00018 0.000 231s Chrysler_capital 0.00083 0.000 231s General.Electric_(Intercept) 0.00000 984.344 231s General.Electric_value 0.00000 -0.451 231s General.Electric_capital 0.00000 -0.173 231s General.Motors_(Intercept) 0.00000 0.000 231s General.Motors_value 0.00000 0.000 231s General.Motors_capital 0.00000 0.000 231s US.Steel_(Intercept) 0.00000 0.000 231s US.Steel_value 0.00000 0.000 231s US.Steel_capital 0.00000 0.000 231s Westinghouse_(Intercept) 0.00000 0.000 231s Westinghouse_value 0.00000 0.000 231s Westinghouse_capital 0.00000 0.000 231s General.Electric_value General.Electric_capital 231s Chrysler_(Intercept) 0.00e+00 0.00e+00 231s Chrysler_value 0.00e+00 0.00e+00 231s Chrysler_capital 0.00e+00 0.00e+00 231s General.Electric_(Intercept) -4.51e-01 -1.73e-01 231s General.Electric_value 2.42e-04 -4.73e-05 231s General.Electric_capital -4.73e-05 6.61e-04 231s General.Motors_(Intercept) 0.00e+00 0.00e+00 231s General.Motors_value 0.00e+00 0.00e+00 231s General.Motors_capital 0.00e+00 0.00e+00 231s US.Steel_(Intercept) 0.00e+00 0.00e+00 231s US.Steel_value 0.00e+00 0.00e+00 231s US.Steel_capital 0.00e+00 0.00e+00 231s Westinghouse_(Intercept) 0.00e+00 0.00e+00 231s Westinghouse_value 0.00e+00 0.00e+00 231s Westinghouse_capital 0.00e+00 0.00e+00 231s General.Motors_(Intercept) General.Motors_value 231s Chrysler_(Intercept) 0.000 0.000000 231s Chrysler_value 0.000 0.000000 231s Chrysler_capital 0.000 0.000000 231s General.Electric_(Intercept) 0.000 0.000000 231s General.Electric_value 0.000 0.000000 231s General.Electric_capital 0.000 0.000000 231s General.Motors_(Intercept) 11202.555 -2.623398 231s General.Motors_value -2.623 0.000667 231s General.Motors_capital 0.907 -0.000415 231s US.Steel_(Intercept) 0.000 0.000000 231s US.Steel_value 0.000 0.000000 231s US.Steel_capital 0.000 0.000000 231s Westinghouse_(Intercept) 0.000 0.000000 231s Westinghouse_value 0.000 0.000000 231s Westinghouse_capital 0.000 0.000000 231s General.Motors_capital US.Steel_(Intercept) 231s Chrysler_(Intercept) 0.000000 0.00 231s Chrysler_value 0.000000 0.00 231s Chrysler_capital 0.000000 0.00 231s General.Electric_(Intercept) 0.000000 0.00 231s General.Electric_value 0.000000 0.00 231s General.Electric_capital 0.000000 0.00 231s General.Motors_(Intercept) 0.906860 0.00 231s General.Motors_value -0.000415 0.00 231s General.Motors_capital 0.001374 0.00 231s US.Steel_(Intercept) 0.000000 24663.98 231s US.Steel_value 0.000000 -11.71 231s US.Steel_capital 0.000000 -3.52 231s Westinghouse_(Intercept) 0.000000 0.00 231s Westinghouse_value 0.000000 0.00 231s Westinghouse_capital 0.000000 0.00 231s US.Steel_value US.Steel_capital 231s Chrysler_(Intercept) 0.00000 0.00000 231s Chrysler_value 0.00000 0.00000 231s Chrysler_capital 0.00000 0.00000 231s General.Electric_(Intercept) 0.00000 0.00000 231s General.Electric_value 0.00000 0.00000 231s General.Electric_capital 0.00000 0.00000 231s General.Motors_(Intercept) 0.00000 0.00000 231s General.Motors_value 0.00000 0.00000 231s General.Motors_capital 0.00000 0.00000 231s US.Steel_(Intercept) -11.70740 -3.52078 231s US.Steel_value 0.00622 -0.00188 231s US.Steel_capital -0.00188 0.02409 231s Westinghouse_(Intercept) 0.00000 0.00000 231s Westinghouse_value 0.00000 0.00000 231s Westinghouse_capital 0.00000 0.00000 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_(Intercept) 0.000 0.000000 231s Chrysler_value 0.000 0.000000 231s Chrysler_capital 0.000 0.000000 231s General.Electric_(Intercept) 0.000 0.000000 231s General.Electric_value 0.000 0.000000 231s General.Electric_capital 0.000 0.000000 231s General.Motors_(Intercept) 0.000 0.000000 231s General.Motors_value 0.000 0.000000 231s General.Motors_capital 0.000 0.000000 231s US.Steel_(Intercept) 0.000 0.000000 231s US.Steel_value 0.000 0.000000 231s US.Steel_capital 0.000 0.000000 231s Westinghouse_(Intercept) 64.245 -0.109545 231s Westinghouse_value -0.110 0.000247 231s Westinghouse_capital 0.169 -0.000653 231s Westinghouse_capital 231s Chrysler_(Intercept) 0.000000 231s Chrysler_value 0.000000 231s Chrysler_capital 0.000000 231s General.Electric_(Intercept) 0.000000 231s General.Electric_value 0.000000 231s General.Electric_capital 0.000000 231s General.Motors_(Intercept) 0.000000 231s General.Motors_value 0.000000 231s General.Motors_capital 0.000000 231s US.Steel_(Intercept) 0.000000 231s US.Steel_value 0.000000 231s US.Steel_capital 0.000000 231s Westinghouse_(Intercept) 0.168911 231s Westinghouse_value -0.000653 231s Westinghouse_capital 0.003147 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 10.622 -2.860 99.14 4.15 3.144 231s X1936 10.425 -14.402 -34.01 81.32 -0.958 231s X1937 -7.404 -5.175 -140.48 31.18 -3.684 231s X1938 7.302 -23.295 -3.28 -99.75 -7.915 231s X1939 -14.682 -28.031 -109.45 -178.23 -10.322 231s X1940 -2.315 -0.562 -19.91 -160.69 -6.613 231s X1941 0.631 40.750 24.12 19.65 17.265 231s X1942 -1.581 16.036 98.02 9.82 8.547 231s X1943 -13.459 -23.719 67.76 -46.76 -2.916 231s X1944 -7.780 -26.780 100.03 -83.74 -3.257 231s X1945 11.757 1.768 35.12 -91.24 -7.753 231s X1946 -16.133 58.737 103.90 28.34 5.796 231s X1947 -6.823 43.936 15.18 57.32 15.050 231s X1948 6.615 31.227 -51.86 140.23 2.969 231s X1949 -7.379 -23.552 -115.39 25.65 -11.433 231s X1950 1.268 -37.511 -63.51 34.88 -13.481 231s X1951 39.502 -4.983 -119.40 115.10 4.619 231s X1952 2.774 1.893 -77.82 149.19 13.138 231s X1953 -6.215 5.087 49.50 89.00 11.308 231s X1954 -7.124 -8.563 142.33 -125.42 -13.505 231s 2.5 % 97.5 % 231s Chrysler_(Intercept) -34.686 22.306 231s Chrysler_value 0.036 0.120 231s Chrysler_capital 0.255 0.377 231s General.Electric_(Intercept) -76.150 56.238 231s General.Electric_value -0.006 0.059 231s General.Electric_capital 0.097 0.206 231s General.Motors_(Intercept) -373.090 73.525 231s General.Motors_value 0.065 0.174 231s General.Motors_capital 0.293 0.450 231s US.Steel_(Intercept) -361.710 300.973 231s US.Steel_value -0.010 0.323 231s US.Steel_capital 0.096 0.751 231s Westinghouse_(Intercept) -17.420 16.401 231s Westinghouse_value 0.020 0.086 231s Westinghouse_capital -0.026 0.211 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 29.7 36.0 218 206 9.79 231s X1936 62.3 59.4 426 274 26.86 231s X1937 73.7 82.4 551 439 38.73 231s X1938 44.3 67.9 261 362 30.81 231s X1939 67.1 76.1 440 409 29.16 231s X1940 71.7 75.0 481 422 35.18 231s X1941 67.7 72.3 488 453 31.25 231s X1942 48.4 75.9 350 436 34.79 231s X1943 60.9 85.0 432 408 39.94 231s X1944 67.3 83.6 447 372 41.07 231s X1945 77.0 91.8 526 350 47.02 231s X1946 90.3 101.2 584 392 47.66 231s X1947 69.5 103.3 554 363 40.51 231s X1948 82.7 115.1 581 354 46.59 231s X1949 86.4 121.9 670 379 43.47 231s X1950 99.4 131.0 706 384 45.72 231s X1951 121.1 140.2 875 473 49.76 231s X1952 142.2 155.4 969 496 58.64 231s X1953 181.1 174.4 1255 552 78.77 231s X1954 179.6 198.2 1344 585 82.11 231s 'log Lik.' -464 (df=16) 231s 'log Lik.' -481 (df=16) 231s [1] 100 231s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 231s X1935 40.3 418 10.5 33.1 231s X1936 72.8 838 10.2 45.0 231s X1937 66.3 884 34.7 77.2 231s X1938 51.6 438 51.8 44.6 231s X1939 52.4 680 64.3 48.1 231s X1940 69.4 728 67.1 74.4 231s X1941 68.3 644 75.2 113.0 231s X1942 46.8 411 71.4 91.9 231s X1943 47.4 588 67.1 61.3 231s X1944 59.6 698 60.5 56.8 231s X1945 88.8 846 54.6 93.6 231s X1946 74.1 894 84.8 159.9 231s X1947 62.7 579 96.8 147.2 231s X1948 89.4 695 110.2 146.3 231s X1949 79.0 590 147.4 98.3 231s X1950 100.7 694 163.2 93.5 231s X1951 160.6 809 203.5 135.2 231s X1952 145.0 727 290.6 157.3 231s X1953 174.9 1002 346.1 179.5 231s X1954 172.5 703 414.9 189.6 231s General.Electric_value General.Electric_capital General.Motors_invest 231s X1935 1171 97.8 318 231s X1936 2016 104.4 392 231s X1937 2803 118.0 411 231s X1938 2040 156.2 258 231s X1939 2256 172.6 331 231s X1940 2132 186.6 461 231s X1941 1834 220.9 512 231s X1942 1588 287.8 448 231s X1943 1749 319.9 500 231s X1944 1687 321.3 548 231s X1945 2008 319.6 561 231s X1946 2208 346.0 688 231s X1947 1657 456.4 569 231s X1948 1604 543.4 529 231s X1949 1432 618.3 555 231s X1950 1610 647.4 643 231s X1951 1819 671.3 756 231s X1952 2080 726.1 891 231s X1953 2372 800.3 1304 231s X1954 2760 888.9 1487 231s General.Motors_value General.Motors_capital US.Steel_invest 231s X1935 3078 2.8 210 231s X1936 4662 52.6 355 231s X1937 5387 156.9 470 231s X1938 2792 209.2 262 231s X1939 4313 203.4 230 231s X1940 4644 207.2 262 231s X1941 4551 255.2 473 231s X1942 3244 303.7 446 231s X1943 4054 264.1 362 231s X1944 4379 201.6 288 231s X1945 4841 265.0 259 231s X1946 4901 402.2 420 231s X1947 3526 761.5 420 231s X1948 3255 922.4 494 231s X1949 3700 1020.1 405 231s X1950 3756 1099.0 419 231s X1951 4833 1207.7 588 231s X1952 4925 1430.5 645 231s X1953 6242 1777.3 641 231s X1954 5594 2226.3 459 231s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 231s X1935 1362 53.8 12.9 192 231s X1936 1807 50.5 25.9 516 231s X1937 2676 118.1 35.0 729 231s X1938 1802 260.2 22.9 560 231s X1939 1957 312.7 18.8 520 231s X1940 2203 254.2 28.6 628 231s X1941 2380 261.4 48.5 537 231s X1942 2169 298.7 43.3 561 231s X1943 1985 301.8 37.0 617 231s X1944 1814 279.1 37.8 627 231s X1945 1850 213.8 39.3 737 231s X1946 2068 232.6 53.5 760 231s X1947 1797 264.8 55.6 581 231s X1948 1626 306.9 49.6 662 231s X1949 1667 351.1 32.0 584 231s X1950 1677 357.8 32.2 635 231s X1951 2290 342.1 54.4 724 231s X1952 2159 444.2 71.8 864 231s X1953 2031 623.6 90.1 1194 231s X1954 2116 669.7 68.6 1189 231s Westinghouse_capital 231s X1935 1.8 231s X1936 0.8 231s X1937 7.4 231s X1938 18.1 231s X1939 23.5 231s X1940 26.5 231s X1941 36.2 231s X1942 60.8 231s X1943 84.4 231s X1944 91.2 231s X1945 92.4 231s X1946 86.0 231s X1947 111.1 231s X1948 130.6 231s X1949 141.8 231s X1950 136.7 231s X1951 129.7 231s X1952 145.5 231s X1953 174.8 231s X1954 213.5 231s Chrysler_(Intercept) Chrysler_value Chrysler_capital 231s Chrysler_X1935 1 418 10.5 231s Chrysler_X1936 1 838 10.2 231s Chrysler_X1937 1 884 34.7 231s Chrysler_X1938 1 438 51.8 231s Chrysler_X1939 1 680 64.3 231s Chrysler_X1940 1 728 67.1 231s Chrysler_X1941 1 644 75.2 231s Chrysler_X1942 1 411 71.4 231s Chrysler_X1943 1 588 67.1 231s Chrysler_X1944 1 698 60.5 231s Chrysler_X1945 1 846 54.6 231s Chrysler_X1946 1 894 84.8 231s Chrysler_X1947 1 579 96.8 231s Chrysler_X1948 1 695 110.2 231s Chrysler_X1949 1 590 147.4 231s Chrysler_X1950 1 694 163.2 231s Chrysler_X1951 1 809 203.5 231s Chrysler_X1952 1 727 290.6 231s Chrysler_X1953 1 1002 346.1 231s Chrysler_X1954 1 703 414.9 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 0 0 0.0 231s US.Steel_X1936 0 0 0.0 231s US.Steel_X1937 0 0 0.0 231s US.Steel_X1938 0 0 0.0 231s US.Steel_X1939 0 0 0.0 231s US.Steel_X1940 0 0 0.0 231s US.Steel_X1941 0 0 0.0 231s US.Steel_X1942 0 0 0.0 231s US.Steel_X1943 0 0 0.0 231s US.Steel_X1944 0 0 0.0 231s US.Steel_X1945 0 0 0.0 231s US.Steel_X1946 0 0 0.0 231s US.Steel_X1947 0 0 0.0 231s US.Steel_X1948 0 0 0.0 231s US.Steel_X1949 0 0 0.0 231s US.Steel_X1950 0 0 0.0 231s US.Steel_X1951 0 0 0.0 231s US.Steel_X1952 0 0 0.0 231s US.Steel_X1953 0 0 0.0 231s US.Steel_X1954 0 0 0.0 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s General.Electric_(Intercept) General.Electric_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 1 1171 231s General.Electric_X1936 1 2016 231s General.Electric_X1937 1 2803 231s General.Electric_X1938 1 2040 231s General.Electric_X1939 1 2256 231s General.Electric_X1940 1 2132 231s General.Electric_X1941 1 1834 231s General.Electric_X1942 1 1588 231s General.Electric_X1943 1 1749 231s General.Electric_X1944 1 1687 231s General.Electric_X1945 1 2008 231s General.Electric_X1946 1 2208 231s General.Electric_X1947 1 1657 231s General.Electric_X1948 1 1604 231s General.Electric_X1949 1 1432 231s General.Electric_X1950 1 1610 231s General.Electric_X1951 1 1819 231s General.Electric_X1952 1 2080 231s General.Electric_X1953 1 2372 231s General.Electric_X1954 1 2760 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 0 0 231s Westinghouse_X1936 0 0 231s Westinghouse_X1937 0 0 231s Westinghouse_X1938 0 0 231s Westinghouse_X1939 0 0 231s Westinghouse_X1940 0 0 231s Westinghouse_X1941 0 0 231s Westinghouse_X1942 0 0 231s Westinghouse_X1943 0 0 231s Westinghouse_X1944 0 0 231s Westinghouse_X1945 0 0 231s Westinghouse_X1946 0 0 231s Westinghouse_X1947 0 0 231s Westinghouse_X1948 0 0 231s Westinghouse_X1949 0 0 231s Westinghouse_X1950 0 0 231s Westinghouse_X1951 0 0 231s Westinghouse_X1952 0 0 231s Westinghouse_X1953 0 0 231s Westinghouse_X1954 0 0 231s General.Electric_capital General.Motors_(Intercept) 231s Chrysler_X1935 0.0 0 231s Chrysler_X1936 0.0 0 231s Chrysler_X1937 0.0 0 231s Chrysler_X1938 0.0 0 231s Chrysler_X1939 0.0 0 231s Chrysler_X1940 0.0 0 231s Chrysler_X1941 0.0 0 231s Chrysler_X1942 0.0 0 231s Chrysler_X1943 0.0 0 231s Chrysler_X1944 0.0 0 231s Chrysler_X1945 0.0 0 231s Chrysler_X1946 0.0 0 231s Chrysler_X1947 0.0 0 231s Chrysler_X1948 0.0 0 231s Chrysler_X1949 0.0 0 231s Chrysler_X1950 0.0 0 231s Chrysler_X1951 0.0 0 231s Chrysler_X1952 0.0 0 231s Chrysler_X1953 0.0 0 231s Chrysler_X1954 0.0 0 231s General.Electric_X1935 97.8 0 231s General.Electric_X1936 104.4 0 231s General.Electric_X1937 118.0 0 231s General.Electric_X1938 156.2 0 231s General.Electric_X1939 172.6 0 231s General.Electric_X1940 186.6 0 231s General.Electric_X1941 220.9 0 231s General.Electric_X1942 287.8 0 231s General.Electric_X1943 319.9 0 231s General.Electric_X1944 321.3 0 231s General.Electric_X1945 319.6 0 231s General.Electric_X1946 346.0 0 231s General.Electric_X1947 456.4 0 231s General.Electric_X1948 543.4 0 231s General.Electric_X1949 618.3 0 231s General.Electric_X1950 647.4 0 231s General.Electric_X1951 671.3 0 231s General.Electric_X1952 726.1 0 231s General.Electric_X1953 800.3 0 231s General.Electric_X1954 888.9 0 231s General.Motors_X1935 0.0 1 231s General.Motors_X1936 0.0 1 231s General.Motors_X1937 0.0 1 231s General.Motors_X1938 0.0 1 231s General.Motors_X1939 0.0 1 231s General.Motors_X1940 0.0 1 231s General.Motors_X1941 0.0 1 231s General.Motors_X1942 0.0 1 231s General.Motors_X1943 0.0 1 231s General.Motors_X1944 0.0 1 231s General.Motors_X1945 0.0 1 231s General.Motors_X1946 0.0 1 231s General.Motors_X1947 0.0 1 231s General.Motors_X1948 0.0 1 231s General.Motors_X1949 0.0 1 231s General.Motors_X1950 0.0 1 231s General.Motors_X1951 0.0 1 231s General.Motors_X1952 0.0 1 231s General.Motors_X1953 0.0 1 231s General.Motors_X1954 0.0 1 231s US.Steel_X1935 0.0 0 231s US.Steel_X1936 0.0 0 231s US.Steel_X1937 0.0 0 231s US.Steel_X1938 0.0 0 231s US.Steel_X1939 0.0 0 231s US.Steel_X1940 0.0 0 231s US.Steel_X1941 0.0 0 231s US.Steel_X1942 0.0 0 231s US.Steel_X1943 0.0 0 231s US.Steel_X1944 0.0 0 231s US.Steel_X1945 0.0 0 231s US.Steel_X1946 0.0 0 231s US.Steel_X1947 0.0 0 231s US.Steel_X1948 0.0 0 231s US.Steel_X1949 0.0 0 231s US.Steel_X1950 0.0 0 231s US.Steel_X1951 0.0 0 231s US.Steel_X1952 0.0 0 231s US.Steel_X1953 0.0 0 231s US.Steel_X1954 0.0 0 231s Westinghouse_X1935 0.0 0 231s Westinghouse_X1936 0.0 0 231s Westinghouse_X1937 0.0 0 231s Westinghouse_X1938 0.0 0 231s Westinghouse_X1939 0.0 0 231s Westinghouse_X1940 0.0 0 231s Westinghouse_X1941 0.0 0 231s Westinghouse_X1942 0.0 0 231s Westinghouse_X1943 0.0 0 231s Westinghouse_X1944 0.0 0 231s Westinghouse_X1945 0.0 0 231s Westinghouse_X1946 0.0 0 231s Westinghouse_X1947 0.0 0 231s Westinghouse_X1948 0.0 0 231s Westinghouse_X1949 0.0 0 231s Westinghouse_X1950 0.0 0 231s Westinghouse_X1951 0.0 0 231s Westinghouse_X1952 0.0 0 231s Westinghouse_X1953 0.0 0 231s Westinghouse_X1954 0.0 0 231s General.Motors_value General.Motors_capital 231s Chrysler_X1935 0 0.0 231s Chrysler_X1936 0 0.0 231s Chrysler_X1937 0 0.0 231s Chrysler_X1938 0 0.0 231s Chrysler_X1939 0 0.0 231s Chrysler_X1940 0 0.0 231s Chrysler_X1941 0 0.0 231s Chrysler_X1942 0 0.0 231s Chrysler_X1943 0 0.0 231s Chrysler_X1944 0 0.0 231s Chrysler_X1945 0 0.0 231s Chrysler_X1946 0 0.0 231s Chrysler_X1947 0 0.0 231s Chrysler_X1948 0 0.0 231s Chrysler_X1949 0 0.0 231s Chrysler_X1950 0 0.0 231s Chrysler_X1951 0 0.0 231s Chrysler_X1952 0 0.0 231s Chrysler_X1953 0 0.0 231s Chrysler_X1954 0 0.0 231s General.Electric_X1935 0 0.0 231s General.Electric_X1936 0 0.0 231s General.Electric_X1937 0 0.0 231s General.Electric_X1938 0 0.0 231s General.Electric_X1939 0 0.0 231s General.Electric_X1940 0 0.0 231s General.Electric_X1941 0 0.0 231s General.Electric_X1942 0 0.0 231s General.Electric_X1943 0 0.0 231s General.Electric_X1944 0 0.0 231s General.Electric_X1945 0 0.0 231s General.Electric_X1946 0 0.0 231s General.Electric_X1947 0 0.0 231s General.Electric_X1948 0 0.0 231s General.Electric_X1949 0 0.0 231s General.Electric_X1950 0 0.0 231s General.Electric_X1951 0 0.0 231s General.Electric_X1952 0 0.0 231s General.Electric_X1953 0 0.0 231s General.Electric_X1954 0 0.0 231s General.Motors_X1935 3078 2.8 231s General.Motors_X1936 4662 52.6 231s General.Motors_X1937 5387 156.9 231s General.Motors_X1938 2792 209.2 231s General.Motors_X1939 4313 203.4 231s General.Motors_X1940 4644 207.2 231s General.Motors_X1941 4551 255.2 231s General.Motors_X1942 3244 303.7 231s General.Motors_X1943 4054 264.1 231s General.Motors_X1944 4379 201.6 231s General.Motors_X1945 4841 265.0 231s General.Motors_X1946 4901 402.2 231s General.Motors_X1947 3526 761.5 231s General.Motors_X1948 3255 922.4 231s General.Motors_X1949 3700 1020.1 231s General.Motors_X1950 3756 1099.0 231s General.Motors_X1951 4833 1207.7 231s General.Motors_X1952 4925 1430.5 231s General.Motors_X1953 6242 1777.3 231s General.Motors_X1954 5594 2226.3 231s US.Steel_X1935 0 0.0 231s US.Steel_X1936 0 0.0 231s US.Steel_X1937 0 0.0 231s US.Steel_X1938 0 0.0 231s US.Steel_X1939 0 0.0 231s US.Steel_X1940 0 0.0 231s US.Steel_X1941 0 0.0 231s US.Steel_X1942 0 0.0 231s US.Steel_X1943 0 0.0 231s US.Steel_X1944 0 0.0 231s US.Steel_X1945 0 0.0 231s US.Steel_X1946 0 0.0 231s US.Steel_X1947 0 0.0 231s US.Steel_X1948 0 0.0 231s US.Steel_X1949 0 0.0 231s US.Steel_X1950 0 0.0 231s US.Steel_X1951 0 0.0 231s US.Steel_X1952 0 0.0 231s US.Steel_X1953 0 0.0 231s US.Steel_X1954 0 0.0 231s Westinghouse_X1935 0 0.0 231s Westinghouse_X1936 0 0.0 231s Westinghouse_X1937 0 0.0 231s Westinghouse_X1938 0 0.0 231s Westinghouse_X1939 0 0.0 231s Westinghouse_X1940 0 0.0 231s Westinghouse_X1941 0 0.0 231s Westinghouse_X1942 0 0.0 231s Westinghouse_X1943 0 0.0 231s Westinghouse_X1944 0 0.0 231s Westinghouse_X1945 0 0.0 231s Westinghouse_X1946 0 0.0 231s Westinghouse_X1947 0 0.0 231s Westinghouse_X1948 0 0.0 231s Westinghouse_X1949 0 0.0 231s Westinghouse_X1950 0 0.0 231s Westinghouse_X1951 0 0.0 231s Westinghouse_X1952 0 0.0 231s Westinghouse_X1953 0 0.0 231s Westinghouse_X1954 0 0.0 231s US.Steel_(Intercept) US.Steel_value US.Steel_capital 231s Chrysler_X1935 0 0 0.0 231s Chrysler_X1936 0 0 0.0 231s Chrysler_X1937 0 0 0.0 231s Chrysler_X1938 0 0 0.0 231s Chrysler_X1939 0 0 0.0 231s Chrysler_X1940 0 0 0.0 231s Chrysler_X1941 0 0 0.0 231s Chrysler_X1942 0 0 0.0 231s Chrysler_X1943 0 0 0.0 231s Chrysler_X1944 0 0 0.0 231s Chrysler_X1945 0 0 0.0 231s Chrysler_X1946 0 0 0.0 231s Chrysler_X1947 0 0 0.0 231s Chrysler_X1948 0 0 0.0 231s Chrysler_X1949 0 0 0.0 231s Chrysler_X1950 0 0 0.0 231s Chrysler_X1951 0 0 0.0 231s Chrysler_X1952 0 0 0.0 231s Chrysler_X1953 0 0 0.0 231s Chrysler_X1954 0 0 0.0 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 1 1362 53.8 231s US.Steel_X1936 1 1807 50.5 231s US.Steel_X1937 1 2676 118.1 231s US.Steel_X1938 1 1802 260.2 231s US.Steel_X1939 1 1957 312.7 231s US.Steel_X1940 1 2203 254.2 231s US.Steel_X1941 1 2380 261.4 231s US.Steel_X1942 1 2169 298.7 231s US.Steel_X1943 1 1985 301.8 231s US.Steel_X1944 1 1814 279.1 231s US.Steel_X1945 1 1850 213.8 231s US.Steel_X1946 1 2068 232.6 231s US.Steel_X1947 1 1797 264.8 231s US.Steel_X1948 1 1626 306.9 231s US.Steel_X1949 1 1667 351.1 231s US.Steel_X1950 1 1677 357.8 231s US.Steel_X1951 1 2290 342.1 231s US.Steel_X1952 1 2159 444.2 231s US.Steel_X1953 1 2031 623.6 231s US.Steel_X1954 1 2116 669.7 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 0 0 231s General.Electric_X1936 0 0 231s General.Electric_X1937 0 0 231s General.Electric_X1938 0 0 231s General.Electric_X1939 0 0 231s General.Electric_X1940 0 0 231s General.Electric_X1941 0 0 231s General.Electric_X1942 0 0 231s General.Electric_X1943 0 0 231s General.Electric_X1944 0 0 231s General.Electric_X1945 0 0 231s General.Electric_X1946 0 0 231s General.Electric_X1947 0 0 231s General.Electric_X1948 0 0 231s General.Electric_X1949 0 0 231s General.Electric_X1950 0 0 231s General.Electric_X1951 0 0 231s General.Electric_X1952 0 0 231s General.Electric_X1953 0 0 231s General.Electric_X1954 0 0 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 1 192 231s Westinghouse_X1936 1 516 231s Westinghouse_X1937 1 729 231s Westinghouse_X1938 1 560 231s Westinghouse_X1939 1 520 231s Westinghouse_X1940 1 628 231s Westinghouse_X1941 1 537 231s Westinghouse_X1942 1 561 231s Westinghouse_X1943 1 617 231s Westinghouse_X1944 1 627 231s Westinghouse_X1945 1 737 231s Westinghouse_X1946 1 760 231s Westinghouse_X1947 1 581 231s Westinghouse_X1948 1 662 231s Westinghouse_X1949 1 584 231s Westinghouse_X1950 1 635 231s Westinghouse_X1951 1 724 231s Westinghouse_X1952 1 864 231s Westinghouse_X1953 1 1194 231s Westinghouse_X1954 1 1189 231s Westinghouse_capital 231s Chrysler_X1935 0.0 231s Chrysler_X1936 0.0 231s Chrysler_X1937 0.0 231s Chrysler_X1938 0.0 231s Chrysler_X1939 0.0 231s Chrysler_X1940 0.0 231s Chrysler_X1941 0.0 231s Chrysler_X1942 0.0 231s Chrysler_X1943 0.0 231s Chrysler_X1944 0.0 231s Chrysler_X1945 0.0 231s Chrysler_X1946 0.0 231s Chrysler_X1947 0.0 231s Chrysler_X1948 0.0 231s Chrysler_X1949 0.0 231s Chrysler_X1950 0.0 231s Chrysler_X1951 0.0 231s Chrysler_X1952 0.0 231s Chrysler_X1953 0.0 231s Chrysler_X1954 0.0 231s General.Electric_X1935 0.0 231s General.Electric_X1936 0.0 231s General.Electric_X1937 0.0 231s General.Electric_X1938 0.0 231s General.Electric_X1939 0.0 231s General.Electric_X1940 0.0 231s General.Electric_X1941 0.0 231s General.Electric_X1942 0.0 231s General.Electric_X1943 0.0 231s General.Electric_X1944 0.0 231s General.Electric_X1945 0.0 231s General.Electric_X1946 0.0 231s General.Electric_X1947 0.0 231s General.Electric_X1948 0.0 231s General.Electric_X1949 0.0 231s General.Electric_X1950 0.0 231s General.Electric_X1951 0.0 231s General.Electric_X1952 0.0 231s General.Electric_X1953 0.0 231s General.Electric_X1954 0.0 231s General.Motors_X1935 0.0 231s General.Motors_X1936 0.0 231s General.Motors_X1937 0.0 231s General.Motors_X1938 0.0 231s General.Motors_X1939 0.0 231s General.Motors_X1940 0.0 231s General.Motors_X1941 0.0 231s General.Motors_X1942 0.0 231s General.Motors_X1943 0.0 231s General.Motors_X1944 0.0 231s General.Motors_X1945 0.0 231s General.Motors_X1946 0.0 231s General.Motors_X1947 0.0 231s General.Motors_X1948 0.0 231s General.Motors_X1949 0.0 231s General.Motors_X1950 0.0 231s General.Motors_X1951 0.0 231s General.Motors_X1952 0.0 231s General.Motors_X1953 0.0 231s General.Motors_X1954 0.0 231s US.Steel_X1935 0.0 231s US.Steel_X1936 0.0 231s US.Steel_X1937 0.0 231s US.Steel_X1938 0.0 231s US.Steel_X1939 0.0 231s US.Steel_X1940 0.0 231s US.Steel_X1941 0.0 231s US.Steel_X1942 0.0 231s US.Steel_X1943 0.0 231s US.Steel_X1944 0.0 231s US.Steel_X1945 0.0 231s US.Steel_X1946 0.0 231s US.Steel_X1947 0.0 231s US.Steel_X1948 0.0 231s US.Steel_X1949 0.0 231s US.Steel_X1950 0.0 231s US.Steel_X1951 0.0 231s US.Steel_X1952 0.0 231s US.Steel_X1953 0.0 231s US.Steel_X1954 0.0 231s Westinghouse_X1935 1.8 231s Westinghouse_X1936 0.8 231s Westinghouse_X1937 7.4 231s Westinghouse_X1938 18.1 231s Westinghouse_X1939 23.5 231s Westinghouse_X1940 26.5 231s Westinghouse_X1941 36.2 231s Westinghouse_X1942 60.8 231s Westinghouse_X1943 84.4 231s Westinghouse_X1944 91.2 231s Westinghouse_X1945 92.4 231s Westinghouse_X1946 86.0 231s Westinghouse_X1947 111.1 231s Westinghouse_X1948 130.6 231s Westinghouse_X1949 141.8 231s Westinghouse_X1950 136.7 231s Westinghouse_X1951 129.7 231s Westinghouse_X1952 145.5 231s Westinghouse_X1953 174.8 231s Westinghouse_X1954 213.5 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s attr(,"variables") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"factors") 231s Chrysler_value Chrysler_capital 231s Chrysler_invest 0 0 231s Chrysler_value 1 0 231s Chrysler_capital 0 1 231s attr(,"term.labels") 231s [1] "Chrysler_value" "Chrysler_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"dataClasses") 231s Chrysler_invest Chrysler_value Chrysler_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s attr(,"variables") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"factors") 231s General.Motors_value General.Motors_capital 231s General.Motors_invest 0 0 231s General.Motors_value 1 0 231s General.Motors_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Motors_value" "General.Motors_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"dataClasses") 231s General.Motors_invest General.Motors_value General.Motors_capital 231s "numeric" "numeric" "numeric" 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s attr(,"variables") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"factors") 231s US.Steel_value US.Steel_capital 231s US.Steel_invest 0 0 231s US.Steel_value 1 0 231s US.Steel_capital 0 1 231s attr(,"term.labels") 231s [1] "US.Steel_value" "US.Steel_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"dataClasses") 231s US.Steel_invest US.Steel_value US.Steel_capital 231s "numeric" "numeric" "numeric" 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s attr(,"variables") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"factors") 231s Westinghouse_value Westinghouse_capital 231s Westinghouse_invest 0 0 231s Westinghouse_value 1 0 231s Westinghouse_capital 0 1 231s attr(,"term.labels") 231s [1] "Westinghouse_value" "Westinghouse_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"dataClasses") 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s "numeric" "numeric" "numeric" 231s 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s > 231s > # OLS Pooled 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greeneOlsPooled <- systemfit( formulaGrunfeld, "OLS", 231s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 231s + print( greeneOlsPooled ) 231s + print( summary( greeneOlsPooled ) ) 231s + print( summary( greeneOlsPooled, useDfSys = FALSE, residCov = FALSE ) ) 231s + print( summary( greeneOlsPooled, residCov = FALSE, equations = FALSE ) ) 231s + print( sum( sapply( greeneOlsPooled$eq, function(x){return(summary(x)$ssr)}) )/97 ) # sigma^2 231s + print( coef( greeneOlsPooled ) ) 231s + print( coef( greeneOlsPooled, modified.regMat = TRUE ) ) 231s + print( coef( summary( greeneOlsPooled ) ) ) 231s + print( coef( summary( greeneOlsPooled ), modified.regMat = TRUE ) ) 231s + print( vcov( greeneOlsPooled ) ) 231s + print( vcov( greeneOlsPooled, modified.regMat = TRUE ) ) 231s + print( residuals( greeneOlsPooled ) ) 231s + print( confint( greeneOlsPooled ) ) 231s + print( fitted( greeneOlsPooled ) ) 231s + print( logLik( greeneOlsPooled ) ) 231s + print( logLik( greeneOlsPooled, residCovDiag = TRUE ) ) 231s + print( nobs( greeneOlsPooled ) ) 231s + print( model.frame( greeneOlsPooled ) ) 231s + print( model.matrix( greeneOlsPooled ) ) 231s + print( formula( greeneOlsPooled ) ) 231s + print( formula( greeneOlsPooled$eq[[ 1 ]] ) ) 231s + print( terms( greeneOlsPooled ) ) 231s + print( terms( greeneOlsPooled$eq[[ 1 ]] ) ) 231s + } 231s 231s systemfit results 231s method: OLS 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_value 231s -48.030 0.105 231s Chrysler_capital General.Electric_(Intercept) 231s 0.305 -48.030 231s General.Electric_value General.Electric_capital 231s 0.105 0.305 231s General.Motors_(Intercept) General.Motors_value 231s -48.030 0.105 231s General.Motors_capital US.Steel_(Intercept) 231s 0.305 -48.030 231s US.Steel_value US.Steel_capital 231s 0.105 0.305 231s Westinghouse_(Intercept) Westinghouse_value 231s -48.030 0.105 231s Westinghouse_capital 231s 0.305 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 97 1570884 4.2e+17 0.294 0.812 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 15117 889 29.8 0.564 0.513 231s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 231s General.Motors 20 17 188218 11072 105.2 0.897 0.884 231s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 231s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 889.2 -4898 -198 4748 -94.6 231s General.Electric -4898.1 40339 -2254 -32821 2658.0 231s General.Motors -197.7 -2254 11072 304 -1328.6 231s US.Steel 4748.1 -32821 304 39359 -1377.3 231s Westinghouse -94.6 2658 -1329 -1377 745.2 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.000 0.144 -0.1852 0.2218 0.186 231s General.Electric 0.144 1.000 -0.2592 -0.1216 0.881 231s General.Motors -0.185 -0.259 1.0000 -0.0155 -0.469 231s US.Steel 0.222 -0.122 -0.0155 1.0000 -0.119 231s Westinghouse 0.186 0.881 -0.4689 -0.1186 1.000 231s 231s 231s OLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 29.82 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 231s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 231s 231s 231s OLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 200.847 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 231s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 231s 231s 231s OLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 105.222 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 231s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 231s 231s 231s OLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 198.392 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 231s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 231s 231s 231s OLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 27.298 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 231s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 231s 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 97 1570884 4.2e+17 0.294 0.812 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 15117 889 29.8 0.564 0.513 231s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 231s General.Motors 20 17 188218 11072 105.2 0.897 0.884 231s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 231s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 231s 231s 231s OLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.039 * 231s value 0.1051 0.0114 9.24 4.9e-08 *** 231s capital 0.3054 0.0435 7.02 2.1e-06 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 29.82 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 231s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 231s 231s 231s OLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.039 * 231s value 0.1051 0.0114 9.24 4.9e-08 *** 231s capital 0.3054 0.0435 7.02 2.1e-06 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 200.847 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 231s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 231s 231s 231s OLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.039 * 231s value 0.1051 0.0114 9.24 4.9e-08 *** 231s capital 0.3054 0.0435 7.02 2.1e-06 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 105.222 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 231s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 231s 231s 231s OLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.039 * 231s value 0.1051 0.0114 9.24 4.9e-08 *** 231s capital 0.3054 0.0435 7.02 2.1e-06 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 198.392 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 231s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 231s 231s 231s OLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.039 * 231s value 0.1051 0.0114 9.24 4.9e-08 *** 231s capital 0.3054 0.0435 7.02 2.1e-06 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 27.298 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 231s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 231s 231s 231s systemfit results 231s method: OLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 97 1570884 4.2e+17 0.294 0.812 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 15117 889 29.8 0.564 0.513 231s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 231s General.Motors 20 17 188218 11072 105.2 0.897 0.884 231s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 231s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) -48.0297 21.4802 -2.24 0.028 * 231s Chrysler_value 0.1051 0.0114 9.24 6.0e-15 *** 231s Chrysler_capital 0.3054 0.0435 7.02 3.1e-10 *** 231s General.Electric_(Intercept) -48.0297 21.4802 -2.24 0.028 * 231s General.Electric_value 0.1051 0.0114 9.24 6.0e-15 *** 231s General.Electric_capital 0.3054 0.0435 7.02 3.1e-10 *** 231s General.Motors_(Intercept) -48.0297 21.4802 -2.24 0.028 * 231s General.Motors_value 0.1051 0.0114 9.24 6.0e-15 *** 231s General.Motors_capital 0.3054 0.0435 7.02 3.1e-10 *** 231s US.Steel_(Intercept) -48.0297 21.4802 -2.24 0.028 * 231s US.Steel_value 0.1051 0.0114 9.24 6.0e-15 *** 231s US.Steel_capital 0.3054 0.0435 7.02 3.1e-10 *** 231s Westinghouse_(Intercept) -48.0297 21.4802 -2.24 0.028 * 231s Westinghouse_value 0.1051 0.0114 9.24 6.0e-15 *** 231s Westinghouse_capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s [1] 16195 231s Chrysler_(Intercept) Chrysler_value 231s -48.030 0.105 231s Chrysler_capital General.Electric_(Intercept) 231s 0.305 -48.030 231s General.Electric_value General.Electric_capital 231s 0.105 0.305 231s General.Motors_(Intercept) General.Motors_value 231s -48.030 0.105 231s General.Motors_capital US.Steel_(Intercept) 231s 0.305 -48.030 231s US.Steel_value US.Steel_capital 231s 0.105 0.305 231s Westinghouse_(Intercept) Westinghouse_value 231s -48.030 0.105 231s Westinghouse_capital 231s 0.305 231s C1 C2 C3 231s -48.030 0.105 0.305 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) -48.030 21.4802 -2.24 2.76e-02 231s Chrysler_value 0.105 0.0114 9.24 6.00e-15 231s Chrysler_capital 0.305 0.0435 7.02 3.06e-10 231s General.Electric_(Intercept) -48.030 21.4802 -2.24 2.76e-02 231s General.Electric_value 0.105 0.0114 9.24 6.00e-15 231s General.Electric_capital 0.305 0.0435 7.02 3.06e-10 231s General.Motors_(Intercept) -48.030 21.4802 -2.24 2.76e-02 231s General.Motors_value 0.105 0.0114 9.24 6.00e-15 231s General.Motors_capital 0.305 0.0435 7.02 3.06e-10 231s US.Steel_(Intercept) -48.030 21.4802 -2.24 2.76e-02 231s US.Steel_value 0.105 0.0114 9.24 6.00e-15 231s US.Steel_capital 0.305 0.0435 7.02 3.06e-10 231s Westinghouse_(Intercept) -48.030 21.4802 -2.24 2.76e-02 231s Westinghouse_value 0.105 0.0114 9.24 6.00e-15 231s Westinghouse_capital 0.305 0.0435 7.02 3.06e-10 231s Estimate Std. Error t value Pr(>|t|) 231s C1 -48.030 21.4802 -2.24 2.76e-02 231s C2 0.105 0.0114 9.24 6.00e-15 231s C3 0.305 0.0435 7.02 3.06e-10 231s Chrysler_(Intercept) Chrysler_value 231s Chrysler_(Intercept) 461.39750 -0.154668 231s Chrysler_value -0.15467 0.000129 231s Chrysler_capital -0.00689 -0.000303 231s General.Electric_(Intercept) 461.39750 -0.154668 231s General.Electric_value -0.15467 0.000129 231s General.Electric_capital -0.00689 -0.000303 231s General.Motors_(Intercept) 461.39750 -0.154668 231s General.Motors_value -0.15467 0.000129 231s General.Motors_capital -0.00689 -0.000303 231s US.Steel_(Intercept) 461.39750 -0.154668 231s US.Steel_value -0.15467 0.000129 231s US.Steel_capital -0.00689 -0.000303 231s Westinghouse_(Intercept) 461.39750 -0.154668 231s Westinghouse_value -0.15467 0.000129 231s Westinghouse_capital -0.00689 -0.000303 231s Chrysler_capital General.Electric_(Intercept) 231s Chrysler_(Intercept) -0.006891 461.39750 231s Chrysler_value -0.000303 -0.15467 231s Chrysler_capital 0.001893 -0.00689 231s General.Electric_(Intercept) -0.006891 461.39750 231s General.Electric_value -0.000303 -0.15467 231s General.Electric_capital 0.001893 -0.00689 231s General.Motors_(Intercept) -0.006891 461.39750 231s General.Motors_value -0.000303 -0.15467 231s General.Motors_capital 0.001893 -0.00689 231s US.Steel_(Intercept) -0.006891 461.39750 231s US.Steel_value -0.000303 -0.15467 231s US.Steel_capital 0.001893 -0.00689 231s Westinghouse_(Intercept) -0.006891 461.39750 231s Westinghouse_value -0.000303 -0.15467 231s Westinghouse_capital 0.001893 -0.00689 231s General.Electric_value General.Electric_capital 231s Chrysler_(Intercept) -0.154668 -0.006891 231s Chrysler_value 0.000129 -0.000303 231s Chrysler_capital -0.000303 0.001893 231s General.Electric_(Intercept) -0.154668 -0.006891 231s General.Electric_value 0.000129 -0.000303 231s General.Electric_capital -0.000303 0.001893 231s General.Motors_(Intercept) -0.154668 -0.006891 231s General.Motors_value 0.000129 -0.000303 231s General.Motors_capital -0.000303 0.001893 231s US.Steel_(Intercept) -0.154668 -0.006891 231s US.Steel_value 0.000129 -0.000303 231s US.Steel_capital -0.000303 0.001893 231s Westinghouse_(Intercept) -0.154668 -0.006891 231s Westinghouse_value 0.000129 -0.000303 231s Westinghouse_capital -0.000303 0.001893 231s General.Motors_(Intercept) General.Motors_value 231s Chrysler_(Intercept) 461.39750 -0.154668 231s Chrysler_value -0.15467 0.000129 231s Chrysler_capital -0.00689 -0.000303 231s General.Electric_(Intercept) 461.39750 -0.154668 231s General.Electric_value -0.15467 0.000129 231s General.Electric_capital -0.00689 -0.000303 231s General.Motors_(Intercept) 461.39750 -0.154668 231s General.Motors_value -0.15467 0.000129 231s General.Motors_capital -0.00689 -0.000303 231s US.Steel_(Intercept) 461.39750 -0.154668 231s US.Steel_value -0.15467 0.000129 231s US.Steel_capital -0.00689 -0.000303 231s Westinghouse_(Intercept) 461.39750 -0.154668 231s Westinghouse_value -0.15467 0.000129 231s Westinghouse_capital -0.00689 -0.000303 231s General.Motors_capital US.Steel_(Intercept) 231s Chrysler_(Intercept) -0.006891 461.39750 231s Chrysler_value -0.000303 -0.15467 231s Chrysler_capital 0.001893 -0.00689 231s General.Electric_(Intercept) -0.006891 461.39750 231s General.Electric_value -0.000303 -0.15467 231s General.Electric_capital 0.001893 -0.00689 231s General.Motors_(Intercept) -0.006891 461.39750 231s General.Motors_value -0.000303 -0.15467 231s General.Motors_capital 0.001893 -0.00689 231s US.Steel_(Intercept) -0.006891 461.39750 231s US.Steel_value -0.000303 -0.15467 231s US.Steel_capital 0.001893 -0.00689 231s Westinghouse_(Intercept) -0.006891 461.39750 231s Westinghouse_value -0.000303 -0.15467 231s Westinghouse_capital 0.001893 -0.00689 231s US.Steel_value US.Steel_capital 231s Chrysler_(Intercept) -0.154668 -0.006891 231s Chrysler_value 0.000129 -0.000303 231s Chrysler_capital -0.000303 0.001893 231s General.Electric_(Intercept) -0.154668 -0.006891 231s General.Electric_value 0.000129 -0.000303 231s General.Electric_capital -0.000303 0.001893 231s General.Motors_(Intercept) -0.154668 -0.006891 231s General.Motors_value 0.000129 -0.000303 231s General.Motors_capital -0.000303 0.001893 231s US.Steel_(Intercept) -0.154668 -0.006891 231s US.Steel_value 0.000129 -0.000303 231s US.Steel_capital -0.000303 0.001893 231s Westinghouse_(Intercept) -0.154668 -0.006891 231s Westinghouse_value 0.000129 -0.000303 231s Westinghouse_capital -0.000303 0.001893 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_(Intercept) 461.39750 -0.154668 231s Chrysler_value -0.15467 0.000129 231s Chrysler_capital -0.00689 -0.000303 231s General.Electric_(Intercept) 461.39750 -0.154668 231s General.Electric_value -0.15467 0.000129 231s General.Electric_capital -0.00689 -0.000303 231s General.Motors_(Intercept) 461.39750 -0.154668 231s General.Motors_value -0.15467 0.000129 231s General.Motors_capital -0.00689 -0.000303 231s US.Steel_(Intercept) 461.39750 -0.154668 231s US.Steel_value -0.15467 0.000129 231s US.Steel_capital -0.00689 -0.000303 231s Westinghouse_(Intercept) 461.39750 -0.154668 231s Westinghouse_value -0.15467 0.000129 231s Westinghouse_capital -0.00689 -0.000303 231s Westinghouse_capital 231s Chrysler_(Intercept) -0.006891 231s Chrysler_value -0.000303 231s Chrysler_capital 0.001893 231s General.Electric_(Intercept) -0.006891 231s General.Electric_value -0.000303 231s General.Electric_capital 0.001893 231s General.Motors_(Intercept) -0.006891 231s General.Motors_value -0.000303 231s General.Motors_capital 0.001893 231s US.Steel_(Intercept) -0.006891 231s US.Steel_value -0.000303 231s US.Steel_capital 0.001893 231s Westinghouse_(Intercept) -0.006891 231s Westinghouse_value -0.000303 231s Westinghouse_capital 0.001893 231s C1 C2 C3 231s C1 461.39750 -0.154668 -0.006891 231s C2 -0.15467 0.000129 -0.000303 231s C3 -0.00689 -0.000303 0.001893 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 41.24 -71.7 41.27 98.333 40.29 231s X1936 29.63 -150.7 -66.11 198.009 19.46 231s X1937 10.81 -205.4 -155.39 200.626 4.21 231s X1938 37.79 -169.4 -51.57 41.520 6.50 231s X1939 9.38 -193.7 -136.54 -22.742 5.06 231s X1940 20.47 -158.6 -42.05 0.513 2.46 231s X1941 25.78 -99.2 3.84 190.851 29.04 231s X1942 29.85 -114.8 62.38 174.529 13.83 231s X1943 13.11 -172.2 41.00 108.865 -5.58 231s X1944 15.73 -170.6 73.77 60.388 -7.87 231s X1945 31.19 -166.9 19.60 47.014 -18.39 231s X1946 2.33 -129.8 98.30 180.017 -4.69 231s X1947 20.31 -118.2 13.81 198.862 8.57 231s X1948 30.75 -140.2 -46.46 277.965 -11.89 231s X1949 19.97 -192.9 -97.21 170.739 -24.58 231s X1950 25.98 -225.4 -39.33 181.300 -28.22 231s X1951 61.49 -213.0 -72.74 291.171 -13.26 231s X1952 27.89 -234.9 -15.13 330.665 -15.43 231s X1953 12.03 -266.1 153.79 285.144 -40.69 231s X1954 19.93 -323.8 267.09 80.518 -73.50 231s 2.5 % 97.5 % 231s Chrysler_(Intercept) -90.662 -5.398 231s Chrysler_value 0.083 0.128 231s Chrysler_capital 0.219 0.392 231s General.Electric_(Intercept) -90.662 -5.398 231s General.Electric_value 0.083 0.128 231s General.Electric_capital 0.219 0.392 231s General.Motors_(Intercept) -90.662 -5.398 231s General.Motors_value 0.083 0.128 231s General.Motors_capital 0.219 0.392 231s US.Steel_(Intercept) -90.662 -5.398 231s US.Steel_value 0.083 0.128 231s US.Steel_capital 0.219 0.392 231s Westinghouse_(Intercept) -90.662 -5.398 231s Westinghouse_value 0.083 0.128 231s Westinghouse_capital 0.219 0.392 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 -0.95 105 276 112 -27.36 231s X1936 43.13 196 458 157 6.44 231s X1937 55.45 283 566 269 30.84 231s X1938 13.81 214 309 221 16.39 231s X1939 43.03 242 467 253 13.78 231s X1940 48.94 233 503 261 26.11 231s X1941 42.57 212 508 282 19.47 231s X1942 16.95 207 386 271 29.51 231s X1943 34.29 233 459 253 42.60 231s X1944 43.84 227 474 228 45.68 231s X1945 57.59 261 542 212 57.66 231s X1946 71.79 290 590 240 58.15 231s X1947 42.37 265 555 222 46.99 231s X1948 58.61 287 576 217 61.45 231s X1949 59.01 291 652 234 56.62 231s X1950 74.68 319 682 238 60.46 231s X1951 99.13 348 829 297 67.64 231s X1952 117.11 392 906 315 87.21 231s X1953 162.90 446 1151 356 130.77 231s X1954 152.56 513 1220 379 142.10 231s 'log Lik.' -540 (df=4) 231s 'log Lik.' -573 (df=4) 231s [1] 100 231s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 231s X1935 40.3 418 10.5 33.1 231s X1936 72.8 838 10.2 45.0 231s X1937 66.3 884 34.7 77.2 231s X1938 51.6 438 51.8 44.6 231s X1939 52.4 680 64.3 48.1 231s X1940 69.4 728 67.1 74.4 231s X1941 68.3 644 75.2 113.0 231s X1942 46.8 411 71.4 91.9 231s X1943 47.4 588 67.1 61.3 231s X1944 59.6 698 60.5 56.8 231s X1945 88.8 846 54.6 93.6 231s X1946 74.1 894 84.8 159.9 231s X1947 62.7 579 96.8 147.2 231s X1948 89.4 695 110.2 146.3 231s X1949 79.0 590 147.4 98.3 231s X1950 100.7 694 163.2 93.5 231s X1951 160.6 809 203.5 135.2 231s X1952 145.0 727 290.6 157.3 231s X1953 174.9 1002 346.1 179.5 231s X1954 172.5 703 414.9 189.6 231s General.Electric_value General.Electric_capital General.Motors_invest 231s X1935 1171 97.8 318 231s X1936 2016 104.4 392 231s X1937 2803 118.0 411 231s X1938 2040 156.2 258 231s X1939 2256 172.6 331 231s X1940 2132 186.6 461 231s X1941 1834 220.9 512 231s X1942 1588 287.8 448 231s X1943 1749 319.9 500 231s X1944 1687 321.3 548 231s X1945 2008 319.6 561 231s X1946 2208 346.0 688 231s X1947 1657 456.4 569 231s X1948 1604 543.4 529 231s X1949 1432 618.3 555 231s X1950 1610 647.4 643 231s X1951 1819 671.3 756 231s X1952 2080 726.1 891 231s X1953 2372 800.3 1304 231s X1954 2760 888.9 1487 231s General.Motors_value General.Motors_capital US.Steel_invest 231s X1935 3078 2.8 210 231s X1936 4662 52.6 355 231s X1937 5387 156.9 470 231s X1938 2792 209.2 262 231s X1939 4313 203.4 230 231s X1940 4644 207.2 262 231s X1941 4551 255.2 473 231s X1942 3244 303.7 446 231s X1943 4054 264.1 362 231s X1944 4379 201.6 288 231s X1945 4841 265.0 259 231s X1946 4901 402.2 420 231s X1947 3526 761.5 420 231s X1948 3255 922.4 494 231s X1949 3700 1020.1 405 231s X1950 3756 1099.0 419 231s X1951 4833 1207.7 588 231s X1952 4925 1430.5 645 231s X1953 6242 1777.3 641 231s X1954 5594 2226.3 459 231s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 231s X1935 1362 53.8 12.9 192 231s X1936 1807 50.5 25.9 516 231s X1937 2676 118.1 35.0 729 231s X1938 1802 260.2 22.9 560 231s X1939 1957 312.7 18.8 520 231s X1940 2203 254.2 28.6 628 231s X1941 2380 261.4 48.5 537 231s X1942 2169 298.7 43.3 561 231s X1943 1985 301.8 37.0 617 231s X1944 1814 279.1 37.8 627 231s X1945 1850 213.8 39.3 737 231s X1946 2068 232.6 53.5 760 231s X1947 1797 264.8 55.6 581 231s X1948 1626 306.9 49.6 662 231s X1949 1667 351.1 32.0 584 231s X1950 1677 357.8 32.2 635 231s X1951 2290 342.1 54.4 724 231s X1952 2159 444.2 71.8 864 231s X1953 2031 623.6 90.1 1194 231s X1954 2116 669.7 68.6 1189 231s Westinghouse_capital 231s X1935 1.8 231s X1936 0.8 231s X1937 7.4 231s X1938 18.1 231s X1939 23.5 231s X1940 26.5 231s X1941 36.2 231s X1942 60.8 231s X1943 84.4 231s X1944 91.2 231s X1945 92.4 231s X1946 86.0 231s X1947 111.1 231s X1948 130.6 231s X1949 141.8 231s X1950 136.7 231s X1951 129.7 231s X1952 145.5 231s X1953 174.8 231s X1954 213.5 231s Chrysler_(Intercept) Chrysler_value Chrysler_capital 231s Chrysler_X1935 1 418 10.5 231s Chrysler_X1936 1 838 10.2 231s Chrysler_X1937 1 884 34.7 231s Chrysler_X1938 1 438 51.8 231s Chrysler_X1939 1 680 64.3 231s Chrysler_X1940 1 728 67.1 231s Chrysler_X1941 1 644 75.2 231s Chrysler_X1942 1 411 71.4 231s Chrysler_X1943 1 588 67.1 231s Chrysler_X1944 1 698 60.5 231s Chrysler_X1945 1 846 54.6 231s Chrysler_X1946 1 894 84.8 231s Chrysler_X1947 1 579 96.8 231s Chrysler_X1948 1 695 110.2 231s Chrysler_X1949 1 590 147.4 231s Chrysler_X1950 1 694 163.2 231s Chrysler_X1951 1 809 203.5 231s Chrysler_X1952 1 727 290.6 231s Chrysler_X1953 1 1002 346.1 231s Chrysler_X1954 1 703 414.9 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 0 0 0.0 231s US.Steel_X1936 0 0 0.0 231s US.Steel_X1937 0 0 0.0 231s US.Steel_X1938 0 0 0.0 231s US.Steel_X1939 0 0 0.0 231s US.Steel_X1940 0 0 0.0 231s US.Steel_X1941 0 0 0.0 231s US.Steel_X1942 0 0 0.0 231s US.Steel_X1943 0 0 0.0 231s US.Steel_X1944 0 0 0.0 231s US.Steel_X1945 0 0 0.0 231s US.Steel_X1946 0 0 0.0 231s US.Steel_X1947 0 0 0.0 231s US.Steel_X1948 0 0 0.0 231s US.Steel_X1949 0 0 0.0 231s US.Steel_X1950 0 0 0.0 231s US.Steel_X1951 0 0 0.0 231s US.Steel_X1952 0 0 0.0 231s US.Steel_X1953 0 0 0.0 231s US.Steel_X1954 0 0 0.0 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s General.Electric_(Intercept) General.Electric_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 1 1171 231s General.Electric_X1936 1 2016 231s General.Electric_X1937 1 2803 231s General.Electric_X1938 1 2040 231s General.Electric_X1939 1 2256 231s General.Electric_X1940 1 2132 231s General.Electric_X1941 1 1834 231s General.Electric_X1942 1 1588 231s General.Electric_X1943 1 1749 231s General.Electric_X1944 1 1687 231s General.Electric_X1945 1 2008 231s General.Electric_X1946 1 2208 231s General.Electric_X1947 1 1657 231s General.Electric_X1948 1 1604 231s General.Electric_X1949 1 1432 231s General.Electric_X1950 1 1610 231s General.Electric_X1951 1 1819 231s General.Electric_X1952 1 2080 231s General.Electric_X1953 1 2372 231s General.Electric_X1954 1 2760 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 0 0 231s Westinghouse_X1936 0 0 231s Westinghouse_X1937 0 0 231s Westinghouse_X1938 0 0 231s Westinghouse_X1939 0 0 231s Westinghouse_X1940 0 0 231s Westinghouse_X1941 0 0 231s Westinghouse_X1942 0 0 231s Westinghouse_X1943 0 0 231s Westinghouse_X1944 0 0 231s Westinghouse_X1945 0 0 231s Westinghouse_X1946 0 0 231s Westinghouse_X1947 0 0 231s Westinghouse_X1948 0 0 231s Westinghouse_X1949 0 0 231s Westinghouse_X1950 0 0 231s Westinghouse_X1951 0 0 231s Westinghouse_X1952 0 0 231s Westinghouse_X1953 0 0 231s Westinghouse_X1954 0 0 231s General.Electric_capital General.Motors_(Intercept) 231s Chrysler_X1935 0.0 0 231s Chrysler_X1936 0.0 0 231s Chrysler_X1937 0.0 0 231s Chrysler_X1938 0.0 0 231s Chrysler_X1939 0.0 0 231s Chrysler_X1940 0.0 0 231s Chrysler_X1941 0.0 0 231s Chrysler_X1942 0.0 0 231s Chrysler_X1943 0.0 0 231s Chrysler_X1944 0.0 0 231s Chrysler_X1945 0.0 0 231s Chrysler_X1946 0.0 0 231s Chrysler_X1947 0.0 0 231s Chrysler_X1948 0.0 0 231s Chrysler_X1949 0.0 0 231s Chrysler_X1950 0.0 0 231s Chrysler_X1951 0.0 0 231s Chrysler_X1952 0.0 0 231s Chrysler_X1953 0.0 0 231s Chrysler_X1954 0.0 0 231s General.Electric_X1935 97.8 0 231s General.Electric_X1936 104.4 0 231s General.Electric_X1937 118.0 0 231s General.Electric_X1938 156.2 0 231s General.Electric_X1939 172.6 0 231s General.Electric_X1940 186.6 0 231s General.Electric_X1941 220.9 0 231s General.Electric_X1942 287.8 0 231s General.Electric_X1943 319.9 0 231s General.Electric_X1944 321.3 0 231s General.Electric_X1945 319.6 0 231s General.Electric_X1946 346.0 0 231s General.Electric_X1947 456.4 0 231s General.Electric_X1948 543.4 0 231s General.Electric_X1949 618.3 0 231s General.Electric_X1950 647.4 0 231s General.Electric_X1951 671.3 0 231s General.Electric_X1952 726.1 0 231s General.Electric_X1953 800.3 0 231s General.Electric_X1954 888.9 0 231s General.Motors_X1935 0.0 1 231s General.Motors_X1936 0.0 1 231s General.Motors_X1937 0.0 1 231s General.Motors_X1938 0.0 1 231s General.Motors_X1939 0.0 1 231s General.Motors_X1940 0.0 1 231s General.Motors_X1941 0.0 1 231s General.Motors_X1942 0.0 1 231s General.Motors_X1943 0.0 1 231s General.Motors_X1944 0.0 1 231s General.Motors_X1945 0.0 1 231s General.Motors_X1946 0.0 1 231s General.Motors_X1947 0.0 1 231s General.Motors_X1948 0.0 1 231s General.Motors_X1949 0.0 1 231s General.Motors_X1950 0.0 1 231s General.Motors_X1951 0.0 1 231s General.Motors_X1952 0.0 1 231s General.Motors_X1953 0.0 1 231s General.Motors_X1954 0.0 1 231s US.Steel_X1935 0.0 0 231s US.Steel_X1936 0.0 0 231s US.Steel_X1937 0.0 0 231s US.Steel_X1938 0.0 0 231s US.Steel_X1939 0.0 0 231s US.Steel_X1940 0.0 0 231s US.Steel_X1941 0.0 0 231s US.Steel_X1942 0.0 0 231s US.Steel_X1943 0.0 0 231s US.Steel_X1944 0.0 0 231s US.Steel_X1945 0.0 0 231s US.Steel_X1946 0.0 0 231s US.Steel_X1947 0.0 0 231s US.Steel_X1948 0.0 0 231s US.Steel_X1949 0.0 0 231s US.Steel_X1950 0.0 0 231s US.Steel_X1951 0.0 0 231s US.Steel_X1952 0.0 0 231s US.Steel_X1953 0.0 0 231s US.Steel_X1954 0.0 0 231s Westinghouse_X1935 0.0 0 231s Westinghouse_X1936 0.0 0 231s Westinghouse_X1937 0.0 0 231s Westinghouse_X1938 0.0 0 231s Westinghouse_X1939 0.0 0 231s Westinghouse_X1940 0.0 0 231s Westinghouse_X1941 0.0 0 231s Westinghouse_X1942 0.0 0 231s Westinghouse_X1943 0.0 0 231s Westinghouse_X1944 0.0 0 231s Westinghouse_X1945 0.0 0 231s Westinghouse_X1946 0.0 0 231s Westinghouse_X1947 0.0 0 231s Westinghouse_X1948 0.0 0 231s Westinghouse_X1949 0.0 0 231s Westinghouse_X1950 0.0 0 231s Westinghouse_X1951 0.0 0 231s Westinghouse_X1952 0.0 0 231s Westinghouse_X1953 0.0 0 231s Westinghouse_X1954 0.0 0 231s General.Motors_value General.Motors_capital 231s Chrysler_X1935 0 0.0 231s Chrysler_X1936 0 0.0 231s Chrysler_X1937 0 0.0 231s Chrysler_X1938 0 0.0 231s Chrysler_X1939 0 0.0 231s Chrysler_X1940 0 0.0 231s Chrysler_X1941 0 0.0 231s Chrysler_X1942 0 0.0 231s Chrysler_X1943 0 0.0 231s Chrysler_X1944 0 0.0 231s Chrysler_X1945 0 0.0 231s Chrysler_X1946 0 0.0 231s Chrysler_X1947 0 0.0 231s Chrysler_X1948 0 0.0 231s Chrysler_X1949 0 0.0 231s Chrysler_X1950 0 0.0 231s Chrysler_X1951 0 0.0 231s Chrysler_X1952 0 0.0 231s Chrysler_X1953 0 0.0 231s Chrysler_X1954 0 0.0 231s General.Electric_X1935 0 0.0 231s General.Electric_X1936 0 0.0 231s General.Electric_X1937 0 0.0 231s General.Electric_X1938 0 0.0 231s General.Electric_X1939 0 0.0 231s General.Electric_X1940 0 0.0 231s General.Electric_X1941 0 0.0 231s General.Electric_X1942 0 0.0 231s General.Electric_X1943 0 0.0 231s General.Electric_X1944 0 0.0 231s General.Electric_X1945 0 0.0 231s General.Electric_X1946 0 0.0 231s General.Electric_X1947 0 0.0 231s General.Electric_X1948 0 0.0 231s General.Electric_X1949 0 0.0 231s General.Electric_X1950 0 0.0 231s General.Electric_X1951 0 0.0 231s General.Electric_X1952 0 0.0 231s General.Electric_X1953 0 0.0 231s General.Electric_X1954 0 0.0 231s General.Motors_X1935 3078 2.8 231s General.Motors_X1936 4662 52.6 231s General.Motors_X1937 5387 156.9 231s General.Motors_X1938 2792 209.2 231s General.Motors_X1939 4313 203.4 231s General.Motors_X1940 4644 207.2 231s General.Motors_X1941 4551 255.2 231s General.Motors_X1942 3244 303.7 231s General.Motors_X1943 4054 264.1 231s General.Motors_X1944 4379 201.6 231s General.Motors_X1945 4841 265.0 231s General.Motors_X1946 4901 402.2 231s General.Motors_X1947 3526 761.5 231s General.Motors_X1948 3255 922.4 231s General.Motors_X1949 3700 1020.1 231s General.Motors_X1950 3756 1099.0 231s General.Motors_X1951 4833 1207.7 231s General.Motors_X1952 4925 1430.5 231s General.Motors_X1953 6242 1777.3 231s General.Motors_X1954 5594 2226.3 231s US.Steel_X1935 0 0.0 231s US.Steel_X1936 0 0.0 231s US.Steel_X1937 0 0.0 231s US.Steel_X1938 0 0.0 231s US.Steel_X1939 0 0.0 231s US.Steel_X1940 0 0.0 231s US.Steel_X1941 0 0.0 231s US.Steel_X1942 0 0.0 231s US.Steel_X1943 0 0.0 231s US.Steel_X1944 0 0.0 231s US.Steel_X1945 0 0.0 231s US.Steel_X1946 0 0.0 231s US.Steel_X1947 0 0.0 231s US.Steel_X1948 0 0.0 231s US.Steel_X1949 0 0.0 231s US.Steel_X1950 0 0.0 231s US.Steel_X1951 0 0.0 231s US.Steel_X1952 0 0.0 231s US.Steel_X1953 0 0.0 231s US.Steel_X1954 0 0.0 231s Westinghouse_X1935 0 0.0 231s Westinghouse_X1936 0 0.0 231s Westinghouse_X1937 0 0.0 231s Westinghouse_X1938 0 0.0 231s Westinghouse_X1939 0 0.0 231s Westinghouse_X1940 0 0.0 231s Westinghouse_X1941 0 0.0 231s Westinghouse_X1942 0 0.0 231s Westinghouse_X1943 0 0.0 231s Westinghouse_X1944 0 0.0 231s Westinghouse_X1945 0 0.0 231s Westinghouse_X1946 0 0.0 231s Westinghouse_X1947 0 0.0 231s Westinghouse_X1948 0 0.0 231s Westinghouse_X1949 0 0.0 231s Westinghouse_X1950 0 0.0 231s Westinghouse_X1951 0 0.0 231s Westinghouse_X1952 0 0.0 231s Westinghouse_X1953 0 0.0 231s Westinghouse_X1954 0 0.0 231s US.Steel_(Intercept) US.Steel_value US.Steel_capital 231s Chrysler_X1935 0 0 0.0 231s Chrysler_X1936 0 0 0.0 231s Chrysler_X1937 0 0 0.0 231s Chrysler_X1938 0 0 0.0 231s Chrysler_X1939 0 0 0.0 231s Chrysler_X1940 0 0 0.0 231s Chrysler_X1941 0 0 0.0 231s Chrysler_X1942 0 0 0.0 231s Chrysler_X1943 0 0 0.0 231s Chrysler_X1944 0 0 0.0 231s Chrysler_X1945 0 0 0.0 231s Chrysler_X1946 0 0 0.0 231s Chrysler_X1947 0 0 0.0 231s Chrysler_X1948 0 0 0.0 231s Chrysler_X1949 0 0 0.0 231s Chrysler_X1950 0 0 0.0 231s Chrysler_X1951 0 0 0.0 231s Chrysler_X1952 0 0 0.0 231s Chrysler_X1953 0 0 0.0 231s Chrysler_X1954 0 0 0.0 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 1 1362 53.8 231s US.Steel_X1936 1 1807 50.5 231s US.Steel_X1937 1 2676 118.1 231s US.Steel_X1938 1 1802 260.2 231s US.Steel_X1939 1 1957 312.7 231s US.Steel_X1940 1 2203 254.2 231s US.Steel_X1941 1 2380 261.4 231s US.Steel_X1942 1 2169 298.7 231s US.Steel_X1943 1 1985 301.8 231s US.Steel_X1944 1 1814 279.1 231s US.Steel_X1945 1 1850 213.8 231s US.Steel_X1946 1 2068 232.6 231s US.Steel_X1947 1 1797 264.8 231s US.Steel_X1948 1 1626 306.9 231s US.Steel_X1949 1 1667 351.1 231s US.Steel_X1950 1 1677 357.8 231s US.Steel_X1951 1 2290 342.1 231s US.Steel_X1952 1 2159 444.2 231s US.Steel_X1953 1 2031 623.6 231s US.Steel_X1954 1 2116 669.7 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 0 0 231s General.Electric_X1936 0 0 231s General.Electric_X1937 0 0 231s General.Electric_X1938 0 0 231s General.Electric_X1939 0 0 231s General.Electric_X1940 0 0 231s General.Electric_X1941 0 0 231s General.Electric_X1942 0 0 231s General.Electric_X1943 0 0 231s General.Electric_X1944 0 0 231s General.Electric_X1945 0 0 231s General.Electric_X1946 0 0 231s General.Electric_X1947 0 0 231s General.Electric_X1948 0 0 231s General.Electric_X1949 0 0 231s General.Electric_X1950 0 0 231s General.Electric_X1951 0 0 231s General.Electric_X1952 0 0 231s General.Electric_X1953 0 0 231s General.Electric_X1954 0 0 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 1 192 231s Westinghouse_X1936 1 516 231s Westinghouse_X1937 1 729 231s Westinghouse_X1938 1 560 231s Westinghouse_X1939 1 520 231s Westinghouse_X1940 1 628 231s Westinghouse_X1941 1 537 231s Westinghouse_X1942 1 561 231s Westinghouse_X1943 1 617 231s Westinghouse_X1944 1 627 231s Westinghouse_X1945 1 737 231s Westinghouse_X1946 1 760 231s Westinghouse_X1947 1 581 231s Westinghouse_X1948 1 662 231s Westinghouse_X1949 1 584 231s Westinghouse_X1950 1 635 231s Westinghouse_X1951 1 724 231s Westinghouse_X1952 1 864 231s Westinghouse_X1953 1 1194 231s Westinghouse_X1954 1 1189 231s Westinghouse_capital 231s Chrysler_X1935 0.0 231s Chrysler_X1936 0.0 231s Chrysler_X1937 0.0 231s Chrysler_X1938 0.0 231s Chrysler_X1939 0.0 231s Chrysler_X1940 0.0 231s Chrysler_X1941 0.0 231s Chrysler_X1942 0.0 231s Chrysler_X1943 0.0 231s Chrysler_X1944 0.0 231s Chrysler_X1945 0.0 231s Chrysler_X1946 0.0 231s Chrysler_X1947 0.0 231s Chrysler_X1948 0.0 231s Chrysler_X1949 0.0 231s Chrysler_X1950 0.0 231s Chrysler_X1951 0.0 231s Chrysler_X1952 0.0 231s Chrysler_X1953 0.0 231s Chrysler_X1954 0.0 231s General.Electric_X1935 0.0 231s General.Electric_X1936 0.0 231s General.Electric_X1937 0.0 231s General.Electric_X1938 0.0 231s General.Electric_X1939 0.0 231s General.Electric_X1940 0.0 231s General.Electric_X1941 0.0 231s General.Electric_X1942 0.0 231s General.Electric_X1943 0.0 231s General.Electric_X1944 0.0 231s General.Electric_X1945 0.0 231s General.Electric_X1946 0.0 231s General.Electric_X1947 0.0 231s General.Electric_X1948 0.0 231s General.Electric_X1949 0.0 231s General.Electric_X1950 0.0 231s General.Electric_X1951 0.0 231s General.Electric_X1952 0.0 231s General.Electric_X1953 0.0 231s General.Electric_X1954 0.0 231s General.Motors_X1935 0.0 231s General.Motors_X1936 0.0 231s General.Motors_X1937 0.0 231s General.Motors_X1938 0.0 231s General.Motors_X1939 0.0 231s General.Motors_X1940 0.0 231s General.Motors_X1941 0.0 231s General.Motors_X1942 0.0 231s General.Motors_X1943 0.0 231s General.Motors_X1944 0.0 231s General.Motors_X1945 0.0 231s General.Motors_X1946 0.0 231s General.Motors_X1947 0.0 231s General.Motors_X1948 0.0 231s General.Motors_X1949 0.0 231s General.Motors_X1950 0.0 231s General.Motors_X1951 0.0 231s General.Motors_X1952 0.0 231s General.Motors_X1953 0.0 231s General.Motors_X1954 0.0 231s US.Steel_X1935 0.0 231s US.Steel_X1936 0.0 231s US.Steel_X1937 0.0 231s US.Steel_X1938 0.0 231s US.Steel_X1939 0.0 231s US.Steel_X1940 0.0 231s US.Steel_X1941 0.0 231s US.Steel_X1942 0.0 231s US.Steel_X1943 0.0 231s US.Steel_X1944 0.0 231s US.Steel_X1945 0.0 231s US.Steel_X1946 0.0 231s US.Steel_X1947 0.0 231s US.Steel_X1948 0.0 231s US.Steel_X1949 0.0 231s US.Steel_X1950 0.0 231s US.Steel_X1951 0.0 231s US.Steel_X1952 0.0 231s US.Steel_X1953 0.0 231s US.Steel_X1954 0.0 231s Westinghouse_X1935 1.8 231s Westinghouse_X1936 0.8 231s Westinghouse_X1937 7.4 231s Westinghouse_X1938 18.1 231s Westinghouse_X1939 23.5 231s Westinghouse_X1940 26.5 231s Westinghouse_X1941 36.2 231s Westinghouse_X1942 60.8 231s Westinghouse_X1943 84.4 231s Westinghouse_X1944 91.2 231s Westinghouse_X1945 92.4 231s Westinghouse_X1946 86.0 231s Westinghouse_X1947 111.1 231s Westinghouse_X1948 130.6 231s Westinghouse_X1949 141.8 231s Westinghouse_X1950 136.7 231s Westinghouse_X1951 129.7 231s Westinghouse_X1952 145.5 231s Westinghouse_X1953 174.8 231s Westinghouse_X1954 213.5 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s attr(,"variables") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"factors") 231s Chrysler_value Chrysler_capital 231s Chrysler_invest 0 0 231s Chrysler_value 1 0 231s Chrysler_capital 0 1 231s attr(,"term.labels") 231s [1] "Chrysler_value" "Chrysler_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"dataClasses") 231s Chrysler_invest Chrysler_value Chrysler_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s attr(,"variables") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"factors") 231s General.Motors_value General.Motors_capital 231s General.Motors_invest 0 0 231s General.Motors_value 1 0 231s General.Motors_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Motors_value" "General.Motors_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"dataClasses") 231s General.Motors_invest General.Motors_value General.Motors_capital 231s "numeric" "numeric" "numeric" 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s attr(,"variables") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"factors") 231s US.Steel_value US.Steel_capital 231s US.Steel_invest 0 0 231s US.Steel_value 1 0 231s US.Steel_capital 0 1 231s attr(,"term.labels") 231s [1] "US.Steel_value" "US.Steel_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"dataClasses") 231s US.Steel_invest US.Steel_value US.Steel_capital 231s "numeric" "numeric" "numeric" 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s attr(,"variables") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"factors") 231s Westinghouse_value Westinghouse_capital 231s Westinghouse_invest 0 0 231s Westinghouse_value 1 0 231s Westinghouse_capital 0 1 231s attr(,"term.labels") 231s [1] "Westinghouse_value" "Westinghouse_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"dataClasses") 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s "numeric" "numeric" "numeric" 231s 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s attr(,"variables") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"factors") 231s Chrysler_value Chrysler_capital 231s Chrysler_invest 0 0 231s Chrysler_value 1 0 231s Chrysler_capital 0 1 231s attr(,"term.labels") 231s [1] "Chrysler_value" "Chrysler_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"dataClasses") 231s Chrysler_invest Chrysler_value Chrysler_capital 231s "numeric" "numeric" "numeric" 231s > 231s > # SUR 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greeneSur <- systemfit( formulaGrunfeld, "SUR", 231s + data = GrunfeldGreene, methodResidCov = "noDfCor", useMatrix = useMatrix ) 231s + print( greeneSur ) 231s + print( summary( greeneSur ) ) 231s + print( summary( greeneSur, useDfSys = TRUE, residCov = FALSE ) ) 231s + print( summary( greeneSur, equations = FALSE ) ) 231s + print( coef( greeneSur ) ) 231s + print( coef( summary( greeneSur ) ) ) 231s + print( vcov( greeneSur ) ) 231s + print( residuals( greeneSur ) ) 231s + print( confint( greeneSur ) ) 231s + print( fitted( greeneSur ) ) 231s + print( logLik( greeneSur ) ) 231s + print( logLik( greeneSur, residCovDiag = TRUE ) ) 231s + print( nobs( greeneSur ) ) 231s + print( model.frame( greeneSur ) ) 231s + print( model.matrix( greeneSur ) ) 231s + print( formula( greeneSur ) ) 231s + print( formula( greeneSur$eq[[ 1 ]] ) ) 231s + print( terms( greeneSur ) ) 231s + print( terms( greeneSur$eq[[ 1 ]] ) ) 231s + } 231s 231s systemfit results 231s method: SUR 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_value 231s 0.5043 0.0695 231s Chrysler_capital General.Electric_(Intercept) 231s 0.3085 -22.4389 231s General.Electric_value General.Electric_capital 231s 0.0373 0.1308 231s General.Motors_(Intercept) General.Motors_value 231s -162.3641 0.1205 231s General.Motors_capital US.Steel_(Intercept) 231s 0.3827 85.4233 231s US.Steel_value US.Steel_capital 231s 0.1015 0.4000 231s Westinghouse_(Intercept) Westinghouse_value 231s 1.0889 0.0570 231s Westinghouse_capital 231s 0.0415 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 85 347048 6.18e+13 0.844 0.869 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 3057 180 13.4 0.912 0.901 231s General.Electric 20 17 14009 824 28.7 0.688 0.651 231s General.Motors 20 17 144321 8489 92.1 0.921 0.911 231s US.Steel 20 17 183763 10810 104.0 0.422 0.354 231s Westinghouse 20 17 1898 112 10.6 0.726 0.694 231s 231s The covariance matrix of the residuals used for estimation 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 149.9 -21.4 -283 418 13.3 231s General.Electric -21.4 660.8 608 905 176.4 231s General.Motors -282.8 607.5 7160 -2222 126.2 231s US.Steel 418.1 905.0 -2222 8896 546.2 231s Westinghouse 13.3 176.4 126 546 88.7 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 152.85 2.05 -314 455 16.7 231s General.Electric 2.05 700.46 605 1224 200.3 231s General.Motors -313.70 605.34 7216 -2687 129.9 231s US.Steel 455.09 1224.41 -2687 9188 652.7 231s Westinghouse 16.66 200.32 130 653 94.9 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 231s General.Electric 0.00626 1.00000 0.269 0.483 0.777 231s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 231s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 231s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 231s 231s 231s SUR estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 0.5043 11.5128 0.04 0.96557 231s value 0.0695 0.0169 4.12 0.00072 *** 231s capital 0.3085 0.0259 11.93 1.1e-09 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 13.41 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 231s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 231s 231s 231s SUR estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -22.4389 25.5186 -0.88 0.3915 231s value 0.0373 0.0123 3.04 0.0074 ** 231s capital 0.1308 0.0220 5.93 1.6e-05 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 28.707 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 231s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 231s 231s 231s SUR estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -162.3641 89.4592 -1.81 0.087 . 231s value 0.1205 0.0216 5.57 3.4e-05 *** 231s capital 0.3827 0.0328 11.68 1.5e-09 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 92.138 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 231s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 231s 231s 231s SUR estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 85.4233 111.8774 0.76 0.4556 231s value 0.1015 0.0548 1.85 0.0814 . 231s capital 0.4000 0.1278 3.13 0.0061 ** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 103.969 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 231s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 231s 231s 231s SUR estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 1.0889 6.2588 0.17 0.86394 231s value 0.0570 0.0114 5.02 0.00011 *** 231s capital 0.0415 0.0412 1.01 0.32787 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 10.567 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 231s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 231s 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 85 347048 6.18e+13 0.844 0.869 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 3057 180 13.4 0.912 0.901 231s General.Electric 20 17 14009 824 28.7 0.688 0.651 231s General.Motors 20 17 144321 8489 92.1 0.921 0.911 231s US.Steel 20 17 183763 10810 104.0 0.422 0.354 231s Westinghouse 20 17 1898 112 10.6 0.726 0.694 231s 231s 231s SUR estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 0.5043 11.5128 0.04 0.97 231s value 0.0695 0.0169 4.12 8.9e-05 *** 231s capital 0.3085 0.0259 11.93 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 13.41 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 231s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 231s 231s 231s SUR estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -22.4389 25.5186 -0.88 0.3817 231s value 0.0373 0.0123 3.04 0.0031 ** 231s capital 0.1308 0.0220 5.93 6.3e-08 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 28.707 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 231s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 231s 231s 231s SUR estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -162.3641 89.4592 -1.81 0.073 . 231s value 0.1205 0.0216 5.57 2.9e-07 *** 231s capital 0.3827 0.0328 11.68 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 92.138 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 231s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 231s 231s 231s SUR estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 85.4233 111.8774 0.76 0.4473 231s value 0.1015 0.0548 1.85 0.0674 . 231s capital 0.4000 0.1278 3.13 0.0024 ** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 103.969 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 231s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 231s 231s 231s SUR estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 1.0889 6.2588 0.17 0.86 231s value 0.0570 0.0114 5.02 2.8e-06 *** 231s capital 0.0415 0.0412 1.01 0.32 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 10.567 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 231s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 231s 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 85 347048 6.18e+13 0.844 0.869 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 3057 180 13.4 0.912 0.901 231s General.Electric 20 17 14009 824 28.7 0.688 0.651 231s General.Motors 20 17 144321 8489 92.1 0.921 0.911 231s US.Steel 20 17 183763 10810 104.0 0.422 0.354 231s Westinghouse 20 17 1898 112 10.6 0.726 0.694 231s 231s The covariance matrix of the residuals used for estimation 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 149.9 -21.4 -283 418 13.3 231s General.Electric -21.4 660.8 608 905 176.4 231s General.Motors -282.8 607.5 7160 -2222 126.2 231s US.Steel 418.1 905.0 -2222 8896 546.2 231s Westinghouse 13.3 176.4 126 546 88.7 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 152.85 2.05 -314 455 16.7 231s General.Electric 2.05 700.46 605 1224 200.3 231s General.Motors -313.70 605.34 7216 -2687 129.9 231s US.Steel 455.09 1224.41 -2687 9188 652.7 231s Westinghouse 16.66 200.32 130 653 94.9 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 231s General.Electric 0.00626 1.00000 0.269 0.483 0.777 231s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 231s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 231s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) 0.5043 11.5128 0.04 0.96557 231s Chrysler_value 0.0695 0.0169 4.12 0.00072 *** 231s Chrysler_capital 0.3085 0.0259 11.93 1.1e-09 *** 231s General.Electric_(Intercept) -22.4389 25.5186 -0.88 0.39149 231s General.Electric_value 0.0373 0.0123 3.04 0.00738 ** 231s General.Electric_capital 0.1308 0.0220 5.93 1.6e-05 *** 231s General.Motors_(Intercept) -162.3641 89.4592 -1.81 0.08722 . 231s General.Motors_value 0.1205 0.0216 5.57 3.4e-05 *** 231s General.Motors_capital 0.3827 0.0328 11.68 1.5e-09 *** 231s US.Steel_(Intercept) 85.4233 111.8774 0.76 0.45561 231s US.Steel_value 0.1015 0.0548 1.85 0.08142 . 231s US.Steel_capital 0.4000 0.1278 3.13 0.00610 ** 231s Westinghouse_(Intercept) 1.0889 6.2588 0.17 0.86394 231s Westinghouse_value 0.0570 0.0114 5.02 0.00011 *** 231s Westinghouse_capital 0.0415 0.0412 1.01 0.32787 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s Chrysler_(Intercept) Chrysler_value 231s 0.5043 0.0695 231s Chrysler_capital General.Electric_(Intercept) 231s 0.3085 -22.4389 231s General.Electric_value General.Electric_capital 231s 0.0373 0.1308 231s General.Motors_(Intercept) General.Motors_value 231s -162.3641 0.1205 231s General.Motors_capital US.Steel_(Intercept) 231s 0.3827 85.4233 231s US.Steel_value US.Steel_capital 231s 0.1015 0.4000 231s Westinghouse_(Intercept) Westinghouse_value 231s 1.0889 0.0570 231s Westinghouse_capital 231s 0.0415 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) 0.5043 11.5128 0.0438 9.66e-01 231s Chrysler_value 0.0695 0.0169 4.1157 7.22e-04 231s Chrysler_capital 0.3085 0.0259 11.9297 1.10e-09 231s General.Electric_(Intercept) -22.4389 25.5186 -0.8793 3.91e-01 231s General.Electric_value 0.0373 0.0123 3.0409 7.38e-03 231s General.Electric_capital 0.1308 0.0220 5.9313 1.64e-05 231s General.Motors_(Intercept) -162.3641 89.4592 -1.8150 8.72e-02 231s General.Motors_value 0.1205 0.0216 5.5709 3.38e-05 231s General.Motors_capital 0.3827 0.0328 11.6805 1.52e-09 231s US.Steel_(Intercept) 85.4233 111.8774 0.7635 4.56e-01 231s US.Steel_value 0.1015 0.0548 1.8523 8.14e-02 231s US.Steel_capital 0.4000 0.1278 3.1300 6.10e-03 231s Westinghouse_(Intercept) 1.0889 6.2588 0.1740 8.64e-01 231s Westinghouse_value 0.0570 0.0114 5.0174 1.06e-04 231s Westinghouse_capital 0.0415 0.0412 1.0074 3.28e-01 231s Chrysler_(Intercept) Chrysler_value 231s Chrysler_(Intercept) 1.33e+02 -1.82e-01 231s Chrysler_value -1.82e-01 2.86e-04 231s Chrysler_capital 9.57e-03 -1.31e-04 231s General.Electric_(Intercept) -2.94e+01 3.74e-02 231s General.Electric_value 1.28e-02 -1.86e-05 231s General.Electric_capital 8.80e-03 -2.96e-06 231s General.Motors_(Intercept) -1.56e+02 1.91e-01 231s General.Motors_value 3.28e-02 -4.91e-05 231s General.Motors_capital -8.18e-04 3.42e-05 231s US.Steel_(Intercept) 1.80e+02 -1.87e-01 231s US.Steel_value -7.46e-02 1.13e-04 231s US.Steel_capital -4.03e-02 -1.22e-04 231s Westinghouse_(Intercept) -3.04e-01 3.03e-03 231s Westinghouse_value 1.14e-03 -3.70e-06 231s Westinghouse_capital 2.42e-03 -6.41e-06 231s Chrysler_capital General.Electric_(Intercept) 231s Chrysler_(Intercept) 9.57e-03 -29.3642 231s Chrysler_value -1.31e-04 0.0374 231s Chrysler_capital 6.69e-04 0.0198 231s General.Electric_(Intercept) 1.98e-02 651.1982 231s General.Electric_value 1.28e-06 -0.2851 231s General.Electric_capital -5.56e-05 -0.1615 231s General.Motors_(Intercept) 7.79e-02 571.3402 231s General.Motors_value 1.03e-05 -0.1196 231s General.Motors_capital -1.89e-04 -0.0352 231s US.Steel_(Intercept) -2.45e-01 644.2920 231s US.Steel_value -3.26e-05 -0.2201 231s US.Steel_capital 1.03e-03 -0.5505 231s Westinghouse_(Intercept) -9.35e-03 102.8679 231s Westinghouse_value 1.18e-05 -0.1700 231s Westinghouse_capital 1.67e-05 0.2338 231s General.Electric_value General.Electric_capital 231s Chrysler_(Intercept) 1.28e-02 8.80e-03 231s Chrysler_value -1.86e-05 -2.96e-06 231s Chrysler_capital 1.28e-06 -5.56e-05 231s General.Electric_(Intercept) -2.85e-01 -1.61e-01 231s General.Electric_value 1.50e-04 -1.70e-05 231s General.Electric_capital -1.70e-05 4.86e-04 231s General.Motors_(Intercept) -2.61e-01 -8.74e-02 231s General.Motors_value 6.35e-05 -9.49e-06 231s General.Motors_capital -2.27e-05 1.98e-04 231s US.Steel_(Intercept) -3.04e-01 -2.30e-02 231s US.Steel_value 1.35e-04 -1.07e-04 231s US.Steel_capital 1.23e-04 7.77e-04 231s Westinghouse_(Intercept) -4.02e-02 -4.02e-02 231s Westinghouse_value 8.74e-05 1.04e-06 231s Westinghouse_capital -2.16e-04 4.61e-04 231s General.Motors_(Intercept) General.Motors_value 231s Chrysler_(Intercept) -1.56e+02 3.28e-02 231s Chrysler_value 1.91e-01 -4.91e-05 231s Chrysler_capital 7.79e-02 1.03e-05 231s General.Electric_(Intercept) 5.71e+02 -1.20e-01 231s General.Electric_value -2.61e-01 6.35e-05 231s General.Electric_capital -8.74e-02 -9.49e-06 231s General.Motors_(Intercept) 8.00e+03 -1.84e+00 231s General.Motors_value -1.84e+00 4.68e-04 231s General.Motors_capital 5.32e-01 -2.83e-04 231s US.Steel_(Intercept) -1.75e+03 3.73e-01 231s US.Steel_value 8.02e-01 -2.06e-04 231s US.Steel_capital 2.01e-01 1.09e-04 231s Westinghouse_(Intercept) 1.10e+02 -2.33e-02 231s Westinghouse_value -2.06e-01 5.10e-05 231s Westinghouse_capital 3.98e-01 -1.28e-04 231s General.Motors_capital US.Steel_(Intercept) 231s Chrysler_(Intercept) -8.18e-04 1.80e+02 231s Chrysler_value 3.42e-05 -1.87e-01 231s Chrysler_capital -1.89e-04 -2.45e-01 231s General.Electric_(Intercept) -3.52e-02 6.44e+02 231s General.Electric_value -2.27e-05 -3.04e-01 231s General.Electric_capital 1.98e-04 -2.30e-02 231s General.Motors_(Intercept) 5.32e-01 -1.75e+03 231s General.Motors_value -2.83e-04 3.73e-01 231s General.Motors_capital 1.07e-03 3.74e-02 231s US.Steel_(Intercept) 3.74e-02 1.25e+04 231s US.Steel_value 1.39e-04 -5.65e+00 231s US.Steel_capital -1.04e-03 -3.12e+00 231s Westinghouse_(Intercept) -4.87e-03 2.74e+02 231s Westinghouse_value -2.38e-05 -5.09e-01 231s Westinghouse_capital 2.43e-04 1.10e+00 231s US.Steel_value US.Steel_capital 231s Chrysler_(Intercept) -7.46e-02 -0.040281 231s Chrysler_value 1.13e-04 -0.000122 231s Chrysler_capital -3.26e-05 0.001031 231s General.Electric_(Intercept) -2.20e-01 -0.550482 231s General.Electric_value 1.35e-04 0.000123 231s General.Electric_capital -1.07e-04 0.000777 231s General.Motors_(Intercept) 8.02e-01 0.200945 231s General.Motors_value -2.06e-04 0.000109 231s General.Motors_capital 1.39e-04 -0.001036 231s US.Steel_(Intercept) -5.65e+00 -3.119830 231s US.Steel_value 3.00e-03 -0.000901 231s US.Steel_capital -9.01e-04 0.016331 231s Westinghouse_(Intercept) -8.35e-02 -0.275101 231s Westinghouse_value 2.23e-04 0.000229 231s Westinghouse_capital -7.74e-04 0.001422 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_(Intercept) -0.30387 1.14e-03 231s Chrysler_value 0.00303 -3.70e-06 231s Chrysler_capital -0.00935 1.18e-05 231s General.Electric_(Intercept) 102.86790 -1.70e-01 231s General.Electric_value -0.04016 8.74e-05 231s General.Electric_capital -0.04021 1.04e-06 231s General.Motors_(Intercept) 110.26166 -2.06e-01 231s General.Motors_value -0.02326 5.10e-05 231s General.Motors_capital -0.00487 -2.38e-05 231s US.Steel_(Intercept) 274.40848 -5.09e-01 231s US.Steel_value -0.08348 2.23e-04 231s US.Steel_capital -0.27510 2.29e-04 231s Westinghouse_(Intercept) 39.17263 -5.99e-02 231s Westinghouse_value -0.05992 1.29e-04 231s Westinghouse_capital 0.06376 -3.12e-04 231s Westinghouse_capital 231s Chrysler_(Intercept) 2.42e-03 231s Chrysler_value -6.41e-06 231s Chrysler_capital 1.67e-05 231s General.Electric_(Intercept) 2.34e-01 231s General.Electric_value -2.16e-04 231s General.Electric_capital 4.61e-04 231s General.Motors_(Intercept) 3.98e-01 231s General.Motors_value -1.28e-04 231s General.Motors_capital 2.43e-04 231s US.Steel_(Intercept) 1.10e+00 231s US.Steel_value -7.74e-04 231s US.Steel_capital 1.42e-03 231s Westinghouse_(Intercept) 6.38e-02 231s Westinghouse_value -3.12e-04 231s Westinghouse_capital 1.70e-03 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 7.511 -0.905 107.95 -35.3 0.849 231s X1936 10.843 -21.387 -27.67 66.3 -4.639 231s X1937 -6.422 -20.333 -136.20 65.7 -7.906 231s X1938 4.659 -29.453 3.55 -110.1 -10.898 231s X1939 -15.204 -36.171 -104.40 -178.7 -12.863 231s X1940 -2.413 -7.078 -15.30 -149.0 -9.449 231s X1941 -0.116 38.153 28.30 41.3 15.299 231s X1942 -4.311 17.481 103.23 20.6 7.734 231s X1943 -14.728 -23.336 72.44 -46.0 -2.758 231s X1944 -8.172 -25.700 105.03 -92.9 -2.792 231s X1945 12.566 -0.629 38.84 -100.0 -7.681 231s X1946 -14.709 54.737 106.00 32.0 5.446 231s X1947 -7.958 48.169 14.88 46.8 16.715 231s X1948 6.548 37.841 -53.65 121.3 5.293 231s X1949 -8.057 -13.518 -118.82 10.1 -8.216 231s X1950 1.571 -28.788 -67.90 20.0 -10.735 231s X1951 41.064 1.996 -126.32 133.6 6.645 231s X1952 4.273 7.222 -87.37 163.0 15.390 231s X1953 -2.011 8.833 34.43 100.0 13.695 231s X1954 -4.934 -7.135 122.97 -108.7 -9.129 231s 2.5 % 97.5 % 231s Chrysler_(Intercept) -23.786 24.794 231s Chrysler_value 0.034 0.105 231s Chrysler_capital 0.254 0.363 231s General.Electric_(Intercept) -76.278 31.401 231s General.Electric_value 0.011 0.063 231s General.Electric_capital 0.084 0.177 231s General.Motors_(Intercept) -351.107 26.378 231s General.Motors_value 0.075 0.166 231s General.Motors_capital 0.314 0.452 231s US.Steel_(Intercept) -150.617 321.464 231s US.Steel_value -0.014 0.217 231s US.Steel_capital 0.130 0.670 231s Westinghouse_(Intercept) -12.116 14.294 231s Westinghouse_value 0.033 0.081 231s Westinghouse_capital -0.045 0.128 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 32.8 34.0 210 245 12.1 231s X1936 61.9 66.4 419 289 30.5 231s X1937 72.7 97.5 547 404 43.0 231s X1938 46.9 74.1 254 372 33.8 231s X1939 67.6 84.3 435 409 31.7 231s X1940 71.8 81.5 476 411 38.0 231s X1941 68.5 74.8 484 432 33.2 231s X1942 51.1 74.4 345 425 35.6 231s X1943 62.1 84.6 427 408 39.8 231s X1944 67.7 82.5 442 381 40.6 231s X1945 76.2 94.2 522 359 47.0 231s X1946 88.8 105.2 582 388 48.0 231s X1947 70.6 99.0 554 374 38.8 231s X1948 82.8 108.5 583 373 44.3 231s X1949 87.0 111.8 674 395 40.3 231s X1950 99.1 122.3 711 399 43.0 231s X1951 119.6 133.2 882 455 47.7 231s X1952 140.7 150.1 979 482 56.4 231s X1953 176.9 170.7 1270 541 76.4 231s X1954 177.4 196.7 1364 568 77.7 231s 'log Lik.' -459 (df=30) 231s 'log Lik.' -483 (df=30) 231s [1] 100 231s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 231s X1935 40.3 418 10.5 33.1 231s X1936 72.8 838 10.2 45.0 231s X1937 66.3 884 34.7 77.2 231s X1938 51.6 438 51.8 44.6 231s X1939 52.4 680 64.3 48.1 231s X1940 69.4 728 67.1 74.4 231s X1941 68.3 644 75.2 113.0 231s X1942 46.8 411 71.4 91.9 231s X1943 47.4 588 67.1 61.3 231s X1944 59.6 698 60.5 56.8 231s X1945 88.8 846 54.6 93.6 231s X1946 74.1 894 84.8 159.9 231s X1947 62.7 579 96.8 147.2 231s X1948 89.4 695 110.2 146.3 231s X1949 79.0 590 147.4 98.3 231s X1950 100.7 694 163.2 93.5 231s X1951 160.6 809 203.5 135.2 231s X1952 145.0 727 290.6 157.3 231s X1953 174.9 1002 346.1 179.5 231s X1954 172.5 703 414.9 189.6 231s General.Electric_value General.Electric_capital General.Motors_invest 231s X1935 1171 97.8 318 231s X1936 2016 104.4 392 231s X1937 2803 118.0 411 231s X1938 2040 156.2 258 231s X1939 2256 172.6 331 231s X1940 2132 186.6 461 231s X1941 1834 220.9 512 231s X1942 1588 287.8 448 231s X1943 1749 319.9 500 231s X1944 1687 321.3 548 231s X1945 2008 319.6 561 231s X1946 2208 346.0 688 231s X1947 1657 456.4 569 231s X1948 1604 543.4 529 231s X1949 1432 618.3 555 231s X1950 1610 647.4 643 231s X1951 1819 671.3 756 231s X1952 2080 726.1 891 231s X1953 2372 800.3 1304 231s X1954 2760 888.9 1487 231s General.Motors_value General.Motors_capital US.Steel_invest 231s X1935 3078 2.8 210 231s X1936 4662 52.6 355 231s X1937 5387 156.9 470 231s X1938 2792 209.2 262 231s X1939 4313 203.4 230 231s X1940 4644 207.2 262 231s X1941 4551 255.2 473 231s X1942 3244 303.7 446 231s X1943 4054 264.1 362 231s X1944 4379 201.6 288 231s X1945 4841 265.0 259 231s X1946 4901 402.2 420 231s X1947 3526 761.5 420 231s X1948 3255 922.4 494 231s X1949 3700 1020.1 405 231s X1950 3756 1099.0 419 231s X1951 4833 1207.7 588 231s X1952 4925 1430.5 645 231s X1953 6242 1777.3 641 231s X1954 5594 2226.3 459 231s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 231s X1935 1362 53.8 12.9 192 231s X1936 1807 50.5 25.9 516 231s X1937 2676 118.1 35.0 729 231s X1938 1802 260.2 22.9 560 231s X1939 1957 312.7 18.8 520 231s X1940 2203 254.2 28.6 628 231s X1941 2380 261.4 48.5 537 231s X1942 2169 298.7 43.3 561 231s X1943 1985 301.8 37.0 617 231s X1944 1814 279.1 37.8 627 231s X1945 1850 213.8 39.3 737 231s X1946 2068 232.6 53.5 760 231s X1947 1797 264.8 55.6 581 231s X1948 1626 306.9 49.6 662 231s X1949 1667 351.1 32.0 584 231s X1950 1677 357.8 32.2 635 231s X1951 2290 342.1 54.4 724 231s X1952 2159 444.2 71.8 864 231s X1953 2031 623.6 90.1 1194 231s X1954 2116 669.7 68.6 1189 231s Westinghouse_capital 231s X1935 1.8 231s X1936 0.8 231s X1937 7.4 231s X1938 18.1 231s X1939 23.5 231s X1940 26.5 231s X1941 36.2 231s X1942 60.8 231s X1943 84.4 231s X1944 91.2 231s X1945 92.4 231s X1946 86.0 231s X1947 111.1 231s X1948 130.6 231s X1949 141.8 231s X1950 136.7 231s X1951 129.7 231s X1952 145.5 231s X1953 174.8 231s X1954 213.5 231s Chrysler_(Intercept) Chrysler_value Chrysler_capital 231s Chrysler_X1935 1 418 10.5 231s Chrysler_X1936 1 838 10.2 231s Chrysler_X1937 1 884 34.7 231s Chrysler_X1938 1 438 51.8 231s Chrysler_X1939 1 680 64.3 231s Chrysler_X1940 1 728 67.1 231s Chrysler_X1941 1 644 75.2 231s Chrysler_X1942 1 411 71.4 231s Chrysler_X1943 1 588 67.1 231s Chrysler_X1944 1 698 60.5 231s Chrysler_X1945 1 846 54.6 231s Chrysler_X1946 1 894 84.8 231s Chrysler_X1947 1 579 96.8 231s Chrysler_X1948 1 695 110.2 231s Chrysler_X1949 1 590 147.4 231s Chrysler_X1950 1 694 163.2 231s Chrysler_X1951 1 809 203.5 231s Chrysler_X1952 1 727 290.6 231s Chrysler_X1953 1 1002 346.1 231s Chrysler_X1954 1 703 414.9 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 0 0 0.0 231s US.Steel_X1936 0 0 0.0 231s US.Steel_X1937 0 0 0.0 231s US.Steel_X1938 0 0 0.0 231s US.Steel_X1939 0 0 0.0 231s US.Steel_X1940 0 0 0.0 231s US.Steel_X1941 0 0 0.0 231s US.Steel_X1942 0 0 0.0 231s US.Steel_X1943 0 0 0.0 231s US.Steel_X1944 0 0 0.0 231s US.Steel_X1945 0 0 0.0 231s US.Steel_X1946 0 0 0.0 231s US.Steel_X1947 0 0 0.0 231s US.Steel_X1948 0 0 0.0 231s US.Steel_X1949 0 0 0.0 231s US.Steel_X1950 0 0 0.0 231s US.Steel_X1951 0 0 0.0 231s US.Steel_X1952 0 0 0.0 231s US.Steel_X1953 0 0 0.0 231s US.Steel_X1954 0 0 0.0 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s General.Electric_(Intercept) General.Electric_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 1 1171 231s General.Electric_X1936 1 2016 231s General.Electric_X1937 1 2803 231s General.Electric_X1938 1 2040 231s General.Electric_X1939 1 2256 231s General.Electric_X1940 1 2132 231s General.Electric_X1941 1 1834 231s General.Electric_X1942 1 1588 231s General.Electric_X1943 1 1749 231s General.Electric_X1944 1 1687 231s General.Electric_X1945 1 2008 231s General.Electric_X1946 1 2208 231s General.Electric_X1947 1 1657 231s General.Electric_X1948 1 1604 231s General.Electric_X1949 1 1432 231s General.Electric_X1950 1 1610 231s General.Electric_X1951 1 1819 231s General.Electric_X1952 1 2080 231s General.Electric_X1953 1 2372 231s General.Electric_X1954 1 2760 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 0 0 231s Westinghouse_X1936 0 0 231s Westinghouse_X1937 0 0 231s Westinghouse_X1938 0 0 231s Westinghouse_X1939 0 0 231s Westinghouse_X1940 0 0 231s Westinghouse_X1941 0 0 231s Westinghouse_X1942 0 0 231s Westinghouse_X1943 0 0 231s Westinghouse_X1944 0 0 231s Westinghouse_X1945 0 0 231s Westinghouse_X1946 0 0 231s Westinghouse_X1947 0 0 231s Westinghouse_X1948 0 0 231s Westinghouse_X1949 0 0 231s Westinghouse_X1950 0 0 231s Westinghouse_X1951 0 0 231s Westinghouse_X1952 0 0 231s Westinghouse_X1953 0 0 231s Westinghouse_X1954 0 0 231s General.Electric_capital General.Motors_(Intercept) 231s Chrysler_X1935 0.0 0 231s Chrysler_X1936 0.0 0 231s Chrysler_X1937 0.0 0 231s Chrysler_X1938 0.0 0 231s Chrysler_X1939 0.0 0 231s Chrysler_X1940 0.0 0 231s Chrysler_X1941 0.0 0 231s Chrysler_X1942 0.0 0 231s Chrysler_X1943 0.0 0 231s Chrysler_X1944 0.0 0 231s Chrysler_X1945 0.0 0 231s Chrysler_X1946 0.0 0 231s Chrysler_X1947 0.0 0 231s Chrysler_X1948 0.0 0 231s Chrysler_X1949 0.0 0 231s Chrysler_X1950 0.0 0 231s Chrysler_X1951 0.0 0 231s Chrysler_X1952 0.0 0 231s Chrysler_X1953 0.0 0 231s Chrysler_X1954 0.0 0 231s General.Electric_X1935 97.8 0 231s General.Electric_X1936 104.4 0 231s General.Electric_X1937 118.0 0 231s General.Electric_X1938 156.2 0 231s General.Electric_X1939 172.6 0 231s General.Electric_X1940 186.6 0 231s General.Electric_X1941 220.9 0 231s General.Electric_X1942 287.8 0 231s General.Electric_X1943 319.9 0 231s General.Electric_X1944 321.3 0 231s General.Electric_X1945 319.6 0 231s General.Electric_X1946 346.0 0 231s General.Electric_X1947 456.4 0 231s General.Electric_X1948 543.4 0 231s General.Electric_X1949 618.3 0 231s General.Electric_X1950 647.4 0 231s General.Electric_X1951 671.3 0 231s General.Electric_X1952 726.1 0 231s General.Electric_X1953 800.3 0 231s General.Electric_X1954 888.9 0 231s General.Motors_X1935 0.0 1 231s General.Motors_X1936 0.0 1 231s General.Motors_X1937 0.0 1 231s General.Motors_X1938 0.0 1 231s General.Motors_X1939 0.0 1 231s General.Motors_X1940 0.0 1 231s General.Motors_X1941 0.0 1 231s General.Motors_X1942 0.0 1 231s General.Motors_X1943 0.0 1 231s General.Motors_X1944 0.0 1 231s General.Motors_X1945 0.0 1 231s General.Motors_X1946 0.0 1 231s General.Motors_X1947 0.0 1 231s General.Motors_X1948 0.0 1 231s General.Motors_X1949 0.0 1 231s General.Motors_X1950 0.0 1 231s General.Motors_X1951 0.0 1 231s General.Motors_X1952 0.0 1 231s General.Motors_X1953 0.0 1 231s General.Motors_X1954 0.0 1 231s US.Steel_X1935 0.0 0 231s US.Steel_X1936 0.0 0 231s US.Steel_X1937 0.0 0 231s US.Steel_X1938 0.0 0 231s US.Steel_X1939 0.0 0 231s US.Steel_X1940 0.0 0 231s US.Steel_X1941 0.0 0 231s US.Steel_X1942 0.0 0 231s US.Steel_X1943 0.0 0 231s US.Steel_X1944 0.0 0 231s US.Steel_X1945 0.0 0 231s US.Steel_X1946 0.0 0 231s US.Steel_X1947 0.0 0 231s US.Steel_X1948 0.0 0 231s US.Steel_X1949 0.0 0 231s US.Steel_X1950 0.0 0 231s US.Steel_X1951 0.0 0 231s US.Steel_X1952 0.0 0 231s US.Steel_X1953 0.0 0 231s US.Steel_X1954 0.0 0 231s Westinghouse_X1935 0.0 0 231s Westinghouse_X1936 0.0 0 231s Westinghouse_X1937 0.0 0 231s Westinghouse_X1938 0.0 0 231s Westinghouse_X1939 0.0 0 231s Westinghouse_X1940 0.0 0 231s Westinghouse_X1941 0.0 0 231s Westinghouse_X1942 0.0 0 231s Westinghouse_X1943 0.0 0 231s Westinghouse_X1944 0.0 0 231s Westinghouse_X1945 0.0 0 231s Westinghouse_X1946 0.0 0 231s Westinghouse_X1947 0.0 0 231s Westinghouse_X1948 0.0 0 231s Westinghouse_X1949 0.0 0 231s Westinghouse_X1950 0.0 0 231s Westinghouse_X1951 0.0 0 231s Westinghouse_X1952 0.0 0 231s Westinghouse_X1953 0.0 0 231s Westinghouse_X1954 0.0 0 231s General.Motors_value General.Motors_capital 231s Chrysler_X1935 0 0.0 231s Chrysler_X1936 0 0.0 231s Chrysler_X1937 0 0.0 231s Chrysler_X1938 0 0.0 231s Chrysler_X1939 0 0.0 231s Chrysler_X1940 0 0.0 231s Chrysler_X1941 0 0.0 231s Chrysler_X1942 0 0.0 231s Chrysler_X1943 0 0.0 231s Chrysler_X1944 0 0.0 231s Chrysler_X1945 0 0.0 231s Chrysler_X1946 0 0.0 231s Chrysler_X1947 0 0.0 231s Chrysler_X1948 0 0.0 231s Chrysler_X1949 0 0.0 231s Chrysler_X1950 0 0.0 231s Chrysler_X1951 0 0.0 231s Chrysler_X1952 0 0.0 231s Chrysler_X1953 0 0.0 231s Chrysler_X1954 0 0.0 231s General.Electric_X1935 0 0.0 231s General.Electric_X1936 0 0.0 231s General.Electric_X1937 0 0.0 231s General.Electric_X1938 0 0.0 231s General.Electric_X1939 0 0.0 231s General.Electric_X1940 0 0.0 231s General.Electric_X1941 0 0.0 231s General.Electric_X1942 0 0.0 231s General.Electric_X1943 0 0.0 231s General.Electric_X1944 0 0.0 231s General.Electric_X1945 0 0.0 231s General.Electric_X1946 0 0.0 231s General.Electric_X1947 0 0.0 231s General.Electric_X1948 0 0.0 231s General.Electric_X1949 0 0.0 231s General.Electric_X1950 0 0.0 231s General.Electric_X1951 0 0.0 231s General.Electric_X1952 0 0.0 231s General.Electric_X1953 0 0.0 231s General.Electric_X1954 0 0.0 231s General.Motors_X1935 3078 2.8 231s General.Motors_X1936 4662 52.6 231s General.Motors_X1937 5387 156.9 231s General.Motors_X1938 2792 209.2 231s General.Motors_X1939 4313 203.4 231s General.Motors_X1940 4644 207.2 231s General.Motors_X1941 4551 255.2 231s General.Motors_X1942 3244 303.7 231s General.Motors_X1943 4054 264.1 231s General.Motors_X1944 4379 201.6 231s General.Motors_X1945 4841 265.0 231s General.Motors_X1946 4901 402.2 231s General.Motors_X1947 3526 761.5 231s General.Motors_X1948 3255 922.4 231s General.Motors_X1949 3700 1020.1 231s General.Motors_X1950 3756 1099.0 231s General.Motors_X1951 4833 1207.7 231s General.Motors_X1952 4925 1430.5 231s General.Motors_X1953 6242 1777.3 231s General.Motors_X1954 5594 2226.3 231s US.Steel_X1935 0 0.0 231s US.Steel_X1936 0 0.0 231s US.Steel_X1937 0 0.0 231s US.Steel_X1938 0 0.0 231s US.Steel_X1939 0 0.0 231s US.Steel_X1940 0 0.0 231s US.Steel_X1941 0 0.0 231s US.Steel_X1942 0 0.0 231s US.Steel_X1943 0 0.0 231s US.Steel_X1944 0 0.0 231s US.Steel_X1945 0 0.0 231s US.Steel_X1946 0 0.0 231s US.Steel_X1947 0 0.0 231s US.Steel_X1948 0 0.0 231s US.Steel_X1949 0 0.0 231s US.Steel_X1950 0 0.0 231s US.Steel_X1951 0 0.0 231s US.Steel_X1952 0 0.0 231s US.Steel_X1953 0 0.0 231s US.Steel_X1954 0 0.0 231s Westinghouse_X1935 0 0.0 231s Westinghouse_X1936 0 0.0 231s Westinghouse_X1937 0 0.0 231s Westinghouse_X1938 0 0.0 231s Westinghouse_X1939 0 0.0 231s Westinghouse_X1940 0 0.0 231s Westinghouse_X1941 0 0.0 231s Westinghouse_X1942 0 0.0 231s Westinghouse_X1943 0 0.0 231s Westinghouse_X1944 0 0.0 231s Westinghouse_X1945 0 0.0 231s Westinghouse_X1946 0 0.0 231s Westinghouse_X1947 0 0.0 231s Westinghouse_X1948 0 0.0 231s Westinghouse_X1949 0 0.0 231s Westinghouse_X1950 0 0.0 231s Westinghouse_X1951 0 0.0 231s Westinghouse_X1952 0 0.0 231s Westinghouse_X1953 0 0.0 231s Westinghouse_X1954 0 0.0 231s US.Steel_(Intercept) US.Steel_value US.Steel_capital 231s Chrysler_X1935 0 0 0.0 231s Chrysler_X1936 0 0 0.0 231s Chrysler_X1937 0 0 0.0 231s Chrysler_X1938 0 0 0.0 231s Chrysler_X1939 0 0 0.0 231s Chrysler_X1940 0 0 0.0 231s Chrysler_X1941 0 0 0.0 231s Chrysler_X1942 0 0 0.0 231s Chrysler_X1943 0 0 0.0 231s Chrysler_X1944 0 0 0.0 231s Chrysler_X1945 0 0 0.0 231s Chrysler_X1946 0 0 0.0 231s Chrysler_X1947 0 0 0.0 231s Chrysler_X1948 0 0 0.0 231s Chrysler_X1949 0 0 0.0 231s Chrysler_X1950 0 0 0.0 231s Chrysler_X1951 0 0 0.0 231s Chrysler_X1952 0 0 0.0 231s Chrysler_X1953 0 0 0.0 231s Chrysler_X1954 0 0 0.0 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 1 1362 53.8 231s US.Steel_X1936 1 1807 50.5 231s US.Steel_X1937 1 2676 118.1 231s US.Steel_X1938 1 1802 260.2 231s US.Steel_X1939 1 1957 312.7 231s US.Steel_X1940 1 2203 254.2 231s US.Steel_X1941 1 2380 261.4 231s US.Steel_X1942 1 2169 298.7 231s US.Steel_X1943 1 1985 301.8 231s US.Steel_X1944 1 1814 279.1 231s US.Steel_X1945 1 1850 213.8 231s US.Steel_X1946 1 2068 232.6 231s US.Steel_X1947 1 1797 264.8 231s US.Steel_X1948 1 1626 306.9 231s US.Steel_X1949 1 1667 351.1 231s US.Steel_X1950 1 1677 357.8 231s US.Steel_X1951 1 2290 342.1 231s US.Steel_X1952 1 2159 444.2 231s US.Steel_X1953 1 2031 623.6 231s US.Steel_X1954 1 2116 669.7 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 0 0 231s General.Electric_X1936 0 0 231s General.Electric_X1937 0 0 231s General.Electric_X1938 0 0 231s General.Electric_X1939 0 0 231s General.Electric_X1940 0 0 231s General.Electric_X1941 0 0 231s General.Electric_X1942 0 0 231s General.Electric_X1943 0 0 231s General.Electric_X1944 0 0 231s General.Electric_X1945 0 0 231s General.Electric_X1946 0 0 231s General.Electric_X1947 0 0 231s General.Electric_X1948 0 0 231s General.Electric_X1949 0 0 231s General.Electric_X1950 0 0 231s General.Electric_X1951 0 0 231s General.Electric_X1952 0 0 231s General.Electric_X1953 0 0 231s General.Electric_X1954 0 0 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 1 192 231s Westinghouse_X1936 1 516 231s Westinghouse_X1937 1 729 231s Westinghouse_X1938 1 560 231s Westinghouse_X1939 1 520 231s Westinghouse_X1940 1 628 231s Westinghouse_X1941 1 537 231s Westinghouse_X1942 1 561 231s Westinghouse_X1943 1 617 231s Westinghouse_X1944 1 627 231s Westinghouse_X1945 1 737 231s Westinghouse_X1946 1 760 231s Westinghouse_X1947 1 581 231s Westinghouse_X1948 1 662 231s Westinghouse_X1949 1 584 231s Westinghouse_X1950 1 635 231s Westinghouse_X1951 1 724 231s Westinghouse_X1952 1 864 231s Westinghouse_X1953 1 1194 231s Westinghouse_X1954 1 1189 231s Westinghouse_capital 231s Chrysler_X1935 0.0 231s Chrysler_X1936 0.0 231s Chrysler_X1937 0.0 231s Chrysler_X1938 0.0 231s Chrysler_X1939 0.0 231s Chrysler_X1940 0.0 231s Chrysler_X1941 0.0 231s Chrysler_X1942 0.0 231s Chrysler_X1943 0.0 231s Chrysler_X1944 0.0 231s Chrysler_X1945 0.0 231s Chrysler_X1946 0.0 231s Chrysler_X1947 0.0 231s Chrysler_X1948 0.0 231s Chrysler_X1949 0.0 231s Chrysler_X1950 0.0 231s Chrysler_X1951 0.0 231s Chrysler_X1952 0.0 231s Chrysler_X1953 0.0 231s Chrysler_X1954 0.0 231s General.Electric_X1935 0.0 231s General.Electric_X1936 0.0 231s General.Electric_X1937 0.0 231s General.Electric_X1938 0.0 231s General.Electric_X1939 0.0 231s General.Electric_X1940 0.0 231s General.Electric_X1941 0.0 231s General.Electric_X1942 0.0 231s General.Electric_X1943 0.0 231s General.Electric_X1944 0.0 231s General.Electric_X1945 0.0 231s General.Electric_X1946 0.0 231s General.Electric_X1947 0.0 231s General.Electric_X1948 0.0 231s General.Electric_X1949 0.0 231s General.Electric_X1950 0.0 231s General.Electric_X1951 0.0 231s General.Electric_X1952 0.0 231s General.Electric_X1953 0.0 231s General.Electric_X1954 0.0 231s General.Motors_X1935 0.0 231s General.Motors_X1936 0.0 231s General.Motors_X1937 0.0 231s General.Motors_X1938 0.0 231s General.Motors_X1939 0.0 231s General.Motors_X1940 0.0 231s General.Motors_X1941 0.0 231s General.Motors_X1942 0.0 231s General.Motors_X1943 0.0 231s General.Motors_X1944 0.0 231s General.Motors_X1945 0.0 231s General.Motors_X1946 0.0 231s General.Motors_X1947 0.0 231s General.Motors_X1948 0.0 231s General.Motors_X1949 0.0 231s General.Motors_X1950 0.0 231s General.Motors_X1951 0.0 231s General.Motors_X1952 0.0 231s General.Motors_X1953 0.0 231s General.Motors_X1954 0.0 231s US.Steel_X1935 0.0 231s US.Steel_X1936 0.0 231s US.Steel_X1937 0.0 231s US.Steel_X1938 0.0 231s US.Steel_X1939 0.0 231s US.Steel_X1940 0.0 231s US.Steel_X1941 0.0 231s US.Steel_X1942 0.0 231s US.Steel_X1943 0.0 231s US.Steel_X1944 0.0 231s US.Steel_X1945 0.0 231s US.Steel_X1946 0.0 231s US.Steel_X1947 0.0 231s US.Steel_X1948 0.0 231s US.Steel_X1949 0.0 231s US.Steel_X1950 0.0 231s US.Steel_X1951 0.0 231s US.Steel_X1952 0.0 231s US.Steel_X1953 0.0 231s US.Steel_X1954 0.0 231s Westinghouse_X1935 1.8 231s Westinghouse_X1936 0.8 231s Westinghouse_X1937 7.4 231s Westinghouse_X1938 18.1 231s Westinghouse_X1939 23.5 231s Westinghouse_X1940 26.5 231s Westinghouse_X1941 36.2 231s Westinghouse_X1942 60.8 231s Westinghouse_X1943 84.4 231s Westinghouse_X1944 91.2 231s Westinghouse_X1945 92.4 231s Westinghouse_X1946 86.0 231s Westinghouse_X1947 111.1 231s Westinghouse_X1948 130.6 231s Westinghouse_X1949 141.8 231s Westinghouse_X1950 136.7 231s Westinghouse_X1951 129.7 231s Westinghouse_X1952 145.5 231s Westinghouse_X1953 174.8 231s Westinghouse_X1954 213.5 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s attr(,"variables") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"factors") 231s Chrysler_value Chrysler_capital 231s Chrysler_invest 0 0 231s Chrysler_value 1 0 231s Chrysler_capital 0 1 231s attr(,"term.labels") 231s [1] "Chrysler_value" "Chrysler_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"dataClasses") 231s Chrysler_invest Chrysler_value Chrysler_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s attr(,"variables") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"factors") 231s General.Motors_value General.Motors_capital 231s General.Motors_invest 0 0 231s General.Motors_value 1 0 231s General.Motors_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Motors_value" "General.Motors_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"dataClasses") 231s General.Motors_invest General.Motors_value General.Motors_capital 231s "numeric" "numeric" "numeric" 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s attr(,"variables") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"factors") 231s US.Steel_value US.Steel_capital 231s US.Steel_invest 0 0 231s US.Steel_value 1 0 231s US.Steel_capital 0 1 231s attr(,"term.labels") 231s [1] "US.Steel_value" "US.Steel_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"dataClasses") 231s US.Steel_invest US.Steel_value US.Steel_capital 231s "numeric" "numeric" "numeric" 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s attr(,"variables") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"factors") 231s Westinghouse_value Westinghouse_capital 231s Westinghouse_invest 0 0 231s Westinghouse_value 1 0 231s Westinghouse_capital 0 1 231s attr(,"term.labels") 231s [1] "Westinghouse_value" "Westinghouse_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"dataClasses") 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s "numeric" "numeric" "numeric" 231s 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s attr(,"variables") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"factors") 231s Chrysler_value Chrysler_capital 231s Chrysler_invest 0 0 231s Chrysler_value 1 0 231s Chrysler_capital 0 1 231s attr(,"term.labels") 231s [1] "Chrysler_value" "Chrysler_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"dataClasses") 231s Chrysler_invest Chrysler_value Chrysler_capital 231s "numeric" "numeric" "numeric" 231s > 231s > # SUR Pooled 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greeneSurPooled <- systemfit( formulaGrunfeld, "SUR", 231s + data = GrunfeldGreene, pooled = TRUE, methodResidCov = "noDfCor", 231s + residCovWeighted = TRUE, useMatrix = useMatrix ) 231s + print( greeneSurPooled ) 231s + print( summary( greeneSurPooled ) ) 231s + print( summary( greeneSurPooled, useDfSys = FALSE, equations = FALSE ) ) 231s + print( summary( greeneSurPooled, residCov = FALSE, equations = FALSE ) ) 231s + print( coef( greeneSurPooled ) ) 231s + print( coef( greeneSurPooled, modified.regMat = TRUE ) ) 231s + print( coef( summary( greeneSurPooled ) ) ) 231s + print( coef( summary( greeneSurPooled ), modified.regMat = TRUE ) ) 231s + print( vcov( greeneSurPooled ) ) 231s + print( vcov( greeneSurPooled, modified.regMat = TRUE ) ) 231s + print( residuals( greeneSurPooled ) ) 231s + print( confint( greeneSurPooled ) ) 231s + print( fitted( greeneSurPooled ) ) 231s + print( logLik( greeneSurPooled ) ) 231s + print( logLik( greeneSurPooled, residCovDiag = TRUE ) ) 231s + print( nobs( greeneSurPooled ) ) 231s + print( model.frame( greeneSurPooled ) ) 231s + print( model.matrix( greeneSurPooled ) ) 231s + print( formula( greeneSurPooled ) ) 231s + print( formula( greeneSurPooled$eq[[ 1 ]] ) ) 231s + print( terms( greeneSurPooled ) ) 231s + print( terms( greeneSurPooled$eq[[ 1 ]] ) ) 231s + } 231s 231s systemfit results 231s method: SUR 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_value 231s -28.2467 0.0891 231s Chrysler_capital General.Electric_(Intercept) 231s 0.3340 -28.2467 231s General.Electric_value General.Electric_capital 231s 0.0891 0.3340 231s General.Motors_(Intercept) General.Motors_value 231s -28.2467 0.0891 231s General.Motors_capital US.Steel_(Intercept) 231s 0.3340 -28.2467 231s US.Steel_value US.Steel_capital 231s 0.0891 0.3340 231s Westinghouse_(Intercept) Westinghouse_value 231s -28.2467 0.0891 231s Westinghouse_capital 231s 0.3340 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 97 1604301 9.95e+16 0.279 0.844 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 6112 360 19.0 0.824 0.803 231s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 231s General.Motors 20 17 201010 11824 108.7 0.890 0.877 231s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 231s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 231s 231s The covariance matrix of the residuals used for estimation 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 409 -2594 -197 2594 -102 231s General.Electric -2594 36563 -3480 -28623 3797 231s General.Motors -197 -3480 8612 996 -971 231s US.Steel 2594 -28623 996 32903 -2272 231s Westinghouse -102 3797 -971 -2272 778 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 305.61 -1967 -4.81 2159 -124 231s General.Electric -1966.65 34557 -7160.67 -28722 4274 231s General.Motors -4.81 -7161 10050.52 4440 -1401 231s US.Steel 2158.60 -28722 4439.99 34469 -2894 231s Westinghouse -123.92 4274 -1400.75 -2894 833 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 231s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 231s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 231s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 231s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 231s 231s 231s SUR estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s value 0.08910 0.00507 17.57 < 2e-16 *** 231s capital 0.33402 0.01671 19.99 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 18.962 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 6112.2 MSE: 359.541 Root MSE: 18.962 231s Multiple R-Squared: 0.824 Adjusted R-Squared: 0.803 231s 231s 231s SUR estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s value 0.08910 0.00507 17.57 < 2e-16 *** 231s capital 0.33402 0.01671 19.99 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 201.63 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 691132.056 MSE: 40654.827 Root MSE: 201.63 231s Multiple R-Squared: -14.41 Adjusted R-Squared: -16.223 231s 231s 231s SUR estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s value 0.08910 0.00507 17.57 < 2e-16 *** 231s capital 0.33402 0.01671 19.99 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 108.739 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 201010.497 MSE: 11824.147 Root MSE: 108.739 231s Multiple R-Squared: 0.89 Adjusted R-Squared: 0.877 231s 231s 231s SUR estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s value 0.08910 0.00507 17.57 < 2e-16 *** 231s capital 0.33402 0.01671 19.99 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 201.375 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 689379.52 MSE: 40551.736 Root MSE: 201.375 231s Multiple R-Squared: -1.168 Adjusted R-Squared: -1.424 231s 231s 231s SUR estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s value 0.08910 0.00507 17.57 < 2e-16 *** 231s capital 0.33402 0.01671 19.99 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 31.312 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 16667.149 MSE: 980.421 Root MSE: 31.312 231s Multiple R-Squared: -1.402 Adjusted R-Squared: -1.685 231s 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 97 1604301 9.95e+16 0.279 0.844 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 6112 360 19.0 0.824 0.803 231s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 231s General.Motors 20 17 201010 11824 108.7 0.890 0.877 231s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 231s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 231s 231s The covariance matrix of the residuals used for estimation 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 409 -2594 -197 2594 -102 231s General.Electric -2594 36563 -3480 -28623 3797 231s General.Motors -197 -3480 8612 996 -971 231s US.Steel 2594 -28623 996 32903 -2272 231s Westinghouse -102 3797 -971 -2272 778 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 305.61 -1967 -4.81 2159 -124 231s General.Electric -1966.65 34557 -7160.67 -28722 4274 231s General.Motors -4.81 -7161 10050.52 4440 -1401 231s US.Steel 2158.60 -28722 4439.99 34469 -2894 231s Westinghouse -123.92 4274 -1400.75 -2894 833 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 231s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 231s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 231s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 231s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 231s Chrysler_value 0.08910 0.00507 17.57 2.5e-12 *** 231s Chrysler_capital 0.33402 0.01671 19.99 3.0e-13 *** 231s General.Electric_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 231s General.Electric_value 0.08910 0.00507 17.57 2.5e-12 *** 231s General.Electric_capital 0.33402 0.01671 19.99 3.0e-13 *** 231s General.Motors_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 231s General.Motors_value 0.08910 0.00507 17.57 2.5e-12 *** 231s General.Motors_capital 0.33402 0.01671 19.99 3.0e-13 *** 231s US.Steel_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 231s US.Steel_value 0.08910 0.00507 17.57 2.5e-12 *** 231s US.Steel_capital 0.33402 0.01671 19.99 3.0e-13 *** 231s Westinghouse_(Intercept) -28.24669 4.88824 -5.78 2.2e-05 *** 231s Westinghouse_value 0.08910 0.00507 17.57 2.5e-12 *** 231s Westinghouse_capital 0.33402 0.01671 19.99 3.0e-13 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s systemfit results 231s method: SUR 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 97 1604301 9.95e+16 0.279 0.844 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 6112 360 19.0 0.824 0.803 231s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 231s General.Motors 20 17 201010 11824 108.7 0.890 0.877 231s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 231s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 231s 231s 231s Coefficients: 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s Chrysler_value 0.08910 0.00507 17.57 < 2e-16 *** 231s Chrysler_capital 0.33402 0.01671 19.99 < 2e-16 *** 231s General.Electric_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s General.Electric_value 0.08910 0.00507 17.57 < 2e-16 *** 231s General.Electric_capital 0.33402 0.01671 19.99 < 2e-16 *** 231s General.Motors_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s General.Motors_value 0.08910 0.00507 17.57 < 2e-16 *** 231s General.Motors_capital 0.33402 0.01671 19.99 < 2e-16 *** 231s US.Steel_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s US.Steel_value 0.08910 0.00507 17.57 < 2e-16 *** 231s US.Steel_capital 0.33402 0.01671 19.99 < 2e-16 *** 231s Westinghouse_(Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 231s Westinghouse_value 0.08910 0.00507 17.57 < 2e-16 *** 231s Westinghouse_capital 0.33402 0.01671 19.99 < 2e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s Chrysler_(Intercept) Chrysler_value 231s -28.2467 0.0891 231s Chrysler_capital General.Electric_(Intercept) 231s 0.3340 -28.2467 231s General.Electric_value General.Electric_capital 231s 0.0891 0.3340 231s General.Motors_(Intercept) General.Motors_value 231s -28.2467 0.0891 231s General.Motors_capital US.Steel_(Intercept) 231s 0.3340 -28.2467 231s US.Steel_value US.Steel_capital 231s 0.0891 0.3340 231s Westinghouse_(Intercept) Westinghouse_value 231s -28.2467 0.0891 231s Westinghouse_capital 231s 0.3340 231s C1 C2 C3 231s -28.2467 0.0891 0.3340 231s Estimate Std. Error t value Pr(>|t|) 231s Chrysler_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 231s Chrysler_value 0.0891 0.00507 17.57 0.00e+00 231s Chrysler_capital 0.3340 0.01671 19.99 0.00e+00 231s General.Electric_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 231s General.Electric_value 0.0891 0.00507 17.57 0.00e+00 231s General.Electric_capital 0.3340 0.01671 19.99 0.00e+00 231s General.Motors_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 231s General.Motors_value 0.0891 0.00507 17.57 0.00e+00 231s General.Motors_capital 0.3340 0.01671 19.99 0.00e+00 231s US.Steel_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 231s US.Steel_value 0.0891 0.00507 17.57 0.00e+00 231s US.Steel_capital 0.3340 0.01671 19.99 0.00e+00 231s Westinghouse_(Intercept) -28.2467 4.88824 -5.78 9.12e-08 231s Westinghouse_value 0.0891 0.00507 17.57 0.00e+00 231s Westinghouse_capital 0.3340 0.01671 19.99 0.00e+00 231s Estimate Std. Error t value Pr(>|t|) 231s C1 -28.2467 4.88824 -5.78 9.12e-08 231s C2 0.0891 0.00507 17.57 0.00e+00 231s C3 0.3340 0.01671 19.99 0.00e+00 231s Chrysler_(Intercept) Chrysler_value 231s Chrysler_(Intercept) 23.89487 -1.73e-02 231s Chrysler_value -0.01729 2.57e-05 231s Chrysler_capital 0.00114 -4.74e-05 231s General.Electric_(Intercept) 23.89487 -1.73e-02 231s General.Electric_value -0.01729 2.57e-05 231s General.Electric_capital 0.00114 -4.74e-05 231s General.Motors_(Intercept) 23.89487 -1.73e-02 231s General.Motors_value -0.01729 2.57e-05 231s General.Motors_capital 0.00114 -4.74e-05 231s US.Steel_(Intercept) 23.89487 -1.73e-02 231s US.Steel_value -0.01729 2.57e-05 231s US.Steel_capital 0.00114 -4.74e-05 231s Westinghouse_(Intercept) 23.89487 -1.73e-02 231s Westinghouse_value -0.01729 2.57e-05 231s Westinghouse_capital 0.00114 -4.74e-05 231s Chrysler_capital General.Electric_(Intercept) 231s Chrysler_(Intercept) 1.14e-03 23.89487 231s Chrysler_value -4.74e-05 -0.01729 231s Chrysler_capital 2.79e-04 0.00114 231s General.Electric_(Intercept) 1.14e-03 23.89487 231s General.Electric_value -4.74e-05 -0.01729 231s General.Electric_capital 2.79e-04 0.00114 231s General.Motors_(Intercept) 1.14e-03 23.89487 231s General.Motors_value -4.74e-05 -0.01729 231s General.Motors_capital 2.79e-04 0.00114 231s US.Steel_(Intercept) 1.14e-03 23.89487 231s US.Steel_value -4.74e-05 -0.01729 231s US.Steel_capital 2.79e-04 0.00114 231s Westinghouse_(Intercept) 1.14e-03 23.89487 231s Westinghouse_value -4.74e-05 -0.01729 231s Westinghouse_capital 2.79e-04 0.00114 231s General.Electric_value General.Electric_capital 231s Chrysler_(Intercept) -1.73e-02 1.14e-03 231s Chrysler_value 2.57e-05 -4.74e-05 231s Chrysler_capital -4.74e-05 2.79e-04 231s General.Electric_(Intercept) -1.73e-02 1.14e-03 231s General.Electric_value 2.57e-05 -4.74e-05 231s General.Electric_capital -4.74e-05 2.79e-04 231s General.Motors_(Intercept) -1.73e-02 1.14e-03 231s General.Motors_value 2.57e-05 -4.74e-05 231s General.Motors_capital -4.74e-05 2.79e-04 231s US.Steel_(Intercept) -1.73e-02 1.14e-03 231s US.Steel_value 2.57e-05 -4.74e-05 231s US.Steel_capital -4.74e-05 2.79e-04 231s Westinghouse_(Intercept) -1.73e-02 1.14e-03 231s Westinghouse_value 2.57e-05 -4.74e-05 231s Westinghouse_capital -4.74e-05 2.79e-04 231s General.Motors_(Intercept) General.Motors_value 231s Chrysler_(Intercept) 23.89487 -1.73e-02 231s Chrysler_value -0.01729 2.57e-05 231s Chrysler_capital 0.00114 -4.74e-05 231s General.Electric_(Intercept) 23.89487 -1.73e-02 231s General.Electric_value -0.01729 2.57e-05 231s General.Electric_capital 0.00114 -4.74e-05 231s General.Motors_(Intercept) 23.89487 -1.73e-02 231s General.Motors_value -0.01729 2.57e-05 231s General.Motors_capital 0.00114 -4.74e-05 231s US.Steel_(Intercept) 23.89487 -1.73e-02 231s US.Steel_value -0.01729 2.57e-05 231s US.Steel_capital 0.00114 -4.74e-05 231s Westinghouse_(Intercept) 23.89487 -1.73e-02 231s Westinghouse_value -0.01729 2.57e-05 231s Westinghouse_capital 0.00114 -4.74e-05 231s General.Motors_capital US.Steel_(Intercept) 231s Chrysler_(Intercept) 1.14e-03 23.89487 231s Chrysler_value -4.74e-05 -0.01729 231s Chrysler_capital 2.79e-04 0.00114 231s General.Electric_(Intercept) 1.14e-03 23.89487 231s General.Electric_value -4.74e-05 -0.01729 231s General.Electric_capital 2.79e-04 0.00114 231s General.Motors_(Intercept) 1.14e-03 23.89487 231s General.Motors_value -4.74e-05 -0.01729 231s General.Motors_capital 2.79e-04 0.00114 231s US.Steel_(Intercept) 1.14e-03 23.89487 231s US.Steel_value -4.74e-05 -0.01729 231s US.Steel_capital 2.79e-04 0.00114 231s Westinghouse_(Intercept) 1.14e-03 23.89487 231s Westinghouse_value -4.74e-05 -0.01729 231s Westinghouse_capital 2.79e-04 0.00114 231s US.Steel_value US.Steel_capital 231s Chrysler_(Intercept) -1.73e-02 1.14e-03 231s Chrysler_value 2.57e-05 -4.74e-05 231s Chrysler_capital -4.74e-05 2.79e-04 231s General.Electric_(Intercept) -1.73e-02 1.14e-03 231s General.Electric_value 2.57e-05 -4.74e-05 231s General.Electric_capital -4.74e-05 2.79e-04 231s General.Motors_(Intercept) -1.73e-02 1.14e-03 231s General.Motors_value 2.57e-05 -4.74e-05 231s General.Motors_capital -4.74e-05 2.79e-04 231s US.Steel_(Intercept) -1.73e-02 1.14e-03 231s US.Steel_value 2.57e-05 -4.74e-05 231s US.Steel_capital -4.74e-05 2.79e-04 231s Westinghouse_(Intercept) -1.73e-02 1.14e-03 231s Westinghouse_value 2.57e-05 -4.74e-05 231s Westinghouse_capital -4.74e-05 2.79e-04 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_(Intercept) 23.89487 -1.73e-02 231s Chrysler_value -0.01729 2.57e-05 231s Chrysler_capital 0.00114 -4.74e-05 231s General.Electric_(Intercept) 23.89487 -1.73e-02 231s General.Electric_value -0.01729 2.57e-05 231s General.Electric_capital 0.00114 -4.74e-05 231s General.Motors_(Intercept) 23.89487 -1.73e-02 231s General.Motors_value -0.01729 2.57e-05 231s General.Motors_capital 0.00114 -4.74e-05 231s US.Steel_(Intercept) 23.89487 -1.73e-02 231s US.Steel_value -0.01729 2.57e-05 231s US.Steel_capital 0.00114 -4.74e-05 231s Westinghouse_(Intercept) 23.89487 -1.73e-02 231s Westinghouse_value -0.01729 2.57e-05 231s Westinghouse_capital 0.00114 -4.74e-05 231s Westinghouse_capital 231s Chrysler_(Intercept) 1.14e-03 231s Chrysler_value -4.74e-05 231s Chrysler_capital 2.79e-04 231s General.Electric_(Intercept) 1.14e-03 231s General.Electric_value -4.74e-05 231s General.Electric_capital 2.79e-04 231s General.Motors_(Intercept) 1.14e-03 231s General.Motors_value -4.74e-05 231s General.Motors_capital 2.79e-04 231s US.Steel_(Intercept) 1.14e-03 231s US.Steel_value -4.74e-05 231s US.Steel_capital 2.79e-04 231s Westinghouse_(Intercept) 1.14e-03 231s Westinghouse_value -4.74e-05 231s Westinghouse_capital 2.79e-04 231s C1 C2 C3 231s C1 23.89487 -1.73e-02 1.14e-03 231s C2 -0.01729 2.57e-05 -4.74e-05 231s C3 0.00114 -4.74e-05 2.79e-04 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 27.830 -75.6 70.61 98.79 23.51 231s X1936 22.951 -141.2 -12.88 205.66 7.90 231s X1937 4.160 -183.7 -93.56 220.24 -4.13 231s X1938 23.527 -161.1 -32.72 43.09 -4.84 231s X1939 -1.382 -182.3 -93.20 -20.20 -7.09 231s X1940 10.397 -149.7 6.46 8.66 -8.03 231s X1941 14.133 -96.0 49.49 201.63 16.81 231s X1942 14.586 -117.5 85.75 180.85 1.28 231s X1943 0.807 -173.2 78.44 112.17 -17.92 231s X1944 5.381 -172.6 118.21 61.60 -20.25 231s X1945 23.374 -163.8 69.60 50.68 -29.03 231s X1946 -5.596 -124.2 145.33 186.62 -14.78 231s X1947 7.005 -124.6 28.58 200.21 -5.11 231s X1948 18.909 -149.9 -40.65 275.38 -24.83 231s X1949 5.397 -207.5 -87.07 167.54 -39.09 231s X1950 12.604 -238.0 -30.56 178.08 -41.77 231s X1951 48.812 -222.9 -49.87 298.18 -25.19 231s X1952 11.406 -242.3 2.83 332.67 -25.56 231s X1953 -1.660 -270.9 182.86 279.96 -46.40 231s X1954 -0.502 -325.0 272.93 75.36 -80.40 231s 2.5 % 97.5 % 231s Chrysler_(Intercept) -37.948 -18.545 231s Chrysler_value 0.079 0.099 231s Chrysler_capital 0.301 0.367 231s General.Electric_(Intercept) -37.948 -18.545 231s General.Electric_value 0.079 0.099 231s General.Electric_capital 0.301 0.367 231s General.Motors_(Intercept) -37.948 -18.545 231s General.Motors_value 0.079 0.099 231s General.Motors_capital 0.301 0.367 231s US.Steel_(Intercept) -37.948 -18.545 231s US.Steel_value 0.079 0.099 231s US.Steel_capital 0.301 0.367 231s Westinghouse_(Intercept) -37.948 -18.545 231s Westinghouse_value 0.079 0.099 231s Westinghouse_capital 0.301 0.367 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s X1935 12.5 109 247 111 -10.6 231s X1936 49.8 186 405 150 18.0 231s X1937 62.1 261 504 250 39.2 231s X1938 28.1 206 290 219 27.7 231s X1939 53.8 230 424 251 25.9 231s X1940 59.0 224 455 253 36.6 231s X1941 54.2 209 463 271 31.7 231s X1942 32.2 209 362 265 42.1 231s X1943 46.6 234 421 249 54.9 231s X1944 54.2 229 429 227 58.1 231s X1945 65.4 257 492 208 68.3 231s X1946 79.7 284 543 234 68.2 231s X1947 55.7 272 540 220 60.7 231s X1948 70.5 296 570 219 74.4 231s X1949 73.6 306 642 238 71.1 231s X1950 88.1 331 673 241 74.0 231s X1951 111.8 358 806 290 79.6 231s X1952 133.6 400 888 313 97.3 231s X1953 176.6 450 1122 361 136.5 231s X1954 173.0 515 1214 384 149.0 231s 'log Lik.' -533 (df=18) 231s 'log Lik.' -568 (df=18) 231s [1] 100 231s Chrysler_invest Chrysler_value Chrysler_capital General.Electric_invest 231s X1935 40.3 418 10.5 33.1 231s X1936 72.8 838 10.2 45.0 231s X1937 66.3 884 34.7 77.2 231s X1938 51.6 438 51.8 44.6 231s X1939 52.4 680 64.3 48.1 231s X1940 69.4 728 67.1 74.4 231s X1941 68.3 644 75.2 113.0 231s X1942 46.8 411 71.4 91.9 231s X1943 47.4 588 67.1 61.3 231s X1944 59.6 698 60.5 56.8 231s X1945 88.8 846 54.6 93.6 231s X1946 74.1 894 84.8 159.9 231s X1947 62.7 579 96.8 147.2 231s X1948 89.4 695 110.2 146.3 231s X1949 79.0 590 147.4 98.3 231s X1950 100.7 694 163.2 93.5 231s X1951 160.6 809 203.5 135.2 231s X1952 145.0 727 290.6 157.3 231s X1953 174.9 1002 346.1 179.5 231s X1954 172.5 703 414.9 189.6 231s General.Electric_value General.Electric_capital General.Motors_invest 231s X1935 1171 97.8 318 231s X1936 2016 104.4 392 231s X1937 2803 118.0 411 231s X1938 2040 156.2 258 231s X1939 2256 172.6 331 231s X1940 2132 186.6 461 231s X1941 1834 220.9 512 231s X1942 1588 287.8 448 231s X1943 1749 319.9 500 231s X1944 1687 321.3 548 231s X1945 2008 319.6 561 231s X1946 2208 346.0 688 231s X1947 1657 456.4 569 231s X1948 1604 543.4 529 231s X1949 1432 618.3 555 231s X1950 1610 647.4 643 231s X1951 1819 671.3 756 231s X1952 2080 726.1 891 231s X1953 2372 800.3 1304 231s X1954 2760 888.9 1487 231s General.Motors_value General.Motors_capital US.Steel_invest 231s X1935 3078 2.8 210 231s X1936 4662 52.6 355 231s X1937 5387 156.9 470 231s X1938 2792 209.2 262 231s X1939 4313 203.4 230 231s X1940 4644 207.2 262 231s X1941 4551 255.2 473 231s X1942 3244 303.7 446 231s X1943 4054 264.1 362 231s X1944 4379 201.6 288 231s X1945 4841 265.0 259 231s X1946 4901 402.2 420 231s X1947 3526 761.5 420 231s X1948 3255 922.4 494 231s X1949 3700 1020.1 405 231s X1950 3756 1099.0 419 231s X1951 4833 1207.7 588 231s X1952 4925 1430.5 645 231s X1953 6242 1777.3 641 231s X1954 5594 2226.3 459 231s US.Steel_value US.Steel_capital Westinghouse_invest Westinghouse_value 231s X1935 1362 53.8 12.9 192 231s X1936 1807 50.5 25.9 516 231s X1937 2676 118.1 35.0 729 231s X1938 1802 260.2 22.9 560 231s X1939 1957 312.7 18.8 520 231s X1940 2203 254.2 28.6 628 231s X1941 2380 261.4 48.5 537 231s X1942 2169 298.7 43.3 561 231s X1943 1985 301.8 37.0 617 231s X1944 1814 279.1 37.8 627 231s X1945 1850 213.8 39.3 737 231s X1946 2068 232.6 53.5 760 231s X1947 1797 264.8 55.6 581 231s X1948 1626 306.9 49.6 662 231s X1949 1667 351.1 32.0 584 231s X1950 1677 357.8 32.2 635 231s X1951 2290 342.1 54.4 724 231s X1952 2159 444.2 71.8 864 231s X1953 2031 623.6 90.1 1194 231s X1954 2116 669.7 68.6 1189 231s Westinghouse_capital 231s X1935 1.8 231s X1936 0.8 231s X1937 7.4 231s X1938 18.1 231s X1939 23.5 231s X1940 26.5 231s X1941 36.2 231s X1942 60.8 231s X1943 84.4 231s X1944 91.2 231s X1945 92.4 231s X1946 86.0 231s X1947 111.1 231s X1948 130.6 231s X1949 141.8 231s X1950 136.7 231s X1951 129.7 231s X1952 145.5 231s X1953 174.8 231s X1954 213.5 231s Chrysler_(Intercept) Chrysler_value Chrysler_capital 231s Chrysler_X1935 1 418 10.5 231s Chrysler_X1936 1 838 10.2 231s Chrysler_X1937 1 884 34.7 231s Chrysler_X1938 1 438 51.8 231s Chrysler_X1939 1 680 64.3 231s Chrysler_X1940 1 728 67.1 231s Chrysler_X1941 1 644 75.2 231s Chrysler_X1942 1 411 71.4 231s Chrysler_X1943 1 588 67.1 231s Chrysler_X1944 1 698 60.5 231s Chrysler_X1945 1 846 54.6 231s Chrysler_X1946 1 894 84.8 231s Chrysler_X1947 1 579 96.8 231s Chrysler_X1948 1 695 110.2 231s Chrysler_X1949 1 590 147.4 231s Chrysler_X1950 1 694 163.2 231s Chrysler_X1951 1 809 203.5 231s Chrysler_X1952 1 727 290.6 231s Chrysler_X1953 1 1002 346.1 231s Chrysler_X1954 1 703 414.9 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 0 0 0.0 231s US.Steel_X1936 0 0 0.0 231s US.Steel_X1937 0 0 0.0 231s US.Steel_X1938 0 0 0.0 231s US.Steel_X1939 0 0 0.0 231s US.Steel_X1940 0 0 0.0 231s US.Steel_X1941 0 0 0.0 231s US.Steel_X1942 0 0 0.0 231s US.Steel_X1943 0 0 0.0 231s US.Steel_X1944 0 0 0.0 231s US.Steel_X1945 0 0 0.0 231s US.Steel_X1946 0 0 0.0 231s US.Steel_X1947 0 0 0.0 231s US.Steel_X1948 0 0 0.0 231s US.Steel_X1949 0 0 0.0 231s US.Steel_X1950 0 0 0.0 231s US.Steel_X1951 0 0 0.0 231s US.Steel_X1952 0 0 0.0 231s US.Steel_X1953 0 0 0.0 231s US.Steel_X1954 0 0 0.0 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s General.Electric_(Intercept) General.Electric_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 1 1171 231s General.Electric_X1936 1 2016 231s General.Electric_X1937 1 2803 231s General.Electric_X1938 1 2040 231s General.Electric_X1939 1 2256 231s General.Electric_X1940 1 2132 231s General.Electric_X1941 1 1834 231s General.Electric_X1942 1 1588 231s General.Electric_X1943 1 1749 231s General.Electric_X1944 1 1687 231s General.Electric_X1945 1 2008 231s General.Electric_X1946 1 2208 231s General.Electric_X1947 1 1657 231s General.Electric_X1948 1 1604 231s General.Electric_X1949 1 1432 231s General.Electric_X1950 1 1610 231s General.Electric_X1951 1 1819 231s General.Electric_X1952 1 2080 231s General.Electric_X1953 1 2372 231s General.Electric_X1954 1 2760 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 0 0 231s Westinghouse_X1936 0 0 231s Westinghouse_X1937 0 0 231s Westinghouse_X1938 0 0 231s Westinghouse_X1939 0 0 231s Westinghouse_X1940 0 0 231s Westinghouse_X1941 0 0 231s Westinghouse_X1942 0 0 231s Westinghouse_X1943 0 0 231s Westinghouse_X1944 0 0 231s Westinghouse_X1945 0 0 231s Westinghouse_X1946 0 0 231s Westinghouse_X1947 0 0 231s Westinghouse_X1948 0 0 231s Westinghouse_X1949 0 0 231s Westinghouse_X1950 0 0 231s Westinghouse_X1951 0 0 231s Westinghouse_X1952 0 0 231s Westinghouse_X1953 0 0 231s Westinghouse_X1954 0 0 231s General.Electric_capital General.Motors_(Intercept) 231s Chrysler_X1935 0.0 0 231s Chrysler_X1936 0.0 0 231s Chrysler_X1937 0.0 0 231s Chrysler_X1938 0.0 0 231s Chrysler_X1939 0.0 0 231s Chrysler_X1940 0.0 0 231s Chrysler_X1941 0.0 0 231s Chrysler_X1942 0.0 0 231s Chrysler_X1943 0.0 0 231s Chrysler_X1944 0.0 0 231s Chrysler_X1945 0.0 0 231s Chrysler_X1946 0.0 0 231s Chrysler_X1947 0.0 0 231s Chrysler_X1948 0.0 0 231s Chrysler_X1949 0.0 0 231s Chrysler_X1950 0.0 0 231s Chrysler_X1951 0.0 0 231s Chrysler_X1952 0.0 0 231s Chrysler_X1953 0.0 0 231s Chrysler_X1954 0.0 0 231s General.Electric_X1935 97.8 0 231s General.Electric_X1936 104.4 0 231s General.Electric_X1937 118.0 0 231s General.Electric_X1938 156.2 0 231s General.Electric_X1939 172.6 0 231s General.Electric_X1940 186.6 0 231s General.Electric_X1941 220.9 0 231s General.Electric_X1942 287.8 0 231s General.Electric_X1943 319.9 0 231s General.Electric_X1944 321.3 0 231s General.Electric_X1945 319.6 0 231s General.Electric_X1946 346.0 0 231s General.Electric_X1947 456.4 0 231s General.Electric_X1948 543.4 0 231s General.Electric_X1949 618.3 0 231s General.Electric_X1950 647.4 0 231s General.Electric_X1951 671.3 0 231s General.Electric_X1952 726.1 0 231s General.Electric_X1953 800.3 0 231s General.Electric_X1954 888.9 0 231s General.Motors_X1935 0.0 1 231s General.Motors_X1936 0.0 1 231s General.Motors_X1937 0.0 1 231s General.Motors_X1938 0.0 1 231s General.Motors_X1939 0.0 1 231s General.Motors_X1940 0.0 1 231s General.Motors_X1941 0.0 1 231s General.Motors_X1942 0.0 1 231s General.Motors_X1943 0.0 1 231s General.Motors_X1944 0.0 1 231s General.Motors_X1945 0.0 1 231s General.Motors_X1946 0.0 1 231s General.Motors_X1947 0.0 1 231s General.Motors_X1948 0.0 1 231s General.Motors_X1949 0.0 1 231s General.Motors_X1950 0.0 1 231s General.Motors_X1951 0.0 1 231s General.Motors_X1952 0.0 1 231s General.Motors_X1953 0.0 1 231s General.Motors_X1954 0.0 1 231s US.Steel_X1935 0.0 0 231s US.Steel_X1936 0.0 0 231s US.Steel_X1937 0.0 0 231s US.Steel_X1938 0.0 0 231s US.Steel_X1939 0.0 0 231s US.Steel_X1940 0.0 0 231s US.Steel_X1941 0.0 0 231s US.Steel_X1942 0.0 0 231s US.Steel_X1943 0.0 0 231s US.Steel_X1944 0.0 0 231s US.Steel_X1945 0.0 0 231s US.Steel_X1946 0.0 0 231s US.Steel_X1947 0.0 0 231s US.Steel_X1948 0.0 0 231s US.Steel_X1949 0.0 0 231s US.Steel_X1950 0.0 0 231s US.Steel_X1951 0.0 0 231s US.Steel_X1952 0.0 0 231s US.Steel_X1953 0.0 0 231s US.Steel_X1954 0.0 0 231s Westinghouse_X1935 0.0 0 231s Westinghouse_X1936 0.0 0 231s Westinghouse_X1937 0.0 0 231s Westinghouse_X1938 0.0 0 231s Westinghouse_X1939 0.0 0 231s Westinghouse_X1940 0.0 0 231s Westinghouse_X1941 0.0 0 231s Westinghouse_X1942 0.0 0 231s Westinghouse_X1943 0.0 0 231s Westinghouse_X1944 0.0 0 231s Westinghouse_X1945 0.0 0 231s Westinghouse_X1946 0.0 0 231s Westinghouse_X1947 0.0 0 231s Westinghouse_X1948 0.0 0 231s Westinghouse_X1949 0.0 0 231s Westinghouse_X1950 0.0 0 231s Westinghouse_X1951 0.0 0 231s Westinghouse_X1952 0.0 0 231s Westinghouse_X1953 0.0 0 231s Westinghouse_X1954 0.0 0 231s General.Motors_value General.Motors_capital 231s Chrysler_X1935 0 0.0 231s Chrysler_X1936 0 0.0 231s Chrysler_X1937 0 0.0 231s Chrysler_X1938 0 0.0 231s Chrysler_X1939 0 0.0 231s Chrysler_X1940 0 0.0 231s Chrysler_X1941 0 0.0 231s Chrysler_X1942 0 0.0 231s Chrysler_X1943 0 0.0 231s Chrysler_X1944 0 0.0 231s Chrysler_X1945 0 0.0 231s Chrysler_X1946 0 0.0 231s Chrysler_X1947 0 0.0 231s Chrysler_X1948 0 0.0 231s Chrysler_X1949 0 0.0 231s Chrysler_X1950 0 0.0 231s Chrysler_X1951 0 0.0 231s Chrysler_X1952 0 0.0 231s Chrysler_X1953 0 0.0 231s Chrysler_X1954 0 0.0 231s General.Electric_X1935 0 0.0 231s General.Electric_X1936 0 0.0 231s General.Electric_X1937 0 0.0 231s General.Electric_X1938 0 0.0 231s General.Electric_X1939 0 0.0 231s General.Electric_X1940 0 0.0 231s General.Electric_X1941 0 0.0 231s General.Electric_X1942 0 0.0 231s General.Electric_X1943 0 0.0 231s General.Electric_X1944 0 0.0 231s General.Electric_X1945 0 0.0 231s General.Electric_X1946 0 0.0 231s General.Electric_X1947 0 0.0 231s General.Electric_X1948 0 0.0 231s General.Electric_X1949 0 0.0 231s General.Electric_X1950 0 0.0 231s General.Electric_X1951 0 0.0 231s General.Electric_X1952 0 0.0 231s General.Electric_X1953 0 0.0 231s General.Electric_X1954 0 0.0 231s General.Motors_X1935 3078 2.8 231s General.Motors_X1936 4662 52.6 231s General.Motors_X1937 5387 156.9 231s General.Motors_X1938 2792 209.2 231s General.Motors_X1939 4313 203.4 231s General.Motors_X1940 4644 207.2 231s General.Motors_X1941 4551 255.2 231s General.Motors_X1942 3244 303.7 231s General.Motors_X1943 4054 264.1 231s General.Motors_X1944 4379 201.6 231s General.Motors_X1945 4841 265.0 231s General.Motors_X1946 4901 402.2 231s General.Motors_X1947 3526 761.5 231s General.Motors_X1948 3255 922.4 231s General.Motors_X1949 3700 1020.1 231s General.Motors_X1950 3756 1099.0 231s General.Motors_X1951 4833 1207.7 231s General.Motors_X1952 4925 1430.5 231s General.Motors_X1953 6242 1777.3 231s General.Motors_X1954 5594 2226.3 231s US.Steel_X1935 0 0.0 231s US.Steel_X1936 0 0.0 231s US.Steel_X1937 0 0.0 231s US.Steel_X1938 0 0.0 231s US.Steel_X1939 0 0.0 231s US.Steel_X1940 0 0.0 231s US.Steel_X1941 0 0.0 231s US.Steel_X1942 0 0.0 231s US.Steel_X1943 0 0.0 231s US.Steel_X1944 0 0.0 231s US.Steel_X1945 0 0.0 231s US.Steel_X1946 0 0.0 231s US.Steel_X1947 0 0.0 231s US.Steel_X1948 0 0.0 231s US.Steel_X1949 0 0.0 231s US.Steel_X1950 0 0.0 231s US.Steel_X1951 0 0.0 231s US.Steel_X1952 0 0.0 231s US.Steel_X1953 0 0.0 231s US.Steel_X1954 0 0.0 231s Westinghouse_X1935 0 0.0 231s Westinghouse_X1936 0 0.0 231s Westinghouse_X1937 0 0.0 231s Westinghouse_X1938 0 0.0 231s Westinghouse_X1939 0 0.0 231s Westinghouse_X1940 0 0.0 231s Westinghouse_X1941 0 0.0 231s Westinghouse_X1942 0 0.0 231s Westinghouse_X1943 0 0.0 231s Westinghouse_X1944 0 0.0 231s Westinghouse_X1945 0 0.0 231s Westinghouse_X1946 0 0.0 231s Westinghouse_X1947 0 0.0 231s Westinghouse_X1948 0 0.0 231s Westinghouse_X1949 0 0.0 231s Westinghouse_X1950 0 0.0 231s Westinghouse_X1951 0 0.0 231s Westinghouse_X1952 0 0.0 231s Westinghouse_X1953 0 0.0 231s Westinghouse_X1954 0 0.0 231s US.Steel_(Intercept) US.Steel_value US.Steel_capital 231s Chrysler_X1935 0 0 0.0 231s Chrysler_X1936 0 0 0.0 231s Chrysler_X1937 0 0 0.0 231s Chrysler_X1938 0 0 0.0 231s Chrysler_X1939 0 0 0.0 231s Chrysler_X1940 0 0 0.0 231s Chrysler_X1941 0 0 0.0 231s Chrysler_X1942 0 0 0.0 231s Chrysler_X1943 0 0 0.0 231s Chrysler_X1944 0 0 0.0 231s Chrysler_X1945 0 0 0.0 231s Chrysler_X1946 0 0 0.0 231s Chrysler_X1947 0 0 0.0 231s Chrysler_X1948 0 0 0.0 231s Chrysler_X1949 0 0 0.0 231s Chrysler_X1950 0 0 0.0 231s Chrysler_X1951 0 0 0.0 231s Chrysler_X1952 0 0 0.0 231s Chrysler_X1953 0 0 0.0 231s Chrysler_X1954 0 0 0.0 231s General.Electric_X1935 0 0 0.0 231s General.Electric_X1936 0 0 0.0 231s General.Electric_X1937 0 0 0.0 231s General.Electric_X1938 0 0 0.0 231s General.Electric_X1939 0 0 0.0 231s General.Electric_X1940 0 0 0.0 231s General.Electric_X1941 0 0 0.0 231s General.Electric_X1942 0 0 0.0 231s General.Electric_X1943 0 0 0.0 231s General.Electric_X1944 0 0 0.0 231s General.Electric_X1945 0 0 0.0 231s General.Electric_X1946 0 0 0.0 231s General.Electric_X1947 0 0 0.0 231s General.Electric_X1948 0 0 0.0 231s General.Electric_X1949 0 0 0.0 231s General.Electric_X1950 0 0 0.0 231s General.Electric_X1951 0 0 0.0 231s General.Electric_X1952 0 0 0.0 231s General.Electric_X1953 0 0 0.0 231s General.Electric_X1954 0 0 0.0 231s General.Motors_X1935 0 0 0.0 231s General.Motors_X1936 0 0 0.0 231s General.Motors_X1937 0 0 0.0 231s General.Motors_X1938 0 0 0.0 231s General.Motors_X1939 0 0 0.0 231s General.Motors_X1940 0 0 0.0 231s General.Motors_X1941 0 0 0.0 231s General.Motors_X1942 0 0 0.0 231s General.Motors_X1943 0 0 0.0 231s General.Motors_X1944 0 0 0.0 231s General.Motors_X1945 0 0 0.0 231s General.Motors_X1946 0 0 0.0 231s General.Motors_X1947 0 0 0.0 231s General.Motors_X1948 0 0 0.0 231s General.Motors_X1949 0 0 0.0 231s General.Motors_X1950 0 0 0.0 231s General.Motors_X1951 0 0 0.0 231s General.Motors_X1952 0 0 0.0 231s General.Motors_X1953 0 0 0.0 231s General.Motors_X1954 0 0 0.0 231s US.Steel_X1935 1 1362 53.8 231s US.Steel_X1936 1 1807 50.5 231s US.Steel_X1937 1 2676 118.1 231s US.Steel_X1938 1 1802 260.2 231s US.Steel_X1939 1 1957 312.7 231s US.Steel_X1940 1 2203 254.2 231s US.Steel_X1941 1 2380 261.4 231s US.Steel_X1942 1 2169 298.7 231s US.Steel_X1943 1 1985 301.8 231s US.Steel_X1944 1 1814 279.1 231s US.Steel_X1945 1 1850 213.8 231s US.Steel_X1946 1 2068 232.6 231s US.Steel_X1947 1 1797 264.8 231s US.Steel_X1948 1 1626 306.9 231s US.Steel_X1949 1 1667 351.1 231s US.Steel_X1950 1 1677 357.8 231s US.Steel_X1951 1 2290 342.1 231s US.Steel_X1952 1 2159 444.2 231s US.Steel_X1953 1 2031 623.6 231s US.Steel_X1954 1 2116 669.7 231s Westinghouse_X1935 0 0 0.0 231s Westinghouse_X1936 0 0 0.0 231s Westinghouse_X1937 0 0 0.0 231s Westinghouse_X1938 0 0 0.0 231s Westinghouse_X1939 0 0 0.0 231s Westinghouse_X1940 0 0 0.0 231s Westinghouse_X1941 0 0 0.0 231s Westinghouse_X1942 0 0 0.0 231s Westinghouse_X1943 0 0 0.0 231s Westinghouse_X1944 0 0 0.0 231s Westinghouse_X1945 0 0 0.0 231s Westinghouse_X1946 0 0 0.0 231s Westinghouse_X1947 0 0 0.0 231s Westinghouse_X1948 0 0 0.0 231s Westinghouse_X1949 0 0 0.0 231s Westinghouse_X1950 0 0 0.0 231s Westinghouse_X1951 0 0 0.0 231s Westinghouse_X1952 0 0 0.0 231s Westinghouse_X1953 0 0 0.0 231s Westinghouse_X1954 0 0 0.0 231s Westinghouse_(Intercept) Westinghouse_value 231s Chrysler_X1935 0 0 231s Chrysler_X1936 0 0 231s Chrysler_X1937 0 0 231s Chrysler_X1938 0 0 231s Chrysler_X1939 0 0 231s Chrysler_X1940 0 0 231s Chrysler_X1941 0 0 231s Chrysler_X1942 0 0 231s Chrysler_X1943 0 0 231s Chrysler_X1944 0 0 231s Chrysler_X1945 0 0 231s Chrysler_X1946 0 0 231s Chrysler_X1947 0 0 231s Chrysler_X1948 0 0 231s Chrysler_X1949 0 0 231s Chrysler_X1950 0 0 231s Chrysler_X1951 0 0 231s Chrysler_X1952 0 0 231s Chrysler_X1953 0 0 231s Chrysler_X1954 0 0 231s General.Electric_X1935 0 0 231s General.Electric_X1936 0 0 231s General.Electric_X1937 0 0 231s General.Electric_X1938 0 0 231s General.Electric_X1939 0 0 231s General.Electric_X1940 0 0 231s General.Electric_X1941 0 0 231s General.Electric_X1942 0 0 231s General.Electric_X1943 0 0 231s General.Electric_X1944 0 0 231s General.Electric_X1945 0 0 231s General.Electric_X1946 0 0 231s General.Electric_X1947 0 0 231s General.Electric_X1948 0 0 231s General.Electric_X1949 0 0 231s General.Electric_X1950 0 0 231s General.Electric_X1951 0 0 231s General.Electric_X1952 0 0 231s General.Electric_X1953 0 0 231s General.Electric_X1954 0 0 231s General.Motors_X1935 0 0 231s General.Motors_X1936 0 0 231s General.Motors_X1937 0 0 231s General.Motors_X1938 0 0 231s General.Motors_X1939 0 0 231s General.Motors_X1940 0 0 231s General.Motors_X1941 0 0 231s General.Motors_X1942 0 0 231s General.Motors_X1943 0 0 231s General.Motors_X1944 0 0 231s General.Motors_X1945 0 0 231s General.Motors_X1946 0 0 231s General.Motors_X1947 0 0 231s General.Motors_X1948 0 0 231s General.Motors_X1949 0 0 231s General.Motors_X1950 0 0 231s General.Motors_X1951 0 0 231s General.Motors_X1952 0 0 231s General.Motors_X1953 0 0 231s General.Motors_X1954 0 0 231s US.Steel_X1935 0 0 231s US.Steel_X1936 0 0 231s US.Steel_X1937 0 0 231s US.Steel_X1938 0 0 231s US.Steel_X1939 0 0 231s US.Steel_X1940 0 0 231s US.Steel_X1941 0 0 231s US.Steel_X1942 0 0 231s US.Steel_X1943 0 0 231s US.Steel_X1944 0 0 231s US.Steel_X1945 0 0 231s US.Steel_X1946 0 0 231s US.Steel_X1947 0 0 231s US.Steel_X1948 0 0 231s US.Steel_X1949 0 0 231s US.Steel_X1950 0 0 231s US.Steel_X1951 0 0 231s US.Steel_X1952 0 0 231s US.Steel_X1953 0 0 231s US.Steel_X1954 0 0 231s Westinghouse_X1935 1 192 231s Westinghouse_X1936 1 516 231s Westinghouse_X1937 1 729 231s Westinghouse_X1938 1 560 231s Westinghouse_X1939 1 520 231s Westinghouse_X1940 1 628 231s Westinghouse_X1941 1 537 231s Westinghouse_X1942 1 561 231s Westinghouse_X1943 1 617 231s Westinghouse_X1944 1 627 231s Westinghouse_X1945 1 737 231s Westinghouse_X1946 1 760 231s Westinghouse_X1947 1 581 231s Westinghouse_X1948 1 662 231s Westinghouse_X1949 1 584 231s Westinghouse_X1950 1 635 231s Westinghouse_X1951 1 724 231s Westinghouse_X1952 1 864 231s Westinghouse_X1953 1 1194 231s Westinghouse_X1954 1 1189 231s Westinghouse_capital 231s Chrysler_X1935 0.0 231s Chrysler_X1936 0.0 231s Chrysler_X1937 0.0 231s Chrysler_X1938 0.0 231s Chrysler_X1939 0.0 231s Chrysler_X1940 0.0 231s Chrysler_X1941 0.0 231s Chrysler_X1942 0.0 231s Chrysler_X1943 0.0 231s Chrysler_X1944 0.0 231s Chrysler_X1945 0.0 231s Chrysler_X1946 0.0 231s Chrysler_X1947 0.0 231s Chrysler_X1948 0.0 231s Chrysler_X1949 0.0 231s Chrysler_X1950 0.0 231s Chrysler_X1951 0.0 231s Chrysler_X1952 0.0 231s Chrysler_X1953 0.0 231s Chrysler_X1954 0.0 231s General.Electric_X1935 0.0 231s General.Electric_X1936 0.0 231s General.Electric_X1937 0.0 231s General.Electric_X1938 0.0 231s General.Electric_X1939 0.0 231s General.Electric_X1940 0.0 231s General.Electric_X1941 0.0 231s General.Electric_X1942 0.0 231s General.Electric_X1943 0.0 231s General.Electric_X1944 0.0 231s General.Electric_X1945 0.0 231s General.Electric_X1946 0.0 231s General.Electric_X1947 0.0 231s General.Electric_X1948 0.0 231s General.Electric_X1949 0.0 231s General.Electric_X1950 0.0 231s General.Electric_X1951 0.0 231s General.Electric_X1952 0.0 231s General.Electric_X1953 0.0 231s General.Electric_X1954 0.0 231s General.Motors_X1935 0.0 231s General.Motors_X1936 0.0 231s General.Motors_X1937 0.0 231s General.Motors_X1938 0.0 231s General.Motors_X1939 0.0 231s General.Motors_X1940 0.0 231s General.Motors_X1941 0.0 231s General.Motors_X1942 0.0 231s General.Motors_X1943 0.0 231s General.Motors_X1944 0.0 231s General.Motors_X1945 0.0 231s General.Motors_X1946 0.0 231s General.Motors_X1947 0.0 231s General.Motors_X1948 0.0 231s General.Motors_X1949 0.0 231s General.Motors_X1950 0.0 231s General.Motors_X1951 0.0 231s General.Motors_X1952 0.0 231s General.Motors_X1953 0.0 231s General.Motors_X1954 0.0 231s US.Steel_X1935 0.0 231s US.Steel_X1936 0.0 231s US.Steel_X1937 0.0 231s US.Steel_X1938 0.0 231s US.Steel_X1939 0.0 231s US.Steel_X1940 0.0 231s US.Steel_X1941 0.0 231s US.Steel_X1942 0.0 231s US.Steel_X1943 0.0 231s US.Steel_X1944 0.0 231s US.Steel_X1945 0.0 231s US.Steel_X1946 0.0 231s US.Steel_X1947 0.0 231s US.Steel_X1948 0.0 231s US.Steel_X1949 0.0 231s US.Steel_X1950 0.0 231s US.Steel_X1951 0.0 231s US.Steel_X1952 0.0 231s US.Steel_X1953 0.0 231s US.Steel_X1954 0.0 231s Westinghouse_X1935 1.8 231s Westinghouse_X1936 0.8 231s Westinghouse_X1937 7.4 231s Westinghouse_X1938 18.1 231s Westinghouse_X1939 23.5 231s Westinghouse_X1940 26.5 231s Westinghouse_X1941 36.2 231s Westinghouse_X1942 60.8 231s Westinghouse_X1943 84.4 231s Westinghouse_X1944 91.2 231s Westinghouse_X1945 92.4 231s Westinghouse_X1946 86.0 231s Westinghouse_X1947 111.1 231s Westinghouse_X1948 130.6 231s Westinghouse_X1949 141.8 231s Westinghouse_X1950 136.7 231s Westinghouse_X1951 129.7 231s Westinghouse_X1952 145.5 231s Westinghouse_X1953 174.8 231s Westinghouse_X1954 213.5 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s $Chrysler 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s attr(,"variables") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"factors") 231s Chrysler_value Chrysler_capital 231s Chrysler_invest 0 0 231s Chrysler_value 1 0 231s Chrysler_capital 0 1 231s attr(,"term.labels") 231s [1] "Chrysler_value" "Chrysler_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"dataClasses") 231s Chrysler_invest Chrysler_value Chrysler_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Electric 231s General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s attr(,"variables") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"factors") 231s General.Electric_value General.Electric_capital 231s General.Electric_invest 0 0 231s General.Electric_value 1 0 231s General.Electric_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Electric_value" "General.Electric_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Electric_invest, General.Electric_value, General.Electric_capital) 231s attr(,"dataClasses") 231s General.Electric_invest General.Electric_value General.Electric_capital 231s "numeric" "numeric" "numeric" 231s 231s $General.Motors 231s General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s attr(,"variables") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"factors") 231s General.Motors_value General.Motors_capital 231s General.Motors_invest 0 0 231s General.Motors_value 1 0 231s General.Motors_capital 0 1 231s attr(,"term.labels") 231s [1] "General.Motors_value" "General.Motors_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(General.Motors_invest, General.Motors_value, General.Motors_capital) 231s attr(,"dataClasses") 231s General.Motors_invest General.Motors_value General.Motors_capital 231s "numeric" "numeric" "numeric" 231s 231s $US.Steel 231s US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s attr(,"variables") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"factors") 231s US.Steel_value US.Steel_capital 231s US.Steel_invest 0 0 231s US.Steel_value 1 0 231s US.Steel_capital 0 1 231s attr(,"term.labels") 231s [1] "US.Steel_value" "US.Steel_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(US.Steel_invest, US.Steel_value, US.Steel_capital) 231s attr(,"dataClasses") 231s US.Steel_invest US.Steel_value US.Steel_capital 231s "numeric" "numeric" "numeric" 231s 231s $Westinghouse 231s Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s attr(,"variables") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"factors") 231s Westinghouse_value Westinghouse_capital 231s Westinghouse_invest 0 0 231s Westinghouse_value 1 0 231s Westinghouse_capital 0 1 231s attr(,"term.labels") 231s [1] "Westinghouse_value" "Westinghouse_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Westinghouse_invest, Westinghouse_value, Westinghouse_capital) 231s attr(,"dataClasses") 231s Westinghouse_invest Westinghouse_value Westinghouse_capital 231s "numeric" "numeric" "numeric" 231s 231s Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s attr(,"variables") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"factors") 231s Chrysler_value Chrysler_capital 231s Chrysler_invest 0 0 231s Chrysler_value 1 0 231s Chrysler_capital 0 1 231s attr(,"term.labels") 231s [1] "Chrysler_value" "Chrysler_capital" 231s attr(,"order") 231s [1] 1 1 231s attr(,"intercept") 231s [1] 1 231s attr(,"response") 231s [1] 1 231s attr(,".Environment") 231s 231s attr(,"predvars") 231s list(Chrysler_invest, Chrysler_value, Chrysler_capital) 231s attr(,"dataClasses") 231s Chrysler_invest Chrysler_value Chrysler_capital 231s "numeric" "numeric" "numeric" 231s > 231s > 231s > ######### IV estimation ####################### 231s > ### 2SLS ### 231s > # instruments = explanatory variables -> 2SLS estimates = OLS estimates 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greene2sls <- systemfit( formulaGrunfeld, inst = ~ value + capital, "2SLS", 231s + data = GrunfeldGreene, useMatrix = useMatrix ) 231s + print( greene2sls ) 231s + print( summary( greene2sls ) ) 231s + print( all.equal( coef( summary( greene2sls ) ), coef( summary( greeneOls ) ) ) ) 231s + print( all.equal( greene2sls[ -c(1,2,6) ], greeneOls[ -c(1,2,6) ] ) ) 231s + for( i in 1:length( greene2sls$eq ) ) { 231s + print( all.equal( greene2sls$eq[[i]][ -c(3,15:17) ], 231s + greeneOls$eq[[i]][-3] ) ) 231s + } 231s + } 231s 231s systemfit results 231s method: 2SLS 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_value 231s -6.1900 0.0779 231s Chrysler_capital General.Electric_(Intercept) 231s 0.3157 -9.9563 231s General.Electric_value General.Electric_capital 231s 0.0266 0.1517 231s General.Motors_(Intercept) General.Motors_value 231s -149.7825 0.1193 231s General.Motors_capital US.Steel_(Intercept) 231s 0.3714 -30.3685 231s US.Steel_value US.Steel_capital 231s 0.1566 0.4239 231s Westinghouse_(Intercept) Westinghouse_value 231s -0.5094 0.0529 231s Westinghouse_capital 231s 0.0924 231s 231s systemfit results 231s method: 2SLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 85 339121 2.09e+14 0.848 0.862 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 2997 176 13.3 0.914 0.903 231s General.Electric 20 17 13217 777 27.9 0.705 0.671 231s General.Motors 20 17 143206 8424 91.8 0.921 0.912 231s US.Steel 20 17 177928 10466 102.3 0.440 0.374 231s Westinghouse 20 17 1773 104 10.2 0.744 0.714 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 176.3 -25.1 -333 492 15.7 231s General.Electric -25.1 777.4 715 1065 207.6 231s General.Motors -332.7 714.7 8424 -2614 148.4 231s US.Steel 491.9 1064.6 -2614 10466 642.6 231s Westinghouse 15.7 207.6 148 643 104.3 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.0000 -0.0679 -0.273 0.362 0.115 231s General.Electric -0.0679 1.0000 0.279 0.373 0.729 231s General.Motors -0.2730 0.2793 1.000 -0.278 0.158 231s US.Steel 0.3621 0.3732 -0.278 1.000 0.615 231s Westinghouse 0.1154 0.7290 0.158 0.615 1.000 231s 231s 231s 2SLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s Instruments: ~Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -6.1900 13.5065 -0.46 0.6525 231s value 0.0779 0.0200 3.90 0.0011 ** 231s capital 0.3157 0.0288 10.96 4e-09 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 13.279 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 2997.444 MSE: 176.32 Root MSE: 13.279 231s Multiple R-Squared: 0.914 Adjusted R-Squared: 0.903 231s 231s 231s 2SLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s Instruments: ~General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -9.9563 31.3742 -0.32 0.75 231s value 0.0266 0.0156 1.71 0.11 231s capital 0.1517 0.0257 5.90 1.7e-05 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 27.883 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 13216.588 MSE: 777.446 Root MSE: 27.883 231s Multiple R-Squared: 0.705 Adjusted R-Squared: 0.671 231s 231s 231s 2SLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s Instruments: ~General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -149.7825 105.8421 -1.42 0.17508 231s value 0.1193 0.0258 4.62 0.00025 *** 231s capital 0.3714 0.0371 10.02 1.5e-08 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 91.782 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 143205.877 MSE: 8423.875 Root MSE: 91.782 231s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.912 231s 231s 231s 2SLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s Instruments: ~US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -30.3685 157.0477 -0.19 0.849 231s value 0.1566 0.0789 1.98 0.064 . 231s capital 0.4239 0.1552 2.73 0.014 * 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 102.305 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 177928.314 MSE: 10466.371 Root MSE: 102.305 231s Multiple R-Squared: 0.44 Adjusted R-Squared: 0.374 231s 231s 231s 2SLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s Instruments: ~Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -0.5094 8.0153 -0.06 0.9501 231s value 0.0529 0.0157 3.37 0.0037 ** 231s capital 0.0924 0.0561 1.65 0.1179 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 10.213 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 1773.234 MSE: 104.308 Root MSE: 10.213 231s Multiple R-Squared: 0.744 Adjusted R-Squared: 0.714 231s 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s > # 'real' IV/2SLS estimation 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greene2slsR <- systemfit( invest ~ capital, inst = ~ value, "2SLS", 231s + data = GrunfeldGreene, useMatrix = useMatrix ) 231s + print( greene2slsR ) 231s + print( summary( greene2slsR ) ) 231s + } 231s 231s systemfit results 231s method: 2SLS 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_capital 231s 4.314 0.675 231s General.Electric_(Intercept) General.Electric_capital 231s -106.788 0.522 231s General.Motors_(Intercept) General.Motors_capital 231s 110.940 0.767 231s US.Steel_(Intercept) US.Steel_capital 231s -323.878 2.432 231s Westinghouse_(Intercept) Westinghouse_capital 231s 13.163 0.347 231s 231s systemfit results 231s method: 2SLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 90 3239824 2.75e+17 -0.456 0.476 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 18 30374 1687 41.1 0.124 0.076 231s General.Electric 20 18 174998 9722 98.6 -2.902 -3.119 231s General.Motors 20 18 1100181 61121 247.2 0.396 0.362 231s US.Steel 20 18 1930347 107242 327.5 -5.072 -5.409 231s Westinghouse 20 18 3924 218 14.8 0.434 0.403 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1687 3089 6820 11741 179 231s General.Electric 3089 9722 20780 23319 886 231s General.Motors 6820 20780 61121 44203 1908 231s US.Steel 11741 23319 44203 107242 1977 231s Westinghouse 179 886 1908 1977 218 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.000 0.763 0.672 0.873 0.295 231s General.Electric 0.763 1.000 0.852 0.722 0.608 231s General.Motors 0.672 0.852 1.000 0.546 0.523 231s US.Steel 0.873 0.722 0.546 1.000 0.409 231s Westinghouse 0.295 0.608 0.523 0.409 1.000 231s 231s 231s 2SLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_capital 231s 231s Instruments: ~Chrysler_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 4.314 34.033 0.13 0.901 231s capital 0.675 0.270 2.50 0.022 * 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 41.078 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 30373.531 MSE: 1687.418 Root MSE: 41.078 231s Multiple R-Squared: 0.124 Adjusted R-Squared: 0.076 231s 231s 231s 2SLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_capital 231s 231s Instruments: ~General.Electric_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -106.788 306.251 -0.35 0.73 231s capital 0.522 0.763 0.68 0.50 231s 231s Residual standard error: 98.601 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 174998.166 MSE: 9722.12 Root MSE: 98.601 231s Multiple R-Squared: -2.902 Adjusted R-Squared: -3.119 231s 231s 231s 2SLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_capital 231s 231s Instruments: ~General.Motors_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 110.940 145.626 0.76 0.4560 231s capital 0.767 0.208 3.69 0.0017 ** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 247.227 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 1100180.666 MSE: 61121.148 Root MSE: 247.227 231s Multiple R-Squared: 0.396 Adjusted R-Squared: 0.362 231s 231s 231s 2SLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_capital 231s 231s Instruments: ~US.Steel_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -323.88 962.57 -0.34 0.74 231s capital 2.43 3.20 0.76 0.46 231s 231s Residual standard error: 327.478 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 1930347.395 MSE: 107241.522 Root MSE: 327.478 231s Multiple R-Squared: -5.072 Adjusted R-Squared: -5.409 231s 231s 231s 2SLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_capital 231s 231s Instruments: ~Westinghouse_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) 13.1626 7.0965 1.85 0.08008 . 231s capital 0.3471 0.0734 4.73 0.00017 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 14.765 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 3923.899 MSE: 217.994 Root MSE: 14.765 231s Multiple R-Squared: 0.434 Adjusted R-Squared: 0.403 231s 231s > 231s > ### 2SLS, pooled ### 231s > # instruments = explanatory variables -> 2SLS estimates = OLS estimates 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greene2slsPooled <- systemfit( formulaGrunfeld, inst = ~ value + capital, "2SLS", 231s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 231s + print( greene2slsPooled ) 231s + print( summary( greene2slsPooled ) ) 231s + print( all.equal( coef( summary( greene2slsPooled ) ), 231s + coef( summary( greeneOlsPooled ) ) ) ) 231s + print( all.equal( greene2slsPooled[ -c(1,2,6) ], greeneOlsPooled[ -c(1,2,6) ] ) ) 231s + for( i in 1:length( greene2slsPooled$eq ) ) { 231s + print( all.equal( greene2slsPooled$eq[[i]][ -c(3,15:17) ], 231s + greeneOlsPooled$eq[[i]][-3] ) ) 231s + } 231s + } 231s 231s systemfit results 231s method: 2SLS 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_value 231s -48.030 0.105 231s Chrysler_capital General.Electric_(Intercept) 231s 0.305 -48.030 231s General.Electric_value General.Electric_capital 231s 0.105 0.305 231s General.Motors_(Intercept) General.Motors_value 231s -48.030 0.105 231s General.Motors_capital US.Steel_(Intercept) 231s 0.305 -48.030 231s US.Steel_value US.Steel_capital 231s 0.105 0.305 231s Westinghouse_(Intercept) Westinghouse_value 231s -48.030 0.105 231s Westinghouse_capital 231s 0.305 231s 231s systemfit results 231s method: 2SLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 97 1570884 4.2e+17 0.294 0.812 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 17 15117 889 29.8 0.564 0.513 231s General.Electric 20 17 685770 40339 200.8 -14.291 -16.090 231s General.Motors 20 17 188218 11072 105.2 0.897 0.884 231s US.Steel 20 17 669110 39359 198.4 -1.105 -1.352 231s Westinghouse 20 17 12668 745 27.3 -0.826 -1.041 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 889.2 -4898 -198 4748 -94.6 231s General.Electric -4898.1 40339 -2254 -32821 2658.0 231s General.Motors -197.7 -2254 11072 304 -1328.6 231s US.Steel 4748.1 -32821 304 39359 -1377.3 231s Westinghouse -94.6 2658 -1329 -1377 745.2 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.000 0.144 -0.1852 0.2218 0.186 231s General.Electric 0.144 1.000 -0.2592 -0.1216 0.881 231s General.Motors -0.185 -0.259 1.0000 -0.0155 -0.469 231s US.Steel 0.222 -0.122 -0.0155 1.0000 -0.119 231s Westinghouse 0.186 0.881 -0.4689 -0.1186 1.000 231s 231s 231s 2SLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 231s 231s Instruments: ~Chrysler_value + Chrysler_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 29.82 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 15117.016 MSE: 889.236 Root MSE: 29.82 231s Multiple R-Squared: 0.564 Adjusted R-Squared: 0.513 231s 231s 231s 2SLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 231s 231s Instruments: ~General.Electric_value + General.Electric_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 200.847 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 685769.815 MSE: 40339.401 Root MSE: 200.847 231s Multiple R-Squared: -14.291 Adjusted R-Squared: -16.09 231s 231s 231s 2SLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 231s 231s Instruments: ~General.Motors_value + General.Motors_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 105.222 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 188218.158 MSE: 11071.656 Root MSE: 105.222 231s Multiple R-Squared: 0.897 Adjusted R-Squared: 0.884 231s 231s 231s 2SLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 231s 231s Instruments: ~US.Steel_value + US.Steel_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 198.392 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 669110.225 MSE: 39359.425 Root MSE: 198.392 231s Multiple R-Squared: -1.105 Adjusted R-Squared: -1.352 231s 231s 231s 2SLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 231s 231s Instruments: ~Westinghouse_value + Westinghouse_capital 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -48.0297 21.4802 -2.24 0.028 * 231s value 0.1051 0.0114 9.24 6.0e-15 *** 231s capital 0.3054 0.0435 7.02 3.1e-10 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 27.298 on 17 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 17 231s SSR: 12668.473 MSE: 745.204 Root MSE: 27.298 231s Multiple R-Squared: -0.826 Adjusted R-Squared: -1.041 231s 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s [1] TRUE 231s > # 'real' IV/2SLS estimation 231s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 231s + greene2slsRPooled <- systemfit( invest ~ capital, inst = ~ value, "2SLS", 231s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix ) 231s + print( greene2slsRPooled ) 231s + print( summary( greene2slsRPooled ) ) 231s + } 231s 231s systemfit results 231s method: 2SLS 231s 231s Coefficients: 231s Chrysler_(Intercept) Chrysler_capital 231s -15.105 0.849 231s General.Electric_(Intercept) General.Electric_capital 231s -15.105 0.849 231s General.Motors_(Intercept) General.Motors_capital 231s -15.105 0.849 231s US.Steel_(Intercept) US.Steel_capital 231s -15.105 0.849 231s Westinghouse_(Intercept) Westinghouse_capital 231s -15.105 0.849 231s 231s systemfit results 231s method: 2SLS 231s 231s N DF SSR detRCov OLS-R2 McElroy-R2 231s system 100 98 4164182 2.53e+19 -0.871 -0.832 231s 231s N DF SSR MSE RMSE R2 Adj R2 231s Chrysler 20 18 64130 3563 59.7 -0.849 -0.952 231s General.Electric 20 18 1575287 87516 295.8 -34.125 -36.076 231s General.Motors 20 18 1655592 91977 303.3 0.091 0.040 231s US.Steel 20 18 833908 46328 215.2 -1.623 -1.769 231s Westinghouse 20 18 35264 1959 44.3 -4.082 -4.365 231s 231s The covariance matrix of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 3563 9506 13222 2659 1862 231s General.Electric 9506 87516 29381 -35898 10615 231s General.Motors 13222 29381 91977 17584 8562 231s US.Steel 2659 -35898 17584 46328 -762 231s Westinghouse 1862 10615 8562 -762 1959 231s 231s The correlations of the residuals 231s Chrysler General.Electric General.Motors US.Steel Westinghouse 231s Chrysler 1.000 0.843 0.763 0.397 0.742 231s General.Electric 0.843 1.000 0.893 0.226 0.933 231s General.Motors 0.763 0.893 1.000 0.114 0.801 231s US.Steel 0.397 0.226 0.114 1.000 0.375 231s Westinghouse 0.742 0.933 0.801 0.375 1.000 231s 231s 231s 2SLS estimates for 'Chrysler' (equation 1) 231s Model Formula: Chrysler_invest ~ Chrysler_capital 231s 231s Instruments: ~Chrysler_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -15.1045 33.8915 -0.45 0.66 231s capital 0.8489 0.0865 9.82 4.4e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 59.689 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 64130.003 MSE: 3562.778 Root MSE: 59.689 231s Multiple R-Squared: -0.849 Adjusted R-Squared: -0.952 231s 231s 231s 2SLS estimates for 'General.Electric' (equation 2) 231s Model Formula: General.Electric_invest ~ General.Electric_capital 231s 231s Instruments: ~General.Electric_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -15.1045 33.8915 -0.45 0.66 231s capital 0.8489 0.0865 9.82 4.4e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 295.831 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 1575287.29 MSE: 87515.961 Root MSE: 295.831 231s Multiple R-Squared: -34.125 Adjusted R-Squared: -36.076 231s 231s 231s 2SLS estimates for 'General.Motors' (equation 3) 231s Model Formula: General.Motors_invest ~ General.Motors_capital 231s 231s Instruments: ~General.Motors_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -15.1045 33.8915 -0.45 0.66 231s capital 0.8489 0.0865 9.82 4.4e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 303.278 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 1655591.854 MSE: 91977.325 Root MSE: 303.278 231s Multiple R-Squared: 0.091 Adjusted R-Squared: 0.04 231s 231s 231s 2SLS estimates for 'US.Steel' (equation 4) 231s Model Formula: US.Steel_invest ~ US.Steel_capital 231s 231s Instruments: ~US.Steel_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -15.1045 33.8915 -0.45 0.66 231s capital 0.8489 0.0865 9.82 4.4e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 215.24 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 833908.389 MSE: 46328.244 Root MSE: 215.24 231s Multiple R-Squared: -1.623 Adjusted R-Squared: -1.769 231s 231s 231s 2SLS estimates for 'Westinghouse' (equation 5) 231s Model Formula: Westinghouse_invest ~ Westinghouse_capital 231s 231s Instruments: ~Westinghouse_value 231s 231s 231s Estimate Std. Error t value Pr(>|t|) 231s (Intercept) -15.1045 33.8915 -0.45 0.66 231s capital 0.8489 0.0865 9.82 4.4e-16 *** 231s --- 231s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 231s 231s Residual standard error: 44.262 on 18 degrees of freedom 231s Number of observations: 20 Degrees of Freedom: 18 231s SSR: 35264.462 MSE: 1959.137 Root MSE: 44.262 231s Multiple R-Squared: -4.082 Adjusted R-Squared: -4.365 231s 231s > 232s > ### 3SLS ### 232s > # instruments = explanatory variables -> 3SLS estimates = SUR estimates 232s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 232s + greene3sls <- systemfit( formulaGrunfeld, inst = ~ value + capital, "3SLS", 232s + data = GrunfeldGreene, useMatrix = useMatrix, methodResidCov = "noDfCor" ) 232s + print( greene3sls ) 232s + print( summary( greene3sls ) ) 232s + print( all.equal( coef( summary( greene3sls ) ), coef( summary( greeneSur ) ) ) ) 232s + print( all.equal( greene3sls[ -c(1,2,7) ], greeneSur[ -c(1,2,7) ] ) ) 232s + for( i in 1:length( greene3sls$eq ) ) { 232s + print( all.equal( greene3sls$eq[[i]][ -c(3,15:17) ], 232s + greeneSur$eq[[i]][-3] ) ) 232s + } 232s + } 232s 232s systemfit results 232s method: 3SLS 232s 232s Coefficients: 232s Chrysler_(Intercept) Chrysler_value 232s 0.5043 0.0695 232s Chrysler_capital General.Electric_(Intercept) 232s 0.3085 -22.4389 232s General.Electric_value General.Electric_capital 232s 0.0373 0.1308 232s General.Motors_(Intercept) General.Motors_value 232s -162.3641 0.1205 232s General.Motors_capital US.Steel_(Intercept) 232s 0.3827 85.4233 232s US.Steel_value US.Steel_capital 232s 0.1015 0.4000 232s Westinghouse_(Intercept) Westinghouse_value 232s 1.0889 0.0570 232s Westinghouse_capital 232s 0.0415 232s 232s systemfit results 232s method: 3SLS 232s 232s N DF SSR detRCov OLS-R2 McElroy-R2 232s system 100 85 347048 6.18e+13 0.844 0.869 232s 232s N DF SSR MSE RMSE R2 Adj R2 232s Chrysler 20 17 3057 180 13.4 0.912 0.901 232s General.Electric 20 17 14009 824 28.7 0.688 0.651 232s General.Motors 20 17 144321 8489 92.1 0.921 0.911 232s US.Steel 20 17 183763 10810 104.0 0.422 0.354 232s Westinghouse 20 17 1898 112 10.6 0.726 0.694 232s 232s The covariance matrix of the residuals used for estimation 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 149.9 -21.4 -283 418 13.3 232s General.Electric -21.4 660.8 608 905 176.4 232s General.Motors -282.8 607.5 7160 -2222 126.2 232s US.Steel 418.1 905.0 -2222 8896 546.2 232s Westinghouse 13.3 176.4 126 546 88.7 232s 232s The covariance matrix of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 152.85 2.05 -314 455 16.7 232s General.Electric 2.05 700.46 605 1224 200.3 232s General.Motors -313.70 605.34 7216 -2687 129.9 232s US.Steel 455.09 1224.41 -2687 9188 652.7 232s Westinghouse 16.66 200.32 130 653 94.9 232s 232s The correlations of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 1.00000 0.00626 -0.299 0.384 0.138 232s General.Electric 0.00626 1.00000 0.269 0.483 0.777 232s General.Motors -0.29870 0.26925 1.000 -0.330 0.157 232s US.Steel 0.38402 0.48264 -0.330 1.000 0.699 232s Westinghouse 0.13832 0.77690 0.157 0.699 1.000 232s 232s 232s 3SLS estimates for 'Chrysler' (equation 1) 232s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 232s 232s Instruments: ~Chrysler_value + Chrysler_capital 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 0.5043 11.5128 0.04 0.96557 232s value 0.0695 0.0169 4.12 0.00072 *** 232s capital 0.3085 0.0259 11.93 1.1e-09 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 13.41 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 3056.985 MSE: 179.823 Root MSE: 13.41 232s Multiple R-Squared: 0.912 Adjusted R-Squared: 0.901 232s 232s 232s 3SLS estimates for 'General.Electric' (equation 2) 232s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 232s 232s Instruments: ~General.Electric_value + General.Electric_capital 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -22.4389 25.5186 -0.88 0.3915 232s value 0.0373 0.0123 3.04 0.0074 ** 232s capital 0.1308 0.0220 5.93 1.6e-05 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 28.707 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 14009.115 MSE: 824.066 Root MSE: 28.707 232s Multiple R-Squared: 0.688 Adjusted R-Squared: 0.651 232s 232s 232s 3SLS estimates for 'General.Motors' (equation 3) 232s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 232s 232s Instruments: ~General.Motors_value + General.Motors_capital 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -162.3641 89.4592 -1.81 0.087 . 232s value 0.1205 0.0216 5.57 3.4e-05 *** 232s capital 0.3827 0.0328 11.68 1.5e-09 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 92.138 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 144320.876 MSE: 8489.463 Root MSE: 92.138 232s Multiple R-Squared: 0.921 Adjusted R-Squared: 0.911 232s 232s 232s 3SLS estimates for 'US.Steel' (equation 4) 232s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 232s 232s Instruments: ~US.Steel_value + US.Steel_capital 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 85.4233 111.8774 0.76 0.4556 232s value 0.1015 0.0548 1.85 0.0814 . 232s capital 0.4000 0.1278 3.13 0.0061 ** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 103.969 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 183763.011 MSE: 10809.589 Root MSE: 103.969 232s Multiple R-Squared: 0.422 Adjusted R-Squared: 0.354 232s 232s 232s 3SLS estimates for 'Westinghouse' (equation 5) 232s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 232s 232s Instruments: ~Westinghouse_value + Westinghouse_capital 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 1.0889 6.2588 0.17 0.86394 232s value 0.0570 0.0114 5.02 0.00011 *** 232s capital 0.0415 0.0412 1.01 0.32787 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 10.567 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 1898.249 MSE: 111.662 Root MSE: 10.567 232s Multiple R-Squared: 0.726 Adjusted R-Squared: 0.694 232s 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s > # 'real' IV/3SLS estimation 232s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 232s + greene3slsR <- systemfit( invest ~ capital, inst = ~ value, "3SLS", 232s + data = GrunfeldGreene, useMatrix = useMatrix ) 232s + print( greene3slsR ) 232s + print( summary( greene3slsR ) ) 232s + } 232s 232s systemfit results 232s method: 3SLS 232s 232s Coefficients: 232s Chrysler_(Intercept) Chrysler_capital 232s 23.499 0.517 232s General.Electric_(Intercept) General.Electric_capital 232s -108.596 0.527 232s General.Motors_(Intercept) General.Motors_capital 232s 199.856 0.629 232s US.Steel_(Intercept) US.Steel_capital 232s 181.691 0.746 232s Westinghouse_(Intercept) Westinghouse_capital 232s 11.668 0.365 232s 232s systemfit results 232s method: 3SLS 232s 232s N DF SSR detRCov OLS-R2 McElroy-R2 232s system 100 90 1026043 4.46e+16 0.539 0.539 232s 232s N DF SSR MSE RMSE R2 Adj R2 232s Chrysler 20 18 12139 674 26.0 0.650 0.631 232s General.Electric 20 18 178965 9942 99.7 -2.990 -3.212 232s General.Motors 20 18 577860 32103 179.2 0.683 0.665 232s US.Steel 20 18 252838 14047 118.5 0.205 0.160 232s Westinghouse 20 18 4241 236 15.3 0.389 0.355 232s 232s The covariance matrix of the residuals used for estimation 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 1687 3089 6820 11741 179 232s General.Electric 3089 9722 20780 23319 886 232s General.Motors 6820 20780 61121 44203 1908 232s US.Steel 11741 23319 44203 107242 1977 232s Westinghouse 179 886 1908 1977 218 232s 232s The covariance matrix of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 674 1587 1944 1371 137 232s General.Electric 1587 9942 13003 2009 996 232s General.Motors 1944 13003 32103 -908 1571 232s US.Steel 1371 2009 -908 14047 888 232s Westinghouse 137 996 1571 888 236 232s 232s The correlations of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 1.000 0.613 0.4178 0.4454 0.343 232s General.Electric 0.613 1.000 0.7278 0.1700 0.651 232s General.Motors 0.418 0.728 1.0000 -0.0428 0.571 232s US.Steel 0.445 0.170 -0.0428 1.0000 0.488 232s Westinghouse 0.343 0.651 0.5713 0.4880 1.000 232s 232s 232s 3SLS estimates for 'Chrysler' (equation 1) 232s Model Formula: Chrysler_invest ~ Chrysler_capital 232s 232s Instruments: ~Chrysler_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 23.499 17.165 1.37 0.18784 232s capital 0.517 0.120 4.32 0.00041 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 25.969 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 12138.974 MSE: 674.387 Root MSE: 25.969 232s Multiple R-Squared: 0.65 Adjusted R-Squared: 0.631 232s 232s 232s 3SLS estimates for 'General.Electric' (equation 2) 232s Model Formula: General.Electric_invest ~ General.Electric_capital 232s 232s Instruments: ~General.Electric_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -108.596 152.939 -0.71 0.49 232s capital 0.527 0.378 1.39 0.18 232s 232s Residual standard error: 99.712 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 178964.956 MSE: 9942.498 Root MSE: 99.712 232s Multiple R-Squared: -2.99 Adjusted R-Squared: -3.212 232s 232s 232s 3SLS estimates for 'General.Motors' (equation 3) 232s Model Formula: General.Motors_invest ~ General.Motors_capital 232s 232s Instruments: ~General.Motors_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 199.856 98.953 2.02 0.059 . 232s capital 0.629 0.127 4.97 9.8e-05 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 179.174 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 577859.714 MSE: 32103.317 Root MSE: 179.174 232s Multiple R-Squared: 0.683 Adjusted R-Squared: 0.665 232s 232s 232s 3SLS estimates for 'US.Steel' (equation 4) 232s Model Formula: US.Steel_invest ~ US.Steel_capital 232s 232s Instruments: ~US.Steel_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 181.691 448.797 0.40 0.69 232s capital 0.746 1.477 0.51 0.62 232s 232s Residual standard error: 118.518 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 252838.286 MSE: 14046.571 Root MSE: 118.518 232s Multiple R-Squared: 0.205 Adjusted R-Squared: 0.16 232s 232s 232s 3SLS estimates for 'Westinghouse' (equation 5) 232s Model Formula: Westinghouse_invest ~ Westinghouse_capital 232s 232s Instruments: ~Westinghouse_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 11.6685 5.9043 1.98 0.064 . 232s capital 0.3646 0.0572 6.38 5.2e-06 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 15.349 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 4240.92 MSE: 235.607 Root MSE: 15.349 232s Multiple R-Squared: 0.389 Adjusted R-Squared: 0.355 232s 232s > 232s > ### 3SLS, Pooled ### 232s > # instruments = explanatory variables -> 3SLS estimates = SUR estimates 232s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 232s + greene3slsPooled <- systemfit( formulaGrunfeld, inst = ~ capital + value, "3SLS", 232s + data = GrunfeldGreene, pooled = TRUE, useMatrix = useMatrix, 232s + residCovWeighted = TRUE, methodResidCov = "noDfCor" ) 232s + print( greene3slsPooled ) 232s + print( summary( greene3slsPooled ) ) 232s + print( all.equal( coef( summary( greene3slsPooled ) ), 232s + coef( summary( greeneSurPooled ) ) ) ) 232s + print( all.equal( greene3slsPooled[ -c(1,2,7) ], greeneSurPooled[ -c(1,2,7) ] ) ) 232s + for( i in 1:length( greene3slsPooled$eq ) ) { 232s + print( all.equal( greene3slsPooled$eq[[i]][ -c(3,15:17) ], 232s + greeneSurPooled$eq[[i]][-3] ) ) 232s + } 232s + } 232s 232s systemfit results 232s method: 3SLS 232s 232s Coefficients: 232s Chrysler_(Intercept) Chrysler_value 232s -28.2467 0.0891 232s Chrysler_capital General.Electric_(Intercept) 232s 0.3340 -28.2467 232s General.Electric_value General.Electric_capital 232s 0.0891 0.3340 232s General.Motors_(Intercept) General.Motors_value 232s -28.2467 0.0891 232s General.Motors_capital US.Steel_(Intercept) 232s 0.3340 -28.2467 232s US.Steel_value US.Steel_capital 232s 0.0891 0.3340 232s Westinghouse_(Intercept) Westinghouse_value 232s -28.2467 0.0891 232s Westinghouse_capital 232s 0.3340 232s 232s systemfit results 232s method: 3SLS 232s 232s N DF SSR detRCov OLS-R2 McElroy-R2 232s system 100 97 1604301 9.95e+16 0.279 0.844 232s 232s N DF SSR MSE RMSE R2 Adj R2 232s Chrysler 20 17 6112 360 19.0 0.824 0.803 232s General.Electric 20 17 691132 40655 201.6 -14.410 -16.223 232s General.Motors 20 17 201010 11824 108.7 0.890 0.877 232s US.Steel 20 17 689380 40552 201.4 -1.168 -1.424 232s Westinghouse 20 17 16667 980 31.3 -1.402 -1.685 232s 232s The covariance matrix of the residuals used for estimation 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 409 -2594 -197 2594 -102 232s General.Electric -2594 36563 -3480 -28623 3797 232s General.Motors -197 -3480 8612 996 -971 232s US.Steel 2594 -28623 996 32903 -2272 232s Westinghouse -102 3797 -971 -2272 778 232s 232s The covariance matrix of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 305.61 -1967 -4.81 2159 -124 232s General.Electric -1966.65 34557 -7160.67 -28722 4274 232s General.Motors -4.81 -7161 10050.52 4440 -1401 232s US.Steel 2158.60 -28722 4439.99 34469 -2894 232s Westinghouse -123.92 4274 -1400.75 -2894 833 232s 232s The correlations of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 1.000 0.220 -0.3447 0.2008 0.2907 232s General.Electric 0.220 1.000 -0.2233 -0.1587 0.8973 232s General.Motors -0.345 -0.223 1.0000 -0.0924 -0.3760 232s US.Steel 0.201 -0.159 -0.0924 1.0000 -0.0757 232s Westinghouse 0.291 0.897 -0.3760 -0.0757 1.0000 232s 232s 232s 3SLS estimates for 'Chrysler' (equation 1) 232s Model Formula: Chrysler_invest ~ Chrysler_value + Chrysler_capital 232s 232s Instruments: ~Chrysler_capital + Chrysler_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 232s value 0.08910 0.00507 17.57 < 2e-16 *** 232s capital 0.33402 0.01671 19.99 < 2e-16 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 18.962 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 6112.2 MSE: 359.541 Root MSE: 18.962 232s Multiple R-Squared: 0.824 Adjusted R-Squared: 0.803 232s 232s 232s 3SLS estimates for 'General.Electric' (equation 2) 232s Model Formula: General.Electric_invest ~ General.Electric_value + General.Electric_capital 232s 232s Instruments: ~General.Electric_capital + General.Electric_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 232s value 0.08910 0.00507 17.57 < 2e-16 *** 232s capital 0.33402 0.01671 19.99 < 2e-16 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 201.63 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 691132.056 MSE: 40654.827 Root MSE: 201.63 232s Multiple R-Squared: -14.41 Adjusted R-Squared: -16.223 232s 232s 232s 3SLS estimates for 'General.Motors' (equation 3) 232s Model Formula: General.Motors_invest ~ General.Motors_value + General.Motors_capital 232s 232s Instruments: ~General.Motors_capital + General.Motors_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 232s value 0.08910 0.00507 17.57 < 2e-16 *** 232s capital 0.33402 0.01671 19.99 < 2e-16 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 108.739 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 201010.497 MSE: 11824.147 Root MSE: 108.739 232s Multiple R-Squared: 0.89 Adjusted R-Squared: 0.877 232s 232s 232s 3SLS estimates for 'US.Steel' (equation 4) 232s Model Formula: US.Steel_invest ~ US.Steel_value + US.Steel_capital 232s 232s Instruments: ~US.Steel_capital + US.Steel_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 232s value 0.08910 0.00507 17.57 < 2e-16 *** 232s capital 0.33402 0.01671 19.99 < 2e-16 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 201.375 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 689379.52 MSE: 40551.736 Root MSE: 201.375 232s Multiple R-Squared: -1.168 Adjusted R-Squared: -1.424 232s 232s 232s 3SLS estimates for 'Westinghouse' (equation 5) 232s Model Formula: Westinghouse_invest ~ Westinghouse_value + Westinghouse_capital 232s 232s Instruments: ~Westinghouse_capital + Westinghouse_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -28.24669 4.88824 -5.78 9.1e-08 *** 232s value 0.08910 0.00507 17.57 < 2e-16 *** 232s capital 0.33402 0.01671 19.99 < 2e-16 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 31.312 on 17 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 17 232s SSR: 16667.149 MSE: 980.421 Root MSE: 31.312 232s Multiple R-Squared: -1.402 Adjusted R-Squared: -1.685 232s 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s [1] TRUE 232s > # 'real' IV/3SLS estimation 232s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 232s + greene3slsRPooled <- systemfit( invest ~ capital, inst = ~ value, "3SLS", 232s + data = GrunfeldGreene, useMatrix = useMatrix ) 232s + print( greene3slsRPooled ) 232s + print( summary( greene3slsRPooled ) ) 232s + } 232s 232s systemfit results 232s method: 3SLS 232s 232s Coefficients: 232s Chrysler_(Intercept) Chrysler_capital 232s 23.499 0.517 232s General.Electric_(Intercept) General.Electric_capital 232s -108.596 0.527 232s General.Motors_(Intercept) General.Motors_capital 232s 199.856 0.629 232s US.Steel_(Intercept) US.Steel_capital 232s 181.691 0.746 232s Westinghouse_(Intercept) Westinghouse_capital 232s 11.668 0.365 232s 232s systemfit results 232s method: 3SLS 232s 232s N DF SSR detRCov OLS-R2 McElroy-R2 232s system 100 90 1026043 4.46e+16 0.539 0.539 232s 232s N DF SSR MSE RMSE R2 Adj R2 232s Chrysler 20 18 12139 674 26.0 0.650 0.631 232s General.Electric 20 18 178965 9942 99.7 -2.990 -3.212 232s General.Motors 20 18 577860 32103 179.2 0.683 0.665 232s US.Steel 20 18 252838 14047 118.5 0.205 0.160 232s Westinghouse 20 18 4241 236 15.3 0.389 0.355 232s 232s The covariance matrix of the residuals used for estimation 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 1687 3089 6820 11741 179 232s General.Electric 3089 9722 20780 23319 886 232s General.Motors 6820 20780 61121 44203 1908 232s US.Steel 11741 23319 44203 107242 1977 232s Westinghouse 179 886 1908 1977 218 232s 232s The covariance matrix of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 674 1587 1944 1371 137 232s General.Electric 1587 9942 13003 2009 996 232s General.Motors 1944 13003 32103 -908 1571 232s US.Steel 1371 2009 -908 14047 888 232s Westinghouse 137 996 1571 888 236 232s 232s The correlations of the residuals 232s Chrysler General.Electric General.Motors US.Steel Westinghouse 232s Chrysler 1.000 0.613 0.4178 0.4454 0.343 232s General.Electric 0.613 1.000 0.7278 0.1700 0.651 232s General.Motors 0.418 0.728 1.0000 -0.0428 0.571 232s US.Steel 0.445 0.170 -0.0428 1.0000 0.488 232s Westinghouse 0.343 0.651 0.5713 0.4880 1.000 232s 232s 232s 3SLS estimates for 'Chrysler' (equation 1) 232s Model Formula: Chrysler_invest ~ Chrysler_capital 232s 232s Instruments: ~Chrysler_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 23.499 17.165 1.37 0.18784 232s capital 0.517 0.120 4.32 0.00041 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 25.969 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 12138.974 MSE: 674.387 Root MSE: 25.969 232s Multiple R-Squared: 0.65 Adjusted R-Squared: 0.631 232s 232s 232s 3SLS estimates for 'General.Electric' (equation 2) 232s Model Formula: General.Electric_invest ~ General.Electric_capital 232s 232s Instruments: ~General.Electric_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) -108.596 152.939 -0.71 0.49 232s capital 0.527 0.378 1.39 0.18 232s 232s Residual standard error: 99.712 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 178964.956 MSE: 9942.498 Root MSE: 99.712 232s Multiple R-Squared: -2.99 Adjusted R-Squared: -3.212 232s 232s 232s 3SLS estimates for 'General.Motors' (equation 3) 232s Model Formula: General.Motors_invest ~ General.Motors_capital 232s 232s Instruments: ~General.Motors_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 199.856 98.953 2.02 0.059 . 232s capital 0.629 0.127 4.97 9.8e-05 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 179.174 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 577859.714 MSE: 32103.317 Root MSE: 179.174 232s Multiple R-Squared: 0.683 Adjusted R-Squared: 0.665 232s 232s 232s 3SLS estimates for 'US.Steel' (equation 4) 232s Model Formula: US.Steel_invest ~ US.Steel_capital 232s 232s Instruments: ~US.Steel_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 181.691 448.797 0.40 0.69 232s capital 0.746 1.477 0.51 0.62 232s 232s Residual standard error: 118.518 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 252838.286 MSE: 14046.571 Root MSE: 118.518 232s Multiple R-Squared: 0.205 Adjusted R-Squared: 0.16 232s 232s 232s 3SLS estimates for 'Westinghouse' (equation 5) 232s Model Formula: Westinghouse_invest ~ Westinghouse_capital 232s 232s Instruments: ~Westinghouse_value 232s 232s 232s Estimate Std. Error t value Pr(>|t|) 232s (Intercept) 11.6685 5.9043 1.98 0.064 . 232s capital 0.3646 0.0572 6.38 5.2e-06 *** 232s --- 232s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 232s 232s Residual standard error: 15.349 on 18 degrees of freedom 232s Number of observations: 20 Degrees of Freedom: 18 232s SSR: 4240.92 MSE: 235.607 Root MSE: 15.349 232s Multiple R-Squared: 0.389 Adjusted R-Squared: 0.355 232s 232s > 232s > 232s > ## **************** estfun ************************ 232s > library( "sandwich" ) 232s > 232s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 232s + print( estfun( theilOls ) ) 232s + print( round( colSums( estfun( theilOls ) ), digits = 7 ) ) 232s + 232s + print( estfun( theilSur ) ) 232s + print( round( colSums( estfun( theilSur ) ), digits = 7 ) ) 232s + 232s + print( estfun( greeneOls ) ) 232s + print( round( colSums( estfun( greeneOls ) ), digits = 7 ) ) 232s + 232s + print( try( estfun( greeneOlsPooled ) ) ) 232s + 232s + print( estfun( greeneSur ) ) 232s + print( round( colSums( estfun( greeneSur ) ), digits = 7 ) ) 232s + 232s + print( try( estfun( greeneSurPooled ) ) ) 232s + } 232s General.Electric_(Intercept) General.Electric_value 232s General.Electric_X1935 -2.860 -3348 232s General.Electric_X1936 -14.402 -29032 232s General.Electric_X1937 -5.175 -14506 232s General.Electric_X1938 -23.295 -47514 232s General.Electric_X1939 -28.031 -63243 232s General.Electric_X1940 -0.562 -1199 232s General.Electric_X1941 40.750 74739 232s General.Electric_X1942 16.036 25464 232s General.Electric_X1943 -23.719 -41494 232s General.Electric_X1944 -26.780 -45183 232s General.Electric_X1945 1.768 3550 232s General.Electric_X1946 58.737 129709 232s General.Electric_X1947 43.936 72789 232s General.Electric_X1948 31.227 50101 232s General.Electric_X1949 -23.552 -33722 232s General.Electric_X1950 -37.511 -60411 232s General.Electric_X1951 -4.983 -9066 232s General.Electric_X1952 1.893 3937 232s General.Electric_X1953 5.087 12064 232s General.Electric_X1954 -8.563 -23633 232s Westinghouse_X1935 0.000 0 232s Westinghouse_X1936 0.000 0 232s Westinghouse_X1937 0.000 0 232s Westinghouse_X1938 0.000 0 232s Westinghouse_X1939 0.000 0 232s Westinghouse_X1940 0.000 0 232s Westinghouse_X1941 0.000 0 232s Westinghouse_X1942 0.000 0 232s Westinghouse_X1943 0.000 0 232s Westinghouse_X1944 0.000 0 232s Westinghouse_X1945 0.000 0 232s Westinghouse_X1946 0.000 0 232s Westinghouse_X1947 0.000 0 232s Westinghouse_X1948 0.000 0 232s Westinghouse_X1949 0.000 0 232s Westinghouse_X1950 0.000 0 232s Westinghouse_X1951 0.000 0 232s Westinghouse_X1952 0.000 0 232s Westinghouse_X1953 0.000 0 232s Westinghouse_X1954 0.000 0 232s General.Electric_capital Westinghouse_(Intercept) 232s General.Electric_X1935 -280 0.000 232s General.Electric_X1936 -1504 0.000 232s General.Electric_X1937 -611 0.000 232s General.Electric_X1938 -3639 0.000 232s General.Electric_X1939 -4838 0.000 232s General.Electric_X1940 -105 0.000 232s General.Electric_X1941 9002 0.000 232s General.Electric_X1942 4615 0.000 232s General.Electric_X1943 -7588 0.000 232s General.Electric_X1944 -8604 0.000 232s General.Electric_X1945 565 0.000 232s General.Electric_X1946 20323 0.000 232s General.Electric_X1947 20052 0.000 232s General.Electric_X1948 16969 0.000 232s General.Electric_X1949 -14562 0.000 232s General.Electric_X1950 -24285 0.000 232s General.Electric_X1951 -3345 0.000 232s General.Electric_X1952 1374 0.000 232s General.Electric_X1953 4071 0.000 232s General.Electric_X1954 -7612 0.000 232s Westinghouse_X1935 0 3.144 232s Westinghouse_X1936 0 -0.958 232s Westinghouse_X1937 0 -3.684 232s Westinghouse_X1938 0 -7.915 232s Westinghouse_X1939 0 -10.322 232s Westinghouse_X1940 0 -6.613 232s Westinghouse_X1941 0 17.265 232s Westinghouse_X1942 0 8.547 232s Westinghouse_X1943 0 -2.916 232s Westinghouse_X1944 0 -3.257 232s Westinghouse_X1945 0 -7.753 232s Westinghouse_X1946 0 5.796 232s Westinghouse_X1947 0 15.050 232s Westinghouse_X1948 0 2.969 232s Westinghouse_X1949 0 -11.433 232s Westinghouse_X1950 0 -13.481 232s Westinghouse_X1951 0 4.619 232s Westinghouse_X1952 0 13.138 232s Westinghouse_X1953 0 11.308 232s Westinghouse_X1954 0 -13.505 232s Westinghouse_value Westinghouse_capital 232s General.Electric_X1935 0 0.000 232s General.Electric_X1936 0 0.000 232s General.Electric_X1937 0 0.000 232s General.Electric_X1938 0 0.000 232s General.Electric_X1939 0 0.000 232s General.Electric_X1940 0 0.000 232s General.Electric_X1941 0 0.000 232s General.Electric_X1942 0 0.000 232s General.Electric_X1943 0 0.000 232s General.Electric_X1944 0 0.000 232s General.Electric_X1945 0 0.000 232s General.Electric_X1946 0 0.000 232s General.Electric_X1947 0 0.000 232s General.Electric_X1948 0 0.000 232s General.Electric_X1949 0 0.000 232s General.Electric_X1950 0 0.000 232s General.Electric_X1951 0 0.000 232s General.Electric_X1952 0 0.000 232s General.Electric_X1953 0 0.000 232s General.Electric_X1954 0 0.000 232s Westinghouse_X1935 602 5.659 232s Westinghouse_X1936 -494 -0.766 232s Westinghouse_X1937 -2686 -27.263 232s Westinghouse_X1938 -4436 -143.262 232s Westinghouse_X1939 -5366 -242.563 232s Westinghouse_X1940 -4156 -175.254 232s Westinghouse_X1941 9273 624.987 232s Westinghouse_X1942 4797 519.651 232s Westinghouse_X1943 -1800 -246.108 232s Westinghouse_X1944 -2041 -297.023 232s Westinghouse_X1945 -5715 -716.333 232s Westinghouse_X1946 4408 498.495 232s Westinghouse_X1947 8750 1672.098 232s Westinghouse_X1948 1967 387.794 232s Westinghouse_X1949 -6675 -1621.262 232s Westinghouse_X1950 -8563 -1842.843 232s Westinghouse_X1951 3344 599.149 232s Westinghouse_X1952 11353 1911.642 232s Westinghouse_X1953 13496 1976.568 232s Westinghouse_X1954 -16056 -2883.365 232s General.Electric_(Intercept) General.Electric_value 232s 0 0 232s General.Electric_capital Westinghouse_(Intercept) 232s 0 0 232s Westinghouse_value Westinghouse_capital 232s 0 0 232s General.Electric_(Intercept) General.Electric_value 232s General.Electric_X1935 0.007671 8.980 232s General.Electric_X1936 -0.061426 -123.822 232s General.Electric_X1937 -0.060974 -170.929 232s General.Electric_X1938 -0.088931 -181.393 232s General.Electric_X1939 -0.111776 -252.189 232s General.Electric_X1940 -0.017793 -37.937 232s General.Electric_X1941 0.128334 235.378 232s General.Electric_X1942 0.060606 96.243 232s General.Electric_X1943 -0.072587 -126.985 232s General.Electric_X1944 -0.080053 -135.065 232s General.Electric_X1945 -0.000104 -0.208 232s General.Electric_X1946 0.177325 391.586 232s General.Electric_X1947 0.154986 256.765 232s General.Electric_X1948 0.119488 191.707 232s General.Electric_X1949 -0.047791 -68.427 232s General.Electric_X1950 -0.098464 -158.576 232s General.Electric_X1951 -0.000379 -0.689 232s General.Electric_X1952 0.014181 29.492 232s General.Electric_X1953 0.016444 38.998 232s General.Electric_X1954 -0.038758 -106.969 232s Westinghouse_X1935 -0.019477 -22.800 232s Westinghouse_X1936 0.016942 34.151 232s Westinghouse_X1937 0.039739 111.402 232s Westinghouse_X1938 0.059843 122.062 232s Westinghouse_X1939 0.073091 164.909 232s Westinghouse_X1940 0.052015 110.907 232s Westinghouse_X1941 -0.105994 -194.404 232s Westinghouse_X1942 -0.053728 -85.321 232s Westinghouse_X1943 0.017332 30.320 232s Westinghouse_X1944 0.018569 31.330 232s Westinghouse_X1945 0.050605 101.599 232s Westinghouse_X1946 -0.034591 -76.387 232s Westinghouse_X1947 -0.104099 -172.460 232s Westinghouse_X1948 -0.027559 -44.215 232s Westinghouse_X1949 0.060567 86.720 232s Westinghouse_X1950 0.076221 122.754 232s Westinghouse_X1951 -0.036128 -65.731 232s Westinghouse_X1952 -0.089492 -186.117 232s Westinghouse_X1953 -0.073054 -173.256 232s Westinghouse_X1954 0.079198 218.578 232s General.Electric_capital Westinghouse_(Intercept) 232s General.Electric_X1935 0.7503 -0.015267 232s General.Electric_X1936 -6.4128 0.122246 232s General.Electric_X1937 -7.1950 0.121347 232s General.Electric_X1938 -13.8911 0.176986 232s General.Electric_X1939 -19.2925 0.222450 232s General.Electric_X1940 -3.3201 0.035410 232s General.Electric_X1941 28.3490 -0.255403 232s General.Electric_X1942 17.4425 -0.120615 232s General.Electric_X1943 -23.2207 0.144459 232s General.Electric_X1944 -25.7209 0.159316 232s General.Electric_X1945 -0.0331 0.000206 232s General.Electric_X1946 61.3543 -0.352901 232s General.Electric_X1947 70.7355 -0.308443 232s General.Electric_X1948 64.9300 -0.237798 232s General.Electric_X1949 -29.5489 0.095110 232s General.Electric_X1950 -63.7453 0.195956 232s General.Electric_X1951 -0.2543 0.000754 232s General.Electric_X1952 10.2966 -0.028221 232s General.Electric_X1953 13.1598 -0.032725 232s General.Electric_X1954 -34.4523 0.077135 232s Westinghouse_X1935 -1.9049 0.072945 232s Westinghouse_X1936 1.7687 -0.063449 232s Westinghouse_X1937 4.6893 -0.148830 232s Westinghouse_X1938 9.3475 -0.224122 232s Westinghouse_X1939 12.6156 -0.273739 232s Westinghouse_X1940 9.7061 -0.194806 232s Westinghouse_X1941 -23.4141 0.396965 232s Westinghouse_X1942 -15.4630 0.201221 232s Westinghouse_X1943 5.5444 -0.064910 232s Westinghouse_X1944 5.9663 -0.069544 232s Westinghouse_X1945 16.1733 -0.189523 232s Westinghouse_X1946 -11.9684 0.129548 232s Westinghouse_X1947 -47.5107 0.389866 232s Westinghouse_X1948 -14.9755 0.103212 232s Westinghouse_X1949 37.4485 -0.226832 232s Westinghouse_X1950 49.3457 -0.285461 232s Westinghouse_X1951 -24.2526 0.135304 232s Westinghouse_X1952 -64.9804 0.335163 232s Westinghouse_X1953 -58.4654 0.273600 232s Westinghouse_X1954 70.3989 -0.296608 232s Westinghouse_value Westinghouse_capital 232s General.Electric_X1935 -2.924 -0.0275 232s General.Electric_X1936 63.079 0.0978 232s General.Electric_X1937 88.462 0.8980 232s General.Electric_X1938 99.183 3.2034 232s General.Electric_X1939 115.652 5.2276 232s General.Electric_X1940 22.255 0.9384 232s General.Electric_X1941 -137.177 -9.2456 232s General.Electric_X1942 -67.689 -7.3334 232s General.Electric_X1943 89.160 12.1924 232s General.Electric_X1944 99.843 14.5296 232s General.Electric_X1945 0.152 0.0190 232s General.Electric_X1946 -268.381 -30.3494 232s General.Electric_X1947 -179.329 -34.2680 232s General.Electric_X1948 -157.494 -31.0565 232s General.Electric_X1949 55.525 13.4866 232s General.Electric_X1950 124.471 26.7872 232s General.Electric_X1951 0.546 0.0978 232s General.Electric_X1952 -24.386 -4.1062 232s General.Electric_X1953 -39.057 -5.7203 232s General.Electric_X1954 91.705 16.4682 232s Westinghouse_X1935 13.969 0.1313 232s Westinghouse_X1936 -32.740 -0.0508 232s Westinghouse_X1937 -108.497 -1.1013 232s Westinghouse_X1938 -125.598 -4.0566 232s Westinghouse_X1939 -142.317 -6.4329 232s Westinghouse_X1940 -122.436 -5.1624 232s Westinghouse_X1941 213.210 14.3701 232s Westinghouse_X1942 112.925 12.2342 232s Westinghouse_X1943 -40.063 -5.4784 232s Westinghouse_X1944 -43.583 -6.3424 232s Westinghouse_X1945 -139.717 -17.5120 232s Westinghouse_X1946 98.521 11.1411 232s Westinghouse_X1947 226.668 43.3141 232s Westinghouse_X1948 68.357 13.4795 232s Westinghouse_X1949 -132.425 -32.1648 232s Westinghouse_X1950 -181.325 -39.0225 232s Westinghouse_X1951 97.933 17.5490 232s Westinghouse_X1952 289.614 48.7662 232s Westinghouse_X1953 326.541 47.8252 232s Westinghouse_X1954 -352.637 -63.3258 232s General.Electric_(Intercept) General.Electric_value 232s 0 0 232s General.Electric_capital Westinghouse_(Intercept) 232s 0 0 232s Westinghouse_value Westinghouse_capital 232s 0 0 232s Chrysler_(Intercept) Chrysler_value Chrysler_capital 232s Chrysler_X1935 10.622 4435 111.5 232s Chrysler_X1936 10.425 8734 106.3 232s Chrysler_X1937 -7.404 -6544 -256.9 232s Chrysler_X1938 7.302 3198 378.3 232s Chrysler_X1939 -14.682 -9979 -944.0 232s Chrysler_X1940 -2.315 -1685 -155.3 232s Chrysler_X1941 0.631 406 47.4 232s Chrysler_X1942 -1.581 -650 -112.9 232s Chrysler_X1943 -13.459 -7919 -903.1 232s Chrysler_X1944 -7.780 -5433 -470.7 232s Chrysler_X1945 11.757 9951 641.9 232s Chrysler_X1946 -16.133 -14419 -1368.1 232s Chrysler_X1947 -6.823 -3951 -660.5 232s Chrysler_X1948 6.615 4595 729.0 232s Chrysler_X1949 -7.379 -4356 -1087.7 232s Chrysler_X1950 1.268 879 206.9 232s Chrysler_X1951 39.502 31957 8038.6 232s Chrysler_X1952 2.774 2017 806.2 232s Chrysler_X1953 -6.215 -6224 -2151.0 232s Chrysler_X1954 -7.124 -5010 -2955.9 232s General.Electric_X1935 0.000 0 0.0 232s General.Electric_X1936 0.000 0 0.0 232s General.Electric_X1937 0.000 0 0.0 232s General.Electric_X1938 0.000 0 0.0 232s General.Electric_X1939 0.000 0 0.0 232s General.Electric_X1940 0.000 0 0.0 232s General.Electric_X1941 0.000 0 0.0 232s General.Electric_X1942 0.000 0 0.0 232s General.Electric_X1943 0.000 0 0.0 232s General.Electric_X1944 0.000 0 0.0 232s General.Electric_X1945 0.000 0 0.0 232s General.Electric_X1946 0.000 0 0.0 232s General.Electric_X1947 0.000 0 0.0 232s General.Electric_X1948 0.000 0 0.0 232s General.Electric_X1949 0.000 0 0.0 232s General.Electric_X1950 0.000 0 0.0 232s General.Electric_X1951 0.000 0 0.0 232s General.Electric_X1952 0.000 0 0.0 232s General.Electric_X1953 0.000 0 0.0 232s General.Electric_X1954 0.000 0 0.0 232s General.Motors_X1935 0.000 0 0.0 232s General.Motors_X1936 0.000 0 0.0 232s General.Motors_X1937 0.000 0 0.0 232s General.Motors_X1938 0.000 0 0.0 232s General.Motors_X1939 0.000 0 0.0 232s General.Motors_X1940 0.000 0 0.0 232s General.Motors_X1941 0.000 0 0.0 232s General.Motors_X1942 0.000 0 0.0 232s General.Motors_X1943 0.000 0 0.0 232s General.Motors_X1944 0.000 0 0.0 232s General.Motors_X1945 0.000 0 0.0 232s General.Motors_X1946 0.000 0 0.0 232s General.Motors_X1947 0.000 0 0.0 232s General.Motors_X1948 0.000 0 0.0 232s General.Motors_X1949 0.000 0 0.0 232s General.Motors_X1950 0.000 0 0.0 232s General.Motors_X1951 0.000 0 0.0 232s General.Motors_X1952 0.000 0 0.0 232s General.Motors_X1953 0.000 0 0.0 232s General.Motors_X1954 0.000 0 0.0 232s US.Steel_X1935 0.000 0 0.0 232s US.Steel_X1936 0.000 0 0.0 232s US.Steel_X1937 0.000 0 0.0 232s US.Steel_X1938 0.000 0 0.0 232s US.Steel_X1939 0.000 0 0.0 232s US.Steel_X1940 0.000 0 0.0 232s US.Steel_X1941 0.000 0 0.0 232s US.Steel_X1942 0.000 0 0.0 232s US.Steel_X1943 0.000 0 0.0 232s US.Steel_X1944 0.000 0 0.0 232s US.Steel_X1945 0.000 0 0.0 232s US.Steel_X1946 0.000 0 0.0 232s US.Steel_X1947 0.000 0 0.0 232s US.Steel_X1948 0.000 0 0.0 232s US.Steel_X1949 0.000 0 0.0 232s US.Steel_X1950 0.000 0 0.0 232s US.Steel_X1951 0.000 0 0.0 232s US.Steel_X1952 0.000 0 0.0 232s US.Steel_X1953 0.000 0 0.0 232s US.Steel_X1954 0.000 0 0.0 232s Westinghouse_X1935 0.000 0 0.0 232s Westinghouse_X1936 0.000 0 0.0 232s Westinghouse_X1937 0.000 0 0.0 232s Westinghouse_X1938 0.000 0 0.0 232s Westinghouse_X1939 0.000 0 0.0 232s Westinghouse_X1940 0.000 0 0.0 232s Westinghouse_X1941 0.000 0 0.0 232s Westinghouse_X1942 0.000 0 0.0 232s Westinghouse_X1943 0.000 0 0.0 232s Westinghouse_X1944 0.000 0 0.0 232s Westinghouse_X1945 0.000 0 0.0 232s Westinghouse_X1946 0.000 0 0.0 232s Westinghouse_X1947 0.000 0 0.0 232s Westinghouse_X1948 0.000 0 0.0 232s Westinghouse_X1949 0.000 0 0.0 232s Westinghouse_X1950 0.000 0 0.0 232s Westinghouse_X1951 0.000 0 0.0 232s Westinghouse_X1952 0.000 0 0.0 232s Westinghouse_X1953 0.000 0 0.0 232s Westinghouse_X1954 0.000 0 0.0 232s General.Electric_(Intercept) General.Electric_value 232s Chrysler_X1935 0.000 0 232s Chrysler_X1936 0.000 0 232s Chrysler_X1937 0.000 0 232s Chrysler_X1938 0.000 0 232s Chrysler_X1939 0.000 0 232s Chrysler_X1940 0.000 0 232s Chrysler_X1941 0.000 0 232s Chrysler_X1942 0.000 0 232s Chrysler_X1943 0.000 0 232s Chrysler_X1944 0.000 0 232s Chrysler_X1945 0.000 0 232s Chrysler_X1946 0.000 0 232s Chrysler_X1947 0.000 0 232s Chrysler_X1948 0.000 0 232s Chrysler_X1949 0.000 0 232s Chrysler_X1950 0.000 0 232s Chrysler_X1951 0.000 0 232s Chrysler_X1952 0.000 0 232s Chrysler_X1953 0.000 0 232s Chrysler_X1954 0.000 0 232s General.Electric_X1935 -2.860 -3348 232s General.Electric_X1936 -14.402 -29032 232s General.Electric_X1937 -5.175 -14506 232s General.Electric_X1938 -23.295 -47514 232s General.Electric_X1939 -28.031 -63243 232s General.Electric_X1940 -0.562 -1199 232s General.Electric_X1941 40.750 74739 232s General.Electric_X1942 16.036 25464 232s General.Electric_X1943 -23.719 -41494 232s General.Electric_X1944 -26.780 -45183 232s General.Electric_X1945 1.768 3550 232s General.Electric_X1946 58.737 129709 232s General.Electric_X1947 43.936 72789 232s General.Electric_X1948 31.227 50101 232s General.Electric_X1949 -23.552 -33722 232s General.Electric_X1950 -37.511 -60411 232s General.Electric_X1951 -4.983 -9066 232s General.Electric_X1952 1.893 3937 232s General.Electric_X1953 5.087 12064 232s General.Electric_X1954 -8.563 -23633 232s General.Motors_X1935 0.000 0 232s General.Motors_X1936 0.000 0 232s General.Motors_X1937 0.000 0 232s General.Motors_X1938 0.000 0 232s General.Motors_X1939 0.000 0 232s General.Motors_X1940 0.000 0 232s General.Motors_X1941 0.000 0 232s General.Motors_X1942 0.000 0 232s General.Motors_X1943 0.000 0 232s General.Motors_X1944 0.000 0 232s General.Motors_X1945 0.000 0 232s General.Motors_X1946 0.000 0 232s General.Motors_X1947 0.000 0 232s General.Motors_X1948 0.000 0 232s General.Motors_X1949 0.000 0 232s General.Motors_X1950 0.000 0 232s General.Motors_X1951 0.000 0 232s General.Motors_X1952 0.000 0 232s General.Motors_X1953 0.000 0 232s General.Motors_X1954 0.000 0 232s US.Steel_X1935 0.000 0 232s US.Steel_X1936 0.000 0 232s US.Steel_X1937 0.000 0 232s US.Steel_X1938 0.000 0 232s US.Steel_X1939 0.000 0 232s US.Steel_X1940 0.000 0 232s US.Steel_X1941 0.000 0 232s US.Steel_X1942 0.000 0 232s US.Steel_X1943 0.000 0 232s US.Steel_X1944 0.000 0 232s US.Steel_X1945 0.000 0 232s US.Steel_X1946 0.000 0 232s US.Steel_X1947 0.000 0 232s US.Steel_X1948 0.000 0 232s US.Steel_X1949 0.000 0 232s US.Steel_X1950 0.000 0 232s US.Steel_X1951 0.000 0 232s US.Steel_X1952 0.000 0 232s US.Steel_X1953 0.000 0 232s US.Steel_X1954 0.000 0 232s Westinghouse_X1935 0.000 0 232s Westinghouse_X1936 0.000 0 232s Westinghouse_X1937 0.000 0 232s Westinghouse_X1938 0.000 0 232s Westinghouse_X1939 0.000 0 232s Westinghouse_X1940 0.000 0 232s Westinghouse_X1941 0.000 0 232s Westinghouse_X1942 0.000 0 232s Westinghouse_X1943 0.000 0 232s Westinghouse_X1944 0.000 0 232s Westinghouse_X1945 0.000 0 232s Westinghouse_X1946 0.000 0 232s Westinghouse_X1947 0.000 0 232s Westinghouse_X1948 0.000 0 232s Westinghouse_X1949 0.000 0 232s Westinghouse_X1950 0.000 0 232s Westinghouse_X1951 0.000 0 232s Westinghouse_X1952 0.000 0 232s Westinghouse_X1953 0.000 0 232s Westinghouse_X1954 0.000 0 232s General.Electric_capital General.Motors_(Intercept) 232s Chrysler_X1935 0 0.00 232s Chrysler_X1936 0 0.00 232s Chrysler_X1937 0 0.00 232s Chrysler_X1938 0 0.00 232s Chrysler_X1939 0 0.00 232s Chrysler_X1940 0 0.00 232s Chrysler_X1941 0 0.00 232s Chrysler_X1942 0 0.00 232s Chrysler_X1943 0 0.00 232s Chrysler_X1944 0 0.00 232s Chrysler_X1945 0 0.00 232s Chrysler_X1946 0 0.00 232s Chrysler_X1947 0 0.00 232s Chrysler_X1948 0 0.00 232s Chrysler_X1949 0 0.00 232s Chrysler_X1950 0 0.00 232s Chrysler_X1951 0 0.00 232s Chrysler_X1952 0 0.00 232s Chrysler_X1953 0 0.00 232s Chrysler_X1954 0 0.00 232s General.Electric_X1935 -280 0.00 232s General.Electric_X1936 -1504 0.00 232s General.Electric_X1937 -611 0.00 232s General.Electric_X1938 -3639 0.00 232s General.Electric_X1939 -4838 0.00 232s General.Electric_X1940 -105 0.00 232s General.Electric_X1941 9002 0.00 232s General.Electric_X1942 4615 0.00 232s General.Electric_X1943 -7588 0.00 232s General.Electric_X1944 -8604 0.00 232s General.Electric_X1945 565 0.00 232s General.Electric_X1946 20323 0.00 232s General.Electric_X1947 20052 0.00 232s General.Electric_X1948 16969 0.00 232s General.Electric_X1949 -14562 0.00 232s General.Electric_X1950 -24285 0.00 232s General.Electric_X1951 -3345 0.00 232s General.Electric_X1952 1374 0.00 232s General.Electric_X1953 4071 0.00 232s General.Electric_X1954 -7612 0.00 232s General.Motors_X1935 0 99.14 232s General.Motors_X1936 0 -34.01 232s General.Motors_X1937 0 -140.48 232s General.Motors_X1938 0 -3.28 232s General.Motors_X1939 0 -109.45 232s General.Motors_X1940 0 -19.91 232s General.Motors_X1941 0 24.12 232s General.Motors_X1942 0 98.02 232s General.Motors_X1943 0 67.76 232s General.Motors_X1944 0 100.03 232s General.Motors_X1945 0 35.12 232s General.Motors_X1946 0 103.90 232s General.Motors_X1947 0 15.18 232s General.Motors_X1948 0 -51.86 232s General.Motors_X1949 0 -115.39 232s General.Motors_X1950 0 -63.51 232s General.Motors_X1951 0 -119.40 232s General.Motors_X1952 0 -77.82 232s General.Motors_X1953 0 49.50 232s General.Motors_X1954 0 142.33 232s US.Steel_X1935 0 0.00 232s US.Steel_X1936 0 0.00 232s US.Steel_X1937 0 0.00 232s US.Steel_X1938 0 0.00 232s US.Steel_X1939 0 0.00 232s US.Steel_X1940 0 0.00 232s US.Steel_X1941 0 0.00 232s US.Steel_X1942 0 0.00 232s US.Steel_X1943 0 0.00 232s US.Steel_X1944 0 0.00 232s US.Steel_X1945 0 0.00 232s US.Steel_X1946 0 0.00 232s US.Steel_X1947 0 0.00 232s US.Steel_X1948 0 0.00 232s US.Steel_X1949 0 0.00 232s US.Steel_X1950 0 0.00 232s US.Steel_X1951 0 0.00 232s US.Steel_X1952 0 0.00 232s US.Steel_X1953 0 0.00 232s US.Steel_X1954 0 0.00 232s Westinghouse_X1935 0 0.00 232s Westinghouse_X1936 0 0.00 232s Westinghouse_X1937 0 0.00 232s Westinghouse_X1938 0 0.00 232s Westinghouse_X1939 0 0.00 232s Westinghouse_X1940 0 0.00 232s Westinghouse_X1941 0 0.00 232s Westinghouse_X1942 0 0.00 232s Westinghouse_X1943 0 0.00 232s Westinghouse_X1944 0 0.00 232s Westinghouse_X1945 0 0.00 232s Westinghouse_X1946 0 0.00 232s Westinghouse_X1947 0 0.00 232s Westinghouse_X1948 0 0.00 232s Westinghouse_X1949 0 0.00 232s Westinghouse_X1950 0 0.00 232s Westinghouse_X1951 0 0.00 232s Westinghouse_X1952 0 0.00 232s Westinghouse_X1953 0 0.00 232s Westinghouse_X1954 0 0.00 232s General.Motors_value General.Motors_capital 232s Chrysler_X1935 0 0 232s Chrysler_X1936 0 0 232s Chrysler_X1937 0 0 232s Chrysler_X1938 0 0 232s Chrysler_X1939 0 0 232s Chrysler_X1940 0 0 232s Chrysler_X1941 0 0 232s Chrysler_X1942 0 0 232s Chrysler_X1943 0 0 232s Chrysler_X1944 0 0 232s Chrysler_X1945 0 0 232s Chrysler_X1946 0 0 232s Chrysler_X1947 0 0 232s Chrysler_X1948 0 0 232s Chrysler_X1949 0 0 232s Chrysler_X1950 0 0 232s Chrysler_X1951 0 0 232s Chrysler_X1952 0 0 232s Chrysler_X1953 0 0 232s Chrysler_X1954 0 0 232s General.Electric_X1935 0 0 232s General.Electric_X1936 0 0 232s General.Electric_X1937 0 0 232s General.Electric_X1938 0 0 232s General.Electric_X1939 0 0 232s General.Electric_X1940 0 0 232s General.Electric_X1941 0 0 232s General.Electric_X1942 0 0 232s General.Electric_X1943 0 0 232s General.Electric_X1944 0 0 232s General.Electric_X1945 0 0 232s General.Electric_X1946 0 0 232s General.Electric_X1947 0 0 232s General.Electric_X1948 0 0 232s General.Electric_X1949 0 0 232s General.Electric_X1950 0 0 232s General.Electric_X1951 0 0 232s General.Electric_X1952 0 0 232s General.Electric_X1953 0 0 232s General.Electric_X1954 0 0 232s General.Motors_X1935 305191 278 232s General.Motors_X1936 -158530 -1789 232s General.Motors_X1937 -756753 -22041 232s General.Motors_X1938 -9158 -686 232s General.Motors_X1939 -472086 -22262 232s General.Motors_X1940 -92456 -4125 232s General.Motors_X1941 109770 6155 232s General.Motors_X1942 317973 29767 232s General.Motors_X1943 274659 17894 232s General.Motors_X1944 438073 20167 232s General.Motors_X1945 170027 9308 232s General.Motors_X1946 509223 41790 232s General.Motors_X1947 53544 11562 232s General.Motors_X1948 -168794 -47837 232s General.Motors_X1949 -426971 -117711 232s General.Motors_X1950 -238505 -69794 232s General.Motors_X1951 -577039 -144194 232s General.Motors_X1952 -383234 -111315 232s General.Motors_X1953 308954 87974 232s General.Motors_X1954 796113 316860 232s US.Steel_X1935 0 0 232s US.Steel_X1936 0 0 232s US.Steel_X1937 0 0 232s US.Steel_X1938 0 0 232s US.Steel_X1939 0 0 232s US.Steel_X1940 0 0 232s US.Steel_X1941 0 0 232s US.Steel_X1942 0 0 232s US.Steel_X1943 0 0 232s US.Steel_X1944 0 0 232s US.Steel_X1945 0 0 232s US.Steel_X1946 0 0 232s US.Steel_X1947 0 0 232s US.Steel_X1948 0 0 232s US.Steel_X1949 0 0 232s US.Steel_X1950 0 0 232s US.Steel_X1951 0 0 232s US.Steel_X1952 0 0 232s US.Steel_X1953 0 0 232s US.Steel_X1954 0 0 232s Westinghouse_X1935 0 0 232s Westinghouse_X1936 0 0 232s Westinghouse_X1937 0 0 232s Westinghouse_X1938 0 0 232s Westinghouse_X1939 0 0 232s Westinghouse_X1940 0 0 232s Westinghouse_X1941 0 0 232s Westinghouse_X1942 0 0 232s Westinghouse_X1943 0 0 232s Westinghouse_X1944 0 0 232s Westinghouse_X1945 0 0 232s Westinghouse_X1946 0 0 232s Westinghouse_X1947 0 0 232s Westinghouse_X1948 0 0 232s Westinghouse_X1949 0 0 232s Westinghouse_X1950 0 0 232s Westinghouse_X1951 0 0 232s Westinghouse_X1952 0 0 232s Westinghouse_X1953 0 0 232s Westinghouse_X1954 0 0 232s US.Steel_(Intercept) US.Steel_value US.Steel_capital 232s Chrysler_X1935 0.00 0 0 232s Chrysler_X1936 0.00 0 0 232s Chrysler_X1937 0.00 0 0 232s Chrysler_X1938 0.00 0 0 232s Chrysler_X1939 0.00 0 0 232s Chrysler_X1940 0.00 0 0 232s Chrysler_X1941 0.00 0 0 232s Chrysler_X1942 0.00 0 0 232s Chrysler_X1943 0.00 0 0 232s Chrysler_X1944 0.00 0 0 232s Chrysler_X1945 0.00 0 0 232s Chrysler_X1946 0.00 0 0 232s Chrysler_X1947 0.00 0 0 232s Chrysler_X1948 0.00 0 0 232s Chrysler_X1949 0.00 0 0 232s Chrysler_X1950 0.00 0 0 232s Chrysler_X1951 0.00 0 0 232s Chrysler_X1952 0.00 0 0 232s Chrysler_X1953 0.00 0 0 232s Chrysler_X1954 0.00 0 0 232s General.Electric_X1935 0.00 0 0 232s General.Electric_X1936 0.00 0 0 232s General.Electric_X1937 0.00 0 0 232s General.Electric_X1938 0.00 0 0 232s General.Electric_X1939 0.00 0 0 232s General.Electric_X1940 0.00 0 0 232s General.Electric_X1941 0.00 0 0 232s General.Electric_X1942 0.00 0 0 232s General.Electric_X1943 0.00 0 0 232s General.Electric_X1944 0.00 0 0 232s General.Electric_X1945 0.00 0 0 232s General.Electric_X1946 0.00 0 0 232s General.Electric_X1947 0.00 0 0 232s General.Electric_X1948 0.00 0 0 232s General.Electric_X1949 0.00 0 0 232s General.Electric_X1950 0.00 0 0 232s General.Electric_X1951 0.00 0 0 232s General.Electric_X1952 0.00 0 0 232s General.Electric_X1953 0.00 0 0 232s General.Electric_X1954 0.00 0 0 232s General.Motors_X1935 0.00 0 0 232s General.Motors_X1936 0.00 0 0 232s General.Motors_X1937 0.00 0 0 232s General.Motors_X1938 0.00 0 0 232s General.Motors_X1939 0.00 0 0 232s General.Motors_X1940 0.00 0 0 232s General.Motors_X1941 0.00 0 0 232s General.Motors_X1942 0.00 0 0 232s General.Motors_X1943 0.00 0 0 232s General.Motors_X1944 0.00 0 0 232s General.Motors_X1945 0.00 0 0 232s General.Motors_X1946 0.00 0 0 232s General.Motors_X1947 0.00 0 0 232s General.Motors_X1948 0.00 0 0 232s General.Motors_X1949 0.00 0 0 232s General.Motors_X1950 0.00 0 0 232s General.Motors_X1951 0.00 0 0 232s General.Motors_X1952 0.00 0 0 232s General.Motors_X1953 0.00 0 0 232s General.Motors_X1954 0.00 0 0 232s US.Steel_X1935 4.15 5657 223 232s US.Steel_X1936 81.32 146961 4107 232s US.Steel_X1937 31.18 83446 3682 232s US.Steel_X1938 -99.75 -179733 -25954 232s US.Steel_X1939 -178.23 -348850 -55733 232s US.Steel_X1940 -160.69 -353980 -40847 232s US.Steel_X1941 19.65 46784 5137 232s US.Steel_X1942 9.82 21296 2933 232s US.Steel_X1943 -46.76 -92829 -14113 232s US.Steel_X1944 -83.74 -151889 -23371 232s US.Steel_X1945 -91.24 -168815 -19507 232s US.Steel_X1946 28.34 58590 6591 232s US.Steel_X1947 57.32 102983 15178 232s US.Steel_X1948 140.23 227988 43037 232s US.Steel_X1949 25.65 42751 9004 232s US.Steel_X1950 34.88 58503 12479 232s US.Steel_X1951 115.10 263510 39374 232s US.Steel_X1952 149.19 322157 66269 232s US.Steel_X1953 89.00 180793 55503 232s US.Steel_X1954 -125.42 -265326 -83994 232s Westinghouse_X1935 0.00 0 0 232s Westinghouse_X1936 0.00 0 0 232s Westinghouse_X1937 0.00 0 0 232s Westinghouse_X1938 0.00 0 0 232s Westinghouse_X1939 0.00 0 0 232s Westinghouse_X1940 0.00 0 0 232s Westinghouse_X1941 0.00 0 0 232s Westinghouse_X1942 0.00 0 0 232s Westinghouse_X1943 0.00 0 0 232s Westinghouse_X1944 0.00 0 0 232s Westinghouse_X1945 0.00 0 0 232s Westinghouse_X1946 0.00 0 0 232s Westinghouse_X1947 0.00 0 0 232s Westinghouse_X1948 0.00 0 0 232s Westinghouse_X1949 0.00 0 0 232s Westinghouse_X1950 0.00 0 0 232s Westinghouse_X1951 0.00 0 0 232s Westinghouse_X1952 0.00 0 0 232s Westinghouse_X1953 0.00 0 0 232s Westinghouse_X1954 0.00 0 0 232s Westinghouse_(Intercept) Westinghouse_value 232s Chrysler_X1935 0.000 0 232s Chrysler_X1936 0.000 0 232s Chrysler_X1937 0.000 0 232s Chrysler_X1938 0.000 0 232s Chrysler_X1939 0.000 0 232s Chrysler_X1940 0.000 0 232s Chrysler_X1941 0.000 0 232s Chrysler_X1942 0.000 0 232s Chrysler_X1943 0.000 0 232s Chrysler_X1944 0.000 0 232s Chrysler_X1945 0.000 0 232s Chrysler_X1946 0.000 0 232s Chrysler_X1947 0.000 0 232s Chrysler_X1948 0.000 0 232s Chrysler_X1949 0.000 0 232s Chrysler_X1950 0.000 0 232s Chrysler_X1951 0.000 0 232s Chrysler_X1952 0.000 0 232s Chrysler_X1953 0.000 0 232s Chrysler_X1954 0.000 0 232s General.Electric_X1935 0.000 0 232s General.Electric_X1936 0.000 0 232s General.Electric_X1937 0.000 0 232s General.Electric_X1938 0.000 0 232s General.Electric_X1939 0.000 0 232s General.Electric_X1940 0.000 0 232s General.Electric_X1941 0.000 0 232s General.Electric_X1942 0.000 0 232s General.Electric_X1943 0.000 0 232s General.Electric_X1944 0.000 0 232s General.Electric_X1945 0.000 0 232s General.Electric_X1946 0.000 0 232s General.Electric_X1947 0.000 0 232s General.Electric_X1948 0.000 0 232s General.Electric_X1949 0.000 0 232s General.Electric_X1950 0.000 0 232s General.Electric_X1951 0.000 0 232s General.Electric_X1952 0.000 0 232s General.Electric_X1953 0.000 0 232s General.Electric_X1954 0.000 0 232s General.Motors_X1935 0.000 0 232s General.Motors_X1936 0.000 0 232s General.Motors_X1937 0.000 0 232s General.Motors_X1938 0.000 0 232s General.Motors_X1939 0.000 0 232s General.Motors_X1940 0.000 0 232s General.Motors_X1941 0.000 0 232s General.Motors_X1942 0.000 0 232s General.Motors_X1943 0.000 0 232s General.Motors_X1944 0.000 0 232s General.Motors_X1945 0.000 0 232s General.Motors_X1946 0.000 0 232s General.Motors_X1947 0.000 0 232s General.Motors_X1948 0.000 0 232s General.Motors_X1949 0.000 0 232s General.Motors_X1950 0.000 0 232s General.Motors_X1951 0.000 0 232s General.Motors_X1952 0.000 0 232s General.Motors_X1953 0.000 0 232s General.Motors_X1954 0.000 0 232s US.Steel_X1935 0.000 0 232s US.Steel_X1936 0.000 0 232s US.Steel_X1937 0.000 0 232s US.Steel_X1938 0.000 0 232s US.Steel_X1939 0.000 0 232s US.Steel_X1940 0.000 0 232s US.Steel_X1941 0.000 0 232s US.Steel_X1942 0.000 0 232s US.Steel_X1943 0.000 0 232s US.Steel_X1944 0.000 0 232s US.Steel_X1945 Error in estfun.systemfit(greeneOlsPooled) : 232s returning the estimation function for models with restrictions has not yet been implemented. 232s 0.000 0 232s US.Steel_X1946 0.000 0 232s US.Steel_X1947 0.000 0 232s US.Steel_X1948 0.000 0 232s US.Steel_X1949 0.000 0 232s US.Steel_X1950 0.000 0 232s US.Steel_X1951 0.000 0 232s US.Steel_X1952 0.000 0 232s US.Steel_X1953 0.000 0 232s US.Steel_X1954 0.000 0 232s Westinghouse_X1935 3.144 602 232s Westinghouse_X1936 -0.958 -494 232s Westinghouse_X1937 -3.684 -2686 232s Westinghouse_X1938 -7.915 -4436 232s Westinghouse_X1939 -10.322 -5366 232s Westinghouse_X1940 -6.613 -4156 232s Westinghouse_X1941 17.265 9273 232s Westinghouse_X1942 8.547 4797 232s Westinghouse_X1943 -2.916 -1800 232s Westinghouse_X1944 -3.257 -2041 232s Westinghouse_X1945 -7.753 -5715 232s Westinghouse_X1946 5.796 4408 232s Westinghouse_X1947 15.050 8750 232s Westinghouse_X1948 2.969 1967 232s Westinghouse_X1949 -11.433 -6675 232s Westinghouse_X1950 -13.481 -8563 232s Westinghouse_X1951 4.619 3344 232s Westinghouse_X1952 13.138 11353 232s Westinghouse_X1953 11.308 13496 232s Westinghouse_X1954 -13.505 -16056 232s Westinghouse_capital 232s Chrysler_X1935 0.000 232s Chrysler_X1936 0.000 232s Chrysler_X1937 0.000 232s Chrysler_X1938 0.000 232s Chrysler_X1939 0.000 232s Chrysler_X1940 0.000 232s Chrysler_X1941 0.000 232s Chrysler_X1942 0.000 232s Chrysler_X1943 0.000 232s Chrysler_X1944 0.000 232s Chrysler_X1945 0.000 232s Chrysler_X1946 0.000 232s Chrysler_X1947 0.000 232s Chrysler_X1948 0.000 232s Chrysler_X1949 0.000 232s Chrysler_X1950 0.000 232s Chrysler_X1951 0.000 232s Chrysler_X1952 0.000 232s Chrysler_X1953 0.000 232s Chrysler_X1954 0.000 232s General.Electric_X1935 0.000 232s General.Electric_X1936 0.000 232s General.Electric_X1937 0.000 232s General.Electric_X1938 0.000 232s General.Electric_X1939 0.000 232s General.Electric_X1940 0.000 232s General.Electric_X1941 0.000 232s General.Electric_X1942 0.000 232s General.Electric_X1943 0.000 232s General.Electric_X1944 0.000 232s General.Electric_X1945 0.000 232s General.Electric_X1946 0.000 232s General.Electric_X1947 0.000 232s General.Electric_X1948 0.000 232s General.Electric_X1949 0.000 232s General.Electric_X1950 0.000 232s General.Electric_X1951 0.000 232s General.Electric_X1952 0.000 232s General.Electric_X1953 0.000 232s General.Electric_X1954 0.000 232s General.Motors_X1935 0.000 232s General.Motors_X1936 0.000 232s General.Motors_X1937 0.000 232s General.Motors_X1938 0.000 232s General.Motors_X1939 0.000 232s General.Motors_X1940 0.000 232s General.Motors_X1941 0.000 232s General.Motors_X1942 0.000 232s General.Motors_X1943 0.000 232s General.Motors_X1944 0.000 232s General.Motors_X1945 0.000 232s General.Motors_X1946 0.000 232s General.Motors_X1947 0.000 232s General.Motors_X1948 0.000 232s General.Motors_X1949 0.000 232s General.Motors_X1950 0.000 232s General.Motors_X1951 0.000 232s General.Motors_X1952 0.000 232s General.Motors_X1953 0.000 232s General.Motors_X1954 0.000 232s US.Steel_X1935 0.000 232s US.Steel_X1936 0.000 232s US.Steel_X1937 0.000 232s US.Steel_X1938 0.000 232s US.Steel_X1939 0.000 232s US.Steel_X1940 0.000 232s US.Steel_X1941 0.000 232s US.Steel_X1942 0.000 232s US.Steel_X1943 0.000 232s US.Steel_X1944 0.000 232s US.Steel_X1945 0.000 232s US.Steel_X1946 0.000 232s US.Steel_X1947 0.000 232s US.Steel_X1948 0.000 232s US.Steel_X1949 0.000 232s US.Steel_X1950 0.000 232s US.Steel_X1951 0.000 232s US.Steel_X1952 0.000 232s US.Steel_X1953 0.000 232s US.Steel_X1954 0.000 232s Westinghouse_X1935 5.659 232s Westinghouse_X1936 -0.766 232s Westinghouse_X1937 -27.263 232s Westinghouse_X1938 -143.262 232s Westinghouse_X1939 -242.563 232s Westinghouse_X1940 -175.254 232s Westinghouse_X1941 624.987 232s Westinghouse_X1942 519.651 232s Westinghouse_X1943 -246.108 232s Westinghouse_X1944 -297.023 232s Westinghouse_X1945 -716.333 232s Westinghouse_X1946 498.495 232s Westinghouse_X1947 1672.098 232s Westinghouse_X1948 387.794 232s Westinghouse_X1949 -1621.262 232s Westinghouse_X1950 -1842.843 232s Westinghouse_X1951 599.149 232s Westinghouse_X1952 1911.642 232s Westinghouse_X1953 1976.568 232s Westinghouse_X1954 -2883.365 232s Chrysler_(Intercept) Chrysler_value 232s 0 0 232s Chrysler_capital General.Electric_(Intercept) 232s 0 0 232s General.Electric_value General.Electric_capital 232s 0 0 232s General.Motors_(Intercept) General.Motors_value 232s 0 0 232s General.Motors_capital US.Steel_(Intercept) 232s 0 0 232s US.Steel_value US.Steel_capital 232s 0 0 232s Westinghouse_(Intercept) Westinghouse_value 232s 0 0 232s Westinghouse_capital 232s 0 232s [1] "Error in estfun.systemfit(greeneOlsPooled) : \n returning the estimation function for models with restrictions has not yet been implemented.\n" 232s attr(,"class") 232s [1] "try-error" 232s attr(,"condition") 232s 232s Chrysler_(Intercept) Chrysler_value Chrysler_capital 232s Chrysler_X1935 0.061827 25.813 0.64918 232s Chrysler_X1936 0.089260 74.782 0.91045 232s Chrysler_X1937 -0.052866 -46.729 -1.83447 232s Chrysler_X1938 0.038353 16.795 1.98668 232s Chrysler_X1939 -0.125156 -85.069 -8.04755 232s Chrysler_X1940 -0.019863 -14.456 -1.33281 232s Chrysler_X1941 -0.000958 -0.617 -0.07206 232s Chrysler_X1942 -0.035485 -14.581 -2.53362 232s Chrysler_X1943 -0.121241 -71.338 -8.13529 232s Chrysler_X1944 -0.067270 -46.981 -4.06984 232s Chrysler_X1945 0.103440 87.551 5.64781 232s Chrysler_X1946 -0.121081 -108.222 -10.26763 232s Chrysler_X1947 -0.065512 -37.931 -6.34155 232s Chrysler_X1948 0.053900 37.439 5.93977 232s Chrysler_X1949 -0.066320 -39.149 -9.77563 232s Chrysler_X1950 0.012935 8.971 2.11101 232s Chrysler_X1951 0.338038 273.472 68.79064 232s Chrysler_X1952 0.035175 25.572 10.22178 232s Chrysler_X1953 -0.016558 -16.583 -5.73086 232s Chrysler_X1954 -0.040615 -28.561 -16.85128 232s General.Electric_X1935 -0.000794 -0.332 -0.00834 232s General.Electric_X1936 -0.018766 -15.722 -0.19142 232s General.Electric_X1937 -0.017841 -15.770 -0.61909 232s General.Electric_X1938 -0.025844 -11.317 -1.33872 232s General.Electric_X1939 -0.031739 -21.573 -2.04083 232s General.Electric_X1940 -0.006211 -4.520 -0.41674 232s General.Electric_X1941 0.033478 21.546 2.51754 232s General.Electric_X1942 0.015339 6.303 1.09520 232s General.Electric_X1943 -0.020477 -12.049 -1.37400 232s General.Electric_X1944 -0.022551 -15.749 -1.36432 232s General.Electric_X1945 -0.000552 -0.467 -0.03015 232s General.Electric_X1946 0.048030 42.930 4.07298 232s General.Electric_X1947 0.042267 24.472 4.09142 232s General.Electric_X1948 0.033204 23.064 3.65913 232s General.Electric_X1949 -0.011862 -7.002 -1.74842 232s General.Electric_X1950 -0.025261 -17.518 -4.12252 232s General.Electric_X1951 0.001752 1.417 0.35646 232s General.Electric_X1952 0.006337 4.607 1.84166 232s General.Electric_X1953 0.007751 7.762 2.68249 232s General.Electric_X1954 -0.006261 -4.402 -2.59748 232s General.Motors_X1935 0.015266 6.374 0.16030 232s General.Motors_X1936 -0.003913 -3.278 -0.03991 232s General.Motors_X1937 -0.019260 -17.024 -0.66833 232s General.Motors_X1938 0.000502 0.220 0.02603 232s General.Motors_X1939 -0.014763 -10.035 -0.94928 232s General.Motors_X1940 -0.002163 -1.575 -0.14517 232s General.Motors_X1941 0.004002 2.576 0.30095 232s General.Motors_X1942 0.014599 5.999 1.04234 232s General.Motors_X1943 0.010244 6.027 0.68736 232s General.Motors_X1944 0.014852 10.373 0.89857 232s General.Motors_X1945 0.005493 4.649 0.29991 232s General.Motors_X1946 0.014990 13.398 1.27114 232s General.Motors_X1947 0.002105 1.219 0.20375 232s General.Motors_X1948 -0.007587 -5.270 -0.83607 232s General.Motors_X1949 -0.016803 -9.919 -2.47682 232s General.Motors_X1950 -0.009602 -6.659 -1.56700 232s General.Motors_X1951 -0.017864 -14.452 -3.63526 232s General.Motors_X1952 -0.012355 -8.982 -3.59050 232s General.Motors_X1953 0.004869 4.876 1.68503 232s General.Motors_X1954 0.017389 12.228 7.21481 232s US.Steel_X1935 0.013928 5.815 0.14625 232s US.Steel_X1936 -0.026161 -21.918 -0.26684 232s US.Steel_X1937 -0.025907 -22.899 -0.89897 232s US.Steel_X1938 0.043429 19.017 2.24961 232s US.Steel_X1939 0.070526 47.937 4.53484 232s US.Steel_X1940 0.058816 42.806 3.94653 232s US.Steel_X1941 -0.016278 -10.476 -1.22408 232s US.Steel_X1942 -0.008142 -3.346 -0.58136 232s US.Steel_X1943 0.018146 10.677 1.21761 232s US.Steel_X1944 0.036672 25.612 2.21866 232s US.Steel_X1945 0.039460 33.399 2.15450 232s US.Steel_X1946 -0.012632 -11.291 -1.07122 232s US.Steel_X1947 -0.018481 -10.700 -1.78894 232s US.Steel_X1948 -0.047880 -33.258 -5.27643 232s US.Steel_X1949 -0.003976 -2.347 -0.58605 232s US.Steel_X1950 -0.007908 -5.484 -1.29060 232s US.Steel_X1951 -0.052722 -42.652 -10.72894 232s US.Steel_X1952 -0.064309 -46.753 -18.68822 232s US.Steel_X1953 -0.039465 -39.524 -13.65875 232s US.Steel_X1954 0.042884 30.156 17.79265 232s Westinghouse_X1935 -0.000639 -0.267 -0.00671 232s Westinghouse_X1936 0.003489 2.923 0.03559 232s Westinghouse_X1937 0.005946 5.256 0.20632 232s Westinghouse_X1938 0.008196 3.589 0.42458 232s Westinghouse_X1939 0.009675 6.576 0.62207 232s Westinghouse_X1940 0.007107 5.172 0.47686 232s Westinghouse_X1941 -0.011506 -7.406 -0.86528 232s Westinghouse_X1942 -0.005817 -2.390 -0.41532 232s Westinghouse_X1943 0.002074 1.221 0.13919 232s Westinghouse_X1944 0.002100 1.466 0.12704 232s Westinghouse_X1945 0.005777 4.890 0.31543 232s Westinghouse_X1946 -0.004096 -3.661 -0.34734 232s Westinghouse_X1947 -0.012571 -7.279 -1.21688 232s Westinghouse_X1948 -0.003981 -2.765 -0.43871 232s Westinghouse_X1949 0.006180 3.648 0.91087 232s Westinghouse_X1950 0.008074 5.599 1.31765 232s Westinghouse_X1951 -0.004997 -4.043 -1.01696 232s Westinghouse_X1952 -0.011575 -8.415 -3.36372 232s Westinghouse_X1953 -0.010300 -10.316 -3.56494 232s Westinghouse_X1954 0.006866 4.828 2.84858 232s General.Electric_(Intercept) General.Electric_value 232s Chrysler_X1935 0.006590 7.715 232s Chrysler_X1936 0.009515 19.180 232s Chrysler_X1937 -0.005635 -15.797 232s Chrysler_X1938 0.004088 8.339 232s Chrysler_X1939 -0.013341 -30.100 232s Chrysler_X1940 -0.002117 -4.514 232s Chrysler_X1941 -0.000102 -0.187 232s Chrysler_X1942 -0.003782 -6.007 232s Chrysler_X1943 -0.012924 -22.609 232s Chrysler_X1944 -0.007171 -12.098 232s Chrysler_X1945 0.011026 22.137 232s Chrysler_X1946 -0.012907 -28.501 232s Chrysler_X1947 -0.006983 -11.569 232s Chrysler_X1948 0.005745 9.218 232s Chrysler_X1949 -0.007069 -10.122 232s Chrysler_X1950 0.001379 2.221 232s Chrysler_X1951 0.036033 65.558 232s Chrysler_X1952 0.003749 7.798 232s Chrysler_X1953 -0.001765 -4.186 232s Chrysler_X1954 -0.004329 -11.949 232s General.Electric_X1935 -0.003192 -3.736 232s General.Electric_X1936 -0.075425 -152.042 232s General.Electric_X1937 -0.071707 -201.016 232s General.Electric_X1938 -0.103871 -211.866 232s General.Electric_X1939 -0.127565 -287.812 232s General.Electric_X1940 -0.024962 -53.224 232s General.Electric_X1941 0.134553 246.784 232s General.Electric_X1942 0.061649 97.899 232s General.Electric_X1943 -0.082300 -143.975 232s General.Electric_X1944 -0.090635 -152.920 232s General.Electric_X1945 -0.002219 -4.456 232s General.Electric_X1946 0.193042 426.295 232s General.Electric_X1947 0.169877 281.435 232s General.Electric_X1948 0.133454 214.114 232s General.Electric_X1949 -0.047674 -68.260 232s General.Electric_X1950 -0.101526 -163.508 232s General.Electric_X1951 0.007040 12.809 232s General.Electric_X1952 0.025471 52.972 232s General.Electric_X1953 0.031151 73.878 232s General.Electric_X1954 -0.025162 -69.445 232s General.Motors_X1935 -0.016212 -18.978 232s General.Motors_X1936 0.004155 8.376 232s General.Motors_X1937 0.020453 57.337 232s General.Motors_X1938 -0.000534 -1.088 232s General.Motors_X1939 0.015678 35.372 232s General.Motors_X1940 0.002297 4.899 232s General.Motors_X1941 -0.004250 -7.795 232s General.Motors_X1942 -0.015503 -24.619 232s General.Motors_X1943 -0.010878 -19.031 232s General.Motors_X1944 -0.015772 -26.611 232s General.Motors_X1945 -0.005833 -11.711 232s General.Motors_X1946 -0.015918 -35.152 232s General.Motors_X1947 -0.002235 -3.703 232s General.Motors_X1948 0.008057 12.926 232s General.Motors_X1949 0.017844 25.549 232s General.Motors_X1950 0.010196 16.421 232s General.Motors_X1951 0.018970 34.514 232s General.Motors_X1952 0.013121 27.287 232s General.Motors_X1953 -0.005170 -12.262 232s General.Motors_X1954 -0.018466 -50.965 232s US.Steel_X1935 0.000660 0.772 232s US.Steel_X1936 -0.001239 -2.497 232s US.Steel_X1937 -0.001227 -3.439 232s US.Steel_X1938 0.002057 4.195 232s US.Steel_X1939 0.003340 7.535 232s US.Steel_X1940 0.002785 5.939 232s US.Steel_X1941 -0.000771 -1.414 232s US.Steel_X1942 -0.000386 -0.612 232s US.Steel_X1943 0.000859 1.503 232s US.Steel_X1944 0.001737 2.930 232s US.Steel_X1945 0.001869 3.752 232s US.Steel_X1946 -0.000598 -1.321 232s US.Steel_X1947 -0.000875 -1.450 232s US.Steel_X1948 -0.002267 -3.638 232s US.Steel_X1949 -0.000188 -0.270 232s US.Steel_X1950 -0.000374 -0.603 232s US.Steel_X1951 -0.002497 -4.542 232s US.Steel_X1952 -0.003045 -6.333 232s US.Steel_X1953 -0.001869 -4.432 232s US.Steel_X1954 0.002031 5.605 232s Westinghouse_X1935 -0.005793 -6.781 232s Westinghouse_X1936 0.031644 63.787 232s Westinghouse_X1937 0.053929 151.178 232s Westinghouse_X1938 0.074341 151.634 232s Westinghouse_X1939 0.087747 197.975 232s Westinghouse_X1940 0.064457 137.434 232s Westinghouse_X1941 -0.104362 -191.410 232s Westinghouse_X1942 -0.052757 -83.779 232s Westinghouse_X1943 0.018814 32.913 232s Westinghouse_X1944 0.019045 32.133 232s Westinghouse_X1945 0.052397 105.198 232s Westinghouse_X1946 -0.037151 -82.040 232s Westinghouse_X1947 -0.114019 -188.895 232s Westinghouse_X1948 -0.036108 -57.931 232s Westinghouse_X1949 0.056048 80.250 232s Westinghouse_X1950 0.073229 117.935 232s Westinghouse_X1951 -0.045325 -82.465 232s Westinghouse_X1952 -0.104985 -218.337 232s Westinghouse_X1953 -0.093423 -221.562 232s Westinghouse_X1954 0.062271 171.863 232s General.Electric_capital General.Motors_(Intercept) 232s Chrysler_X1935 0.6445 1.06e-03 232s Chrysler_X1936 0.9933 1.53e-03 232s Chrysler_X1937 -0.6650 -9.08e-04 232s Chrysler_X1938 0.6386 6.59e-04 232s Chrysler_X1939 -2.3026 -2.15e-03 232s Chrysler_X1940 -0.3951 -3.41e-04 232s Chrysler_X1941 -0.0226 -1.65e-05 232s Chrysler_X1942 -1.0886 -6.10e-04 232s Chrysler_X1943 -4.1343 -2.08e-03 232s Chrysler_X1944 -2.3039 -1.16e-03 232s Chrysler_X1945 3.5239 1.78e-03 232s Chrysler_X1946 -4.4657 -2.08e-03 232s Chrysler_X1947 -3.1871 -1.13e-03 232s Chrysler_X1948 3.1221 9.26e-04 232s Chrysler_X1949 -4.3710 -1.14e-03 232s Chrysler_X1950 0.8926 2.22e-04 232s Chrysler_X1951 24.1889 5.81e-03 232s Chrysler_X1952 2.7225 6.04e-04 232s Chrysler_X1953 -1.4126 -2.84e-04 232s Chrysler_X1954 -3.8484 -6.98e-04 232s General.Electric_X1935 -0.3121 1.36e-04 232s General.Electric_X1936 -7.8744 3.21e-03 232s General.Electric_X1937 -8.4614 3.05e-03 232s General.Electric_X1938 -16.2246 4.42e-03 232s General.Electric_X1939 -22.0177 5.43e-03 232s General.Electric_X1940 -4.6579 1.06e-03 232s General.Electric_X1941 29.7228 -5.73e-03 232s General.Electric_X1942 17.7427 -2.63e-03 232s General.Electric_X1943 -26.3277 3.50e-03 232s General.Electric_X1944 -29.1212 3.86e-03 232s General.Electric_X1945 -0.7094 9.45e-05 232s General.Electric_X1946 66.7926 -8.22e-03 232s General.Electric_X1947 77.5319 -7.23e-03 232s General.Electric_X1948 72.5190 -5.68e-03 232s General.Electric_X1949 -29.4770 2.03e-03 232s General.Electric_X1950 -65.7280 4.32e-03 232s General.Electric_X1951 4.7261 -3.00e-04 232s General.Electric_X1952 18.4946 -1.08e-03 232s General.Electric_X1953 24.9302 -1.33e-03 232s General.Electric_X1954 -22.3665 1.07e-03 232s General.Motors_X1935 -1.5855 2.13e-02 232s General.Motors_X1936 0.4338 -5.46e-03 232s General.Motors_X1937 2.4135 -2.69e-02 232s General.Motors_X1938 -0.0833 7.00e-04 232s General.Motors_X1939 2.7060 -2.06e-02 232s General.Motors_X1940 0.4287 -3.02e-03 232s General.Motors_X1941 -0.9388 5.58e-03 232s General.Motors_X1942 -4.4617 2.04e-02 232s General.Motors_X1943 -3.4800 1.43e-02 232s General.Motors_X1944 -5.0677 2.07e-02 232s General.Motors_X1945 -1.8642 7.66e-03 232s General.Motors_X1946 -5.5077 2.09e-02 232s General.Motors_X1947 -1.0202 2.93e-03 232s General.Motors_X1948 4.3781 -1.06e-02 232s General.Motors_X1949 11.0331 -2.34e-02 232s General.Motors_X1950 6.6012 -1.34e-02 232s General.Motors_X1951 12.7347 -2.49e-02 232s General.Motors_X1952 9.5270 -1.72e-02 232s General.Motors_X1953 -4.1377 6.79e-03 232s General.Motors_X1954 -16.4148 2.42e-02 232s US.Steel_X1935 0.0645 -3.30e-03 232s US.Steel_X1936 -0.1293 6.19e-03 232s US.Steel_X1937 -0.1448 6.13e-03 232s US.Steel_X1938 0.3212 -1.03e-02 232s US.Steel_X1939 0.5764 -1.67e-02 232s US.Steel_X1940 0.5197 -1.39e-02 232s US.Steel_X1941 -0.1703 3.85e-03 232s US.Steel_X1942 -0.1110 1.93e-03 232s US.Steel_X1943 0.2749 -4.29e-03 232s US.Steel_X1944 0.5580 -8.68e-03 232s US.Steel_X1945 0.5972 -9.34e-03 232s US.Steel_X1946 -0.2070 2.99e-03 232s US.Steel_X1947 -0.3994 4.37e-03 232s US.Steel_X1948 -1.2321 1.13e-02 232s US.Steel_X1949 -0.1164 9.41e-04 232s US.Steel_X1950 -0.2424 1.87e-03 232s US.Steel_X1951 -1.6760 1.25e-02 232s US.Steel_X1952 -2.2112 1.52e-02 232s US.Steel_X1953 -1.4956 9.34e-03 232s US.Steel_X1954 1.8051 -1.01e-02 232s Westinghouse_X1935 -0.5665 -4.91e-04 232s Westinghouse_X1936 3.3036 2.68e-03 232s Westinghouse_X1937 6.3636 4.57e-03 232s Westinghouse_X1938 11.6121 6.30e-03 232s Westinghouse_X1939 15.1452 7.44e-03 232s Westinghouse_X1940 12.0276 5.46e-03 232s Westinghouse_X1941 -23.0535 -8.84e-03 232s Westinghouse_X1942 -15.1836 -4.47e-03 232s Westinghouse_X1943 6.0186 1.59e-03 232s Westinghouse_X1944 6.1191 1.61e-03 232s Westinghouse_X1945 16.7462 4.44e-03 232s Westinghouse_X1946 -12.8541 -3.15e-03 232s Westinghouse_X1947 -52.0382 -9.66e-03 232s Westinghouse_X1948 -19.6209 -3.06e-03 232s Westinghouse_X1949 34.6547 4.75e-03 232s Westinghouse_X1950 47.4084 6.21e-03 232s Westinghouse_X1951 -30.4270 -3.84e-03 232s Westinghouse_X1952 -76.2296 -8.90e-03 232s Westinghouse_X1953 -74.7663 -7.92e-03 232s Westinghouse_X1954 55.3529 5.28e-03 232s General.Motors_value General.Motors_capital 232s Chrysler_X1935 3.2697 2.97e-03 232s Chrysler_X1936 7.1482 8.07e-02 232s Chrysler_X1937 -4.8925 -1.42e-01 232s Chrysler_X1938 1.8397 1.38e-01 232s Chrysler_X1939 -9.2736 -4.37e-01 232s Chrysler_X1940 -1.5846 -7.07e-02 232s Chrysler_X1941 -0.0749 -4.20e-03 232s Chrysler_X1942 -1.9776 -1.85e-01 232s Chrysler_X1943 -8.4430 -5.50e-01 232s Chrysler_X1944 -5.0608 -2.33e-01 232s Chrysler_X1945 8.6022 4.71e-01 232s Chrysler_X1946 -10.1940 -8.37e-01 232s Chrysler_X1947 -3.9688 -8.57e-01 232s Chrysler_X1948 3.0137 8.54e-01 232s Chrysler_X1949 -4.2157 -1.16e+00 232s Chrysler_X1950 0.8345 2.44e-01 232s Chrysler_X1951 28.0658 7.01e+00 232s Chrysler_X1952 2.9759 8.64e-01 232s Chrysler_X1953 -1.7755 -5.06e-01 232s Chrysler_X1954 -3.9028 -1.55e+00 232s General.Electric_X1935 0.4184 3.81e-04 232s General.Electric_X1936 14.9723 1.69e-01 232s General.Electric_X1937 16.4491 4.79e-01 232s General.Electric_X1938 12.3500 9.25e-01 232s General.Electric_X1939 23.4292 1.10e+00 232s General.Electric_X1940 4.9361 2.20e-01 232s General.Electric_X1941 -26.0763 -1.46e+00 232s General.Electric_X1942 -8.5163 -7.97e-01 232s General.Electric_X1943 14.2062 9.26e-01 232s General.Electric_X1944 16.9016 7.78e-01 232s General.Electric_X1945 0.4575 2.50e-02 232s General.Electric_X1946 -40.2860 -3.31e+00 232s General.Electric_X1947 -25.5097 -5.51e+00 232s General.Electric_X1948 -18.4956 -5.24e+00 232s General.Electric_X1949 7.5116 2.07e+00 232s General.Electric_X1950 16.2362 4.75e+00 232s General.Electric_X1951 -1.4489 -3.62e-01 232s General.Electric_X1952 -5.3416 -1.55e+00 232s General.Electric_X1953 -8.2795 -2.36e+00 232s General.Electric_X1954 5.9933 2.39e+00 232s General.Motors_X1935 65.5183 5.96e-02 232s General.Motors_X1936 -25.4300 -2.87e-01 232s General.Motors_X1937 -144.6452 -4.21e+00 232s General.Motors_X1938 1.9558 1.47e-01 232s General.Motors_X1939 -88.7707 -4.19e+00 232s General.Motors_X1940 -14.0060 -6.25e-01 232s General.Motors_X1941 25.3914 1.42e+00 232s General.Motors_X1942 66.0227 6.18e+00 232s General.Motors_X1943 57.8898 3.77e+00 232s General.Motors_X1944 90.6754 4.17e+00 232s General.Motors_X1945 37.0686 2.03e+00 232s General.Motors_X1946 102.4144 8.40e+00 232s General.Motors_X1947 10.3479 2.23e+00 232s General.Motors_X1948 -34.4239 -9.76e+00 232s General.Motors_X1949 -86.6782 -2.39e+01 232s General.Motors_X1950 -50.2708 -1.47e+01 232s General.Motors_X1951 -120.3581 -3.01e+01 232s General.Motors_X1952 -84.8289 -2.46e+01 232s General.Motors_X1953 42.3640 1.21e+01 232s General.Motors_X1954 135.6002 5.40e+01 232s US.Steel_X1935 -10.1444 -9.23e-03 232s US.Steel_X1936 28.8526 3.26e-01 232s US.Steel_X1937 33.0183 9.62e-01 232s US.Steel_X1938 -28.6886 -2.15e+00 232s US.Steel_X1939 -71.9676 -3.39e+00 232s US.Steel_X1940 -64.6193 -2.88e+00 232s US.Steel_X1941 17.5269 9.83e-01 232s US.Steel_X1942 6.2492 5.85e-01 232s US.Steel_X1943 -17.4030 -1.13e+00 232s US.Steel_X1944 -37.9949 -1.75e+00 232s US.Steel_X1945 -45.1924 -2.47e+00 232s US.Steel_X1946 14.6469 1.20e+00 232s US.Steel_X1947 15.4188 3.33e+00 232s US.Steel_X1948 36.8685 1.04e+01 232s US.Steel_X1949 3.4806 9.60e-01 232s US.Steel_X1950 7.0265 2.06e+00 232s US.Steel_X1951 60.2830 1.51e+01 232s US.Steel_X1952 74.9299 2.18e+01 232s US.Steel_X1953 58.2771 1.66e+01 232s US.Steel_X1954 -56.7511 -2.26e+01 232s Westinghouse_X1935 -1.5111 -1.37e-03 232s Westinghouse_X1936 12.4999 1.41e-01 232s Westinghouse_X1937 24.6178 7.17e-01 232s Westinghouse_X1938 17.5894 1.32e+00 232s Westinghouse_X1939 32.0707 1.51e+00 232s Westinghouse_X1940 25.3645 1.13e+00 232s Westinghouse_X1941 -40.2479 -2.26e+00 232s Westinghouse_X1942 -14.5028 -1.36e+00 232s Westinghouse_X1943 6.4627 4.21e-01 232s Westinghouse_X1944 7.0674 3.25e-01 232s Westinghouse_X1945 21.4937 1.18e+00 232s Westinghouse_X1946 -15.4283 -1.27e+00 232s Westinghouse_X1947 -34.0718 -7.36e+00 232s Westinghouse_X1948 -9.9583 -2.82e+00 232s Westinghouse_X1949 17.5737 4.84e+00 232s Westinghouse_X1950 23.3044 6.82e+00 232s Westinghouse_X1951 -18.5624 -4.64e+00 232s Westinghouse_X1952 -43.8127 -1.27e+01 232s Westinghouse_X1953 -49.4119 -1.41e+01 232s Westinghouse_X1954 29.5158 1.17e+01 232s US.Steel_(Intercept) US.Steel_value US.Steel_capital 232s Chrysler_X1935 -2.96e-03 -4.0379 -0.15945 232s Chrysler_X1936 -4.28e-03 -7.7323 -0.21608 232s Chrysler_X1937 2.53e-03 6.7824 0.29930 232s Chrysler_X1938 -1.84e-03 -3.3128 -0.47838 232s Chrysler_X1939 6.00e-03 11.7430 1.87608 232s Chrysler_X1940 9.52e-04 2.0975 0.24204 232s Chrysler_X1941 4.59e-05 0.1094 0.01201 232s Chrysler_X1942 1.70e-03 3.6889 0.50810 232s Chrysler_X1943 5.81e-03 11.5373 1.75404 232s Chrysler_X1944 3.22e-03 5.8493 0.90002 232s Chrysler_X1945 -4.96e-03 -9.1744 -1.06014 232s Chrysler_X1946 5.80e-03 12.0014 1.35006 232s Chrysler_X1947 3.14e-03 5.6424 0.83159 232s Chrysler_X1948 -2.58e-03 -4.2007 -0.79297 232s Chrysler_X1949 3.18e-03 5.2997 1.11622 232s Chrysler_X1950 -6.20e-04 -1.0401 -0.22186 232s Chrysler_X1951 -1.62e-02 -37.1002 -5.54355 232s Chrysler_X1952 -1.69e-03 -3.6411 -0.74900 232s Chrysler_X1953 7.94e-04 1.6124 0.49499 232s Chrysler_X1954 1.95e-03 4.1188 1.30389 232s General.Electric_X1935 1.69e-05 0.0230 0.00091 232s General.Electric_X1936 4.00e-04 0.7222 0.02018 232s General.Electric_X1937 3.80e-04 1.0168 0.04487 232s General.Electric_X1938 5.50e-04 0.9917 0.14321 232s General.Electric_X1939 6.76e-04 1.3230 0.21136 232s General.Electric_X1940 1.32e-04 0.2914 0.03362 232s General.Electric_X1941 -7.13e-04 -1.6972 -0.18636 232s General.Electric_X1942 -3.27e-04 -0.7084 -0.09757 232s General.Electric_X1943 4.36e-04 0.8656 0.13161 232s General.Electric_X1944 4.80e-04 0.8711 0.13403 232s General.Electric_X1945 1.18e-05 0.0218 0.00251 232s General.Electric_X1946 -1.02e-03 -2.1149 -0.23791 232s General.Electric_X1947 -9.00e-04 -1.6172 -0.23835 232s General.Electric_X1948 -7.07e-04 -1.1496 -0.21701 232s General.Electric_X1949 2.53e-04 0.4211 0.08869 232s General.Electric_X1950 5.38e-04 0.9023 0.19248 232s General.Electric_X1951 -3.73e-05 -0.0854 -0.01276 232s General.Electric_X1952 -1.35e-04 -0.2914 -0.05995 232s General.Electric_X1953 -1.65e-04 -0.3353 -0.10293 232s General.Electric_X1954 1.33e-04 0.2820 0.08929 232s General.Motors_X1935 1.01e-02 13.7309 0.54222 232s General.Motors_X1936 -2.58e-03 -4.6683 -0.13046 232s General.Motors_X1937 -1.27e-02 -34.0295 -1.50166 232s General.Motors_X1938 3.32e-04 0.5977 0.08631 232s General.Motors_X1939 -9.75e-03 -19.0765 -3.04769 232s General.Motors_X1940 -1.43e-03 -3.1463 -0.36306 232s General.Motors_X1941 2.64e-03 6.2893 0.69062 232s General.Motors_X1942 9.64e-03 20.9002 2.87877 232s General.Motors_X1943 6.76e-03 13.4247 2.04099 232s General.Motors_X1944 9.81e-03 17.7857 2.73663 232s General.Motors_X1945 3.63e-03 6.7092 0.77528 232s General.Motors_X1946 9.90e-03 20.4619 2.30180 232s General.Motors_X1947 1.39e-03 2.4966 0.36796 232s General.Motors_X1948 -5.01e-03 -8.1431 -1.53716 232s General.Motors_X1949 -1.11e-02 -18.4924 -3.89482 232s General.Motors_X1950 -6.34e-03 -10.6327 -2.26803 232s General.Motors_X1951 -1.18e-02 -27.0005 -4.03445 232s General.Motors_X1952 -8.16e-03 -17.6138 -3.62324 232s General.Motors_X1953 3.21e-03 6.5289 2.00435 232s General.Motors_X1954 1.15e-02 24.2859 7.68815 232s US.Steel_X1935 -8.99e-03 -12.2508 -0.48377 232s US.Steel_X1936 1.69e-02 30.5206 0.85291 232s US.Steel_X1937 1.67e-02 44.7615 1.97524 232s US.Steel_X1938 -2.80e-02 -50.5201 -7.29526 232s US.Steel_X1939 -4.55e-02 -89.1179 -14.23756 232s US.Steel_X1940 -3.80e-02 -83.6458 -9.65217 232s US.Steel_X1941 1.05e-02 25.0160 2.74698 232s US.Steel_X1942 5.26e-03 11.3993 1.57013 232s US.Steel_X1943 -1.17e-02 -23.2554 -3.53559 232s US.Steel_X1944 -2.37e-02 -42.9442 -6.60771 232s US.Steel_X1945 -2.55e-02 -47.1333 -5.44650 232s US.Steel_X1946 8.16e-03 16.8627 1.89692 232s US.Steel_X1947 1.19e-02 21.4365 3.15933 232s US.Steel_X1948 3.09e-02 50.2553 9.48663 232s US.Steel_X1949 2.57e-03 4.2789 0.90121 232s US.Steel_X1950 5.11e-03 8.5638 1.82670 232s US.Steel_X1951 3.40e-02 77.9272 11.64398 232s US.Steel_X1952 4.15e-02 89.6523 18.44196 232s US.Steel_X1953 2.55e-02 51.7535 15.88809 232s US.Steel_X1954 -2.77e-02 -58.5688 -18.54102 232s Westinghouse_X1935 -1.36e-03 -1.8578 -0.07336 232s Westinghouse_X1936 7.45e-03 13.4613 0.37618 232s Westinghouse_X1937 1.27e-02 33.9762 1.49930 232s Westinghouse_X1938 1.75e-02 31.5341 4.55362 232s Westinghouse_X1939 2.07e-02 40.4306 6.45923 232s Westinghouse_X1940 1.52e-02 33.4258 3.85712 232s Westinghouse_X1941 -2.46e-02 -58.4830 -6.42196 232s Westinghouse_X1942 -1.24e-02 -26.9329 -3.70970 232s Westinghouse_X1943 4.43e-03 8.7920 1.33667 232s Westinghouse_X1944 4.48e-03 8.1323 1.25129 232s Westinghouse_X1945 1.23e-02 22.8217 2.63717 232s Westinghouse_X1946 -8.75e-03 -18.0831 -2.03421 232s Westinghouse_X1947 -2.68e-02 -48.2250 -7.10746 232s Westinghouse_X1948 -8.50e-03 -13.8193 -2.60865 232s Westinghouse_X1949 1.32e-02 21.9947 4.63248 232s Westinghouse_X1950 1.72e-02 28.9161 6.16798 232s Westinghouse_X1951 -1.07e-02 -24.4289 -3.65019 232s Westinghouse_X1952 -2.47e-02 -53.3679 -10.97807 232s Westinghouse_X1953 -2.20e-02 -44.6732 -13.71448 232s Westinghouse_X1954 1.47e-02 31.0114 9.81721 232s Westinghouse_(Intercept) Westinghouse_value 232s Chrysler_X1935 -5.65e-03 -1.082 232s Chrysler_X1936 -8.16e-03 -4.208 232s Chrysler_X1937 4.83e-03 3.521 232s Chrysler_X1938 -3.50e-03 -1.964 232s Chrysler_X1939 1.14e-02 5.945 232s Chrysler_X1940 1.81e-03 1.141 232s Chrysler_X1941 8.76e-05 0.047 232s Chrysler_X1942 3.24e-03 1.819 232s Chrysler_X1943 1.11e-02 6.837 232s Chrysler_X1944 6.15e-03 3.852 232s Chrysler_X1945 -9.45e-03 -6.967 232s Chrysler_X1946 1.11e-02 8.413 232s Chrysler_X1947 5.99e-03 3.480 232s Chrysler_X1948 -4.92e-03 -3.262 232s Chrysler_X1949 6.06e-03 3.537 232s Chrysler_X1950 -1.18e-03 -0.751 232s Chrysler_X1951 -3.09e-02 -22.354 232s Chrysler_X1952 -3.21e-03 -2.777 232s Chrysler_X1953 1.51e-03 1.806 232s Chrysler_X1954 3.71e-03 4.412 232s General.Electric_X1935 6.17e-03 1.182 232s General.Electric_X1936 1.46e-01 75.280 232s General.Electric_X1937 1.39e-01 101.111 232s General.Electric_X1938 2.01e-01 112.591 232s General.Electric_X1939 2.47e-01 128.281 232s General.Electric_X1940 4.83e-02 30.346 232s General.Electric_X1941 -2.60e-01 -139.785 232s General.Electric_X1942 -1.19e-01 -66.920 232s General.Electric_X1943 1.59e-01 98.251 232s General.Electric_X1944 1.75e-01 109.867 232s General.Electric_X1945 4.29e-03 3.165 232s General.Electric_X1946 -3.73e-01 -283.963 232s General.Electric_X1947 -3.29e-01 -191.038Error in estfun.systemfit(greeneSurPooled) : 232s returning the estimation function for models with restrictions has not yet been implemented. 232s 232s General.Electric_X1948 -2.58e-01 -170.961 232s General.Electric_X1949 9.22e-02 53.834 232s General.Electric_X1950 1.96e-01 124.738 232s General.Electric_X1951 -1.36e-02 -9.856 232s General.Electric_X1952 -4.93e-02 -42.572 232s General.Electric_X1953 -6.03e-02 -71.913 232s General.Electric_X1954 4.87e-02 57.863 232s General.Motors_X1935 -6.24e-02 -11.950 232s General.Motors_X1936 1.60e-02 8.253 232s General.Motors_X1937 7.87e-02 57.392 232s General.Motors_X1938 -2.05e-03 -1.151 232s General.Motors_X1939 6.03e-02 31.373 232s General.Motors_X1940 8.84e-03 5.558 232s General.Motors_X1941 -1.64e-02 -8.786 232s General.Motors_X1942 -5.97e-02 -33.488 232s General.Motors_X1943 -4.19e-02 -25.843 232s General.Motors_X1944 -6.07e-02 -38.047 232s General.Motors_X1945 -2.25e-02 -16.552 232s General.Motors_X1946 -6.13e-02 -46.597 232s General.Motors_X1947 -8.60e-03 -5.002 232s General.Motors_X1948 3.10e-02 20.539 232s General.Motors_X1949 6.87e-02 40.098 232s General.Motors_X1950 3.92e-02 24.930 232s General.Motors_X1951 7.30e-02 52.851 232s General.Motors_X1952 5.05e-02 43.640 232s General.Motors_X1953 -1.99e-02 -23.751 232s General.Motors_X1954 -7.11e-02 -84.506 232s US.Steel_X1935 5.67e-02 10.854 232s US.Steel_X1936 -1.06e-01 -54.933 232s US.Steel_X1937 -1.05e-01 -76.855 232s US.Steel_X1938 1.77e-01 99.039 232s US.Steel_X1939 2.87e-01 149.211 232s US.Steel_X1940 2.39e-01 150.428 232s US.Steel_X1941 -6.62e-02 -35.578 232s US.Steel_X1942 -3.31e-02 -18.595 232s US.Steel_X1943 7.38e-02 45.577 232s US.Steel_X1944 1.49e-01 93.525 232s US.Steel_X1945 1.61e-01 118.378 232s US.Steel_X1946 -5.14e-02 -39.094 232s US.Steel_X1947 -7.52e-02 -43.725 232s US.Steel_X1948 -1.95e-01 -129.046 232s US.Steel_X1949 -1.62e-02 -9.446 232s US.Steel_X1950 -3.22e-02 -20.441 232s US.Steel_X1951 -2.15e-01 -155.289 232s US.Steel_X1952 -2.62e-01 -226.135 232s US.Steel_X1953 -1.61e-01 -191.674 232s US.Steel_X1954 1.75e-01 207.479 232s Westinghouse_X1935 3.03e-02 5.802 232s Westinghouse_X1936 -1.66e-01 -85.410 232s Westinghouse_X1937 -2.82e-01 -205.647 232s Westinghouse_X1938 -3.89e-01 -217.923 232s Westinghouse_X1939 -4.59e-01 -238.632 232s Westinghouse_X1940 -3.37e-01 -211.909 232s Westinghouse_X1941 5.46e-01 293.206 232s Westinghouse_X1942 2.76e-01 154.873 232s Westinghouse_X1943 -9.84e-02 -60.742 232s Westinghouse_X1944 -9.96e-02 -62.433 232s Westinghouse_X1945 -2.74e-01 -202.055 232s Westinghouse_X1946 1.94e-01 147.788 232s Westinghouse_X1947 5.96e-01 346.758 232s Westinghouse_X1948 1.89e-01 125.092 232s Westinghouse_X1949 -2.93e-01 -171.160 232s Westinghouse_X1950 -3.83e-01 -243.315 232s Westinghouse_X1951 2.37e-01 171.608 232s Westinghouse_X1952 5.49e-01 474.533 232s Westinghouse_X1953 4.89e-01 583.245 232s Westinghouse_X1954 -3.26e-01 -387.265 232s Westinghouse_capital 232s Chrysler_X1935 -0.01017 232s Chrysler_X1936 -0.00652 232s Chrysler_X1937 0.03574 232s Chrysler_X1938 -0.06342 232s Chrysler_X1939 0.26872 232s Chrysler_X1940 0.04809 232s Chrysler_X1941 0.00317 232s Chrysler_X1942 0.19712 232s Chrysler_X1943 0.93491 232s Chrysler_X1944 0.56053 232s Chrysler_X1945 -0.87325 232s Chrysler_X1946 0.95137 232s Chrysler_X1947 0.66499 232s Chrysler_X1948 -0.64315 232s Chrysler_X1949 0.85922 232s Chrysler_X1950 -0.16155 232s Chrysler_X1951 -4.00575 232s Chrysler_X1952 -0.46760 232s Chrysler_X1953 0.26445 232s Chrysler_X1954 0.79226 232s General.Electric_X1935 0.01111 232s General.Electric_X1936 0.11671 232s General.Electric_X1937 1.02637 232s General.Electric_X1938 3.63650 232s General.Electric_X1939 5.79842 232s General.Electric_X1940 1.27948 232s General.Electric_X1941 -9.42136 232s General.Electric_X1942 -7.25009 232s General.Electric_X1943 13.43544 232s General.Electric_X1944 15.98834 232s General.Electric_X1945 0.39668 232s General.Electric_X1946 -32.11157 232s General.Electric_X1947 -36.50562 232s General.Electric_X1948 -33.71211 232s General.Electric_X1949 13.07588 232s General.Electric_X1950 26.84462 232s General.Electric_X1951 -1.76618 232s General.Electric_X1952 -7.16842 232s General.Electric_X1953 -10.53235 232s General.Electric_X1954 10.39092 232s General.Motors_X1935 -0.11232 232s General.Motors_X1936 0.01280 232s General.Motors_X1937 0.58258 232s General.Motors_X1938 -0.03717 232s General.Motors_X1939 1.41811 232s General.Motors_X1940 0.23434 232s General.Motors_X1941 -0.59216 232s General.Motors_X1942 -3.62807 232s General.Motors_X1943 -3.53399 232s General.Motors_X1944 -5.53672 232s General.Motors_X1945 -2.07456 232s General.Motors_X1946 -5.26934 232s General.Motors_X1947 -0.95586 232s General.Motors_X1948 4.05009 232s General.Motors_X1949 9.73943 232s General.Motors_X1950 5.36510 232s General.Motors_X1951 9.47046 232s General.Motors_X1952 7.34822 232s General.Motors_X1953 -3.47863 232s General.Motors_X1954 -15.17538 232s US.Steel_X1935 0.10202 232s US.Steel_X1936 -0.08517 232s US.Steel_X1937 -0.78015 232s US.Steel_X1938 3.19880 232s US.Steel_X1939 6.74450 232s US.Steel_X1940 6.34264 232s US.Steel_X1941 -2.39791 232s US.Steel_X1942 -2.01455 232s US.Steel_X1943 6.23245 232s US.Steel_X1944 13.61008 232s US.Steel_X1945 14.83734 232s US.Steel_X1946 -4.42093 232s US.Steel_X1947 -8.35538 232s US.Steel_X1948 -25.44676 232s US.Steel_X1949 -2.29427 232s US.Steel_X1950 -4.39917 232s US.Steel_X1951 -27.82678 232s US.Steel_X1952 -38.07729 232s US.Steel_X1953 -28.07253 232s US.Steel_X1954 37.25854 232s Westinghouse_X1935 0.05454 232s Westinghouse_X1936 -0.13242 232s Westinghouse_X1937 -2.08750 232s Westinghouse_X1938 -7.03855 232s Westinghouse_X1939 -10.78640 232s Westinghouse_X1940 -8.93489 232s Westinghouse_X1941 19.76178 232s Westinghouse_X1942 16.77886 232s Westinghouse_X1943 -8.30621 232s Westinghouse_X1944 -9.08553 232s Westinghouse_X1945 -25.32546 232s Westinghouse_X1946 16.71244 232s Westinghouse_X1947 66.26222 232s Westinghouse_X1948 24.66709 232s Westinghouse_X1949 -41.57334 232s Westinghouse_X1950 -52.36326 232s Westinghouse_X1951 30.75091 232s Westinghouse_X1952 79.90351 232s Westinghouse_X1953 85.42211 232s Westinghouse_X1954 -69.54427 232s Chrysler_(Intercept) Chrysler_value 232s 0 0 232s Chrysler_capital General.Electric_(Intercept) 232s 0 0 232s General.Electric_value General.Electric_capital 232s 0 0 232s General.Motors_(Intercept) General.Motors_value 232s 0 0 232s General.Motors_capital US.Steel_(Intercept) 232s 0 0 232s US.Steel_value US.Steel_capital 232s 0 0 232s Westinghouse_(Intercept) Westinghouse_value 232s 0 0 232s Westinghouse_capital 232s 0 232s [1] "Error in estfun.systemfit(greeneSurPooled) : \n returning the estimation function for models with restrictions has not yet been implemented.\n" 232s attr(,"class") 232s [1] "try-error" 232s attr(,"condition") 232s 232s > 232s > ## **************** bread ************************ 232s > if(requireNamespace( 'plm', quietly = TRUE ) ) { 232s + print( bread( theilOls ) ) 232s + 232s + print( bread( theilSur ) ) 232s + 232s + print( bread( greeneOls ) ) 232s + 232s + print( try( bread( greeneOlsPooled ) ) ) 232s + 232s + print( bread( greeneSur ) ) 232s + 232s + print( try( bread( greeneSurPooled ) ) ) 232s + } 232s General.Electric_(Intercept) 232s General.Electric_(Intercept) 50.64496 232s General.Electric_value -0.02323 232s General.Electric_capital -0.00888 232s Westinghouse_(Intercept) 0.00000 232s Westinghouse_value 0.00000 232s Westinghouse_capital 0.00000 232s General.Electric_value General.Electric_capital 232s General.Electric_(Intercept) -2.32e-02 -8.88e-03 232s General.Electric_value 1.25e-05 -2.43e-06 232s General.Electric_capital -2.43e-06 3.40e-05 232s Westinghouse_(Intercept) 0.00e+00 0.00e+00 232s Westinghouse_value 0.00e+00 0.00e+00 232s Westinghouse_capital 0.00e+00 0.00e+00 232s Westinghouse_(Intercept) Westinghouse_value 232s General.Electric_(Intercept) 0.0000 0.00e+00 232s General.Electric_value 0.0000 0.00e+00 232s General.Electric_capital 0.0000 0.00e+00 232s Westinghouse_(Intercept) 24.6366 -4.20e-02 232s Westinghouse_value -0.0420 9.46e-05 232s Westinghouse_capital 0.0648 -2.51e-04 232s Westinghouse_capital 232s General.Electric_(Intercept) 0.000000 232s General.Electric_value 0.000000 232s General.Electric_capital 0.000000 232s Westinghouse_(Intercept) 0.064774 232s Westinghouse_value -0.000251 232s Westinghouse_capital 0.001207 232s General.Electric_(Intercept) General.Electric_value 232s [1,] 29230.95 -13.17064 232s [2,] -13.17 0.00707 232s [3,] -5.85 -0.00136 232s [4,] 5078.50 -2.10754 232s [5,] -9.05 0.00480 232s [6,] 15.70 -0.01299 232s General.Electric_capital Westinghouse_(Intercept) Westinghouse_value 232s [1,] -5.849668 5078.50 -9.047719 232s [2,] -0.001362 -2.11 0.004800 232s [3,] 0.021226 -1.58 -0.000675 232s [4,] -1.584851 1935.63 -3.200900 232s [5,] -0.000675 -3.20 0.007194 232s [6,] 0.023793 4.54 -0.018984 232s Westinghouse_capital 232s [1,] 15.7006 232s [2,] -0.0130 232s [3,] 0.0238 232s [4,] 4.5447 232s [5,] -0.0190 232s [6,] 0.0957 232s Chrysler_(Intercept) Chrysler_value 232s Chrysler_(Intercept) 103.4623 -0.144448 232s Chrysler_value -0.1444 0.000226 232s Chrysler_capital 0.0138 -0.000102 232s General.Electric_(Intercept) 0.0000 0.000000 232s General.Electric_value 0.0000 0.000000 232s General.Electric_capital 0.0000 0.000000 232s General.Motors_(Intercept) 0.0000 0.000000 232s General.Motors_value 0.0000 0.000000 232s General.Motors_capital 0.0000 0.000000 232s US.Steel_(Intercept) 0.0000 0.000000 232s US.Steel_value 0.0000 0.000000 232s US.Steel_capital 0.0000 0.000000 232s Westinghouse_(Intercept) 0.0000 0.000000 232s Westinghouse_value 0.0000 0.000000 232s Westinghouse_capital 0.0000 0.000000 232s Chrysler_capital General.Electric_(Intercept) 232s Chrysler_(Intercept) 0.013776 0.0000 232s Chrysler_value -0.000102 0.0000 232s Chrysler_capital 0.000471 0.0000 232s General.Electric_(Intercept) 0.000000 126.6124 232s General.Electric_value 0.000000Error in bread.systemfit(greeneOlsPooled) : 232s returning the 'bread' for models with restrictions has not yet been implemented. 232s Error in bread.systemfit(greeneSurPooled) : 232s returning the 'bread' for models with restrictions has not yet been implemented. 232s -0.0581 232s General.Electric_capital 0.000000 -0.0222 232s General.Motors_(Intercept) 0.000000 0.0000 232s General.Motors_value 0.000000 0.0000 232s General.Motors_capital 0.000000 0.0000 232s US.Steel_(Intercept) 0.000000 0.0000 232s US.Steel_value 0.000000 0.0000 232s US.Steel_capital 0.000000 0.0000 232s Westinghouse_(Intercept) 0.000000 0.0000 232s Westinghouse_value 0.000000 0.0000 232s Westinghouse_capital 0.000000 0.0000 232s General.Electric_value General.Electric_capital 232s Chrysler_(Intercept) 0.00e+00 0.00e+00 232s Chrysler_value 0.00e+00 0.00e+00 232s Chrysler_capital 0.00e+00 0.00e+00 232s General.Electric_(Intercept) -5.81e-02 -2.22e-02 232s General.Electric_value 3.12e-05 -6.09e-06 232s General.Electric_capital -6.09e-06 8.50e-05 232s General.Motors_(Intercept) 0.00e+00 0.00e+00 232s General.Motors_value 0.00e+00 0.00e+00 232s General.Motors_capital 0.00e+00 0.00e+00 232s US.Steel_(Intercept) 0.00e+00 0.00e+00 232s US.Steel_value 0.00e+00 0.00e+00 232s US.Steel_capital 0.00e+00 0.00e+00 232s Westinghouse_(Intercept) 0.00e+00 0.00e+00 232s Westinghouse_value 0.00e+00 0.00e+00 232s Westinghouse_capital 0.00e+00 0.00e+00 232s General.Motors_(Intercept) General.Motors_value 232s Chrysler_(Intercept) 0.0000 0.00e+00 232s Chrysler_value 0.0000 0.00e+00 232s Chrysler_capital 0.0000 0.00e+00 232s General.Electric_(Intercept) 0.0000 0.00e+00 232s General.Electric_value 0.0000 0.00e+00 232s General.Electric_capital 0.0000 0.00e+00 232s General.Motors_(Intercept) 132.9858 -3.11e-02 232s General.Motors_value -0.0311 7.92e-06 232s General.Motors_capital 0.0108 -4.93e-06 232s US.Steel_(Intercept) 0.0000 0.00e+00 232s US.Steel_value 0.0000 0.00e+00 232s US.Steel_capital 0.0000 0.00e+00 232s Westinghouse_(Intercept) 0.0000 0.00e+00 232s Westinghouse_value 0.0000 0.00e+00 232s Westinghouse_capital 0.0000 0.00e+00 232s General.Motors_capital US.Steel_(Intercept) 232s Chrysler_(Intercept) 0.00e+00 0.0000 232s Chrysler_value 0.00e+00 0.0000 232s Chrysler_capital 0.00e+00 0.0000 232s General.Electric_(Intercept) 0.00e+00 0.0000 232s General.Electric_value 0.00e+00 0.0000 232s General.Electric_capital 0.00e+00 0.0000 232s General.Motors_(Intercept) 1.08e-02 0.0000 232s General.Motors_value -4.93e-06 0.0000 232s General.Motors_capital 1.63e-05 0.0000 232s US.Steel_(Intercept) 0.00e+00 235.6498 232s US.Steel_value 0.00e+00 -0.1119 232s US.Steel_capital 0.00e+00 -0.0336 232s Westinghouse_(Intercept) 0.00e+00 0.0000 232s Westinghouse_value 0.00e+00 0.0000 232s Westinghouse_capital 0.00e+00 0.0000 232s US.Steel_value US.Steel_capital 232s Chrysler_(Intercept) 0.00e+00 0.00e+00 232s Chrysler_value 0.00e+00 0.00e+00 232s Chrysler_capital 0.00e+00 0.00e+00 232s General.Electric_(Intercept) 0.00e+00 0.00e+00 232s General.Electric_value 0.00e+00 0.00e+00 232s General.Electric_capital 0.00e+00 0.00e+00 232s General.Motors_(Intercept) 0.00e+00 0.00e+00 232s General.Motors_value 0.00e+00 0.00e+00 232s General.Motors_capital 0.00e+00 0.00e+00 232s US.Steel_(Intercept) -1.12e-01 -3.36e-02 232s US.Steel_value 5.95e-05 -1.79e-05 232s US.Steel_capital -1.79e-05 2.30e-04 232s Westinghouse_(Intercept) 0.00e+00 0.00e+00 232s Westinghouse_value 0.00e+00 0.00e+00 232s Westinghouse_capital 0.00e+00 0.00e+00 232s Westinghouse_(Intercept) Westinghouse_value 232s Chrysler_(Intercept) 0.000 0.000000 232s Chrysler_value 0.000 0.000000 232s Chrysler_capital 0.000 0.000000 232s General.Electric_(Intercept) 0.000 0.000000 232s General.Electric_value 0.000 0.000000 232s General.Electric_capital 0.000 0.000000 232s General.Motors_(Intercept) 0.000 0.000000 232s General.Motors_value 0.000 0.000000 232s General.Motors_capital 0.000 0.000000 232s US.Steel_(Intercept) 0.000 0.000000 232s US.Steel_value 0.000 0.000000 232s US.Steel_capital 0.000 0.000000 232s Westinghouse_(Intercept) 61.592 -0.105021 232s Westinghouse_value -0.105 0.000237 232s Westinghouse_capital 0.162 -0.000626 232s Westinghouse_capital 232s Chrysler_(Intercept) 0.000000 232s Chrysler_value 0.000000 232s Chrysler_capital 0.000000 232s General.Electric_(Intercept) 0.000000 232s General.Electric_value 0.000000 232s General.Electric_capital 0.000000 232s General.Motors_(Intercept) 0.000000 232s General.Motors_value 0.000000 232s General.Motors_capital 0.000000 232s US.Steel_(Intercept) 0.000000 232s US.Steel_value 0.000000 232s US.Steel_capital 0.000000 232s Westinghouse_(Intercept) 0.161935 232s Westinghouse_value -0.000626 232s Westinghouse_capital 0.003017 232s [1] "Error in bread.systemfit(greeneOlsPooled) : \n returning the 'bread' for models with restrictions has not yet been implemented.\n" 232s attr(,"class") 232s [1] "try-error" 232s attr(,"condition") 232s 232s Chrysler_(Intercept) Chrysler_value Chrysler_capital 232s [1,] 1.33e+04 -1.82e+01 9.57e-01 232s [2,] -1.82e+01 2.86e-02 -1.31e-02 232s [3,] 9.57e-01 -1.31e-02 6.69e-02 232s [4,] -2.94e+03 3.74e+00 1.98e+00 232s [5,] 1.28e+00 -1.86e-03 1.28e-04 232s [6,] 8.80e-01 -2.96e-04 -5.56e-03 232s [7,] -1.56e+04 1.91e+01 7.79e+00 232s [8,] 3.28e+00 -4.91e-03 1.03e-03 232s [9,] -8.18e-02 3.42e-03 -1.89e-02 232s [10,] 1.80e+04 -1.87e+01 -2.45e+01 232s [11,] -7.46e+00 1.13e-02 -3.26e-03 232s [12,] -4.03e+00 -1.22e-02 1.03e-01 232s [13,] -3.04e+01 3.03e-01 -9.35e-01 232s [14,] 1.14e-01 -3.70e-04 1.18e-03 232s [15,] 2.42e-01 -6.41e-04 1.67e-03 232s General.Electric_(Intercept) General.Electric_value 232s [1,] -2936.42 1.28e+00 232s [2,] 3.74 -1.86e-03 232s [3,] 1.98 1.28e-04 232s [4,] 65119.82 -2.85e+01 232s [5,] -28.51 1.50e-02 232s [6,] -16.15 -1.70e-03 232s [7,] 57134.02 -2.61e+01 232s [8,] -11.96 6.35e-03 232s [9,] -3.52 -2.27e-03 232s [10,] 64429.20 -3.04e+01 232s [11,] -22.01 1.35e-02 232s [12,] -55.05 1.23e-02 232s [13,] 10286.79 -4.02e+00 232s [14,] -17.00 8.74e-03 232s [15,] 23.38 -2.16e-02 232s General.Electric_capital General.Motors_(Intercept) General.Motors_value 232s [1,] 8.80e-01 -1.56e+04 3.28e+00 232s [2,] -2.96e-04 1.91e+01 -4.91e-03 232s [3,] -5.56e-03 7.79e+00 1.03e-03 232s [4,] -1.61e+01 5.71e+04 -1.20e+01 232s [5,] -1.70e-03 -2.61e+01 6.35e-03 232s [6,] 4.86e-02 -8.74e+00 -9.49e-04 232s [7,] -8.74e+00 8.00e+05 -1.84e+02 232s [8,] -9.49e-04 -1.84e+02 4.68e-02 232s [9,] 1.98e-02 5.32e+01 -2.83e-02 232s [10,] -2.30e+00 -1.75e+05 3.73e+01 232s [11,] -1.07e-02 8.02e+01 -2.06e-02 232s [12,] 7.77e-02 2.01e+01 1.09e-02 232s [13,] -4.02e+00 1.10e+04 -2.33e+00 232s [14,] 1.04e-04 -2.06e+01 5.10e-03 232s [15,] 4.61e-02 3.98e+01 -1.28e-02 232s General.Motors_capital US.Steel_(Intercept) US.Steel_value 232s [1,] -0.08183 1.80e+04 -7.46e+00 232s [2,] 0.00342 -1.87e+01 1.13e-02 232s [3,] -0.01889 -2.45e+01 -3.26e-03 232s [4,] -3.51957 6.44e+04 -2.20e+01 232s [5,] -0.00227 -3.04e+01 1.35e-02 232s [6,] 0.01982 -2.30e+00 -1.07e-02 232s [7,] 53.22544 -1.75e+05 8.02e+01 232s [8,] -0.02835 3.73e+01 -2.06e-02 232s [9,] 0.10737 3.74e+00 1.39e-02 232s [10,] 3.74276 1.25e+06 -5.65e+02 232s [11,] 0.01386 -5.65e+02 3.00e-01 232s [12,] -0.10360 -3.12e+02 -9.01e-02 232s [13,] -0.48733 2.74e+04 -8.35e+00 232s [14,] -0.00238 -5.09e+01 2.23e-02 232s [15,] 0.02432 1.10e+02 -7.74e-02 232s US.Steel_capital Westinghouse_(Intercept) Westinghouse_value 232s [1,] -4.0281 -30.387 1.14e-01 232s [2,] -0.0122 0.303 -3.70e-04 232s [3,] 0.1031 -0.935 1.18e-03 232s [4,] -55.0482 10286.790 -1.70e+01 232s [5,] 0.0123 -4.016 8.74e-03 232s [6,] 0.0777 -4.021 1.04e-04 232s [7,] 20.0945 11026.166 -2.06e+01 232s [8,] 0.0109 -2.326 5.10e-03 232s [9,] -0.1036 -0.487 -2.38e-03 232s [10,] -311.9830 27440.848 -5.09e+01 232s [11,] -0.0901 -8.348 2.23e-02 232s [12,] 1.6331 -27.510 2.29e-02 232s [13,] -27.5101 3917.263 -5.99e+00 232s [14,] 0.0229 -5.992 1.29e-02 232s [15,] 0.1422 6.376 -3.12e-02 232s Westinghouse_capital 232s [1,] 2.42e-01 232s [2,] -6.41e-04 232s [3,] 1.67e-03 232s [4,] 2.34e+01 232s [5,] -2.16e-02 232s [6,] 4.61e-02 232s [7,] 3.98e+01 232s [8,] -1.28e-02 232s [9,] 2.43e-02 232s [10,] 1.10e+02 232s [11,] -7.74e-02 232s [12,] 1.42e-01 232s [13,] 6.38e+00 232s [14,] -3.12e-02 232s [15,] 1.70e-01 232s [1] "Error in bread.systemfit(greeneSurPooled) : \n returning the 'bread' for models with restrictions has not yet been implemented.\n" 232s attr(,"class") 232s [1] "try-error" 232s attr(,"condition") 232s 232s > 232s BEGIN TEST test_sur.R 232s 232s R version 4.3.2 (2023-10-31) -- "Eye Holes" 232s Copyright (C) 2023 The R Foundation for Statistical Computing 232s Platform: aarch64-unknown-linux-gnu (64-bit) 232s 232s R is free software and comes with ABSOLUTELY NO WARRANTY. 232s You are welcome to redistribute it under certain conditions. 232s Type 'license()' or 'licence()' for distribution details. 232s 232s R is a collaborative project with many contributors. 232s Type 'contributors()' for more information and 232s 'citation()' on how to cite R or R packages in publications. 232s 232s Type 'demo()' for some demos, 'help()' for on-line help, or 232s 'help.start()' for an HTML browser interface to help. 232s Type 'q()' to quit R. 232s 232s > library( systemfit ) 232s Loading required package: Matrix 233s Loading required package: car 233s Loading required package: carData 233s Loading required package: lmtest 233s Loading required package: zoo 233s 233s Attaching package: ‘zoo’ 233s 233s The following objects are masked from ‘package:base’: 233s 233s as.Date, as.Date.numeric 233s 233s 233s Please cite the 'systemfit' package as: 233s 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/. 233s 233s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 233s https://r-forge.r-project.org/projects/systemfit/ 233s > options( digits = 3 ) 233s > 233s > data( "Kmenta" ) 233s > useMatrix <- FALSE 233s > 233s > demand <- consump ~ price + income 233s > supply <- consump ~ price + farmPrice + trend 233s > system <- list( demand = demand, supply = supply ) 233s > restrm <- matrix(0,1,7) # restriction matrix "R" 233s > restrm[1,3] <- 1 233s > restrm[1,7] <- -1 233s > restrict <- "demand_income - supply_trend = 0" 233s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 233s > restr2m[1,3] <- 1 233s > restr2m[1,7] <- -1 233s > restr2m[2,2] <- -1 233s > restr2m[2,5] <- 1 233s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 233s > restrict2 <- c( "demand_income - supply_trend = 0", 233s + "- demand_price + supply_price = 0.5" ) 233s > restrict2i <- c( "demand_income - supply_trend = 0", 233s + "- demand_price + supply_income = 0.5" ) 233s > tc <- matrix(0,7,6) 233s > tc[1,1] <- 1 233s > tc[2,2] <- 1 233s > tc[3,3] <- 1 233s > tc[4,4] <- 1 233s > tc[5,5] <- 1 233s > tc[6,6] <- 1 233s > tc[7,3] <- 1 233s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 233s > restr3m[1,2] <- -1 233s > restr3m[1,5] <- 1 233s > restr3q <- c( 0.5 ) # restriction vector "q" 2 233s > restrict3 <- "- C2 + C5 = 0.5" 233s > 233s > # the standard equations do not converge and lead to a singular weighting matrix 233s > # both in R and in EViews, since both equations have the same endogenous variable 233s > supply2 <- price ~ income + farmPrice + trend 233s > system2 <- list( demand = demand, supply = supply2 ) 233s > 233s > 233s > ## *************** SUR estimation ************************ 233s > fitsur1 <- systemfit( system, "SUR", data = Kmenta, useMatrix = useMatrix ) 233s > print( summary( fitsur1 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 170 0.879 0.683 0.789 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 65.7 3.86 1.97 0.755 0.726 233s supply 20 16 104.1 6.50 2.55 0.612 0.539 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.73 4.14 233s supply 4.14 5.78 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.86 4.92 233s supply 4.92 6.50 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.982 233s supply 0.982 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 99.3329 7.5145 13.22 2.3e-10 *** 233s price -0.2755 0.0885 -3.11 0.0063 ** 233s income 0.2986 0.0419 7.12 1.7e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.966 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 65.683 MSE: 3.864 Root MSE: 1.966 233s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 61.9662 11.0808 5.59 4.0e-05 *** 233s price 0.1469 0.0944 1.56 0.13941 233s farmPrice 0.2140 0.0399 5.37 6.3e-05 *** 233s trend 0.3393 0.0679 5.00 0.00013 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.55 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 104.058 MSE: 6.504 Root MSE: 2.55 233s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 233s 233s > nobs( fitsur1 ) 233s [1] 40 233s > 233s > ## ********************* SUR (EViews-like) ***************** 233s > fitsur1e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur1e, useDfSys = TRUE ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 170 0.598 0.683 0.748 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.2 3.89 1.97 0.753 0.724 233s supply 20 16 103.5 6.47 2.54 0.614 0.541 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.17 3.41 233s supply 3.41 4.63 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.31 4.07 233s supply 4.07 5.18 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.982 233s supply 0.982 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 99.2757 6.9280 14.33 8.9e-16 *** 233s price -0.2713 0.0816 -3.33 0.0022 ** 233s income 0.2949 0.0387 7.63 8.9e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.973 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.186 MSE: 3.893 Root MSE: 1.973 233s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 62.2942 9.9110 6.29 4.2e-07 *** 233s price 0.1461 0.0845 1.73 0.093 . 233s farmPrice 0.2121 0.0357 5.95 1.1e-06 *** 233s trend 0.3322 0.0607 5.47 4.6e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.544 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 103.55 MSE: 6.472 Root MSE: 2.544 233s Multiple R-Squared: 0.614 Adjusted R-Squared: 0.541 233s 233s > nobs( fitsur1e ) 233s [1] 40 233s > 233s > ## ********************* SUR (methodResidCov="Theil") ***************** 233s > fitsur1r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur1r2 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 172 -0.896 0.679 1.01 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.8 3.93 1.98 0.751 0.722 233s supply 20 16 105.3 6.58 2.57 0.607 0.534 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.73 4.28 233s supply 4.28 5.78 233s 233s warning: this covariance matrix is NOT positive semidefinit! 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.93 5.17 233s supply 5.17 6.58 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.984 233s supply 0.984 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 99.2120 7.5127 13.21 2.3e-10 *** 233s price -0.2667 0.0877 -3.04 0.0074 ** 233s income 0.2908 0.0406 7.16 1.6e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.982 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 233s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 63.0768 10.9735 5.75 3.0e-05 *** 233s price 0.1439 0.0943 1.52 0.15 233s farmPrice 0.2064 0.0384 5.37 6.2e-05 *** 233s trend 0.3325 0.0640 5.19 8.9e-05 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.566 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 233s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 233s 233s > 233s > ## *************** SUR (methodResidCov="Theil", useDfSys = TRUE ) *************** 233s > fitsur1e2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 233s + x = TRUE, useMatrix = useMatrix ) 233s > print( summary( fitsur1e2, useDfSys = TRUE ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 172 -0.896 0.679 1.01 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.8 3.93 1.98 0.751 0.722 233s supply 20 16 105.3 6.58 2.57 0.607 0.534 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.73 4.28 233s supply 4.28 5.78 233s 233s warning: this covariance matrix is NOT positive semidefinit! 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.93 5.17 233s supply 5.17 6.58 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.984 233s supply 0.984 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 233s price -0.2667 0.0877 -3.04 0.0046 ** 233s income 0.2908 0.0406 7.16 3.3e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.982 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 233s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 233s price 0.1439 0.0943 1.52 0.14 233s farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 233s trend 0.3325 0.0640 5.19 1.0e-05 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.566 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 233s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 233s 233s > 233s > ## ********************* SUR (methodResidCov="max") ***************** 233s > fitsur1r3 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur1r3 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 172 -0.735 0.68 0.957 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.7 3.92 1.98 0.751 0.722 233s supply 20 16 105.2 6.57 2.56 0.608 0.534 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.73 4.26 233s supply 4.26 5.78 233s 233s warning: this covariance matrix is NOT positive semidefinit! 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.92 5.15 233s supply 5.15 6.57 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.984 233s supply 0.984 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 99.2250 7.5129 13.21 2.3e-10 *** 233s price -0.2677 0.0878 -3.05 0.0073 ** 233s income 0.2916 0.0408 7.15 1.6e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.98 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.671 MSE: 3.922 Root MSE: 1.98 233s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 62.9575 10.9850 5.73 3.1e-05 *** 233s price 0.1442 0.0944 1.53 0.15 233s farmPrice 0.2072 0.0386 5.37 6.2e-05 *** 233s trend 0.3333 0.0644 5.18 9.2e-05 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.564 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 105.187 MSE: 6.574 Root MSE: 2.564 233s Multiple R-Squared: 0.608 Adjusted R-Squared: 0.534 233s 233s > 233s > ## *************** WSUR estimation ************************ 233s > fitsur1w <- systemfit( system, "SUR", data = Kmenta, residCovWeighted = TRUE, 233s + useMatrix = useMatrix ) 233s > summary( fitsur1w ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 170 0.879 0.683 0.789 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 65.7 3.86 1.97 0.755 0.726 233s supply 20 16 104.1 6.50 2.55 0.612 0.539 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.73 4.14 233s supply 4.14 5.78 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.86 4.92 233s supply 4.92 6.50 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.982 233s supply 0.982 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 99.3329 7.5145 13.22 2.3e-10 *** 233s price -0.2755 0.0885 -3.11 0.0063 ** 233s income 0.2986 0.0419 7.12 1.7e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.966 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 65.683 MSE: 3.864 Root MSE: 1.966 233s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 61.9662 11.0808 5.59 4.0e-05 *** 233s price 0.1469 0.0944 1.56 0.13941 233s farmPrice 0.2140 0.0399 5.37 6.3e-05 *** 233s trend 0.3393 0.0679 5.00 0.00013 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.55 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 104.058 MSE: 6.504 Root MSE: 2.55 233s Multiple R-Squared: 0.612 Adjusted R-Squared: 0.539 233s 233s > nobs( fitsur1w ) 233s [1] 40 233s > 233s > ## *************** WSUR (methodResidCov="Theil", useDfSys = TRUE ) *************** 233s > fitsur1we2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 233s + residCovWeighted = TRUE, useMatrix = useMatrix ) 233s > summary( fitsur1we2, useDfSys = TRUE ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 172 -0.896 0.679 1.01 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.8 3.93 1.98 0.751 0.722 233s supply 20 16 105.3 6.58 2.57 0.607 0.534 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.73 4.28 233s supply 4.28 5.78 233s 233s warning: this covariance matrix is NOT positive semidefinit! 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.93 5.17 233s supply 5.17 6.58 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.984 233s supply 0.984 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 233s price -0.2667 0.0877 -3.04 0.0046 ** 233s income 0.2908 0.0406 7.16 3.3e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.982 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.802 MSE: 3.93 Root MSE: 1.982 233s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 233s price 0.1439 0.0943 1.52 0.14 233s farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 233s trend 0.3325 0.0640 5.19 1.0e-05 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.566 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 105.322 MSE: 6.583 Root MSE: 2.566 233s Multiple R-Squared: 0.607 Adjusted R-Squared: 0.534 233s 233s > 233s > 233s > ## *************** SUR with cross-equation restriction ************** 233s > fitsur2 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur2 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 179 0.933 0.665 0.753 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 71.6 4.21 2.05 0.733 0.702 233s supply 20 16 107.8 6.74 2.60 0.598 0.523 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.78 4.47 233s supply 4.47 5.94 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 4.21 5.24 233s supply 5.24 6.74 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.983 233s supply 0.983 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 233s price -0.2398 0.0860 -2.79 0.0086 ** 233s income 0.2670 0.0368 7.25 2.2e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.052 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 71.597 MSE: 4.212 Root MSE: 2.052 233s Multiple R-Squared: 0.733 Adjusted R-Squared: 0.702 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 233s price 0.1332 0.0953 1.40 0.17 233s farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 233s trend 0.2670 0.0368 7.25 2.2e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.596 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 107.806 MSE: 6.738 Root MSE: 2.596 233s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 233s 233s > nobs( fitsur2 ) 233s [1] 40 233s > # the same with symbolically specified restrictions 233s > fitsur2Sym <- systemfit( system, "SUR", data = Kmenta, 233s + restrict.matrix = restrict, useMatrix = useMatrix ) 233s > all.equal( fitsur2, fitsur2Sym ) 233s [1] "Component “call”: target, current do not match when deparsed" 233s > nobs( fitsur2Sym ) 233s [1] 40 233s > 233s > ## *************** SUR with cross-equation restriction (EViews-like) ** 233s > fitsur2e <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 233s + methodResidCov = "noDfCor", x = TRUE, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur2e ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 180 0.62 0.663 0.707 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 72.6 4.27 2.07 0.729 0.697 233s supply 20 16 107.9 6.75 2.60 0.597 0.522 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.21 3.68 233s supply 3.68 4.75 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.63 4.35 233s supply 4.35 5.40 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.984 233s supply 0.984 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.7799 6.9687 14.17 8.9e-16 *** 233s price -0.2354 0.0795 -2.96 0.0056 ** 233s income 0.2631 0.0344 7.66 6.7e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.066 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 233s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 67.6039 9.5712 7.06 3.7e-08 *** 233s price 0.1328 0.0853 1.56 0.13 233s farmPrice 0.1785 0.0305 5.85 1.3e-06 *** 233s trend 0.2631 0.0344 7.66 6.7e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.597 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 233s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 233s 233s > 233s > ## *************** WSUR with cross-equation restriction (EViews-like) ** 233s > fitsur2we <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restrm, 233s + methodResidCov = "noDfCor", residCovWeighted = TRUE, 233s + x = TRUE, useMatrix = useMatrix ) 233s > summary( fitsur2we ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 182 0.609 0.661 0.711 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 73 4.29 2.07 0.728 0.696 233s supply 20 16 109 6.79 2.61 0.595 0.519 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.19 3.69 233s supply 3.69 4.78 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.65 4.38 233s supply 4.38 5.43 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.985 233s supply 0.985 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.7542 6.9468 14.22 6.7e-16 *** 233s price -0.2335 0.0790 -2.96 0.0056 ** 233s income 0.2614 0.0338 7.74 5.3e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.072 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 73.009 MSE: 4.295 Root MSE: 2.072 233s Multiple R-Squared: 0.728 Adjusted R-Squared: 0.696 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 67.8882 9.5640 7.10 3.4e-08 *** 233s price 0.1320 0.0855 1.55 0.13 233s farmPrice 0.1765 0.0301 5.86 1.3e-06 *** 233s trend 0.2614 0.0338 7.74 5.3e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.606 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 108.634 MSE: 6.79 Root MSE: 2.606 233s Multiple R-Squared: 0.595 Adjusted R-Squared: 0.519 233s 233s > 233s > 233s > ## *************** SUR with restriction via restrict.regMat ******************* 233s > fitsur3 <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur3 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 179 0.933 0.665 0.753 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 71.6 4.21 2.05 0.733 0.702 233s supply 20 16 107.8 6.74 2.60 0.598 0.523 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.78 4.47 233s supply 4.47 5.94 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 4.21 5.24 233s supply 5.24 6.74 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.983 233s supply 0.983 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 233s price -0.2398 0.0860 -2.79 0.0086 ** 233s income 0.2670 0.0368 7.25 2.2e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.052 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 71.597 MSE: 4.212 Root MSE: 2.052 233s Multiple R-Squared: 0.733 Adjusted R-Squared: 0.702 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 233s price 0.1332 0.0953 1.40 0.17 233s farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 233s trend 0.2670 0.0368 7.25 2.2e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.596 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 107.806 MSE: 6.738 Root MSE: 2.596 233s Multiple R-Squared: 0.598 Adjusted R-Squared: 0.523 233s 233s > nobs( fitsur3 ) 233s [1] 40 233s > 233s > ## *************** SUR with restriction via restrict.regMat (EViews-like) ************** 233s > fitsur3e <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 233s + methodResidCov = "noDfCor", x = TRUE, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur3e ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 180 0.62 0.663 0.707 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 72.6 4.27 2.07 0.729 0.697 233s supply 20 16 107.9 6.75 2.60 0.597 0.522 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.21 3.68 233s supply 3.68 4.75 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.63 4.35 233s supply 4.35 5.40 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.984 233s supply 0.984 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.7799 6.9687 14.17 8.9e-16 *** 233s price -0.2354 0.0795 -2.96 0.0056 ** 233s income 0.2631 0.0344 7.66 6.7e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.066 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 233s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 67.6039 9.5712 7.06 3.7e-08 *** 233s price 0.1328 0.0853 1.56 0.13 233s farmPrice 0.1785 0.0305 5.85 1.3e-06 *** 233s trend 0.2631 0.0344 7.66 6.7e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.597 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 233s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 233s 233s > 233s > ## *************** WSUR with restriction via restrict.regMat ******************* 233s > fitsur3w <- systemfit( system, "SUR", data = Kmenta, restrict.regMat = tc, 233s + residCovWeighted = TRUE, x = TRUE, useMatrix = useMatrix ) 233s > summary( fitsur3w ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 181 0.919 0.663 0.757 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 72 4.24 2.06 0.731 0.700 233s supply 20 16 109 6.79 2.60 0.595 0.519 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.75 4.48 233s supply 4.48 5.98 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 4.24 5.28 233s supply 5.28 6.79 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.984 233s supply 0.984 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.8139 7.5317 13.12 7.3e-15 *** 233s price -0.2378 0.0854 -2.79 0.0087 ** 233s income 0.2653 0.0361 7.34 1.7e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.058 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 72.023 MSE: 4.237 Root MSE: 2.058 233s Multiple R-Squared: 0.731 Adjusted R-Squared: 0.7 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 67.7366 10.6556 6.36 3.0e-07 *** 233s price 0.1324 0.0955 1.39 0.17 233s farmPrice 0.1774 0.0332 5.35 6.1e-06 *** 233s trend 0.2653 0.0361 7.34 1.7e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.605 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 108.579 MSE: 6.786 Root MSE: 2.605 233s Multiple R-Squared: 0.595 Adjusted R-Squared: 0.519 233s 233s > 233s > 233s > ## *************** SUR with 2 restrictions *************************** 233s > fitsur4 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 233s + restrict.rhs = restr2q, useMatrix = useMatrix ) 233s > print( summary( fitsur4 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 165 1.76 0.691 0.69 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 64 3.76 1.94 0.761 0.733 233s supply 20 16 101 6.34 2.52 0.622 0.551 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.76 4.46 233s supply 4.46 5.99 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.76 4.70 233s supply 4.70 6.34 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.962 233s supply 0.962 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 233s price -0.2798 0.0840 -3.33 0.002 ** 233s income 0.3286 0.0206 15.93 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.94 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 63.987 MSE: 3.764 Root MSE: 1.94 233s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 233s price 0.2202 0.0840 2.62 0.013 * 233s farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 233s trend 0.3286 0.0206 15.93 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.518 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 101.473 MSE: 6.342 Root MSE: 2.518 233s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 233s 233s > nobs( fitsur4 ) 233s [1] 40 233s > # the same with symbolically specified restrictions 233s > fitsur4Sym <- systemfit( system, "SUR", data = Kmenta, 233s + restrict.matrix = restrict2, useMatrix = useMatrix ) 233s > all.equal( fitsur4, fitsur4Sym ) 233s [1] "Component “call”: target, current do not match when deparsed" 233s > 233s > ## *************** SUR with 2 restrictions (EViews-like) ************** 233s > fitsur4e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 233s + restrict.matrix = restr2m, restrict.rhs = restr2q, useMatrix = useMatrix ) 233s > print( summary( fitsur4e ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 165 1.2 0.693 0.653 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 63.8 3.75 1.94 0.762 0.734 233s supply 20 16 100.8 6.30 2.51 0.624 0.553 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.20 3.67 233s supply 3.67 4.79 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.19 3.86 233s supply 3.86 5.04 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.962 233s supply 0.962 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 97.2678 6.9200 14.06 4.4e-16 *** 233s price -0.2851 0.0767 -3.72 7e-04 *** 233s income 0.3296 0.0184 17.86 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.937 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 63.811 MSE: 3.754 Root MSE: 1.937 233s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 53.3040 7.1045 7.5 8.7e-09 *** 233s price 0.2149 0.0767 2.8 0.0082 ** 233s farmPrice 0.2343 0.0187 12.6 1.6e-14 *** 233s trend 0.3296 0.0184 17.9 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.51 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 100.835 MSE: 6.302 Root MSE: 2.51 233s Multiple R-Squared: 0.624 Adjusted R-Squared: 0.553 233s 233s > 233s > ## *************** SUR with 2 restrictions (methodResidCov = "Theil") ************** 233s > fitsur4r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 233s + restrict.matrix = restr2m, restrict.rhs = restr2q, useMatrix = useMatrix ) 233s > print( summary( fitsur4r2 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 175 0.034 0.673 0.708 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67 3.94 1.99 0.750 0.721 233s supply 20 16 108 6.76 2.60 0.596 0.521 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.76 4.61 233s supply 4.61 5.99 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.94 5.16 233s supply 5.16 6.76 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.967 233s supply 0.967 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 92.5266 7.2896 12.69 1.2e-14 *** 233s price -0.2304 0.0827 -2.79 0.0086 ** 233s income 0.3221 0.0166 19.37 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.986 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.048 MSE: 3.944 Root MSE: 1.986 233s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 48.7011 7.4034 6.58 1.3e-07 *** 233s price 0.2696 0.0827 3.26 0.0025 ** 233s farmPrice 0.2261 0.0166 13.62 1.6e-15 *** 233s trend 0.3221 0.0166 19.37 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.601 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 108.217 MSE: 6.764 Root MSE: 2.601 233s Multiple R-Squared: 0.596 Adjusted R-Squared: 0.521 233s 233s > 233s > ## *************** SUR with 2 restrictions (methodResidCov = "max") ************** 233s > fitsur4r3 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 233s + restrict.matrix = restr2m, restrict.rhs = restr2q, 233s + x = TRUE, useMatrix = useMatrix ) 233s > print( summary( fitsur4r3 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 173 0.217 0.677 0.702 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.4 3.91 1.98 0.752 0.723 233s supply 20 16 106.9 6.68 2.58 0.601 0.526 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.76 4.59 233s supply 4.59 5.99 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.91 5.09 233s supply 5.09 6.68 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.966 233s supply 0.966 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 93.1978 7.3168 12.74 1.1e-14 *** 233s price -0.2381 0.0829 -2.87 0.0069 ** 233s income 0.3231 0.0170 18.96 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.976 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.405 MSE: 3.906 Root MSE: 1.976 233s Multiple R-Squared: 0.752 Adjusted R-Squared: 0.723 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 49.3676 7.4381 6.64 1.1e-07 *** 233s price 0.2619 0.0829 3.16 0.0033 ** 233s farmPrice 0.2271 0.0171 13.29 3.1e-15 *** 233s trend 0.3231 0.0170 18.96 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.585 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 106.924 MSE: 6.683 Root MSE: 2.585 233s Multiple R-Squared: 0.601 Adjusted R-Squared: 0.526 233s 233s > 233s > ## *************** WSUR with 2 restrictions (EViews-like) ************** 233s > fitsur4we <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 233s + restrict.matrix = restr2m, restrict.rhs = restr2q, residCovWeighted = TRUE, 233s + useMatrix = useMatrix ) 233s > summary( fitsur4we ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 165 1.2 0.692 0.654 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 63.9 3.76 1.94 0.762 0.733 233s supply 20 16 101.2 6.33 2.52 0.623 0.552 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.18 3.69 233s supply 3.69 4.81 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.20 3.87 233s supply 3.87 5.06 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.962 233s supply 0.962 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 96.9414 6.8894 14.07 4.4e-16 *** 233s price -0.2814 0.0766 -3.67 8e-04 *** 233s income 0.3291 0.0181 18.18 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.939 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 63.936 MSE: 3.761 Root MSE: 1.939 233s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.733 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 52.9963 7.0652 7.50 8.7e-09 *** 233s price 0.2186 0.0766 2.85 0.0072 ** 233s farmPrice 0.2337 0.0183 12.76 1.0e-14 *** 233s trend 0.3291 0.0181 18.18 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.515 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 101.201 MSE: 6.325 Root MSE: 2.515 233s Multiple R-Squared: 0.623 Adjusted R-Squared: 0.552 233s 233s > 233s > 233s > ## *************** SUR with 2 restrictions via R and restrict.regMat **************** 233s > fitsur5 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 233s + restrict.rhs = restr3q, restrict.regMat = tc, 233s + x = TRUE, useMatrix = useMatrix ) 233s > print( summary( fitsur5 ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 165 1.76 0.691 0.69 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 64 3.76 1.94 0.761 0.733 233s supply 20 16 101 6.34 2.52 0.622 0.551 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.76 4.46 233s supply 4.46 5.99 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.76 4.70 233s supply 4.70 6.34 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.962 233s supply 0.962 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 233s price -0.2798 0.0840 -3.33 0.002 ** 233s income 0.3286 0.0206 15.93 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.94 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 63.987 MSE: 3.764 Root MSE: 1.94 233s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 233s price 0.2202 0.0840 2.62 0.013 * 233s farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 233s trend 0.3286 0.0206 15.93 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.518 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 101.473 MSE: 6.342 Root MSE: 2.518 233s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 233s 233s > nobs( fitsur5 ) 233s [1] 40 233s > # the same with symbolically specified restrictions 233s > fitsur5Sym <- systemfit( system, "SUR", data = Kmenta, 233s + restrict.matrix = restrict3, restrict.regMat = tc, 233s + x = TRUE, useMatrix = useMatrix ) 233s > all.equal( fitsur5, fitsur5Sym ) 233s [1] "Component “call”: target, current do not match when deparsed" 233s > 233s > ## *************** SUR with 2 restrictions via R and restrict.regMat (EViews-like) ************** 233s > fitsur5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 233s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsur5e ) ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 165 1.2 0.693 0.653 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 63.8 3.75 1.94 0.762 0.734 233s supply 20 16 100.8 6.30 2.51 0.624 0.553 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.20 3.67 233s supply 3.67 4.79 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.19 3.86 233s supply 3.86 5.04 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.962 233s supply 0.962 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 97.2678 6.9200 14.06 4.4e-16 *** 233s price -0.2851 0.0767 -3.72 7e-04 *** 233s income 0.3296 0.0184 17.86 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.937 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 63.811 MSE: 3.754 Root MSE: 1.937 233s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 53.3040 7.1045 7.5 8.7e-09 *** 233s price 0.2149 0.0767 2.8 0.0082 ** 233s farmPrice 0.2343 0.0187 12.6 1.6e-14 *** 233s trend 0.3296 0.0184 17.9 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.51 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 100.835 MSE: 6.302 Root MSE: 2.51 233s Multiple R-Squared: 0.624 Adjusted R-Squared: 0.553 233s 233s > 233s > ## ************ WSUR with 2 restrictions via R and restrict.regMat ************ 233s > fitsur5w <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 233s + restrict.rhs = restr3q, restrict.regMat = tc, residCovWeighted = TRUE, 233s + useMatrix = useMatrix ) 233s > summary( fitsur5w ) 233s 233s systemfit results 233s method: SUR 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 166 1.75 0.69 0.691 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 64.2 3.77 1.94 0.761 0.733 233s supply 20 16 102.0 6.37 2.52 0.620 0.548 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.74 4.47 233s supply 4.47 6.02 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.77 4.72 233s supply 4.72 6.37 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.963 233s supply 0.963 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 96.4421 7.4234 12.99 6e-15 *** 233s price -0.2753 0.0838 -3.29 0.0023 ** 233s income 0.3280 0.0202 16.21 <2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.943 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 64.16 MSE: 3.774 Root MSE: 1.943 233s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 52.5761 7.6099 6.91 5.0e-08 *** 233s price 0.2247 0.0838 2.68 0.011 * 233s farmPrice 0.2318 0.0208 11.14 4.7e-13 *** 233s trend 0.3280 0.0202 16.21 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.524 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 101.967 MSE: 6.373 Root MSE: 2.524 233s Multiple R-Squared: 0.62 Adjusted R-Squared: 0.548 233s 233s > 233s > 233s > ## ************** iterated SUR **************************** 233s > fitsuri1 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsuri1 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 6 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 108 4.42 0.885 0.958 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.3 3.90 1.98 0.753 0.724 233s supply 20 16 41.4 2.59 1.61 0.938 0.926 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.90 -2.38 233s supply -2.38 2.59 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.90 -2.38 233s supply -2.38 2.59 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 -0.749 233s supply -0.749 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 94.0537 7.4051 12.70 4.2e-10 *** 233s price -0.2355 0.0882 -2.67 0.016 * 233s income 0.3117 0.0457 6.81 3.0e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.975 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.286 MSE: 3.899 Root MSE: 1.975 233s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 89.2982 3.3822 26.4 1.3e-14 *** 233s income 0.6655 0.0423 15.7 3.7e-11 *** 233s farmPrice -0.4742 0.0372 -12.7 8.7e-10 *** 233s trend -0.7966 0.0656 -12.2 1.7e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.609 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 41.411 MSE: 2.588 Root MSE: 1.609 233s Multiple R-Squared: 0.938 Adjusted R-Squared: 0.926 233s 233s > nobs( fitsuri1 ) 233s [1] 40 233s > 233s > ## ************** iterated SUR (EViews-like) ***************** 233s > fitsuri1e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 233s + maxit = 100, useMatrix = useMatrix ) 233s > print( summary( fitsuri1e, useDfSys = TRUE ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 7 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 108 3.01 0.885 0.959 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.7 3.93 1.98 0.751 0.722 233s supply 20 16 41.2 2.57 1.60 0.938 0.927 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.34 -1.97 233s supply -1.97 2.06 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.34 -1.97 233s supply -1.97 2.06 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.00 -0.75 233s supply -0.75 1.00 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 93.6193 6.8499 13.67 4.0e-15 *** 233s price -0.2295 0.0816 -2.81 0.0082 ** 233s income 0.3100 0.0423 7.33 2.1e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.981 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.742 MSE: 3.926 Root MSE: 1.981 233s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.722 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 89.2690 3.0165 29.6 < 2e-16 *** 233s income 0.6641 0.0377 17.6 < 2e-16 *** 233s farmPrice -0.4730 0.0332 -14.2 1.3e-15 *** 233s trend -0.7919 0.0585 -13.6 4.9e-15 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.604 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 41.176 MSE: 2.573 Root MSE: 1.604 233s Multiple R-Squared: 0.938 Adjusted R-Squared: 0.927 233s 233s > 233s > ## ************** iterated SUR (methodResidCov = "Theil") **************************** 233s > fitsuri1r2 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 233s + methodResidCov = "Theil", useMatrix = useMatrix ) 233s > print( summary( fitsuri1r2 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 7 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 109 4 0.884 0.961 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.9 3.94 1.98 0.750 0.721 233s supply 20 16 41.8 2.61 1.62 0.937 0.926 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.94 -2.51 233s supply -2.51 2.61 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.94 -2.51 233s supply -2.51 2.61 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 -0.754 233s supply -0.754 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 93.4405 7.3821 12.66 4.4e-10 *** 233s price -0.2271 0.0877 -2.59 0.019 * 233s income 0.3093 0.0458 6.75 3.4e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.984 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.939 MSE: 3.938 Root MSE: 1.984 233s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 89.1602 3.3868 26.3 1.3e-14 *** 233s income 0.6635 0.0423 15.7 3.9e-11 *** 233s farmPrice -0.4710 0.0369 -12.8 8.5e-10 *** 233s trend -0.7952 0.0643 -12.4 1.3e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.616 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 41.764 MSE: 2.61 Root MSE: 1.616 233s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 233s 233s > 233s > ## ************** iterated SUR (methodResidCov="Theil", useDfSys=TRUE) ***************** 233s > fitsuri1e2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 233s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 233s > print( summary( fitsuri1e2, useDfSys = TRUE ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 7 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 109 4 0.884 0.961 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.9 3.94 1.98 0.750 0.721 233s supply 20 16 41.8 2.61 1.62 0.937 0.926 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.94 -2.51 233s supply -2.51 2.61 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.94 -2.51 233s supply -2.51 2.61 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 -0.754 233s supply -0.754 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 93.4405 7.3821 12.66 3.3e-14 *** 233s price -0.2271 0.0877 -2.59 0.014 * 233s income 0.3093 0.0458 6.75 1.1e-07 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.984 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.939 MSE: 3.938 Root MSE: 1.984 233s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 89.1602 3.3868 26.3 < 2e-16 *** 233s income 0.6635 0.0423 15.7 < 2e-16 *** 233s farmPrice -0.4710 0.0369 -12.8 2.7e-14 *** 233s trend -0.7952 0.0643 -12.4 6.0e-14 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.616 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 41.764 MSE: 2.61 Root MSE: 1.616 233s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 233s 233s > 233s > ## ************** iterated SUR (methodResidCov = "max") **************************** 233s > fitsuri1r3 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 233s + methodResidCov = "max", useMatrix = useMatrix ) 233s > print( summary( fitsuri1r3 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 7 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 109 4.06 0.884 0.96 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.8 3.93 1.98 0.751 0.721 233s supply 20 16 41.7 2.61 1.61 0.937 0.926 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.93 -2.49 233s supply -2.49 2.61 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.93 -2.49 233s supply -2.49 2.61 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 -0.754 233s supply -0.754 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 233s price -0.2285 0.0877 -2.60 0.019 * 233s income 0.3097 0.0458 6.76 3.3e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.983 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 233s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 233s income 0.6639 0.0423 15.7 3.8e-11 *** 233s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 233s trend -0.7955 0.0645 -12.3 1.4e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.615 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 233s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 233s 233s > 233s > ## ************** iterated WSUR (methodResidCov = "max") **************************** 233s > fitsuri1wr3 <- systemfit( system2, "SUR", data = Kmenta, maxit = 100, 233s + methodResidCov = "max", residCovWeighted = TRUE, useMatrix = useMatrix ) 233s > summary( fitsuri1wr3 ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 7 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 33 109 4.06 0.884 0.96 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.8 3.93 1.98 0.751 0.721 233s supply 20 16 41.7 2.61 1.61 0.937 0.926 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.93 -2.49 233s supply -2.49 2.61 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.93 -2.49 233s supply -2.49 2.61 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 -0.754 233s supply -0.754 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 233s price -0.2285 0.0877 -2.60 0.019 * 233s income 0.3097 0.0458 6.76 3.3e-06 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.983 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 233s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 233s income 0.6639 0.0423 15.7 3.8e-11 *** 233s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 233s trend -0.7955 0.0645 -12.3 1.4e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.615 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 233s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 233s 233s > 233s > 233s > ## *********** iterated SUR with restriction ******************* 233s > fitsuri2 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 233s + maxit = 100, useMatrix = useMatrix ) 233s > print( summary( fitsuri2 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 21 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 587 110 0.372 0.669 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67 3.94 1.99 0.75 0.721 233s supply 20 16 520 32.52 5.70 0.22 0.074 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.94 4.24 233s supply 4.24 32.52 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.94 4.24 233s supply 4.24 32.52 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.375 233s supply 0.375 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 233s price -0.3945 0.0912 -4.33 0.00013 *** 233s income 0.3382 0.0466 7.25 2.1e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.986 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 233s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 233s income 0.3125 0.1233 2.53 0.016 * 233s farmPrice -0.1972 0.1157 -1.70 0.097 . 233s trend 0.3382 0.0466 7.25 2.1e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.703 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 233s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 233s 233s > 233s > ## *********** iterated SUR with restriction (EViews-like) *************** 233s > fitsuri2e <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 233s + methodResidCov = "noDfCor", maxit = 100, x = TRUE, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsuri2e ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 22 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 588 74.9 0.372 0.664 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67.5 3.97 1.99 0.748 0.719 233s supply 20 16 520.2 32.51 5.70 0.220 0.074 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.37 3.58 233s supply 3.58 26.01 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.37 3.58 233s supply 3.58 26.01 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.382 233s supply 0.382 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 233s price -0.3986 0.0843 -4.73 3.8e-05 *** 233s income 0.3379 0.0431 7.84 4.0e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.992 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.47 MSE: 3.969 Root MSE: 1.992 233s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 233s income 0.3106 0.1101 2.82 0.0079 ** 233s farmPrice -0.1960 0.1034 -1.89 0.0667 . 233s trend 0.3379 0.0431 7.84 4.0e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.702 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 520.205 MSE: 32.513 Root MSE: 5.702 233s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 233s 233s > 233s > ## *********** iterated WSUR with restriction ******************* 233s > fitsuri2w <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restrm, 233s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 233s > summary( fitsuri2w ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 18 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 587 110 0.372 0.669 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67 3.94 1.99 0.75 0.721 233s supply 20 16 520 32.52 5.70 0.22 0.074 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.94 4.24 233s supply 4.24 32.52 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.94 4.24 233s supply 4.24 32.52 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.375 233s supply 0.375 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 107.3672 7.4986 14.32 4.4e-16 *** 233s price -0.3945 0.0912 -4.33 0.00013 *** 233s income 0.3382 0.0466 7.25 2.1e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.986 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.023 MSE: 3.943 Root MSE: 1.986 233s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 233s income 0.3125 0.1233 2.53 0.016 * 233s farmPrice -0.1972 0.1157 -1.70 0.097 . 233s trend 0.3382 0.0466 7.25 2.1e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.703 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 520.327 MSE: 32.52 Root MSE: 5.703 233s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 233s 233s > 233s > 233s > ## *********** iterated SUR with restriction via restrict.regMat ******************** 233s > fitsuri3 <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 233s + maxit = 100, useMatrix = useMatrix ) 233s > print( summary( fitsuri3 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 21 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 587 110 0.372 0.669 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67 3.94 1.99 0.75 0.721 233s supply 20 16 520 32.52 5.70 0.22 0.074 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.94 4.24 233s supply 4.24 32.52 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.94 4.24 233s supply 4.24 32.52 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.375 233s supply 0.375 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 233s price -0.3945 0.0912 -4.33 0.00013 *** 233s income 0.3382 0.0466 7.25 2.1e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.986 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 233s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 233s income 0.3125 0.1233 2.53 0.016 * 233s farmPrice -0.1972 0.1157 -1.70 0.097 . 233s trend 0.3382 0.0466 7.25 2.1e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.703 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 233s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 233s 233s > 233s > ## *********** iterated SUR with restriction via restrict.regMat (EViews-like) *************** 233s > fitsuri3e <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 233s + methodResidCov = "noDfCor", maxit = 100, x = TRUE, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsuri3e ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 22 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 588 74.9 0.372 0.664 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67.5 3.97 1.99 0.748 0.719 233s supply 20 16 520.2 32.51 5.70 0.220 0.074 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.37 3.58 233s supply 3.58 26.01 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.37 3.58 233s supply 3.58 26.01 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.382 233s supply 0.382 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 233s price -0.3986 0.0843 -4.73 3.8e-05 *** 233s income 0.3379 0.0431 7.84 4.0e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.992 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.47 MSE: 3.969 Root MSE: 1.992 233s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 233s income 0.3106 0.1101 2.82 0.0079 ** 233s farmPrice -0.1960 0.1034 -1.89 0.0667 . 233s trend 0.3379 0.0431 7.84 4.0e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.702 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 520.205 MSE: 32.513 Root MSE: 5.702 233s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 233s 233s > 233s > ## *********** iterated WSUR with restriction via restrict.regMat (EViews-like) *************** 233s > fitsuri3we <- systemfit( system2, "SUR", data = Kmenta, restrict.regMat = tc, 233s + methodResidCov = "noDfCor", maxit = 100, residCovWeighted = TRUE, 233s + useMatrix = useMatrix ) 233s > summary( fitsuri3we ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 20 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 34 588 74.9 0.372 0.664 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67.5 3.97 1.99 0.748 0.719 233s supply 20 16 520.2 32.51 5.70 0.220 0.074 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.37 3.58 233s supply 3.58 26.01 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.37 3.58 233s supply 3.58 26.01 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.382 233s supply 0.382 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 107.8055 6.9270 15.56 < 2e-16 *** 233s price -0.3986 0.0843 -4.73 3.8e-05 *** 233s income 0.3379 0.0431 7.84 4.0e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.992 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.471 MSE: 3.969 Root MSE: 1.992 233s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 85.1071 10.8288 7.86 3.8e-09 *** 233s income 0.3106 0.1101 2.82 0.008 ** 233s farmPrice -0.1960 0.1034 -1.89 0.067 . 233s trend 0.3379 0.0431 7.84 4.0e-09 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.702 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 520.206 MSE: 32.513 Root MSE: 5.702 233s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 233s 233s > 233s > 233s > ## *************** iterated SUR with 2 restrictions *************************** 233s > fitsurio4 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 233s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 233s > print( summary( fitsurio4 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 10 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 176 1.74 0.671 0.705 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67.2 3.95 1.99 0.749 0.720 233s supply 20 16 109.2 6.83 2.61 0.593 0.516 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.95 5.02 233s supply 5.02 6.83 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.95 5.02 233s supply 5.02 6.83 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.967 233s supply 0.967 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 233s price -0.2276 0.0850 -2.68 0.011 * 233s income 0.3203 0.0185 17.32 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.988 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 233s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 233s price 0.2724 0.0850 3.20 0.0029 ** 233s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 233s trend 0.3203 0.0185 17.32 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.613 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 233s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 233s 233s > fitsuri4 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr2m, 233s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 233s > print( summary( fitsuri4 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 19 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 575 121 0.385 0.637 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 65.5 3.85 1.96 0.756 0.727 233s supply 20 16 509.3 31.83 5.64 0.237 0.094 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.85 1.23 233s supply 1.23 31.83 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.85 1.23 233s supply 1.23 31.83 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.111 233s supply 0.111 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 233s price -0.2646 0.0777 -3.40 0.0017 ** 233s income 0.3007 0.0436 6.89 5.3e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.963 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 65.532 MSE: 3.855 Root MSE: 1.963 233s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 233s income 0.2354 0.0777 3.03 0.0046 ** 233s farmPrice -0.1667 0.1108 -1.50 0.1416 233s trend 0.3007 0.0436 6.89 5.3e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.642 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 509.345 MSE: 31.834 Root MSE: 5.642 233s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 233s 233s > 233s > ## *************** iterated SUR with 2 restrictions (EViews-like) ************** 233s > fitsurio4e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 233s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsurio4e ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 9 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 173 1.18 0.677 0.665 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66.3 3.90 1.97 0.753 0.724 233s supply 20 16 106.7 6.67 2.58 0.602 0.527 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.31 4.06 233s supply 4.06 5.34 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.31 4.06 233s supply 4.06 5.34 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.966 233s supply 0.966 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 93.3596 6.8576 13.61 1.6e-15 *** 233s price -0.2398 0.0779 -3.08 0.0041 ** 233s income 0.3232 0.0163 19.81 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.974 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 66.265 MSE: 3.898 Root MSE: 1.974 233s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 49.5456 6.9727 7.11 2.8e-08 *** 233s price 0.2602 0.0779 3.34 0.002 ** 233s farmPrice 0.2270 0.0164 13.81 8.9e-16 *** 233s trend 0.3232 0.0163 19.81 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.583 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 106.722 MSE: 6.67 Root MSE: 2.583 233s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.527 233s 233s > fitsuri4e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 233s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsuri4e ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 20 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 570 82.4 0.391 0.629 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 66 3.88 1.97 0.754 0.725 233s supply 20 16 504 31.50 5.61 0.245 0.103 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.300 0.876 233s supply 0.876 25.203 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.300 0.876 233s supply 0.876 25.203 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.0000 0.0961 233s supply 0.0961 1.0000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 97.6297 6.1560 15.86 < 2e-16 *** 233s price -0.2576 0.0709 -3.63 0.00089 *** 233s income 0.2976 0.0403 7.38 1.2e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.97 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 65.995 MSE: 3.882 Root MSE: 1.97 233s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 89.5437 9.3372 9.59 2.5e-11 *** 233s income 0.2424 0.0709 3.42 0.0016 ** 233s farmPrice -0.1687 0.0988 -1.71 0.0967 . 233s trend 0.2976 0.0403 7.38 1.2e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.613 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 504.066 MSE: 31.504 Root MSE: 5.613 233s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.103 233s 233s > 233s > ## *************** iterated WSUR with 2 restrictions *************************** 233s > fitsurio4w <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr2m, 233s + restrict.rhs = restr2q, maxit = 100, residCovWeighted = TRUE, 233s + useMatrix = useMatrix ) 233s > summary( fitsurio4w ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 10 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 176 1.74 0.671 0.705 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67.2 3.95 1.99 0.749 0.720 233s supply 20 16 109.2 6.83 2.61 0.593 0.516 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.95 5.02 233s supply 5.02 6.83 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.95 5.02 233s supply 5.02 6.83 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.967 233s supply 0.967 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 233s price -0.2276 0.0850 -2.68 0.011 * 233s income 0.3203 0.0185 17.32 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.988 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 233s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 48.7294 7.4587 6.53 1.5e-07 *** 233s price 0.2724 0.0850 3.20 0.0029 ** 233s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 233s trend 0.3203 0.0185 17.32 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.613 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 233s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 233s 233s > fitsuri4w <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr2m, 233s + restrict.rhs = restr2q, maxit = 100, residCovWeighted = TRUE, 233s + useMatrix = useMatrix ) 233s > summary( fitsuri4w ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 18 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 575 121 0.385 0.637 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 65.5 3.85 1.96 0.756 0.727 233s supply 20 16 509.3 31.83 5.64 0.237 0.094 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.85 1.23 233s supply 1.23 31.83 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.85 1.23 233s supply 1.23 31.83 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.111 233s supply 0.111 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 98.0361 6.7437 14.54 2.2e-16 *** 233s price -0.2646 0.0777 -3.40 0.0017 ** 233s income 0.3007 0.0436 6.89 5.3e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.963 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 65.531 MSE: 3.855 Root MSE: 1.963 233s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: price ~ income + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 90.0052 10.4368 8.62 3.5e-10 *** 233s income 0.2354 0.0777 3.03 0.0046 ** 233s farmPrice -0.1667 0.1108 -1.50 0.1416 233s trend 0.3007 0.0436 6.89 5.3e-08 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 5.642 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 509.349 MSE: 31.834 Root MSE: 5.642 233s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 233s 233s > 233s > 233s > ## *************** iterated SUR with 2 restrictions via R and restrict.regMat **************** 233s > fitsurio5 <- systemfit( system, "SUR", data = Kmenta, restrict.matrix = restr3m, 233s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 233s + useMatrix = useMatrix ) 233s > print( summary( fitsurio5 ) ) 233s 233s systemfit results 233s method: iterated SUR 233s 233s convergence achieved after 10 iterations 233s 233s N DF SSR detRCov OLS-R2 McElroy-R2 233s system 40 35 176 1.74 0.671 0.705 233s 233s N DF SSR MSE RMSE R2 Adj R2 233s demand 20 17 67.2 3.95 1.99 0.749 0.720 233s supply 20 16 109.2 6.83 2.61 0.593 0.516 233s 233s The covariance matrix of the residuals used for estimation 233s demand supply 233s demand 3.95 5.02 233s supply 5.02 6.83 233s 233s The covariance matrix of the residuals 233s demand supply 233s demand 3.95 5.02 233s supply 5.02 6.83 233s 233s The correlations of the residuals 233s demand supply 233s demand 1.000 0.967 233s supply 0.967 1.000 233s 233s 233s SUR estimates for 'demand' (equation 1) 233s Model Formula: consump ~ price + income 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 233s price -0.2276 0.0850 -2.68 0.011 * 233s income 0.3203 0.0185 17.32 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 1.988 on 17 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 17 233s SSR: 67.206 MSE: 3.953 Root MSE: 1.988 233s Multiple R-Squared: 0.749 Adjusted R-Squared: 0.72 233s 233s 233s SUR estimates for 'supply' (equation 2) 233s Model Formula: consump ~ price + farmPrice + trend 233s 233s Estimate Std. Error t value Pr(>|t|) 233s (Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 233s price 0.2724 0.0850 3.20 0.0029 ** 233s farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 233s trend 0.3203 0.0185 17.32 < 2e-16 *** 233s --- 233s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 233s 233s Residual standard error: 2.613 on 16 degrees of freedom 233s Number of observations: 20 Degrees of Freedom: 16 233s SSR: 109.234 MSE: 6.827 Root MSE: 2.613 233s Multiple R-Squared: 0.593 Adjusted R-Squared: 0.516 233s 233s > fitsuri5 <- systemfit( system2, "SUR", data = Kmenta, restrict.matrix = restr3m, 233s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 233s + useMatrix = useMatrix ) 234s > print( summary( fitsuri5 ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 19 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 575 121 0.385 0.637 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 65.5 3.85 1.96 0.756 0.727 234s supply 20 16 509.3 31.83 5.64 0.237 0.094 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.85 1.23 234s supply 1.23 31.83 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 3.85 1.23 234s supply 1.23 31.83 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.111 234s supply 0.111 1.000 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 234s price -0.2646 0.0777 -3.40 0.0017 ** 234s income 0.3007 0.0436 6.89 5.3e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.963 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 65.532 MSE: 3.855 Root MSE: 1.963 234s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: price ~ income + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 234s income 0.2354 0.0777 3.03 0.0046 ** 234s farmPrice -0.1667 0.1108 -1.50 0.1416 234s trend 0.3007 0.0436 6.89 5.3e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 5.642 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 509.345 MSE: 31.834 Root MSE: 5.642 234s Multiple R-Squared: 0.237 Adjusted R-Squared: 0.094 234s 234s > 234s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (EViews-like) ********** 234s > fitsurio5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "noDfCor", 234s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 234s + maxit = 100, useMatrix = useMatrix ) 234s > print( summary( fitsurio5e ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 9 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 173 1.18 0.677 0.665 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 66.3 3.90 1.97 0.753 0.724 234s supply 20 16 106.7 6.67 2.58 0.602 0.527 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.31 4.06 234s supply 4.06 5.34 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 3.31 4.06 234s supply 4.06 5.34 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.966 234s supply 0.966 1.000 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 93.3596 6.8576 13.61 1.6e-15 *** 234s price -0.2398 0.0779 -3.08 0.0041 ** 234s income 0.3232 0.0163 19.81 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.974 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 66.265 MSE: 3.898 Root MSE: 1.974 234s Multiple R-Squared: 0.753 Adjusted R-Squared: 0.724 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: consump ~ price + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 49.5456 6.9727 7.11 2.8e-08 *** 234s price 0.2602 0.0779 3.34 0.002 ** 234s farmPrice 0.2270 0.0164 13.81 8.9e-16 *** 234s trend 0.3232 0.0163 19.81 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 2.583 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 106.722 MSE: 6.67 Root MSE: 2.583 234s Multiple R-Squared: 0.602 Adjusted R-Squared: 0.527 234s 234s > fitsuri5e <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "noDfCor", 234s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 234s + maxit = 100, useMatrix = useMatrix ) 234s > print( summary( fitsuri5e ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 20 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 570 82.4 0.391 0.629 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 66 3.88 1.97 0.754 0.725 234s supply 20 16 504 31.50 5.61 0.245 0.103 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.300 0.876 234s supply 0.876 25.203 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 3.300 0.876 234s supply 0.876 25.203 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.0000 0.0961 234s supply 0.0961 1.0000 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 97.6297 6.1560 15.86 < 2e-16 *** 234s price -0.2576 0.0709 -3.63 0.00089 *** 234s income 0.2976 0.0403 7.38 1.2e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.97 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 65.995 MSE: 3.882 Root MSE: 1.97 234s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: price ~ income + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 89.5437 9.3372 9.59 2.5e-11 *** 234s income 0.2424 0.0709 3.42 0.0016 ** 234s farmPrice -0.1687 0.0988 -1.71 0.0967 . 234s trend 0.2976 0.0403 7.38 1.2e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 5.613 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 504.066 MSE: 31.504 Root MSE: 5.613 234s Multiple R-Squared: 0.245 Adjusted R-Squared: 0.103 234s 234s > nobs( fitsuri5e ) 234s [1] 40 234s > 234s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (methodResidCov="Theil") ********** 234s > fitsurio5r2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 234s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 234s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 234s > print( summary( fitsurio5r2 ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s warning: convergence not achieved after 100 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 253 -1.67 0.527 0.927 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 95.8 5.63 2.37 0.643 0.601 234s supply 20 16 157.7 9.86 3.14 0.412 0.301 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 4.26 5.29 234s supply 5.29 6.69 234s 234s warning: this covariance matrix is NOT positive semidefinit! 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 5.63 7.56 234s supply 7.56 9.86 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.982 234s supply 0.982 1.000 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 234s price -0.0647 0.0815 -0.79 0.43 234s income 0.3007 0.0131 23.01 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 2.373 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 95.76 MSE: 5.633 Root MSE: 2.373 234s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.601 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: consump ~ price + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 234s price 0.4353 0.0815 5.34 5.7e-06 *** 234s farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 234s trend 0.3007 0.0131 23.01 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 3.14 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 157.737 MSE: 9.859 Root MSE: 3.14 234s Multiple R-Squared: 0.412 Adjusted R-Squared: 0.301 234s 234s > fitsuri5r2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 234s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 234s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 234s > print( summary( fitsuri5r2 ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 21 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 576 121 0.384 0.637 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 65.4 3.85 1.96 0.756 0.727 234s supply 20 16 510.8 31.92 5.65 0.235 0.091 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.85 1.34 234s supply 1.34 31.92 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 3.85 1.34 234s supply 1.34 31.92 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.117 234s supply 0.117 1.000 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 234s price -0.2669 0.0778 -3.43 0.0016 ** 234s income 0.3011 0.0435 6.92 4.9e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.962 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 234s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: price ~ income + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 90.2167 10.4342 8.65 3.3e-10 *** 234s income 0.2331 0.0778 3.00 0.005 ** 234s farmPrice -0.1666 0.1111 -1.50 0.143 234s trend 0.3011 0.0435 6.92 4.9e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 5.65 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 234s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 234s 234s > 234s > ## ********* iterated SUR with 2 restrictions via R and restrict.regMat (methodResidCov="max") ********** 234s > # fitsuri5e <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "max", 234s > # restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 234s > # maxit = 100, useMatrix = useMatrix ) 234s > # print( summary( fitsuri5e ) ) 234s > # print( round( vcov( fitsuri5e ), digits = 6 ) ) 234s > # disabled, because the estimation does not converge 234s > 234s > ## ********* iterated WSUR with 2 restrictions via R and restrict.regMat (methodResidCov="Theil") ********** 234s > fitsurio5wr2 <- systemfit( system, "SUR", data = Kmenta, methodResidCov = "Theil", 234s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 234s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 234s > summary( fitsurio5wr2 ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s warning: convergence not achieved after 100 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 253 -1.67 0.527 0.927 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 95.8 5.63 2.37 0.643 0.601 234s supply 20 16 157.7 9.86 3.14 0.412 0.301 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 4.26 5.29 234s supply 5.29 6.69 234s 234s warning: this covariance matrix is NOT positive semidefinit! 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 5.63 7.56 234s supply 7.56 9.86 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.982 234s supply 0.982 1.000 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 234s price -0.0647 0.0815 -0.79 0.43 234s income 0.3007 0.0131 23.01 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 2.373 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 95.76 MSE: 5.633 Root MSE: 2.373 234s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.601 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: consump ~ price + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 234s price 0.4353 0.0815 5.34 5.7e-06 *** 234s farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 234s trend 0.3007 0.0131 23.01 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 3.14 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 157.737 MSE: 9.859 Root MSE: 3.14 234s Multiple R-Squared: 0.412 Adjusted R-Squared: 0.301 234s 234s > fitsuri5wr2 <- systemfit( system2, "SUR", data = Kmenta, methodResidCov = "Theil", 234s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 234s + maxit = 100, residCovWeighted = TRUE, useMatrix = useMatrix ) 234s > summary( fitsuri5wr2 ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 19 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 576 121 0.384 0.637 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 65.4 3.85 1.96 0.756 0.727 234s supply 20 16 510.8 31.92 5.65 0.235 0.091 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.85 1.34 234s supply 1.34 31.92 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 3.85 1.34 234s supply 1.34 31.92 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.117 234s supply 0.117 1.000 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 234s price -0.2669 0.0778 -3.43 0.0016 ** 234s income 0.3011 0.0435 6.92 4.9e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.962 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 234s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: price ~ income + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 90.2168 10.4342 8.65 3.3e-10 *** 234s income 0.2331 0.0778 3.00 0.005 ** 234s farmPrice -0.1666 0.1111 -1.50 0.143 234s trend 0.3011 0.0435 6.92 4.9e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 5.65 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 234s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 234s 234s > 234s > 234s > ## *********** estimations with a single regressor ************ 234s > fitsurS1 <- systemfit( 234s + list( price ~ consump - 1, farmPrice ~ consump + trend ), "SUR", 234s + data = Kmenta, useMatrix = useMatrix ) 234s > print( summary( fitsurS1 ) ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 36 2060 2543 0.449 0.465 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s eq1 20 19 848 44.6 6.68 -0.271 -0.271 234s eq2 20 17 1211 71.3 8.44 0.605 0.559 234s 234s The covariance matrix of the residuals used for estimation 234s eq1 eq2 234s eq1 44.6 -20.5 234s eq2 -20.5 68.9 234s 234s The covariance matrix of the residuals 234s eq1 eq2 234s eq1 44.6 -25.3 234s eq2 -25.3 71.3 234s 234s The correlations of the residuals 234s eq1 eq2 234s eq1 1.000 -0.448 234s eq2 -0.448 1.000 234s 234s 234s SUR estimates for 'eq1' (equation 1) 234s Model Formula: price ~ consump - 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s consump 0.9902 0.0148 66.9 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 6.682 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 848.208 MSE: 44.643 Root MSE: 6.682 234s Multiple R-Squared: -0.271 Adjusted R-Squared: -0.271 234s 234s 234s SUR estimates for 'eq2' (equation 2) 234s Model Formula: farmPrice ~ consump + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) -108.487 47.754 -2.27 0.03638 * 234s consump 2.123 0.477 4.45 0.00035 *** 234s trend -0.862 0.303 -2.85 0.01111 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 8.441 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 1211.393 MSE: 71.258 Root MSE: 8.441 234s Multiple R-Squared: 0.605 Adjusted R-Squared: 0.559 234s 234s > nobs( fitsurS1 ) 234s [1] 40 234s > fitsurS2 <- systemfit( 234s + list( consump ~ price - 1, consump ~ trend - 1 ), "SUR", 234s + data = Kmenta, useMatrix = useMatrix ) 234s > print( summary( fitsurS2 ) ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 38 47370 110949 -87.3 -5.28 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s eq1 20 19 861 45.3 6.73 -2.21 -2.21 234s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 234s 234s The covariance matrix of the residuals used for estimation 234s eq1 eq2 234s eq1 45.34 -5.15 234s eq2 -5.15 2447.84 234s 234s The covariance matrix of the residuals 234s eq1 eq2 234s eq1 45.34 -6.37 234s eq2 -6.37 2447.84 234s 234s The correlations of the residuals 234s eq1 eq2 234s eq1 1.0000 -0.0439 234s eq2 -0.0439 1.0000 234s 234s 234s SUR estimates for 'eq1' (equation 1) 234s Model Formula: consump ~ price - 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s price 1.006 0.015 67 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 6.734 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 861.496 MSE: 45.342 Root MSE: 6.734 234s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 234s 234s 234s SUR estimates for 'eq2' (equation 2) 234s Model Formula: consump ~ trend - 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s trend 7.410 0.924 8.02 1.6e-07 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 49.476 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 46508.986 MSE: 2447.841 Root MSE: 49.476 234s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 234s 234s > nobs( fitsurS2 ) 234s [1] 40 234s > fitsurS3 <- systemfit( 234s + list( consump ~ trend - 1, price ~ trend - 1 ), "SUR", 234s + data = Kmenta, useMatrix = useMatrix ) 234s > nobs( fitsurS3 ) 234s [1] 40 234s > print( summary( fitsurS3 ) ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 38 93537 108970 -99 -0.977 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s eq1 20 19 46509 2448 49.5 -172.5 -172.5 234s eq2 20 19 47028 2475 49.8 -69.5 -69.5 234s 234s The covariance matrix of the residuals used for estimation 234s eq1 eq2 234s eq1 2448 2439 234s eq2 2439 2475 234s 234s The covariance matrix of the residuals 234s eq1 eq2 234s eq1 2448 2439 234s eq2 2439 2475 234s 234s The correlations of the residuals 234s eq1 eq2 234s eq1 1.000 0.988 234s eq2 0.988 1.000 234s 234s 234s SUR estimates for 'eq1' (equation 1) 234s Model Formula: consump ~ trend - 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s trend 7.405 0.924 8.02 1.6e-07 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 49.476 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 234s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 234s 234s 234s SUR estimates for 'eq2' (equation 2) 234s Model Formula: price ~ trend - 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s trend 7.318 0.929 7.88 2.1e-07 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 49.751 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 234s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 234s 234s > fitsurS4 <- systemfit( 234s + list( consump ~ trend - 1, price ~ trend - 1 ), "SUR", 234s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 234s + useMatrix = useMatrix ) 234s > print( summary( fitsurS4 ) ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 39 93552 111731 -99 -1.03 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s eq1 20 19 46510 2448 49.5 -172.5 -172.5 234s eq2 20 19 47042 2476 49.8 -69.5 -69.5 234s 234s The covariance matrix of the residuals used for estimation 234s eq1 eq2 234s eq1 2448 2439 234s eq2 2439 2475 234s 234s The covariance matrix of the residuals 234s eq1 eq2 234s eq1 2448 2439 234s eq2 2439 2476 234s 234s The correlations of the residuals 234s eq1 eq2 234s eq1 1.000 0.988 234s eq2 0.988 1.000 234s 234s 234s SUR estimates for 'eq1' (equation 1) 234s Model Formula: consump ~ trend - 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s trend 7.388 0.923 8 9.4e-10 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 49.476 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 46509.787 MSE: 2447.884 Root MSE: 49.476 234s Multiple R-Squared: -172.47 Adjusted R-Squared: -172.47 234s 234s 234s SUR estimates for 'eq2' (equation 2) 234s Model Formula: price ~ trend - 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s trend 7.388 0.923 8 9.4e-10 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 49.758 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 47041.803 MSE: 2475.884 Root MSE: 49.758 234s Multiple R-Squared: -69.501 Adjusted R-Squared: -69.501 234s 234s > nobs( fitsurS4 ) 234s [1] 40 234s > fitsurS5 <- systemfit( 234s + list( consump ~ 1, price ~ 1 ), "SUR", 234s + data = Kmenta, useMatrix = useMatrix ) 234s > print( summary( fitsurS5 ) ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 38 935 491 0 0 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s eq1 20 19 268 14.1 3.76 0 0 234s eq2 20 19 667 35.1 5.93 0 0 234s 234s The covariance matrix of the residuals used for estimation 234s eq1 eq2 234s eq1 14.11 2.18 234s eq2 2.18 35.12 234s 234s The covariance matrix of the residuals 234s eq1 eq2 234s eq1 14.11 2.18 234s eq2 2.18 35.12 234s 234s The correlations of the residuals 234s eq1 eq2 234s eq1 1.0000 0.0981 234s eq2 0.0981 1.0000 234s 234s 234s SUR estimates for 'eq1' (equation 1) 234s Model Formula: consump ~ 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 100.90 0.84 120 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 3.756 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 234s Multiple R-Squared: 0 Adjusted R-Squared: 0 234s 234s 234s SUR estimates for 'eq2' (equation 2) 234s Model Formula: price ~ 1 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 100.02 1.33 75.5 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 5.926 on 19 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 19 234s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 234s Multiple R-Squared: 0 Adjusted R-Squared: 0 234s 234s > nobs( fitsurS5 ) 234s [1] 40 234s > 234s > 234s > ## **************** shorter summaries ********************** 234s > print( summary( fitsur1e2, useDfSys = TRUE, equations = FALSE ) ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 33 172 -0.896 0.679 1.01 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 66.8 3.93 1.98 0.751 0.722 234s supply 20 16 105.3 6.58 2.57 0.607 0.534 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.73 4.28 234s supply 4.28 5.78 234s 234s warning: this covariance matrix is NOT positive semidefinit! 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 3.93 5.17 234s supply 5.17 6.58 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.984 234s supply 0.984 1.000 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 99.2120 7.5127 13.21 1.0e-14 *** 234s demand_price -0.2667 0.0877 -3.04 0.0046 ** 234s demand_income 0.2908 0.0406 7.16 3.3e-08 *** 234s supply_(Intercept) 63.0768 10.9735 5.75 2.0e-06 *** 234s supply_price 0.1439 0.0943 1.52 0.1368 234s supply_farmPrice 0.2064 0.0384 5.37 6.1e-06 *** 234s supply_trend 0.3325 0.0640 5.19 1.0e-05 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( summary( fitsur2e, useDfSys = FALSE, residCov = FALSE ) ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 34 180 0.62 0.663 0.707 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 72.6 4.27 2.07 0.729 0.697 234s supply 20 16 107.9 6.75 2.60 0.597 0.522 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 98.7799 6.9687 14.17 7.6e-11 *** 234s price -0.2354 0.0795 -2.96 0.0088 ** 234s income 0.2631 0.0344 7.66 6.6e-07 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 2.066 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 72.577 MSE: 4.269 Root MSE: 2.066 234s Multiple R-Squared: 0.729 Adjusted R-Squared: 0.697 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: consump ~ price + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 67.6039 9.5712 7.06 2.7e-06 *** 234s price 0.1328 0.0853 1.56 0.14 234s farmPrice 0.1785 0.0305 5.85 2.5e-05 *** 234s trend 0.2631 0.0344 7.66 9.7e-07 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 2.597 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 107.917 MSE: 6.745 Root MSE: 2.597 234s Multiple R-Squared: 0.597 Adjusted R-Squared: 0.522 234s 234s > 234s > print( summary( fitsur3 ), equations = FALSE ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 34 179 0.933 0.665 0.753 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 71.6 4.21 2.05 0.733 0.702 234s supply 20 16 107.8 6.74 2.60 0.598 0.523 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.78 4.47 234s supply 4.47 5.94 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 4.21 5.24 234s supply 5.24 6.74 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.983 234s supply 0.983 1.000 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 98.8408 7.5581 13.08 8.0e-15 *** 234s demand_price -0.2398 0.0860 -2.79 0.0086 ** 234s demand_income 0.2670 0.0368 7.25 2.2e-08 *** 234s supply_(Intercept) 67.4283 10.6647 6.32 3.3e-07 *** 234s supply_price 0.1332 0.0953 1.40 0.1713 234s supply_farmPrice 0.1795 0.0337 5.33 6.3e-06 *** 234s supply_trend 0.2670 0.0368 7.25 2.2e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( summary( fitsur4r3 ), residCov = FALSE, equations = FALSE ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 173 0.217 0.677 0.702 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 66.4 3.91 1.98 0.752 0.723 234s supply 20 16 106.9 6.68 2.58 0.601 0.526 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 93.1978 7.3168 12.74 1.1e-14 *** 234s demand_price -0.2381 0.0829 -2.87 0.0069 ** 234s demand_income 0.3231 0.0170 18.96 < 2e-16 *** 234s supply_(Intercept) 49.3676 7.4381 6.64 1.1e-07 *** 234s supply_price 0.2619 0.0829 3.16 0.0033 ** 234s supply_farmPrice 0.2271 0.0171 13.29 3.1e-15 *** 234s supply_trend 0.3231 0.0170 18.96 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( summary( fitsur5, residCov = FALSE ), equations = FALSE ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 165 1.76 0.691 0.69 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 64 3.76 1.94 0.761 0.733 234s supply 20 16 101 6.34 2.52 0.622 0.551 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 96.8275 7.4665 12.97 6.2e-15 *** 234s demand_price -0.2798 0.0840 -3.33 0.002 ** 234s demand_income 0.3286 0.0206 15.93 < 2e-16 *** 234s supply_(Intercept) 52.9386 7.6655 6.91 5.1e-08 *** 234s supply_price 0.2202 0.0840 2.62 0.013 * 234s supply_farmPrice 0.2327 0.0212 10.97 7.2e-13 *** 234s supply_trend 0.3286 0.0206 15.93 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( summary( fitsur5w, equations = FALSE, residCov = FALSE ), 234s + equations = TRUE ) 234s 234s systemfit results 234s method: SUR 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 166 1.75 0.69 0.691 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 64.2 3.77 1.94 0.761 0.733 234s supply 20 16 102.0 6.37 2.52 0.620 0.548 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 96.4421 7.4234 12.99 6e-15 *** 234s price -0.2753 0.0838 -3.29 0.0023 ** 234s income 0.3280 0.0202 16.21 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.943 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 64.16 MSE: 3.774 Root MSE: 1.943 234s Multiple R-Squared: 0.761 Adjusted R-Squared: 0.733 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: consump ~ price + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 52.5761 7.6099 6.91 5.0e-08 *** 234s price 0.2247 0.0838 2.68 0.011 * 234s farmPrice 0.2318 0.0208 11.14 4.7e-13 *** 234s trend 0.3280 0.0202 16.21 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 2.524 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 101.967 MSE: 6.373 Root MSE: 2.524 234s Multiple R-Squared: 0.62 Adjusted R-Squared: 0.548 234s 234s > 234s > print( summary( fitsuri1r3, useDfSys = FALSE ), residCov = FALSE ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 7 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 33 109 4.06 0.884 0.96 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 66.8 3.93 1.98 0.751 0.721 234s supply 20 16 41.7 2.61 1.61 0.937 0.926 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 93.5427 7.3858 12.67 4.4e-10 *** 234s price -0.2285 0.0877 -2.60 0.019 * 234s income 0.3097 0.0458 6.76 3.3e-06 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.983 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 66.826 MSE: 3.931 Root MSE: 1.983 234s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: price ~ income + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 89.1830 3.3861 26.3 1.3e-14 *** 234s income 0.6639 0.0423 15.7 3.8e-11 *** 234s farmPrice -0.4715 0.0370 -12.8 8.5e-10 *** 234s trend -0.7955 0.0645 -12.3 1.4e-09 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.615 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 41.708 MSE: 2.607 Root MSE: 1.615 234s Multiple R-Squared: 0.937 Adjusted R-Squared: 0.926 234s 234s > 234s > print( summary( fitsuri2 ), residCov = FALSE ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 21 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 34 587 110 0.372 0.669 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 67 3.94 1.99 0.75 0.721 234s supply 20 16 520 32.52 5.70 0.22 0.074 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 107.3678 7.4986 14.32 4.4e-16 *** 234s price -0.3945 0.0912 -4.33 0.00013 *** 234s income 0.3382 0.0466 7.25 2.1e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.986 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 67.024 MSE: 3.943 Root MSE: 1.986 234s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: price ~ income + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 85.0448 12.1069 7.02 4.2e-08 *** 234s income 0.3125 0.1233 2.53 0.016 * 234s farmPrice -0.1972 0.1157 -1.70 0.097 . 234s trend 0.3382 0.0466 7.25 2.1e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 5.703 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 520.329 MSE: 32.521 Root MSE: 5.703 234s Multiple R-Squared: 0.22 Adjusted R-Squared: 0.074 234s 234s > 234s > print( summary( fitsuri3e, residCov = FALSE, equations = FALSE ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 22 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 34 588 74.9 0.372 0.664 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 67.5 3.97 1.99 0.748 0.719 234s supply 20 16 520.2 32.51 5.70 0.220 0.074 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 107.8051 6.9270 15.56 < 2e-16 *** 234s demand_price -0.3986 0.0843 -4.73 3.8e-05 *** 234s demand_income 0.3379 0.0431 7.84 4.0e-09 *** 234s supply_(Intercept) 85.1071 10.8287 7.86 3.8e-09 *** 234s supply_income 0.3106 0.1101 2.82 0.0079 ** 234s supply_farmPrice -0.1960 0.1034 -1.89 0.0667 . 234s supply_trend 0.3379 0.0431 7.84 4.0e-09 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( summary( fitsurio4, residCov = FALSE ), equations = FALSE ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 10 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 176 1.74 0.671 0.705 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 67.2 3.95 1.99 0.749 0.720 234s supply 20 16 109.2 6.83 2.61 0.593 0.516 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 92.4262 7.3543 12.57 1.6e-14 *** 234s demand_price -0.2276 0.0850 -2.68 0.0112 * 234s demand_income 0.3203 0.0185 17.32 < 2e-16 *** 234s supply_(Intercept) 48.7295 7.4587 6.53 1.5e-07 *** 234s supply_price 0.2724 0.0850 3.20 0.0029 ** 234s supply_farmPrice 0.2232 0.0190 11.76 1.0e-13 *** 234s supply_trend 0.3203 0.0185 17.32 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( summary( fitsuri4, equations = FALSE ), residCov = FALSE ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 19 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 575 121 0.385 0.637 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 65.5 3.85 1.96 0.756 0.727 234s supply 20 16 509.3 31.83 5.64 0.237 0.094 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 98.0356 6.7437 14.54 2.2e-16 *** 234s demand_price -0.2646 0.0777 -3.40 0.0017 ** 234s demand_income 0.3007 0.0436 6.89 5.3e-08 *** 234s supply_(Intercept) 90.0046 10.4367 8.62 3.5e-10 *** 234s supply_income 0.2354 0.0777 3.03 0.0046 ** 234s supply_farmPrice -0.1667 0.1108 -1.50 0.1416 234s supply_trend 0.3007 0.0436 6.89 5.3e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( summary( fitsuri4w, useDfSys = FALSE, equations = FALSE ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 18 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 575 121 0.385 0.637 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 65.5 3.85 1.96 0.756 0.727 234s supply 20 16 509.3 31.83 5.64 0.237 0.094 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 3.85 1.23 234s supply 1.23 31.83 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 3.85 1.23 234s supply 1.23 31.83 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.111 234s supply 0.111 1.000 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 98.0361 6.7437 14.54 5.1e-11 *** 234s demand_price -0.2646 0.0777 -3.40 0.0034 ** 234s demand_income 0.3007 0.0436 6.89 2.6e-06 *** 234s supply_(Intercept) 90.0052 10.4368 8.62 2.1e-07 *** 234s supply_income 0.2354 0.0777 3.03 0.0080 ** 234s supply_farmPrice -0.1667 0.1108 -1.50 0.1521 234s supply_trend 0.3007 0.0436 6.89 3.6e-06 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( summary( fitsurio5r2, equations = FALSE ) ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s warning: convergence not achieved after 100 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 253 -1.67 0.527 0.927 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 95.8 5.63 2.37 0.643 0.601 234s supply 20 16 157.7 9.86 3.14 0.412 0.301 234s 234s The covariance matrix of the residuals used for estimation 234s demand supply 234s demand 4.26 5.29 234s supply 5.29 6.69 234s 234s warning: this covariance matrix is NOT positive semidefinit! 234s 234s The covariance matrix of the residuals 234s demand supply 234s demand 5.63 7.56 234s supply 7.56 9.86 234s 234s The correlations of the residuals 234s demand supply 234s demand 1.000 0.982 234s supply 0.982 1.000 234s 234s 234s Coefficients: 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 78.0342 7.1638 10.89 8.6e-13 *** 234s demand_price -0.0647 0.0815 -0.79 0.43 234s demand_income 0.3007 0.0131 23.01 < 2e-16 *** 234s supply_(Intercept) 34.1958 7.2257 4.73 3.6e-05 *** 234s supply_price 0.4353 0.0815 5.34 5.7e-06 *** 234s supply_farmPrice 0.2070 0.0124 16.68 < 2e-16 *** 234s supply_trend 0.3007 0.0131 23.01 < 2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( summary( fitsuri5r2 ), residCov = FALSE ) 234s 234s systemfit results 234s method: iterated SUR 234s 234s convergence achieved after 21 iterations 234s 234s N DF SSR detRCov OLS-R2 McElroy-R2 234s system 40 35 576 121 0.384 0.637 234s 234s N DF SSR MSE RMSE R2 Adj R2 234s demand 20 17 65.4 3.85 1.96 0.756 0.727 234s supply 20 16 510.8 31.92 5.65 0.235 0.091 234s 234s 234s SUR estimates for 'demand' (equation 1) 234s Model Formula: consump ~ price + income 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 98.2200 6.7593 14.53 2.2e-16 *** 234s price -0.2669 0.0778 -3.43 0.0016 ** 234s income 0.3011 0.0435 6.92 4.9e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 1.962 on 17 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 17 234s SSR: 65.447 MSE: 3.85 Root MSE: 1.962 234s Multiple R-Squared: 0.756 Adjusted R-Squared: 0.727 234s 234s 234s SUR estimates for 'supply' (equation 2) 234s Model Formula: price ~ income + farmPrice + trend 234s 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 90.2167 10.4342 8.65 3.3e-10 *** 234s income 0.2331 0.0778 3.00 0.005 ** 234s farmPrice -0.1666 0.1111 -1.50 0.143 234s trend 0.3011 0.0435 6.92 4.9e-08 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s Residual standard error: 5.65 on 16 degrees of freedom 234s Number of observations: 20 Degrees of Freedom: 16 234s SSR: 510.75 MSE: 31.922 Root MSE: 5.65 234s Multiple R-Squared: 0.235 Adjusted R-Squared: 0.091 234s 234s > 234s > 234s > ## ****************** residuals ************************** 234s > print( residuals( fitsur1e2 ) ) 234s demand supply 234s 1 0.615 0.41825 234s 2 -0.598 -0.00625 234s 3 2.419 2.75649 234s 4 1.609 1.81727 234s 5 2.145 2.53566 234s 6 1.332 1.53338 234s 7 1.727 2.25581 234s 8 -2.718 -3.56834 234s 9 -1.229 -2.02733 234s 10 2.088 2.53245 234s 11 -0.789 -1.40733 234s 12 -2.799 -3.01416 234s 13 -1.831 -2.30119 234s 14 -0.461 0.01871 234s 15 1.974 2.93624 234s 16 -3.291 -4.00484 234s 17 -0.652 -0.45580 234s 18 -1.899 -3.18683 234s 19 2.030 2.18284 234s 20 0.329 0.98497 234s > print( residuals( fitsur1e2$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 234s 0.41825 -0.00625 2.75649 1.81727 2.53566 1.53338 2.25581 -3.56834 234s 9 10 11 12 13 14 15 16 234s -2.02733 2.53245 -1.40733 -3.01416 -2.30119 0.01871 2.93624 -4.00484 234s 17 18 19 20 234s -0.45580 -3.18683 2.18284 0.98497 234s > 234s > print( residuals( fitsur1w ) ) 234s demand supply 234s 1 0.696 0.4713 234s 2 -0.561 0.0197 234s 3 2.455 2.7782 234s 4 1.643 1.8366 234s 5 2.110 2.4709 234s 6 1.304 1.4773 234s 7 1.692 2.2079 234s 8 -2.756 -3.6663 234s 9 -1.253 -2.0985 234s 10 2.078 2.5321 234s 11 -0.675 -1.2705 234s 12 -2.649 -2.8068 234s 13 -1.706 -2.1305 234s 14 -0.419 0.1150 234s 15 1.887 2.8772 234s 16 -3.364 -4.1013 234s 17 -0.762 -0.5650 234s 18 -1.918 -3.2183 234s 19 1.978 2.1637 234s 20 0.218 0.9075 234s > print( residuals( fitsur1w$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 0.4713 0.0197 2.7782 1.8366 2.4709 1.4773 2.2079 -3.6663 -2.0985 2.5321 234s 11 12 13 14 15 16 17 18 19 20 234s -1.2705 -2.8068 -2.1305 0.1150 2.8772 -4.1013 -0.5650 -3.2183 2.1637 0.9075 234s > 234s > print( residuals( fitsur2e ) ) 234s demand supply 234s 1 0.325 -0.200 234s 2 -0.729 -0.481 234s 3 2.288 2.342 234s 4 1.487 1.457 234s 5 2.271 2.527 234s 6 1.432 1.537 234s 7 1.851 2.275 234s 8 -2.582 -3.322 234s 9 -1.143 -1.834 234s 10 2.124 2.512 234s 11 -1.193 -1.885 234s 12 -3.332 -3.705 234s 13 -2.280 -2.813 234s 14 -0.614 -0.177 234s 15 2.281 3.353 234s 16 -3.032 -3.407 234s 17 -0.260 0.233 234s 18 -1.834 -2.737 234s 19 2.215 2.632 234s 20 0.726 1.692 234s > print( residuals( fitsur2e$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 234s 0.325 -0.729 2.288 1.487 2.271 1.432 1.851 -2.582 -1.143 2.124 -1.193 234s 12 13 14 15 16 17 18 19 20 234s -3.332 -2.280 -0.614 2.281 -3.032 -0.260 -1.834 2.215 0.726 234s > 234s > print( residuals( fitsur3 ) ) 234s demand supply 234s 1 0.366 -0.164 234s 2 -0.711 -0.452 234s 3 2.307 2.368 234s 4 1.504 1.479 234s 5 2.253 2.535 234s 6 1.418 1.544 234s 7 1.833 2.279 234s 8 -2.601 -3.327 234s 9 -1.155 -1.839 234s 10 2.119 2.513 234s 11 -1.136 -1.869 234s 12 -3.257 -3.682 234s 13 -2.217 -2.798 234s 14 -0.593 -0.175 234s 15 2.238 3.332 234s 16 -3.069 -3.436 234s 17 -0.315 0.199 234s 18 -1.844 -2.764 234s 19 2.189 2.604 234s 20 0.671 1.654 234s > print( residuals( fitsur3$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 234s -0.164 -0.452 2.368 1.479 2.535 1.544 2.279 -3.327 -1.839 2.513 -1.869 234s 12 13 14 15 16 17 18 19 20 234s -3.682 -2.798 -0.175 3.332 -3.436 0.199 -2.764 2.604 1.654 234s > 234s > print( residuals( fitsur4r3 ) ) 234s demand supply 234s 1 0.934 0.265 234s 2 -0.721 -0.638 234s 3 2.348 2.232 234s 4 1.459 1.196 234s 5 2.129 2.428 234s 6 1.253 1.318 234s 7 1.514 1.913 234s 8 -3.185 -4.425 234s 9 -1.097 -1.870 234s 10 2.619 3.483 234s 11 0.135 -0.260 234s 12 -2.097 -2.275 234s 13 -1.496 -2.085 234s 14 -0.201 0.516 234s 15 1.934 3.439 234s 16 -3.491 -3.942 234s 17 -0.229 0.913 234s 18 -2.236 -3.503 234s 19 1.440 1.736 234s 20 -1.012 -0.441 234s > print( residuals( fitsur4r3$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 234s 0.934 -0.721 2.348 1.459 2.129 1.253 1.514 -3.185 -1.097 2.619 0.135 234s 12 13 14 15 16 17 18 19 20 234s -2.097 -1.496 -0.201 1.934 -3.491 -0.229 -2.236 1.440 -1.012 234s > 234s > print( residuals( fitsur5 ) ) 234s demand supply 234s 1 1.0025 0.3219 234s 2 -0.5449 -0.4286 234s 3 2.4949 2.4014 234s 4 1.6426 1.4106 234s 5 2.0329 2.2956 234s 6 1.2129 1.2545 234s 7 1.5260 1.9262 234s 8 -3.0444 -4.2868 234s 9 -1.2406 -2.0779 234s 10 2.3001 3.0973 234s 11 -0.0303 -0.4650 234s 12 -2.0337 -2.1783 234s 13 -1.3041 -1.8356 234s 14 -0.2155 0.5292 234s 15 1.6991 3.1787 234s 16 -3.5980 -4.0840 234s 17 -0.7860 0.2371 234s 18 -2.1070 -3.3544 234s 19 1.6070 1.9694 234s 20 -0.6134 0.0885 234s > print( residuals( fitsur5$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 0.3219 -0.4286 2.4014 1.4106 2.2956 1.2545 1.9262 -4.2868 -2.0779 3.0973 234s 11 12 13 14 15 16 17 18 19 20 234s -0.4650 -2.1783 -1.8356 0.5292 3.1787 -4.0840 0.2371 -3.3544 1.9694 0.0885 234s > 234s > print( residuals( fitsuri1r3 ) ) 234s demand supply 234s 1 0.7952 0.123 234s 2 -0.7614 -1.393 234s 3 2.3039 -0.829 234s 4 1.4250 -0.430 234s 5 2.1792 -1.213 234s 6 1.2979 -0.653 234s 7 1.5795 -1.266 234s 8 -3.0935 2.153 234s 9 -1.0750 1.548 234s 10 2.5876 -1.582 234s 11 -0.0991 0.990 234s 12 -2.3616 0.460 234s 13 -1.6970 1.335 234s 14 -0.2819 -1.054 234s 15 2.0557 -2.339 234s 16 -3.3745 1.734 234s 17 -0.1140 -1.054 234s 18 -2.1822 3.461 234s 19 1.5612 0.318 234s 20 -0.7450 -0.308 234s > print( residuals( fitsuri1r3$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 0.7952 -0.7614 2.3039 1.4250 2.1792 1.2979 1.5795 -3.0935 -1.0750 2.5876 234s 11 12 13 14 15 16 17 18 19 20 234s -0.0991 -2.3616 -1.6970 -0.2819 2.0557 -3.3745 -0.1140 -2.1822 1.5612 -0.7450 234s > 234s > print( residuals( fitsuri2 ) ) 234s demand supply 234s 1 1.1341 6.955 234s 2 -0.0587 7.587 234s 3 2.8946 6.701 234s 4 2.1508 6.768 234s 5 1.7798 1.930 234s 6 1.1200 2.315 234s 7 1.5920 2.230 234s 8 -2.5983 4.980 234s 9 -1.6414 -0.392 234s 10 1.3742 -5.140 234s 11 -0.6115 -3.174 234s 12 -1.9764 -0.804 234s 13 -0.8493 1.012 234s 14 -0.2942 -3.282 234s 15 1.0840 -7.042 234s 16 -3.8500 -4.140 234s 17 -2.3259 -12.628 234s 18 -1.7141 -1.498 234s 19 2.1409 -2.683 234s 20 0.6494 0.305 234s > print( residuals( fitsuri2$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 6.955 7.587 6.701 6.768 1.930 2.315 2.230 4.980 -0.392 -5.140 234s 11 12 13 14 15 16 17 18 19 20 234s -3.174 -0.804 1.012 -3.282 -7.042 -4.140 -12.628 -1.498 -2.683 0.305 234s > 234s > print( residuals( fitsuri3e ) ) 234s demand supply 234s 1 1.1327 6.932 234s 2 -0.0412 7.582 234s 3 2.9085 6.695 234s 4 2.1695 6.766 234s 5 1.7721 1.915 234s 6 1.1185 2.305 234s 7 1.5978 2.229 234s 8 -2.5761 4.982 234s 9 -1.6564 -0.410 234s 10 1.3358 -5.161 234s 11 -0.6458 -3.196 234s 12 -1.9868 -0.807 234s 13 -0.8408 1.021 234s 14 -0.3012 -3.275 234s 15 1.0652 -7.037 234s 16 -3.8545 -4.135 234s 17 -2.3819 -12.646 234s 18 -1.6959 -1.478 234s 19 2.1679 -2.647 234s 20 0.7125 0.366 234s > print( residuals( fitsuri3e$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 1.1327 -0.0412 2.9085 2.1695 1.7721 1.1185 1.5978 -2.5761 -1.6564 1.3358 234s 11 12 13 14 15 16 17 18 19 20 234s -0.6458 -1.9868 -0.8408 -0.3012 1.0652 -3.8545 -2.3819 -1.6959 2.1679 0.7125 234s > 234s > print( residuals( fitsurio4 ) ) 234s demand supply 234s 1 0.9019 0.240 234s 2 -0.7658 -0.697 234s 3 2.3097 2.184 234s 4 1.4141 1.136 234s 5 2.1571 2.490 234s 6 1.2670 1.356 234s 7 1.5188 1.928 234s 8 -3.2060 -4.430 234s 9 -1.0620 -1.789 234s 10 2.6864 3.589 234s 11 0.1438 -0.248 234s 12 -2.1427 -2.369 234s 13 -1.5629 -2.210 234s 14 -0.2076 0.479 234s 15 2.0012 3.526 234s 16 -3.4530 -3.876 234s 17 -0.0902 1.129 234s 18 -2.2581 -3.539 234s 19 1.4172 1.671 234s 20 -1.0688 -0.569 234s > print( residuals( fitsurio4$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 234s 0.240 -0.697 2.184 1.136 2.490 1.356 1.928 -4.430 -1.789 3.589 -0.248 234s 12 13 14 15 16 17 18 19 20 234s -2.369 -2.210 0.479 3.526 -3.876 1.129 -3.539 1.671 -0.569 234s > print( residuals( fitsuri4 ) ) 234s demand supply 234s 1 0.7146 5.775 234s 2 -0.6076 7.198 234s 3 2.4197 6.280 234s 4 1.5931 6.531 234s 5 2.1268 1.465 234s 6 1.3043 2.021 234s 7 1.6685 2.261 234s 8 -2.8295 5.275 234s 9 -1.2125 -0.890 234s 10 2.1921 -5.945 234s 11 -0.5521 -4.407 234s 12 -2.5920 -1.482 234s 13 -1.7095 0.895 234s 14 -0.3902 -3.220 234s 15 1.9290 -6.617 234s 16 -3.3627 -3.607 234s 17 -0.6125 -12.896 234s 18 -1.9758 -0.562 234s 19 1.8877 -1.126 234s 20 0.0085 3.051 234s > print( residuals( fitsuri4$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 5.775 7.198 6.280 6.531 1.465 2.021 2.261 5.275 -0.890 -5.945 234s 11 12 13 14 15 16 17 18 19 20 234s -4.407 -1.482 0.895 -3.220 -6.617 -3.607 -12.896 -0.562 -1.126 3.051 234s > 234s > print( residuals( fitsuri4w ) ) 234s demand supply 234s 1 0.71463 5.775 234s 2 -0.60754 7.198 234s 3 2.41972 6.280 234s 4 1.59308 6.531 234s 5 2.12679 1.465 234s 6 1.30430 2.021 234s 7 1.66846 2.262 234s 8 -2.82945 5.275 234s 9 -1.21248 -0.890 234s 10 2.19209 -5.946 234s 11 -0.55215 -4.407 234s 12 -2.59194 -1.482 234s 13 -1.70948 0.895 234s 14 -0.39018 -3.220 234s 15 1.92897 -6.617 234s 16 -3.36276 -3.607 234s 17 -0.61256 -12.896 234s 18 -1.97579 -0.562 234s 19 1.88776 -1.126 234s 20 0.00854 3.051 234s > print( residuals( fitsuri4w$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 5.775 7.198 6.280 6.531 1.465 2.021 2.262 5.275 -0.890 -5.946 234s 11 12 13 14 15 16 17 18 19 20 234s -4.407 -1.482 0.895 -3.220 -6.617 -3.607 -12.896 -0.562 -1.126 3.051 234s > 234s > print( residuals( fitsurio5r2 ) ) 234s demand supply 234s 1 0.655 0.0269 234s 2 -1.456 -1.5152 234s 3 1.737 1.5210 234s 4 0.696 0.3020 234s 5 2.530 2.9397 234s 6 1.417 1.5469 234s 7 1.459 1.8336 234s 8 -3.779 -5.0391 234s 9 -0.498 -1.0416 234s 10 3.950 5.0761 234s 11 0.836 0.6398 234s 12 -2.347 -2.5930 234s 13 -2.286 -3.0468 234s 14 -0.137 0.5081 234s 15 2.908 4.5036 234s 16 -3.050 -3.3786 234s 17 2.091 3.6824 234s 18 -2.775 -4.1107 234s 19 0.737 0.7819 234s 20 -2.686 -2.6370 234s > print( residuals( fitsurio5r2$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 234s 0.655 -1.456 1.737 0.696 2.530 1.417 1.459 -3.779 -0.498 3.950 0.836 234s 12 13 14 15 16 17 18 19 20 234s -2.347 -2.286 -0.137 2.908 -3.050 2.091 -2.775 0.737 -2.686 234s > print( residuals( fitsuri5r2 ) ) 234s demand supply 234s 1 0.7199 5.756 234s 2 -0.5979 7.202 234s 3 2.4279 6.281 234s 4 1.6030 6.535 234s 5 2.1212 1.472 234s 6 1.3017 2.029 234s 7 1.6683 2.275 234s 8 -2.8233 5.299 234s 9 -1.2202 -0.892 234s 10 2.1760 -5.965 234s 11 -0.5578 -4.458 234s 12 -2.5854 -1.528 234s 13 -1.6970 0.866 234s 14 -0.3899 -3.237 234s 15 1.9153 -6.607 234s 16 -3.3698 -3.593 234s 17 -0.6429 -12.902 234s 18 -1.9698 -0.549 234s 19 1.8949 -1.099 234s 20 0.0259 3.114 234s > print( residuals( fitsuri5r2$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 234s 0.7199 -0.5979 2.4279 1.6030 2.1212 1.3017 1.6683 -2.8233 -1.2202 2.1760 234s 11 12 13 14 15 16 17 18 19 20 234s -0.5578 -2.5854 -1.6970 -0.3899 1.9153 -3.3698 -0.6429 -1.9698 1.8949 0.0259 234s > 234s > 234s > ## *************** coefficients ********************* 234s > print( round( coef( fitsur1r3 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income supply_(Intercept) 234s 99.225 -0.268 0.292 62.958 234s supply_price supply_farmPrice supply_trend 234s 0.144 0.207 0.333 234s > print( round( coef( fitsur1r3$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) price farmPrice trend 234s 62.958 0.144 0.207 0.333 234s > 234s > print( round( coef( fitsuri2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income supply_(Intercept) 234s 107.368 -0.394 0.338 85.045 234s supply_income supply_farmPrice supply_trend 234s 0.312 -0.197 0.338 234s > print( round( coef( fitsuri2$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s 107.368 -0.394 0.338 234s > 234s > print( round( coef( fitsur2we ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income supply_(Intercept) 234s 98.754 -0.234 0.261 67.888 234s supply_price supply_farmPrice supply_trend 234s 0.132 0.177 0.261 234s > print( round( coef( fitsur2we$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s 98.754 -0.234 0.261 234s > 234s > print( round( coef( fitsur3 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income supply_(Intercept) 234s 98.841 -0.240 0.267 67.428 234s supply_price supply_farmPrice supply_trend 234s 0.133 0.179 0.267 234s > print( round( coef( fitsur3, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s 98.841 -0.240 0.267 67.428 0.133 0.179 234s > print( round( coef( fitsur3$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) price farmPrice trend 234s 67.428 0.133 0.179 0.267 234s > 234s > print( round( coef( fitsur4r2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income supply_(Intercept) 234s 92.527 -0.230 0.322 48.701 234s supply_price supply_farmPrice supply_trend 234s 0.270 0.226 0.322 234s > print( round( coef( fitsur4r2$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s 92.527 -0.230 0.322 234s > 234s > print( round( coef( fitsuri5e ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income supply_(Intercept) 234s 97.630 -0.258 0.298 89.544 234s supply_income supply_farmPrice supply_trend 234s 0.242 -0.169 0.298 234s > print( round( coef( fitsuri5e, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s 97.630 -0.258 0.298 89.544 0.242 -0.169 234s > print( round( coef( fitsuri5e$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) income farmPrice trend 234s 89.544 0.242 -0.169 0.298 234s > 234s > print( round( coef( fitsur5w ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income supply_(Intercept) 234s 96.442 -0.275 0.328 52.576 234s supply_price supply_farmPrice supply_trend 234s 0.225 0.232 0.328 234s > print( round( coef( fitsur5w, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s 96.442 -0.275 0.328 52.576 0.225 0.232 234s > print( round( coef( fitsur5w$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s 96.442 -0.275 0.328 234s > 234s > 234s > ## *************** coefficients with stats ********************* 234s > print( round( coef( summary( fitsur1r3 ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 99.225 7.5129 13.21 0.000000 234s demand_price -0.268 0.0878 -3.05 0.007262 234s demand_income 0.292 0.0408 7.15 0.000002 234s supply_(Intercept) 62.958 10.9850 5.73 0.000031 234s supply_price 0.144 0.0944 1.53 0.145991 234s supply_farmPrice 0.207 0.0386 5.37 0.000062 234s supply_trend 0.333 0.0644 5.18 0.000092 234s > print( round( coef( summary( fitsur1r3$eq[[ 2 ]] ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 62.958 10.9850 5.73 0.000031 234s price 0.144 0.0944 1.53 0.145991 234s farmPrice 0.207 0.0386 5.37 0.000062 234s trend 0.333 0.0644 5.18 0.000092 234s > 234s > print( round( coef( summary( fitsuri2, useDfSys = FALSE ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 107.368 7.4986 14.32 0.000000 234s demand_price -0.394 0.0912 -4.33 0.000459 234s demand_income 0.338 0.0466 7.25 0.000001 234s supply_(Intercept) 85.045 12.1069 7.02 0.000003 234s supply_income 0.312 0.1233 2.53 0.022132 234s supply_farmPrice -0.197 0.1157 -1.70 0.107654 234s supply_trend 0.338 0.0466 7.25 0.000002 234s > print( round( coef( summary( fitsuri2$eq[[ 1 ]], useDfSys = FALSE ) ), 234s + digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 107.368 7.4986 14.32 0.000000 234s price -0.394 0.0912 -4.33 0.000459 234s income 0.338 0.0466 7.25 0.000001 234s > 234s > print( round( coef( summary( fitsur3 ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 98.841 7.5581 13.08 0.000000 234s demand_price -0.240 0.0860 -2.79 0.008613 234s demand_income 0.267 0.0368 7.25 0.000000 234s supply_(Intercept) 67.428 10.6647 6.32 0.000000 234s supply_price 0.133 0.0953 1.40 0.171250 234s supply_farmPrice 0.179 0.0337 5.33 0.000006 234s supply_trend 0.267 0.0368 7.25 0.000000 234s > print( round( coef( summary( fitsur3 ), modified.regMat = TRUE ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s C1 98.841 7.5581 13.08 0.000000 234s C2 -0.240 0.0860 -2.79 0.008613 234s C3 0.267 0.0368 7.25 0.000000 234s C4 67.428 10.6647 6.32 0.000000 234s C5 0.133 0.0953 1.40 0.171250 234s C6 0.179 0.0337 5.33 0.000006 234s > print( round( coef( summary( fitsur3$eq[[ 2 ]] ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 67.428 10.6647 6.32 0.000000 234s price 0.133 0.0953 1.40 0.171250 234s farmPrice 0.179 0.0337 5.33 0.000006 234s trend 0.267 0.0368 7.25 0.000000 234s > 234s > print( round( coef( summary( fitsuri3we ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 107.806 6.9270 15.56 0.000000 234s demand_price -0.399 0.0843 -4.73 0.000038 234s demand_income 0.338 0.0431 7.84 0.000000 234s supply_(Intercept) 85.107 10.8288 7.86 0.000000 234s supply_income 0.311 0.1101 2.82 0.007950 234s supply_farmPrice -0.196 0.1034 -1.89 0.066671 234s supply_trend 0.338 0.0431 7.84 0.000000 234s > print( round( coef( summary( fitsuri3we ), modified.regMat = TRUE ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s C1 107.806 6.9270 15.56 0.000000 234s C2 -0.399 0.0843 -4.73 0.000038 234s C3 0.338 0.0431 7.84 0.000000 234s C4 85.107 10.8288 7.86 0.000000 234s C5 0.311 0.1101 2.82 0.007950 234s C6 -0.196 0.1034 -1.89 0.066671 234s > print( round( coef( summary( fitsuri3we$eq[[ 1 ]] ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 107.806 6.9270 15.56 0.0e+00 234s price -0.399 0.0843 -4.73 3.8e-05 234s income 0.338 0.0431 7.84 0.0e+00 234s > 234s > print( round( coef( summary( fitsur4r2 ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 92.527 7.2896 12.69 0.00000 234s demand_price -0.230 0.0827 -2.79 0.00855 234s demand_income 0.322 0.0166 19.37 0.00000 234s supply_(Intercept) 48.701 7.4034 6.58 0.00000 234s supply_price 0.270 0.0827 3.26 0.00248 234s supply_farmPrice 0.226 0.0166 13.62 0.00000 234s supply_trend 0.322 0.0166 19.37 0.00000 234s > print( round( coef( summary( fitsur4r2$eq[[ 1 ]] ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 92.527 7.2896 12.69 0.00000 234s price -0.230 0.0827 -2.79 0.00855 234s income 0.322 0.0166 19.37 0.00000 234s > 234s > print( round( coef( summary( fitsur4we ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 96.941 6.8894 14.07 0.000000 234s demand_price -0.281 0.0766 -3.67 0.000796 234s demand_income 0.329 0.0181 18.18 0.000000 234s supply_(Intercept) 52.996 7.0652 7.50 0.000000 234s supply_price 0.219 0.0766 2.85 0.007215 234s supply_farmPrice 0.234 0.0183 12.76 0.000000 234s supply_trend 0.329 0.0181 18.18 0.000000 234s > print( round( coef( summary( fitsur4we$eq[[ 2 ]] ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 52.996 7.0652 7.50 0.00000 234s price 0.219 0.0766 2.85 0.00722 234s farmPrice 0.234 0.0183 12.76 0.00000 234s trend 0.329 0.0181 18.18 0.00000 234s > 234s > print( round( coef( summary( fitsuri5e, useDfSys = FALSE ) ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s demand_(Intercept) 97.630 6.1560 15.86 0.000000 234s demand_price -0.258 0.0709 -3.63 0.002060 234s demand_income 0.298 0.0403 7.38 0.000001 234s supply_(Intercept) 89.544 9.3372 9.59 0.000000 234s supply_income 0.242 0.0709 3.42 0.003516 234s supply_farmPrice -0.169 0.0988 -1.71 0.107123 234s supply_trend 0.298 0.0403 7.38 0.000002 234s > print( round( coef( summary( fitsuri5e, useDfSys = FALSE ), 234s + modified.regMat = TRUE ), digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s C1 97.630 6.1560 15.86 NA 234s C2 -0.258 0.0709 -3.63 NA 234s C3 0.298 0.0403 7.38 NA 234s C4 89.544 9.3372 9.59 NA 234s C5 0.242 0.0709 3.42 NA 234s C6 -0.169 0.0988 -1.71 NA 234s > print( round( coef( summary( fitsuri5e$eq[[ 2 ]], useDfSys = FALSE ) ), 234s + digits = 6 ) ) 234s Estimate Std. Error t value Pr(>|t|) 234s (Intercept) 89.544 9.3372 9.59 0.000000 234s income 0.242 0.0709 3.42 0.003516 234s farmPrice -0.169 0.0988 -1.71 0.107123 234s trend 0.298 0.0403 7.38 0.000002 234s > 234s > 234s > ## *********** variance covariance matrix of the coefficients ******* 234s > print( round( vcov( fitsur1e2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 56.4403 -0.58751 0.025716 234s demand_price -0.5875 0.00769 -0.001866 234s demand_income 0.0257 -0.00187 0.001650 234s supply_(Intercept) 61.0550 -0.40370 -0.209805 234s supply_price -0.6325 0.00579 0.000546 234s supply_farmPrice 0.0215 -0.00156 0.001379 234s supply_trend 0.0327 -0.00237 0.002095 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 61.055 -0.632489 0.021495 234s demand_price -0.404 0.005792 -0.001559 234s demand_income -0.210 0.000546 0.001379 234s supply_(Intercept) 120.418 -0.954714 -0.221454 234s supply_price -0.955 0.008900 0.000584 234s supply_farmPrice -0.221 0.000584 0.001476 234s supply_trend -0.309 0.000772 0.001950 234s supply_trend 234s demand_(Intercept) 0.032652 234s demand_price -0.002369 234s demand_income 0.002095 234s supply_(Intercept) -0.308674 234s supply_price 0.000772 234s supply_farmPrice 0.001950 234s supply_trend 0.004100 234s > print( round( vcov( fitsur1e2$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 56.4403 -0.58751 0.02572 234s price -0.5875 0.00769 -0.00187 234s income 0.0257 -0.00187 0.00165 234s > 234s > print( round( vcov( fitsur1r3 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 56.4432 -0.58772 0.025901 234s demand_price -0.5877 0.00771 -0.001879 234s demand_income 0.0259 -0.00188 0.001662 234s supply_(Intercept) 60.8607 -0.40086 -0.210729 234s supply_price -0.6307 0.00577 0.000548 234s supply_farmPrice 0.0216 -0.00157 0.001385 234s supply_trend 0.0328 -0.00238 0.002104 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 60.861 -0.630659 0.021589 234s demand_price -0.401 0.005771 -0.001566 234s demand_income -0.211 0.000548 0.001385 234s supply_(Intercept) 120.671 -0.955395 -0.223176 234s supply_price -0.955 0.008902 0.000589 234s supply_farmPrice -0.223 0.000589 0.001487 234s supply_trend -0.310 0.000776 0.001959 234s supply_trend 234s demand_(Intercept) 0.032796 234s demand_price -0.002379 234s demand_income 0.002104 234s supply_(Intercept) -0.310422 234s supply_price 0.000776 234s supply_farmPrice 0.001959 234s supply_trend 0.004149 234s > print( round( vcov( fitsur1r3$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) price farmPrice trend 234s (Intercept) 120.671 -0.955395 -0.223176 -0.310422 234s price -0.955 0.008902 0.000589 0.000776 234s farmPrice -0.223 0.000589 0.001487 0.001959 234s trend -0.310 0.000776 0.001959 0.004149 234s > 234s > print( round( vcov( fitsur2e ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 48.5631 -0.50188 0.018400 234s demand_price -0.5019 0.00632 -0.001335 234s demand_income 0.0184 -0.00134 0.001180 234s supply_(Intercept) 53.2014 -0.39283 -0.140738 234s supply_price -0.5462 0.00510 0.000373 234s supply_farmPrice 0.0147 -0.00107 0.000942 234s supply_trend 0.0184 -0.00134 0.001180 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 53.201 -0.546194 0.014689 234s demand_price -0.393 0.005097 -0.001066 234s demand_income -0.141 0.000373 0.000942 234s supply_(Intercept) 91.607 -0.766739 -0.136644 234s supply_price -0.767 0.007271 0.000368 234s supply_farmPrice -0.137 0.000368 0.000931 234s supply_trend -0.141 0.000373 0.000942 234s supply_trend 234s demand_(Intercept) 0.018400 234s demand_price -0.001335 234s demand_income 0.001180 234s supply_(Intercept) -0.140738 234s supply_price 0.000373 234s supply_farmPrice 0.000942 234s supply_trend 0.001180 234s > print( round( vcov( fitsur2e$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 48.5631 -0.50188 0.01840 234s price -0.5019 0.00632 -0.00134 234s income 0.0184 -0.00134 0.00118 234s > 234s > print( round( vcov( fitsur3 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 57.1254 -0.58989 0.02116 234s demand_price -0.5899 0.00739 -0.00153 234s demand_income 0.0212 -0.00153 0.00136 234s supply_(Intercept) 64.5952 -0.48211 -0.16560 234s supply_price -0.6626 0.00619 0.00044 234s supply_farmPrice 0.0173 -0.00126 0.00111 234s supply_trend 0.0212 -0.00153 0.00136 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 64.595 -0.662552 0.017322 234s demand_price -0.482 0.006195 -0.001257 234s demand_income -0.166 0.000440 0.001111 234s supply_(Intercept) 113.736 -0.956493 -0.165927 234s supply_price -0.956 0.009084 0.000448 234s supply_farmPrice -0.166 0.000448 0.001133 234s supply_trend -0.166 0.000440 0.001111 234s supply_trend 234s demand_(Intercept) 0.02116 234s demand_price -0.00153 234s demand_income 0.00136 234s supply_(Intercept) -0.16560 234s supply_price 0.00044 234s supply_farmPrice 0.00111 234s supply_trend 0.00136 234s > print( round( vcov( fitsur3, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s C1 57.1254 -0.58989 0.02116 64.595 -0.662552 0.017322 234s C2 -0.5899 0.00739 -0.00153 -0.482 0.006195 -0.001257 234s C3 0.0212 -0.00153 0.00136 -0.166 0.000440 0.001111 234s C4 64.5952 -0.48211 -0.16560 113.736 -0.956493 -0.165927 234s C5 -0.6626 0.00619 0.00044 -0.956 0.009084 0.000448 234s C6 0.0173 -0.00126 0.00111 -0.166 0.000448 0.001133 234s > print( round( vcov( fitsur3$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) price farmPrice trend 234s (Intercept) 113.736 -0.956493 -0.165927 -0.16560 234s price -0.956 0.009084 0.000448 0.00044 234s farmPrice -0.166 0.000448 0.001133 0.00111 234s trend -0.166 0.000440 0.001111 0.00136 234s > 234s > print( round( vcov( fitsur3w ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 56.7267 -0.58513 0.020348 234s demand_price -0.5851 0.00729 -0.001476 234s demand_income 0.0203 -0.00148 0.001305 234s supply_(Intercept) 64.8820 -0.48999 -0.160451 234s supply_price -0.6648 0.00623 0.000426 234s supply_farmPrice 0.0168 -0.00122 0.001077 234s supply_trend 0.0203 -0.00148 0.001305 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 64.882 -0.664819 0.016795 234s demand_price -0.490 0.006231 -0.001219 234s demand_income -0.160 0.000426 0.001077 234s supply_(Intercept) 113.543 -0.959668 -0.161181 234s supply_price -0.960 0.009129 0.000435 234s supply_farmPrice -0.161 0.000435 0.001100 234s supply_trend -0.160 0.000426 0.001077 234s supply_trend 234s demand_(Intercept) 0.020348 234s demand_price -0.001476 234s demand_income 0.001305 234s supply_(Intercept) -0.160451 234s supply_price 0.000426 234s supply_farmPrice 0.001077 234s supply_trend 0.001305 234s > print( round( vcov( fitsur3w, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s C1 56.7267 -0.58513 0.020348 64.882 -0.664819 0.016795 234s C2 -0.5851 0.00729 -0.001476 -0.490 0.006231 -0.001219 234s C3 0.0203 -0.00148 0.001305 -0.160 0.000426 0.001077 234s C4 64.8820 -0.48999 -0.160451 113.543 -0.959668 -0.161181 234s C5 -0.6648 0.00623 0.000426 -0.960 0.009129 0.000435 234s C6 0.0168 -0.00122 0.001077 -0.161 0.000435 0.001100 234s > print( round( vcov( fitsur3w$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 56.7267 -0.58513 0.02035 234s price -0.5851 0.00729 -0.00148 234s income 0.0203 -0.00148 0.00130 234s > 234s > print( round( vcov( fitsur4r2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 53.1384 -0.593514 0.065746 234s demand_price -0.5935 0.006838 -0.000927 234s demand_income 0.0657 -0.000927 0.000276 234s supply_(Intercept) 53.3903 -0.599312 0.069540 234s supply_price -0.5935 0.006838 -0.000927 234s supply_farmPrice 0.0570 -0.000775 0.000210 234s supply_trend 0.0657 -0.000927 0.000276 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 53.3903 -0.593514 0.057048 234s demand_price -0.5993 0.006838 -0.000775 234s demand_income 0.0695 -0.000927 0.000210 234s supply_(Intercept) 54.8108 -0.599312 0.048653 234s supply_price -0.5993 0.006838 -0.000775 234s supply_farmPrice 0.0487 -0.000775 0.000276 234s supply_trend 0.0695 -0.000927 0.000210 234s supply_trend 234s demand_(Intercept) 0.065746 234s demand_price -0.000927 234s demand_income 0.000276 234s supply_(Intercept) 0.069540 234s supply_price -0.000927 234s supply_farmPrice 0.000210 234s supply_trend 0.000276 234s > print( round( vcov( fitsur4r2$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 53.1384 -0.593514 0.065746 234s price -0.5935 0.006838 -0.000927 234s income 0.0657 -0.000927 0.000276 234s > 234s > print( round( vcov( fitsur5e ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 47.8867 -0.516747 0.040579 234s demand_price -0.5167 0.005886 -0.000738 234s demand_income 0.0406 -0.000738 0.000340 234s supply_(Intercept) 48.2187 -0.526670 0.047594 234s supply_price -0.5167 0.005886 -0.000738 234s supply_farmPrice 0.0334 -0.000562 0.000234 234s supply_trend 0.0406 -0.000738 0.000340 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 48.2187 -0.516747 0.033361 234s demand_price -0.5267 0.005886 -0.000562 234s demand_income 0.0476 -0.000738 0.000234 234s supply_(Intercept) 50.4739 -0.526670 0.020109 234s supply_price -0.5267 0.005886 -0.000562 234s supply_farmPrice 0.0201 -0.000562 0.000348 234s supply_trend 0.0476 -0.000738 0.000234 234s supply_trend 234s demand_(Intercept) 0.040579 234s demand_price -0.000738 234s demand_income 0.000340 234s supply_(Intercept) 0.047594 234s supply_price -0.000738 234s supply_farmPrice 0.000234 234s supply_trend 0.000340 234s > print( round( vcov( fitsur5e, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s C1 47.8867 -0.516747 0.040579 48.2187 -0.516747 0.033361 234s C2 -0.5167 0.005886 -0.000738 -0.5267 0.005886 -0.000562 234s C3 0.0406 -0.000738 0.000340 0.0476 -0.000738 0.000234 234s C4 48.2187 -0.526670 0.047594 50.4739 -0.526670 0.020109 234s C5 -0.5167 0.005886 -0.000738 -0.5267 0.005886 -0.000562 234s C6 0.0334 -0.000562 0.000234 0.0201 -0.000562 0.000348 234s > print( round( vcov( fitsur5e$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) price farmPrice trend 234s (Intercept) 50.4739 -0.526670 0.020109 0.047594 234s price -0.5267 0.005886 -0.000562 -0.000738 234s farmPrice 0.0201 -0.000562 0.000348 0.000234 234s trend 0.0476 -0.000738 0.000234 0.000340 234s > 234s > print( round( vcov( fitsuri1r3 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 54.5505 -0.55698 0.013891 234s demand_price -0.5570 0.00770 -0.002185 234s demand_income 0.0139 -0.00218 0.002098 234s supply_(Intercept) -2.7032 -0.08733 0.115993 234s supply_income 0.2249 -0.00185 -0.000411 234s supply_farmPrice -0.1721 0.00238 -0.000675 234s supply_trend -0.2597 0.00359 -0.001019 234s supply_(Intercept) supply_income supply_farmPrice 234s demand_(Intercept) -2.7032 0.224902 -0.172110 234s demand_price -0.0873 -0.001848 0.002379 234s demand_income 0.1160 -0.000411 -0.000675 234s supply_(Intercept) 11.4659 -0.058750 -0.051728 234s supply_income -0.0587 0.001787 -0.001018 234s supply_farmPrice -0.0517 -0.001018 0.001368 234s supply_trend -0.0578 -0.001631 0.001794 234s supply_trend 234s demand_(Intercept) -0.25970 234s demand_price 0.00359 234s demand_income -0.00102 234s supply_(Intercept) -0.05784 234s supply_income -0.00163 234s supply_farmPrice 0.00179 234s supply_trend 0.00416 234s > print( round( vcov( fitsuri1r3$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 54.5505 -0.55698 0.01389 234s price -0.5570 0.00770 -0.00218 234s income 0.0139 -0.00218 0.00210 234s > 234s > print( round( vcov( fitsuri2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 56.2287 -0.59260 0.033216 234s demand_price -0.5926 0.00831 -0.002451 234s demand_income 0.0332 -0.00245 0.002173 234s supply_(Intercept) 5.9548 0.14141 -0.203885 234s supply_income -0.2516 0.00201 0.000518 234s supply_farmPrice 0.1910 -0.00323 0.001351 234s supply_trend 0.0332 -0.00245 0.002173 234s supply_(Intercept) supply_income supply_farmPrice 234s demand_(Intercept) 5.955 -0.251647 0.19097 234s demand_price 0.141 0.002011 -0.00323 234s demand_income -0.204 0.000518 0.00135 234s supply_(Intercept) 146.577 -0.828954 -0.64122 234s supply_income -0.829 0.015214 -0.00683 234s supply_farmPrice -0.641 -0.006835 0.01339 234s supply_trend -0.204 0.000518 0.00135 234s supply_trend 234s demand_(Intercept) 0.033216 234s demand_price -0.002451 234s demand_income 0.002173 234s supply_(Intercept) -0.203885 234s supply_income 0.000518 234s supply_farmPrice 0.001351 234s supply_trend 0.002173 234s > print( round( vcov( fitsuri2$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) income farmPrice trend 234s (Intercept) 146.577 -0.828954 -0.64122 -0.203885 234s income -0.829 0.015214 -0.00683 0.000518 234s farmPrice -0.641 -0.006835 0.01339 0.001351 234s trend -0.204 0.000518 0.00135 0.002173 234s > 234s > print( round( vcov( fitsuri3e ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 47.9834 -0.50592 0.028570 234s demand_price -0.5059 0.00710 -0.002098 234s demand_income 0.0286 -0.00210 0.001859 234s supply_(Intercept) 4.9860 0.11975 -0.172089 234s supply_income -0.2118 0.00170 0.000428 234s supply_farmPrice 0.1609 -0.00273 0.001147 234s supply_trend 0.0286 -0.00210 0.001859 234s supply_(Intercept) supply_income supply_farmPrice 234s demand_(Intercept) 4.986 -0.211763 0.16090 234s demand_price 0.120 0.001700 -0.00273 234s demand_income -0.172 0.000428 0.00115 234s supply_(Intercept) 117.261 -0.661134 -0.51405 234s supply_income -0.661 0.012132 -0.00545 234s supply_farmPrice -0.514 -0.005450 0.01070 234s supply_trend -0.172 0.000428 0.00115 234s supply_trend 234s demand_(Intercept) 0.028570 234s demand_price -0.002098 234s demand_income 0.001859 234s supply_(Intercept) -0.172089 234s supply_income 0.000428 234s supply_farmPrice 0.001147 234s supply_trend 0.001859 234s > print( round( vcov( fitsuri3e, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s C1 47.9834 -0.50592 0.028570 4.986 -0.211763 0.16090 234s C2 -0.5059 0.00710 -0.002098 0.120 0.001700 -0.00273 234s C3 0.0286 -0.00210 0.001859 -0.172 0.000428 0.00115 234s C4 4.9860 0.11975 -0.172089 117.261 -0.661134 -0.51405 234s C5 -0.2118 0.00170 0.000428 -0.661 0.012132 -0.00545 234s C6 0.1609 -0.00273 0.001147 -0.514 -0.005450 0.01070 234s > print( round( vcov( fitsuri3e$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 47.9834 -0.5059 0.02857 234s price -0.5059 0.0071 -0.00210 234s income 0.0286 -0.0021 0.00186 234s > 234s > print( round( vcov( fitsurio4e ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 47.0268 -0.525375 0.058300 234s demand_price -0.5254 0.006074 -0.000842 234s demand_income 0.0583 -0.000842 0.000266 234s supply_(Intercept) 47.2346 -0.530682 0.061997 234s supply_price -0.5254 0.006074 -0.000842 234s supply_farmPrice 0.0508 -0.000704 0.000201 234s supply_trend 0.0583 -0.000842 0.000266 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 47.2346 -0.525375 0.050751 234s demand_price -0.5307 0.006074 -0.000704 234s demand_income 0.0620 -0.000842 0.000201 234s supply_(Intercept) 48.6183 -0.530682 0.042182 234s supply_price -0.5307 0.006074 -0.000704 234s supply_farmPrice 0.0422 -0.000704 0.000270 234s supply_trend 0.0620 -0.000842 0.000201 234s supply_trend 234s demand_(Intercept) 0.058300 234s demand_price -0.000842 234s demand_income 0.000266 234s supply_(Intercept) 0.061997 234s supply_price -0.000842 234s supply_farmPrice 0.000201 234s supply_trend 0.000266 234s > print( round( vcov( fitsurio4e$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) price farmPrice trend 234s (Intercept) 48.6183 -0.530682 0.042182 0.061997 234s price -0.5307 0.006074 -0.000704 -0.000842 234s farmPrice 0.0422 -0.000704 0.000270 0.000201 234s trend 0.0620 -0.000842 0.000201 0.000266 234s > print( round( vcov( fitsuri4e ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 37.8960 -0.36274 -0.01487 234s demand_price -0.3627 0.00503 -0.00144 234s demand_income -0.0149 -0.00144 0.00163 234s supply_(Intercept) 19.0822 -0.20611 0.01617 234s supply_income -0.3627 0.00503 -0.00144 234s supply_farmPrice 0.1707 -0.00279 0.00111 234s supply_trend -0.0149 -0.00144 0.00163 234s supply_(Intercept) supply_income supply_farmPrice 234s demand_(Intercept) 19.0822 -0.36274 0.17073 234s demand_price -0.2061 0.00503 -0.00279 234s demand_income 0.0162 -0.00144 0.00111 234s supply_(Intercept) 87.1827 -0.20611 -0.68294 234s supply_income -0.2061 0.00503 -0.00279 234s supply_farmPrice -0.6829 -0.00279 0.00976 234s supply_trend 0.0162 -0.00144 0.00111 234s supply_trend 234s demand_(Intercept) -0.01487 234s demand_price -0.00144 234s demand_income 0.00163 234s supply_(Intercept) 0.01617 234s supply_income -0.00144 234s supply_farmPrice 0.00111 234s supply_trend 0.00163 234s > print( round( vcov( fitsuri4e$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) income farmPrice trend 234s (Intercept) 87.1827 -0.20611 -0.68294 0.01617 234s income -0.2061 0.00503 -0.00279 -0.00144 234s farmPrice -0.6829 -0.00279 0.00976 0.00111 234s trend 0.0162 -0.00144 0.00111 0.00163 234s > 234s > print( round( vcov( fitsurio5r2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 51.3196 -0.579747 0.070528 234s demand_price -0.5797 0.006646 -0.000872 234s demand_income 0.0705 -0.000872 0.000171 234s supply_(Intercept) 51.5518 -0.583025 0.072036 234s supply_price -0.5797 0.006646 -0.000872 234s supply_farmPrice 0.0617 -0.000751 0.000138 234s supply_trend 0.0705 -0.000872 0.000171 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 51.5518 -0.579747 0.061658 234s demand_price -0.5830 0.006646 -0.000751 234s demand_income 0.0720 -0.000872 0.000138 234s supply_(Intercept) 52.2109 -0.583025 0.058794 234s supply_price -0.5830 0.006646 -0.000751 234s supply_farmPrice 0.0588 -0.000751 0.000154 234s supply_trend 0.0720 -0.000872 0.000138 234s supply_trend 234s demand_(Intercept) 0.070528 234s demand_price -0.000872 234s demand_income 0.000171 234s supply_(Intercept) 0.072036 234s supply_price -0.000872 234s supply_farmPrice 0.000138 234s supply_trend 0.000171 234s > print( round( vcov( fitsurio5r2, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s C1 51.3196 -0.579747 0.070528 51.5518 -0.579747 0.061658 234s C2 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 234s C3 0.0705 -0.000872 0.000171 0.0720 -0.000872 0.000138 234s C4 51.5518 -0.583025 0.072036 52.2109 -0.583025 0.058794 234s C5 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 234s C6 0.0617 -0.000751 0.000138 0.0588 -0.000751 0.000154 234s > print( round( vcov( fitsurio5r2$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 51.3196 -0.579747 0.070528 234s price -0.5797 0.006646 -0.000872 234s income 0.0705 -0.000872 0.000171 234s > print( round( vcov( fitsuri5r2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 45.6881 -0.44008 -0.01517 234s demand_price -0.4401 0.00605 -0.00170 234s demand_income -0.0152 -0.00170 0.00190 234s supply_(Intercept) 22.8172 -0.23903 0.01186 234s supply_income -0.4401 0.00605 -0.00170 234s supply_farmPrice 0.2104 -0.00345 0.00138 234s supply_trend -0.0152 -0.00170 0.00190 234s supply_(Intercept) supply_income supply_farmPrice 234s demand_(Intercept) 22.8172 -0.44008 0.21042 234s demand_price -0.2390 0.00605 -0.00345 234s demand_income 0.0119 -0.00170 0.00138 234s supply_(Intercept) 108.8722 -0.23903 -0.87024 234s supply_income -0.2390 0.00605 -0.00345 234s supply_farmPrice -0.8702 -0.00345 0.01234 234s supply_trend 0.0119 -0.00170 0.00138 234s supply_trend 234s demand_(Intercept) -0.01517 234s demand_price -0.00170 234s demand_income 0.00190 234s supply_(Intercept) 0.01186 234s supply_income -0.00170 234s supply_farmPrice 0.00138 234s supply_trend 0.00190 234s > print( round( vcov( fitsuri5r2, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s C1 45.6881 -0.44008 -0.01517 22.8172 -0.44008 0.21042 234s C2 -0.4401 0.00605 -0.00170 -0.2390 0.00605 -0.00345 234s C3 -0.0152 -0.00170 0.00190 0.0119 -0.00170 0.00138 234s C4 22.8172 -0.23903 0.01186 108.8722 -0.23903 -0.87024 234s C5 -0.4401 0.00605 -0.00170 -0.2390 0.00605 -0.00345 234s C6 0.2104 -0.00345 0.00138 -0.8702 -0.00345 0.01234 234s > print( round( vcov( fitsuri5r2$eq[[ 1 ]] ), digits = 6 ) ) 234s (Intercept) price income 234s (Intercept) 45.6881 -0.44008 -0.0152 234s price -0.4401 0.00605 -0.0017 234s income -0.0152 -0.00170 0.0019 234s > 234s > print( round( vcov( fitsurio5wr2 ), digits = 6 ) ) 234s demand_(Intercept) demand_price demand_income 234s demand_(Intercept) 51.3196 -0.579747 0.070528 234s demand_price -0.5797 0.006646 -0.000872 234s demand_income 0.0705 -0.000872 0.000171 234s supply_(Intercept) 51.5518 -0.583025 0.072036 234s supply_price -0.5797 0.006646 -0.000872 234s supply_farmPrice 0.0617 -0.000751 0.000138 234s supply_trend 0.0705 -0.000872 0.000171 234s supply_(Intercept) supply_price supply_farmPrice 234s demand_(Intercept) 51.5518 -0.579747 0.061658 234s demand_price -0.5830 0.006646 -0.000751 234s demand_income 0.0720 -0.000872 0.000138 234s supply_(Intercept) 52.2109 -0.583025 0.058794 234s supply_price -0.5830 0.006646 -0.000751 234s supply_farmPrice 0.0588 -0.000751 0.000154 234s supply_trend 0.0720 -0.000872 0.000138 234s supply_trend 234s demand_(Intercept) 0.070528 234s demand_price -0.000872 234s demand_income 0.000171 234s supply_(Intercept) 0.072036 234s supply_price -0.000872 234s supply_farmPrice 0.000138 234s supply_trend 0.000171 234s > print( round( vcov( fitsurio5wr2, modified.regMat = TRUE ), digits = 6 ) ) 234s C1 C2 C3 C4 C5 C6 234s C1 51.3196 -0.579747 0.070528 51.5518 -0.579747 0.061658 234s C2 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 234s C3 0.0705 -0.000872 0.000171 0.0720 -0.000872 0.000138 234s C4 51.5518 -0.583025 0.072036 52.2109 -0.583025 0.058794 234s C5 -0.5797 0.006646 -0.000872 -0.5830 0.006646 -0.000751 234s C6 0.0617 -0.000751 0.000138 0.0588 -0.000751 0.000154 234s > print( round( vcov( fitsurio5wr2$eq[[ 2 ]] ), digits = 6 ) ) 234s (Intercept) price farmPrice trend 234s (Intercept) 52.2109 -0.583025 0.058794 0.072036 234s price -0.5830 0.006646 -0.000751 -0.000872 234s farmPrice 0.0588 -0.000751 0.000154 0.000138 234s trend 0.0720 -0.000872 0.000138 0.000171 234s > 234s > 234s > ## *********** confidence intervals of coefficients ************* 234s > print( confint( fitsur1e2, useDfSys = TRUE ) ) 234s 2.5 % 97.5 % 234s demand_(Intercept) 83.927 114.497 234s demand_price -0.445 -0.088 234s demand_income 0.208 0.373 234s supply_(Intercept) 40.751 85.403 234s supply_price -0.048 0.336 234s supply_farmPrice 0.128 0.285 234s supply_trend 0.202 0.463 234s > print( confint( fitsur1e2$eq[[ 2 ]], level = 0.9, useDfSys = TRUE ) ) 234s 5 % 95 % 234s (Intercept) 44.506 81.648 234s price -0.016 0.304 234s farmPrice 0.141 0.271 234s trend 0.224 0.441 234s > 234s > print( confint( fitsur1we2, useDfSys = TRUE ) ) 234s 2.5 % 97.5 % 234s demand_(Intercept) 83.927 114.497 234s demand_price -0.445 -0.088 234s demand_income 0.208 0.373 234s supply_(Intercept) 40.751 85.403 234s supply_price -0.048 0.336 234s supply_farmPrice 0.128 0.285 234s supply_trend 0.202 0.463 234s > print( confint( fitsur1we2$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 234s 5 % 95 % 234s (Intercept) 86.498 111.926 234s price -0.415 -0.118 234s income 0.222 0.360 234s > 234s > print( confint( fitsur2e, level = 0.9 ) ) 234s 5 % 95 % 234s demand_(Intercept) 84.618 112.942 234s demand_price -0.397 -0.074 234s demand_income 0.193 0.333 234s supply_(Intercept) 48.153 87.055 234s supply_price -0.040 0.306 234s supply_farmPrice 0.116 0.240 234s supply_trend 0.193 0.333 234s > print( confint( fitsur2e$eq[[ 1 ]], level = 0.99 ) ) 234s 0.5 % 99.5 % 234s (Intercept) 79.767 117.793 234s price -0.452 -0.018 234s income 0.169 0.357 234s > 234s > print( confint( fitsur3, level = 0.99 ) ) 234s 0.5 % 99.5 % 234s demand_(Intercept) 83.481 114.201 234s demand_price -0.415 -0.065 234s demand_income 0.192 0.342 234s supply_(Intercept) 45.755 89.102 234s supply_price -0.060 0.327 234s supply_farmPrice 0.111 0.248 234s supply_trend 0.192 0.342 234s > print( confint( fitsur3$eq[[ 2 ]], level = 0.5 ) ) 234s 25 % 75 % 234s (Intercept) 60.157 74.699 234s price 0.068 0.198 234s farmPrice 0.157 0.202 234s trend 0.242 0.292 234s > 234s > print( confint( fitsur4r3, level = 0.5 ) ) 234s 25 % 75 % 234s demand_(Intercept) 78.344 108.052 234s demand_price -0.406 -0.070 234s demand_income 0.289 0.358 234s supply_(Intercept) 34.267 64.468 234s supply_price 0.094 0.430 234s supply_farmPrice 0.192 0.262 234s supply_trend 0.289 0.358 234s > print( confint( fitsur4r3$eq[[ 1 ]], level = 0.25 ) ) 234s 37.5 % 62.5 % 234s (Intercept) 90.848 95.548 234s price -0.265 -0.211 234s income 0.318 0.329 234s > 234s > print( confint( fitsur5, level = 0.25 ) ) 234s 37.5 % 62.5 % 234s demand_(Intercept) 81.670 111.985 234s demand_price -0.450 -0.109 234s demand_income 0.287 0.371 234s supply_(Intercept) 37.377 68.500 234s supply_price 0.050 0.391 234s supply_farmPrice 0.190 0.276 234s supply_trend 0.287 0.371 234s > print( confint( fitsur5$eq[[ 2 ]], level = 0.975 ) ) 234s 1.3 % 98.8 % 234s (Intercept) 34.986 70.891 234s price 0.024 0.417 234s farmPrice 0.183 0.282 234s trend 0.280 0.377 234s > 234s > print( confint( fitsuri1r3, level = 0.975 ) ) 234s 1.3 % 98.8 % 234s demand_(Intercept) 77.960 109.125 234s demand_price -0.414 -0.043 234s demand_income 0.213 0.406 234s supply_(Intercept) 82.005 96.361 234s supply_income 0.574 0.753 234s supply_farmPrice -0.550 -0.393 234s supply_trend -0.932 -0.659 234s > print( confint( fitsuri1r3$eq[[ 1 ]], level = 0.999 ) ) 234s 0.1 % 100 % 234s (Intercept) 64.257 122.828 234s price -0.576 0.119 234s income 0.128 0.491 234s > 234s > print( confint( fitsuri2, level = 0.999 ) ) 234s 0.1 % 100 % 234s demand_(Intercept) 92.129 122.607 234s demand_price -0.580 -0.209 234s demand_income 0.243 0.433 234s supply_(Intercept) 60.441 109.649 234s supply_income 0.062 0.563 234s supply_farmPrice -0.432 0.038 234s supply_trend 0.243 0.433 234s > print( confint( fitsuri2$eq[[ 2 ]], level = 0.1 ) ) 234s 45 % 55 % 234s (Intercept) 83.512 86.578 234s income 0.297 0.328 234s farmPrice -0.212 -0.183 234s trend 0.332 0.344 234s > 234s > print( confint( fitsuri3e, level = 0.1 ) ) 234s 45 % 55 % 234s demand_(Intercept) 93.728 121.882 234s demand_price -0.570 -0.227 234s demand_income 0.250 0.426 234s supply_(Intercept) 63.100 107.114 234s supply_income 0.087 0.534 234s supply_farmPrice -0.406 0.014 234s supply_trend 0.250 0.426 234s > print( confint( fitsuri3e$eq[[ 1 ]], level = 0.01 ) ) 234s 49.5 % 50.5 % 234s (Intercept) 107.718 107.893 234s price -0.400 -0.398 234s income 0.337 0.338 234s > 234s > print( confint( fitsurio4, level = 0.01 ) ) 234s 49.5 % 50.5 % 234s demand_(Intercept) 77.496 107.356 234s demand_price -0.400 -0.055 234s demand_income 0.283 0.358 234s supply_(Intercept) 33.588 63.871 234s supply_price 0.100 0.445 234s supply_farmPrice 0.185 0.262 234s supply_trend 0.283 0.358 234s > print( confint( fitsurio4$eq[[ 2 ]], level = 0.33 ) ) 234s 33.5 % 66.5 % 234s (Intercept) 45.524 51.935 234s price 0.236 0.309 234s farmPrice 0.215 0.231 234s trend 0.312 0.328 234s > print( confint( fitsuri4, level = 0.01 ) ) 234s 49.5 % 50.5 % 234s demand_(Intercept) 84.345 111.726 234s demand_price -0.422 -0.107 234s demand_income 0.212 0.389 234s supply_(Intercept) 68.817 111.192 234s supply_income 0.078 0.393 234s supply_farmPrice -0.392 0.058 234s supply_trend 0.212 0.389 234s > print( confint( fitsuri4$eq[[ 2 ]], level = 0.33 ) ) 234s 33.5 % 66.5 % 234s (Intercept) 85.519 94.490 234s income 0.202 0.269 234s farmPrice -0.214 -0.119 234s trend 0.282 0.319 234s > 234s > print( confint( fitsurio4w, level = 0.01 ) ) 234s 49.5 % 50.5 % 234s demand_(Intercept) 77.496 107.356 234s demand_price -0.400 -0.055 234s demand_income 0.283 0.358 234s supply_(Intercept) 33.587 63.871 234s supply_price 0.100 0.445 234s supply_farmPrice 0.185 0.262 234s supply_trend 0.283 0.358 234s > print( confint( fitsurio4w$eq[[ 1 ]], level = 0.33 ) ) 234s 33.5 % 66.5 % 234s (Intercept) 89.266 95.587 234s price -0.264 -0.191 234s income 0.312 0.328 234s > 234s > print( confint( fitsurio5r2, level = 0.33 ) ) 234s 33.5 % 66.5 % 234s demand_(Intercept) 63.491 92.577 234s demand_price -0.230 0.101 234s demand_income 0.274 0.327 234s supply_(Intercept) 19.527 48.865 234s supply_price 0.270 0.601 234s supply_farmPrice 0.182 0.232 234s supply_trend 0.274 0.327 234s > print( confint( fitsurio5r2$eq[[ 1 ]] ) ) 234s 2.5 % 97.5 % 234s (Intercept) 63.491 92.577 234s price -0.230 0.101 234s income 0.274 0.327 234s > print( confint( fitsuri5r2, level = 0.33 ) ) 234s 33.5 % 66.5 % 234s demand_(Intercept) 84.498 111.942 234s demand_price -0.425 -0.109 234s demand_income 0.213 0.390 234s supply_(Intercept) 69.034 111.399 234s supply_income 0.075 0.391 234s supply_farmPrice -0.392 0.059 234s supply_trend 0.213 0.390 234s > print( confint( fitsuri5r2$eq[[ 1 ]] ) ) 234s 2.5 % 97.5 % 234s (Intercept) 84.498 111.942 234s price -0.425 -0.109 234s income 0.213 0.390 234s > 234s > 234s > ## *********** fitted values ************* 234s > print( fitted( fitsur1e2 ) ) 234s demand supply 234s 1 97.9 98.1 234s 2 99.8 99.2 234s 3 99.7 99.4 234s 4 99.9 99.7 234s 5 102.1 101.7 234s 6 101.9 101.7 234s 7 102.3 101.7 234s 8 102.6 103.5 234s 9 101.6 102.4 234s 10 100.7 100.3 234s 11 96.2 96.8 234s 12 95.2 95.4 234s 13 96.4 96.8 234s 14 99.2 98.7 234s 15 103.8 102.9 234s 16 103.5 104.2 234s 17 104.2 104.0 234s 18 101.8 103.1 234s 19 103.2 103.0 234s 20 105.9 105.2 234s > print( fitted( fitsur1e2$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 98.1 99.2 99.4 99.7 101.7 101.7 101.7 103.5 102.4 100.3 96.8 95.4 96.8 234s 14 15 16 17 18 19 20 234s 98.7 102.9 104.2 104.0 103.1 103.0 105.2 234s > 234s > print( fitted( fitsur2e ) ) 234s demand supply 234s 1 98.2 98.7 234s 2 99.9 99.7 234s 3 99.9 99.8 234s 4 100.0 100.0 234s 5 102.0 101.7 234s 6 101.8 101.7 234s 7 102.1 101.7 234s 8 102.5 103.2 234s 9 101.5 102.2 234s 10 100.7 100.3 234s 11 96.6 97.3 234s 12 95.8 96.1 234s 13 96.8 97.3 234s 14 99.4 98.9 234s 15 103.5 102.4 234s 16 103.3 103.6 234s 17 103.8 103.3 234s 18 101.8 102.7 234s 19 103.0 102.6 234s 20 105.5 104.5 234s > print( fitted( fitsur2e$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 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 234s 14 15 16 17 18 19 20 234s 99.4 103.5 103.3 103.8 101.8 103.0 105.5 234s > 234s > print( fitted( fitsur2we ) ) 234s demand supply 234s 1 98.2 98.7 234s 2 99.9 99.7 234s 3 99.9 99.8 234s 4 100.0 100.1 234s 5 102.0 101.7 234s 6 101.8 101.7 234s 7 102.1 101.7 234s 8 102.5 103.2 234s 9 101.5 102.2 234s 10 100.7 100.3 234s 11 96.7 97.4 234s 12 95.8 96.2 234s 13 96.8 97.4 234s 14 99.4 99.0 234s 15 103.5 102.4 234s 16 103.2 103.6 234s 17 103.8 103.3 234s 18 101.8 102.7 234s 19 103.0 102.6 234s 20 105.5 104.5 234s > print( fitted( fitsur2we$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 98.7 99.7 99.8 100.1 101.7 101.7 101.7 103.2 102.2 100.3 97.4 96.2 97.4 234s 14 15 16 17 18 19 20 234s 99.0 102.4 103.6 103.3 102.7 102.6 104.5 234s > 234s > print( fitted( fitsur3 ) ) 234s demand supply 234s 1 98.1 98.6 234s 2 99.9 99.6 234s 3 99.9 99.8 234s 4 100.0 100.0 234s 5 102.0 101.7 234s 6 101.8 101.7 234s 7 102.2 101.7 234s 8 102.5 103.2 234s 9 101.5 102.2 234s 10 100.7 100.3 234s 11 96.6 97.3 234s 12 95.7 96.1 234s 13 96.8 97.3 234s 14 99.3 98.9 234s 15 103.6 102.5 234s 16 103.3 103.7 234s 17 103.8 103.3 234s 18 101.8 102.7 234s 19 103.0 102.6 234s 20 105.6 104.6 234s > print( fitted( fitsur3$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 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 234s 14 15 16 17 18 19 20 234s 98.9 102.5 103.7 103.3 102.7 102.6 104.6 234s > 234s > print( fitted( fitsur4r3 ) ) 234s demand supply 234s 1 97.6 98.2 234s 2 99.9 99.8 234s 3 99.8 99.9 234s 4 100.0 100.3 234s 5 102.1 101.8 234s 6 102.0 101.9 234s 7 102.5 102.1 234s 8 103.1 104.3 234s 9 101.4 102.2 234s 10 100.2 99.3 234s 11 95.3 95.7 234s 12 94.5 94.7 234s 13 96.0 96.6 234s 14 99.0 98.2 234s 15 103.9 102.4 234s 16 103.7 104.2 234s 17 103.8 102.6 234s 18 102.2 103.4 234s 19 103.8 103.5 234s 20 107.2 106.7 234s > print( fitted( fitsur4r3$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 97.6 99.9 99.8 100.0 102.1 102.0 102.5 103.1 101.4 100.2 95.3 94.5 96.0 234s 14 15 16 17 18 19 20 234s 99.0 103.9 103.7 103.8 102.2 103.8 107.2 234s > 234s > print( fitted( fitsur5 ) ) 234s demand supply 234s 1 97.5 98.2 234s 2 99.7 99.6 234s 3 99.7 99.8 234s 4 99.9 100.1 234s 5 102.2 101.9 234s 6 102.0 102.0 234s 7 102.5 102.1 234s 8 102.9 104.2 234s 9 101.6 102.4 234s 10 100.5 99.7 234s 11 95.5 95.9 234s 12 94.5 94.6 234s 13 95.8 96.4 234s 14 99.0 98.2 234s 15 104.1 102.6 234s 16 103.8 104.3 234s 17 104.3 103.3 234s 18 102.0 103.3 234s 19 103.6 103.3 234s 20 106.8 106.1 234s > print( fitted( fitsur5$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 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 234s 14 15 16 17 18 19 20 234s 98.2 102.6 104.3 103.3 103.3 103.3 106.1 234s > 234s > print( fitted( fitsuri1r3 ) ) 234s demand supply 234s 1 97.7 100.2 234s 2 99.9 105.7 234s 3 99.9 104.3 234s 4 100.1 104.9 234s 5 102.1 99.2 234s 6 101.9 100.1 234s 7 102.4 102.3 234s 8 103.0 102.6 234s 9 101.4 94.9 234s 10 100.2 92.8 234s 11 95.5 92.1 234s 12 94.8 98.3 234s 13 96.2 101.6 234s 14 99.0 99.8 234s 15 103.7 97.5 234s 16 103.6 96.7 234s 17 103.6 87.6 234s 18 102.1 100.6 234s 19 103.7 105.5 234s 20 107.0 113.8 234s > print( fitted( fitsuri1r3$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 97.7 99.9 99.9 100.1 102.1 101.9 102.4 103.0 101.4 100.2 95.5 94.8 96.2 234s 14 15 16 17 18 19 20 234s 99.0 103.7 103.6 103.6 102.1 103.7 107.0 234s > 234s > print( fitted( fitsuri1wr3 ) ) 234s demand supply 234s 1 97.7 100.2 234s 2 99.9 105.7 234s 3 99.9 104.3 234s 4 100.1 104.9 234s 5 102.1 99.2 234s 6 101.9 100.1 234s 7 102.4 102.3 234s 8 103.0 102.6 234s 9 101.4 94.9 234s 10 100.2 92.8 234s 11 95.5 92.1 234s 12 94.8 98.3 234s 13 96.2 101.6 234s 14 99.0 99.8 234s 15 103.7 97.5 234s 16 103.6 96.7 234s 17 103.6 87.6 234s 18 102.1 100.6 234s 19 103.7 105.5 234s 20 107.0 113.8 234s > print( fitted( fitsuri1wr3$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 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 234s 14 15 16 17 18 19 20 234s 99.8 97.5 96.7 87.6 100.6 105.5 113.8 234s > 234s > print( fitted( fitsuri2 ) ) 234s demand supply 234s 1 97.4 93.4 234s 2 99.2 96.7 234s 3 99.3 96.7 234s 4 99.4 97.7 234s 5 102.5 96.1 234s 6 102.1 97.1 234s 7 102.4 98.8 234s 8 102.5 99.8 234s 9 102.0 96.8 234s 10 101.4 96.4 234s 11 96.0 96.3 234s 12 94.4 99.6 234s 13 95.4 101.9 234s 14 99.1 102.0 234s 15 104.7 102.2 234s 16 104.1 102.6 234s 17 105.8 99.1 234s 18 101.6 105.5 234s 19 103.1 108.5 234s 20 105.6 113.2 234s > print( fitted( fitsuri2$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 93.4 96.7 96.7 97.7 96.1 97.1 98.8 99.8 96.8 96.4 96.3 99.6 101.9 234s 14 15 16 17 18 19 20 234s 102.0 102.2 102.6 99.1 105.5 108.5 113.2 234s > 234s > print( fitted( fitsuri3e ) ) 234s demand supply 234s 1 97.4 93.4 234s 2 99.2 96.7 234s 3 99.3 96.7 234s 4 99.3 97.7 234s 5 102.5 96.1 234s 6 102.1 97.2 234s 7 102.4 98.8 234s 8 102.5 99.8 234s 9 102.0 96.9 234s 10 101.5 96.4 234s 11 96.1 96.3 234s 12 94.4 99.6 234s 13 95.4 101.9 234s 14 99.1 102.0 234s 15 104.7 102.2 234s 16 104.1 102.6 234s 17 105.9 99.1 234s 18 101.6 105.5 234s 19 103.1 108.4 234s 20 105.5 113.1 234s > print( fitted( fitsuri3e$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 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 234s 14 15 16 17 18 19 20 234s 99.1 104.7 104.1 105.9 101.6 103.1 105.5 234s > 234s > print( fitted( fitsurio4 ) ) 234s demand supply 234s 1 97.6 98.2 234s 2 100.0 99.9 234s 3 99.9 100.0 234s 4 100.1 100.4 234s 5 102.1 101.8 234s 6 102.0 101.9 234s 7 102.5 102.1 234s 8 103.1 104.3 234s 9 101.4 102.1 234s 10 100.1 99.2 234s 11 95.3 95.7 234s 12 94.6 94.8 234s 13 96.1 96.7 234s 14 99.0 98.3 234s 15 103.8 102.3 234s 16 103.7 104.1 234s 17 103.6 102.4 234s 18 102.2 103.5 234s 19 103.8 103.6 234s 20 107.3 106.8 234s > print( fitted( fitsurio4$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 98.2 99.9 100.0 100.4 101.8 101.9 102.1 104.3 102.1 99.2 95.7 94.8 96.7 234s 14 15 16 17 18 19 20 234s 98.3 102.3 104.1 102.4 103.5 103.6 106.8 234s > print( fitted( fitsuri4 ) ) 234s demand supply 234s 1 97.8 94.5 234s 2 99.8 97.1 234s 3 99.7 97.2 234s 4 99.9 98.0 234s 5 102.1 96.5 234s 6 101.9 97.4 234s 7 102.3 98.8 234s 8 102.7 99.5 234s 9 101.6 97.3 234s 10 100.6 97.2 234s 11 96.0 97.5 234s 12 95.0 100.3 234s 13 96.2 102.0 234s 14 99.1 102.0 234s 15 103.9 101.7 234s 16 103.6 102.1 234s 17 104.1 99.4 234s 18 101.9 104.6 234s 19 103.3 106.9 234s 20 106.2 110.4 234s > print( fitted( fitsuri4$eq[[ 2 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 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 234s 14 15 16 17 18 19 20 234s 102.0 101.7 102.1 99.4 104.6 106.9 110.4 234s > 234s > print( fitted( fitsurio5r2 ) ) 234s demand supply 234s 1 97.8 98.5 234s 2 100.6 100.7 234s 3 100.4 100.6 234s 4 100.8 101.2 234s 5 101.7 101.3 234s 6 101.8 101.7 234s 7 102.5 102.2 234s 8 103.7 104.9 234s 9 100.8 101.4 234s 10 98.9 97.7 234s 11 94.6 94.8 234s 12 94.8 95.0 234s 13 96.8 97.6 234s 14 98.9 98.2 234s 15 102.9 101.3 234s 16 103.3 103.6 234s 17 101.4 99.8 234s 18 102.7 104.0 234s 19 104.5 104.4 234s 20 108.9 108.9 234s > print( fitted( fitsurio5r2$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 97.8 100.6 100.4 100.8 101.7 101.8 102.5 103.7 100.8 98.9 94.6 94.8 96.8 234s 14 15 16 17 18 19 20 234s 98.9 102.9 103.3 101.4 102.7 104.5 108.9 234s > print( fitted( fitsuri5r2 ) ) 234s demand supply 234s 1 97.8 94.6 234s 2 99.8 97.1 234s 3 99.7 97.2 234s 4 99.9 98.0 234s 5 102.1 96.5 234s 6 101.9 97.4 234s 7 102.3 98.8 234s 8 102.7 99.5 234s 9 101.6 97.3 234s 10 100.6 97.2 234s 11 96.0 97.5 234s 12 95.0 100.3 234s 13 96.2 102.0 234s 14 99.1 102.0 234s 15 103.9 101.7 234s 16 103.6 102.0 234s 17 104.2 99.4 234s 18 101.9 104.6 234s 19 103.3 106.9 234s 20 106.2 110.4 234s > print( fitted( fitsuri5r2$eq[[ 1 ]] ) ) 234s 1 2 3 4 5 6 7 8 9 10 11 12 13 234s 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 234s 14 15 16 17 18 19 20 234s 99.1 103.9 103.6 104.2 101.9 103.3 106.2 234s > 234s > 234s > ## *********** predicted values ************* 234s > predictData <- Kmenta 234s > predictData$consump <- NULL 234s > predictData$price <- Kmenta$price * 0.9 234s > predictData$income <- Kmenta$income * 1.1 234s > 234s > print( predict( fitsur1e2, se.fit = TRUE, interval = "prediction", 234s + useDfSys = TRUE ) ) 234s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 234s 1 97.9 0.607 93.7 102.1 98.1 0.780 234s 2 99.8 0.569 95.6 104.0 99.2 0.793 234s 3 99.7 0.537 95.6 103.9 99.4 0.728 234s 4 99.9 0.575 95.7 104.1 99.7 0.755 234s 5 102.1 0.493 97.9 106.3 101.7 0.652 234s 6 101.9 0.458 97.8 106.0 101.7 0.605 234s 7 102.3 0.475 98.1 106.4 101.7 0.592 234s 8 102.6 0.593 98.4 106.8 103.5 0.835 234s 9 101.6 0.523 97.4 105.8 102.4 0.717 234s 10 100.7 0.788 96.4 105.1 100.3 0.980 234s 11 96.2 0.898 91.8 100.7 96.8 1.081 234s 12 95.2 0.898 90.8 99.7 95.4 1.159 234s 13 96.4 0.816 92.0 100.7 96.8 1.019 234s 14 99.2 0.495 95.1 103.4 98.7 0.710 234s 15 103.8 0.724 99.5 108.1 102.9 0.816 234s 16 103.5 0.586 99.3 107.7 104.2 0.830 234s 17 104.2 1.240 99.4 108.9 104.0 1.540 234s 18 101.8 0.533 97.7 106.0 103.1 0.770 234s 19 103.2 0.666 98.9 107.4 103.0 0.862 234s 20 105.9 1.240 101.1 110.7 105.2 1.517 234s supply.lwr supply.upr 234s 1 92.6 104 234s 2 93.7 105 234s 3 94.0 105 234s 4 94.2 105 234s 5 96.3 107 234s 6 96.3 107 234s 7 96.4 107 234s 8 98.0 109 234s 9 97.0 108 234s 10 94.7 106 234s 11 91.2 103 234s 12 89.7 101 234s 13 91.2 102 234s 14 93.3 104 234s 15 97.4 108 234s 16 98.7 110 234s 17 97.9 110 234s 18 97.7 109 234s 19 97.5 109 234s 20 99.2 111 234s > print( predict( fitsur1e2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 234s + useDfSys = TRUE ) ) 234s fit se.fit lwr upr 234s 1 98.1 0.780 92.6 104 234s 2 99.2 0.793 93.7 105 234s 3 99.4 0.728 94.0 105 234s 4 99.7 0.755 94.2 105 234s 5 101.7 0.652 96.3 107 234s 6 101.7 0.605 96.3 107 234s 7 101.7 0.592 96.4 107 234s 8 103.5 0.835 98.0 109 234s 9 102.4 0.717 97.0 108 234s 10 100.3 0.980 94.7 106 234s 11 96.8 1.081 91.2 103 234s 12 95.4 1.159 89.7 101 234s 13 96.8 1.019 91.2 102 234s 14 98.7 0.710 93.3 104 234s 15 102.9 0.816 97.4 108 234s 16 104.2 0.830 98.7 110 234s 17 104.0 1.540 97.9 110 234s 18 103.1 0.770 97.7 109 234s 19 103.0 0.862 97.5 109 234s 20 105.2 1.517 99.2 111 234s > 234s > print( predict( fitsur2e, se.pred = TRUE, interval = "confidence", 234s + level = 0.999, newdata = predictData ) ) 234s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 234s 1 103 2.23 99.8 106 97.4 2.80 234s 2 105 2.22 102.0 108 98.3 2.71 234s 3 105 2.23 101.8 108 98.4 2.72 234s 4 105 2.23 102.1 108 98.7 2.70 234s 5 107 2.42 102.3 111 100.4 2.83 234s 6 107 2.39 102.5 111 100.4 2.79 234s 7 107 2.37 103.0 111 100.4 2.75 234s 8 108 2.34 103.8 112 101.8 2.70 234s 9 106 2.44 101.7 111 100.9 2.87 234s 10 105 2.54 99.8 111 99.1 3.05 234s 11 101 2.39 96.5 105 96.1 3.05 234s 12 100 2.24 97.0 103 94.8 2.96 234s 13 101 2.17 99.1 104 96.0 2.83 234s 14 104 2.30 100.5 108 97.6 2.85 234s 15 108 2.58 102.9 114 101.2 2.91 234s 16 108 2.49 103.4 113 102.3 2.83 234s 17 108 2.85 101.3 115 102.1 3.26 234s 18 107 2.31 103.2 111 101.3 2.70 234s 19 108 2.36 104.3 113 101.2 2.68 234s 20 112 2.52 106.4 117 103.0 2.66 234s supply.lwr supply.upr 234s 1 93.6 101.1 234s 2 95.5 101.1 234s 3 95.5 101.3 234s 4 96.0 101.3 234s 5 96.4 104.4 234s 6 96.7 104.1 234s 7 97.1 103.7 234s 8 99.2 104.5 234s 9 96.5 105.3 234s 10 93.4 104.8 234s 11 90.3 101.8 234s 12 89.7 99.9 234s 13 91.9 100.0 234s 14 93.4 101.8 234s 15 96.4 105.9 234s 16 98.3 106.4 234s 17 95.1 109.2 234s 18 98.6 103.9 234s 19 98.9 103.5 234s 20 101.0 105.1 234s > print( predict( fitsur2e$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 234s + level = 0.999, newdata = predictData ) ) 234s fit se.pred lwr upr 234s 1 103 2.23 99.8 106 234s 2 105 2.22 102.0 108 234s 3 105 2.23 101.8 108 234s 4 105 2.23 102.1 108 234s 5 107 2.42 102.3 111 234s 6 107 2.39 102.5 111 234s 7 107 2.37 103.0 111 234s 8 108 2.34 103.8 112 234s 9 106 2.44 101.7 111 234s 10 105 2.54 99.8 111 234s 11 101 2.39 96.5 105 234s 12 100 2.24 97.0 103 234s 13 101 2.17 99.1 104 234s 14 104 2.30 100.5 108 234s 15 108 2.58 102.9 114 234s 16 108 2.49 103.4 113 234s 17 108 2.85 101.3 115 234s 18 107 2.31 103.2 111 234s 19 108 2.36 104.3 113 234s 20 112 2.52 106.4 117 234s > 234s > print( predict( fitsur3, se.pred = TRUE, interval = "prediction", 234s + level = 0.975 ) ) 234s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 234s 1 98.1 2.13 93.1 103 98.6 2.67 234s 2 99.9 2.13 94.9 105 99.6 2.69 234s 3 99.9 2.12 94.9 105 99.8 2.68 234s 4 100.0 2.13 95.0 105 100.0 2.69 234s 5 102.0 2.11 97.0 107 101.7 2.67 234s 6 101.8 2.10 96.9 107 101.7 2.66 234s 7 102.2 2.11 97.2 107 101.7 2.66 234s 8 102.5 2.14 97.5 108 103.2 2.72 234s 9 101.5 2.12 96.5 106 102.2 2.69 234s 10 100.7 2.20 95.5 106 100.3 2.78 234s 11 96.6 2.23 91.3 102 97.3 2.80 234s 12 95.7 2.22 90.5 101 96.1 2.81 234s 13 96.8 2.19 91.6 102 97.3 2.77 234s 14 99.3 2.11 94.4 104 98.9 2.69 234s 15 103.6 2.17 98.5 109 102.5 2.71 234s 16 103.3 2.13 98.3 108 103.7 2.69 234s 17 103.8 2.39 98.2 109 103.3 2.99 234s 18 101.8 2.12 96.8 107 102.7 2.69 234s 19 103.0 2.16 98.0 108 102.6 2.71 234s 20 105.6 2.39 100.0 111 104.6 2.97 234s supply.lwr supply.upr 234s 1 92.4 105 234s 2 93.3 106 234s 3 93.5 106 234s 4 93.7 106 234s 5 95.4 108 234s 6 95.5 108 234s 7 95.5 108 234s 8 96.8 110 234s 9 95.9 109 234s 10 93.8 107 234s 11 90.7 104 234s 12 89.5 103 234s 13 90.8 104 234s 14 92.6 105 234s 15 96.1 109 234s 16 97.3 110 234s 17 96.3 110 234s 18 96.4 109 234s 19 96.3 109 234s 20 97.6 112 234s > print( predict( fitsur3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 234s + level = 0.975 ) ) 234s fit se.pred lwr upr 234s 1 98.6 2.67 92.4 105 234s 2 99.6 2.69 93.3 106 234s 3 99.8 2.68 93.5 106 234s 4 100.0 2.69 93.7 106 234s 5 101.7 2.67 95.4 108 234s 6 101.7 2.66 95.5 108 234s 7 101.7 2.66 95.5 108 234s 8 103.2 2.72 96.8 110 234s 9 102.2 2.69 95.9 109 234s 10 100.3 2.78 93.8 107 234s 11 97.3 2.80 90.7 104 234s 12 96.1 2.81 89.5 103 234s 13 97.3 2.77 90.8 104 234s 14 98.9 2.69 92.6 105 234s 15 102.5 2.71 96.1 109 234s 16 103.7 2.69 97.3 110 234s 17 103.3 2.99 96.3 110 234s 18 102.7 2.69 96.4 109 234s 19 102.6 2.71 96.3 109 234s 20 104.6 2.97 97.6 112 234s > 234s > print( predict( fitsur4r3, se.fit = TRUE, interval = "confidence", 234s + level = 0.25 ) ) 234s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 234s 1 97.6 0.474 97.4 97.7 98.2 0.571 234s 2 99.9 0.558 99.7 100.1 99.8 0.699 234s 3 99.8 0.523 99.6 100.0 99.9 0.651 234s 4 100.0 0.567 99.9 100.2 100.3 0.701 234s 5 102.1 0.476 102.0 102.3 101.8 0.620 234s 6 102.0 0.443 101.8 102.1 101.9 0.574 234s 7 102.5 0.440 102.3 102.6 102.1 0.559 234s 8 103.1 0.532 102.9 103.3 104.3 0.646 234s 9 101.4 0.520 101.3 101.6 102.2 0.692 234s 10 100.2 0.774 100.0 100.4 99.3 0.939 234s 11 95.3 0.612 95.1 95.5 95.7 0.732 234s 12 94.5 0.525 94.4 94.7 94.7 0.687 234s 13 96.0 0.603 95.8 96.2 96.6 0.791 234s 14 99.0 0.444 98.8 99.1 98.2 0.580 234s 15 103.9 0.643 103.7 104.1 102.4 0.759 234s 16 103.7 0.494 103.6 103.9 104.2 0.634 234s 17 103.8 1.191 103.4 104.1 102.6 1.456 234s 18 102.2 0.510 102.0 102.3 103.4 0.622 234s 19 103.8 0.570 103.6 104.0 103.5 0.714 234s 20 107.2 0.973 106.9 107.6 106.7 1.183 234s supply.lwr supply.upr 234s 1 98.0 98.4 234s 2 99.6 100.0 234s 3 99.7 100.1 234s 4 100.1 100.5 234s 5 101.6 102.0 234s 6 101.7 102.1 234s 7 101.9 102.3 234s 8 104.1 104.5 234s 9 102.0 102.4 234s 10 99.0 99.6 234s 11 95.5 95.9 234s 12 94.5 94.9 234s 13 96.4 96.9 234s 14 98.1 98.4 234s 15 102.1 102.6 234s 16 104.0 104.4 234s 17 102.1 103.1 234s 18 103.2 103.6 234s 19 103.3 103.7 234s 20 106.3 107.1 234s > print( predict( fitsur4r3$eq[[ 1 ]], se.fit = TRUE, interval = "confidence", 234s + level = 0.25 ) ) 234s fit se.fit lwr upr 234s 1 97.6 0.474 97.4 97.7 234s 2 99.9 0.558 99.7 100.1 234s 3 99.8 0.523 99.6 100.0 234s 4 100.0 0.567 99.9 100.2 234s 5 102.1 0.476 102.0 102.3 234s 6 102.0 0.443 101.8 102.1 234s 7 102.5 0.440 102.3 102.6 234s 8 103.1 0.532 102.9 103.3 234s 9 101.4 0.520 101.3 101.6 234s 10 100.2 0.774 100.0 100.4 234s 11 95.3 0.612 95.1 95.5 234s 12 94.5 0.525 94.4 94.7 234s 13 96.0 0.603 95.8 96.2 234s 14 99.0 0.444 98.8 99.1 234s 15 103.9 0.643 103.7 104.1 234s 16 103.7 0.494 103.6 103.9 234s 17 103.8 1.191 103.4 104.1 234s 18 102.2 0.510 102.0 102.3 234s 19 103.8 0.570 103.6 104.0 234s 20 107.2 0.973 106.9 107.6 234s > 234s > print( predict( fitsur4we, se.fit = TRUE, interval = "confidence", 234s + level = 0.25 ) ) 234s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 234s 1 97.5 0.445 97.3 97.6 98.2 0.519 234s 2 99.7 0.514 99.6 99.9 99.6 0.636 234s 3 99.7 0.482 99.5 99.8 99.8 0.591 234s 4 99.9 0.523 99.7 100.0 100.1 0.636 234s 5 102.2 0.438 102.1 102.4 102.0 0.568 234s 6 102.0 0.408 101.9 102.2 102.0 0.523 234s 7 102.5 0.409 102.3 102.6 102.1 0.508 234s 8 102.9 0.503 102.8 103.1 104.2 0.603 234s 9 101.6 0.479 101.4 101.7 102.4 0.631 234s 10 100.5 0.724 100.3 100.8 99.7 0.856 234s 11 95.5 0.612 95.3 95.7 95.9 0.694 234s 12 94.4 0.520 94.3 94.6 94.6 0.677 234s 13 95.8 0.565 95.6 96.0 96.3 0.748 234s 14 99.0 0.414 98.8 99.1 98.2 0.540 234s 15 104.1 0.592 103.9 104.3 102.6 0.690 234s 16 103.8 0.458 103.7 104.0 104.3 0.581 234s 17 104.3 1.100 104.0 104.7 103.3 1.334 234s 18 102.0 0.477 101.9 102.2 103.3 0.564 234s 19 103.6 0.545 103.4 103.8 103.2 0.651 234s 20 106.8 0.958 106.5 107.1 106.1 1.091 234s supply.lwr supply.upr 234s 1 98.0 98.3 234s 2 99.4 99.8 234s 3 99.6 99.9 234s 4 99.9 100.3 234s 5 101.8 102.1 234s 6 101.8 102.2 234s 7 101.9 102.2 234s 8 104.0 104.4 234s 9 102.2 102.6 234s 10 99.5 100.0 234s 11 95.7 96.1 234s 12 94.4 94.8 234s 13 96.1 96.6 234s 14 98.0 98.4 234s 15 102.4 102.9 234s 16 104.1 104.5 234s 17 102.9 103.8 234s 18 103.1 103.5 234s 19 103.0 103.5 234s 20 105.8 106.5 234s > print( predict( fitsur4we$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 234s + level = 0.25 ) ) 234s fit se.fit lwr upr 234s 1 98.2 0.519 98.0 98.3 234s 2 99.6 0.636 99.4 99.8 234s 3 99.8 0.591 99.6 99.9 234s 4 100.1 0.636 99.9 100.3 234s 5 102.0 0.568 101.8 102.1 234s 6 102.0 0.523 101.8 102.2 234s 7 102.1 0.508 101.9 102.2 234s 8 104.2 0.603 104.0 104.4 234s 9 102.4 0.631 102.2 102.6 234s 10 99.7 0.856 99.5 100.0 234s 11 95.9 0.694 95.7 96.1 234s 12 94.6 0.677 94.4 94.8 234s 13 96.3 0.748 96.1 96.6 234s 14 98.2 0.540 98.0 98.4 234s 15 102.6 0.690 102.4 102.9 234s 16 104.3 0.581 104.1 104.5 234s 17 103.3 1.334 102.9 103.8 234s 18 103.3 0.564 103.1 103.5 234s 19 103.2 0.651 103.0 103.5 234s 20 106.1 1.091 105.8 106.5 234s > 234s > print( predict( fitsur5, se.fit = TRUE, se.pred = TRUE, 234s + interval = "prediction", level = 0.5, newdata = predictData ) ) 234s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 234s 1 103.2 0.911 2.14 101.7 105 96.0 234s 2 105.9 0.786 2.09 104.4 107 97.3 234s 3 105.7 0.824 2.11 104.3 107 97.5 234s 4 106.0 0.780 2.09 104.6 107 97.8 234s 5 108.2 1.233 2.30 106.7 110 99.8 234s 6 108.1 1.143 2.25 106.6 110 99.8 234s 7 108.7 1.076 2.22 107.2 110 99.8 234s 8 109.4 0.919 2.15 108.0 111 101.9 234s 9 107.5 1.295 2.33 105.9 109 100.3 234s 10 106.0 1.568 2.49 104.3 108 97.7 234s 11 100.5 1.292 2.33 98.9 102 93.8 234s 12 99.7 0.921 2.15 98.3 101 92.4 234s 13 101.5 0.720 2.07 100.1 103 94.1 234s 14 104.7 1.054 2.21 103.2 106 96.1 234s 15 110.1 1.485 2.44 108.5 112 100.5 234s 16 110.0 1.284 2.33 108.4 112 102.1 234s 17 109.9 2.013 2.80 108.0 112 101.4 234s 18 108.4 0.906 2.14 106.9 110 101.0 234s 19 110.2 0.911 2.14 108.8 112 100.9 234s 20 114.2 0.898 2.14 112.7 116 103.6 234s supply.se.fit supply.se.pred supply.lwr supply.upr 234s 1 0.916 2.68 94.1 97.8 234s 2 0.715 2.62 95.5 99.1 234s 3 0.760 2.63 95.7 99.3 234s 4 0.708 2.62 96.0 99.6 234s 5 1.213 2.80 97.9 101.7 234s 6 1.100 2.75 97.9 101.7 234s 7 0.982 2.70 98.0 101.7 234s 8 0.825 2.65 100.1 103.7 234s 9 1.339 2.85 98.4 102.2 234s 10 1.631 3.00 95.7 99.8 234s 11 1.375 2.87 91.9 95.8 234s 12 1.025 2.72 90.6 94.3 234s 13 0.831 2.65 92.3 95.9 234s 14 1.033 2.72 94.2 97.9 234s 15 1.434 2.90 98.5 102.5 234s 16 1.249 2.81 100.2 104.1 234s 17 2.163 3.32 99.1 103.6 234s 18 0.809 2.65 99.2 102.8 234s 19 0.712 2.62 99.1 102.7 234s 20 0.572 2.58 101.9 105.4 234s > print( predict( fitsur5$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 234s + interval = "prediction", level = 0.5, newdata = predictData ) ) 234s fit se.fit se.pred lwr upr 234s 1 96.0 0.916 2.68 94.1 97.8 234s 2 97.3 0.715 2.62 95.5 99.1 234s 3 97.5 0.760 2.63 95.7 99.3 234s 4 97.8 0.708 2.62 96.0 99.6 234s 5 99.8 1.213 2.80 97.9 101.7 234s 6 99.8 1.100 2.75 97.9 101.7 234s 7 99.8 0.982 2.70 98.0 101.7 234s 8 101.9 0.825 2.65 100.1 103.7 234s 9 100.3 1.339 2.85 98.4 102.2 234s 10 97.7 1.631 3.00 95.7 99.8 234s 11 93.8 1.375 2.87 91.9 95.8 234s 12 92.4 1.025 2.72 90.6 94.3 234s 13 94.1 0.831 2.65 92.3 95.9 234s 14 96.1 1.033 2.72 94.2 97.9 234s 15 100.5 1.434 2.90 98.5 102.5 234s 16 102.1 1.249 2.81 100.2 104.1 234s 17 101.4 2.163 3.32 99.1 103.6 234s 18 101.0 0.809 2.65 99.2 102.8 234s 19 100.9 0.712 2.62 99.1 102.7 234s 20 103.6 0.572 2.58 101.9 105.4 234s > 234s > print( predict( fitsuri1r3, se.fit = TRUE, se.pred = TRUE, 234s + interval = "confidence", level = 0.99 ) ) 234s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 234s 1 97.7 0.653 2.09 95.8 99.6 100.2 234s 2 99.9 0.578 2.07 98.3 101.6 105.7 234s 3 99.9 0.548 2.06 98.3 101.4 104.3 234s 4 100.1 0.583 2.07 98.4 101.8 104.9 234s 5 102.1 0.509 2.05 100.6 103.5 99.2 234s 6 101.9 0.474 2.04 100.6 103.3 100.1 234s 7 102.4 0.496 2.04 101.0 103.9 102.3 234s 8 103.0 0.615 2.08 101.2 104.8 102.6 234s 9 101.4 0.531 2.05 99.9 103.0 94.9 234s 10 100.2 0.785 2.13 98.0 102.5 92.8 234s 11 95.5 0.971 2.21 92.7 98.3 92.1 234s 12 94.8 0.996 2.22 91.9 97.7 98.3 234s 13 96.2 0.880 2.17 93.7 98.8 101.6 234s 14 99.0 0.521 2.05 97.5 100.5 99.8 234s 15 103.7 0.752 2.12 101.6 105.9 97.5 234s 16 103.6 0.622 2.08 101.8 105.4 96.7 234s 17 103.6 1.241 2.34 100.0 107.2 87.6 234s 18 102.1 0.546 2.06 100.5 103.7 100.6 234s 19 103.7 0.696 2.10 101.6 105.7 105.5 234s 20 107.0 1.299 2.37 103.2 110.7 113.8 234s supply.se.fit supply.se.pred supply.lwr supply.upr 234s 1 0.599 1.72 98.4 101.9 234s 2 0.604 1.72 103.9 107.4 234s 3 0.539 1.70 102.7 105.8 234s 4 0.536 1.70 103.4 106.5 234s 5 0.486 1.69 97.8 100.6 234s 6 0.448 1.68 98.8 101.4 234s 7 0.444 1.67 101.0 103.6 234s 8 0.522 1.70 101.1 104.1 234s 9 0.542 1.70 93.3 96.5 234s 10 0.579 1.72 91.1 94.5 234s 11 0.812 1.81 89.7 94.5 234s 12 0.865 1.83 95.8 100.9 234s 13 0.747 1.78 99.4 103.8 234s 14 0.507 1.69 98.3 101.3 234s 15 0.509 1.69 96.0 98.9 234s 16 0.596 1.72 95.0 98.5 234s 17 0.975 1.89 84.7 90.4 234s 18 0.500 1.69 99.1 102.0 234s 19 0.649 1.74 103.6 107.3 234s 20 1.124 1.97 110.5 117.1 234s > print( predict( fitsuri1r3$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 234s + interval = "confidence", level = 0.99 ) ) 234s fit se.fit se.pred lwr upr 234s 1 97.7 0.653 2.09 95.8 99.6 234s 2 99.9 0.578 2.07 98.3 101.6 234s 3 99.9 0.548 2.06 98.3 101.4 234s 4 100.1 0.583 2.07 98.4 101.8 234s 5 102.1 0.509 2.05 100.6 103.5 234s 6 101.9 0.474 2.04 100.6 103.3 234s 7 102.4 0.496 2.04 101.0 103.9 234s 8 103.0 0.615 2.08 101.2 104.8 234s 9 101.4 0.531 2.05 99.9 103.0 234s 10 100.2 0.785 2.13 98.0 102.5 234s 11 95.5 0.971 2.21 92.7 98.3 234s 12 94.8 0.996 2.22 91.9 97.7 234s 13 96.2 0.880 2.17 93.7 98.8 234s 14 99.0 0.521 2.05 97.5 100.5 234s 15 103.7 0.752 2.12 101.6 105.9 234s 16 103.6 0.622 2.08 101.8 105.4 234s 17 103.6 1.241 2.34 100.0 107.2 234s 18 102.1 0.546 2.06 100.5 103.7 234s 19 103.7 0.696 2.10 101.6 105.7 234s 20 107.0 1.299 2.37 103.2 110.7 234s > 234s > print( predict( fitsuri2, se.fit = TRUE, interval = "prediction", 234s + level = 0.9, newdata = predictData ) ) 234s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 234s 1 104 0.960 100.5 108 96.1 1.37 234s 2 107 1.011 102.9 110 99.7 1.69 234s 3 107 1.032 102.8 110 99.8 1.61 234s 4 107 1.019 103.0 111 100.8 1.76 234s 5 110 1.547 105.4 114 99.2 2.00 234s 6 109 1.468 105.3 114 100.3 1.94 234s 7 110 1.465 105.7 114 102.1 2.12 234s 8 110 1.423 106.1 114 103.2 2.60 234s 9 109 1.543 104.8 113 99.9 1.80 234s 10 108 1.699 103.6 112 99.1 1.35 234s 11 102 1.299 98.2 106 98.6 2.25 234s 12 101 0.939 97.2 105 102.0 3.10 234s 13 102 0.731 98.7 106 104.5 3.01 234s 14 106 1.164 102.1 110 104.9 2.27 234s 15 112 1.896 107.3 117 105.4 2.20 234s 16 112 1.733 107.1 116 105.9 2.40 234s 17 113 2.316 107.4 118 102.1 2.02 234s 18 109 1.316 105.2 113 108.8 2.75 234s 19 111 1.497 106.8 115 111.9 3.73 234s 20 114 1.918 109.7 119 117.2 5.62 234s supply.lwr supply.upr 234s 1 86.2 106 234s 2 89.7 110 234s 3 89.7 110 234s 4 90.7 111 234s 5 89.0 109 234s 6 90.1 110 234s 7 91.8 112 234s 8 92.6 114 234s 9 89.7 110 234s 10 89.2 109 234s 11 88.2 109 234s 12 91.0 113 234s 13 93.6 115 234s 14 94.5 115 234s 15 95.0 116 234s 16 95.4 116 234s 17 91.9 112 234s 18 98.1 119 234s 19 100.4 123 234s 20 103.6 131 234s > print( predict( fitsuri2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 234s + level = 0.9, newdata = predictData ) ) 234s fit se.fit lwr upr 234s 1 96.1 1.37 86.2 106 234s 2 99.7 1.69 89.7 110 234s 3 99.8 1.61 89.7 110 234s 4 100.8 1.76 90.7 111 234s 5 99.2 2.00 89.0 109 234s 6 100.3 1.94 90.1 110 234s 7 102.1 2.12 91.8 112 234s 8 103.2 2.60 92.6 114 234s 9 99.9 1.80 89.7 110 234s 10 99.1 1.35 89.2 109 234s 11 98.6 2.25 88.2 109 234s 12 102.0 3.10 91.0 113 234s 13 104.5 3.01 93.6 115 234s 14 104.9 2.27 94.5 115 234s 15 105.4 2.20 95.0 116 234s 16 105.9 2.40 95.4 116 234s 17 102.1 2.02 91.9 112 234s 18 108.8 2.75 98.1 119 234s 19 111.9 3.73 100.4 123 234s 20 117.2 5.62 103.6 131 234s > 234s > print( predict( fitsuri2w, se.fit = TRUE, interval = "prediction", 234s + level = 0.9, newdata = predictData ) ) 234s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 234s 1 104 0.960 100.5 108 96.1 1.37 234s 2 107 1.011 102.9 110 99.7 1.69 234s 3 107 1.032 102.8 110 99.8 1.61 234s 4 107 1.019 103.0 111 100.8 1.76 234s 5 110 1.547 105.4 114 99.2 2.00 234s 6 109 1.468 105.3 114 100.3 1.94 234s 7 110 1.465 105.7 114 102.1 2.12 234s 8 110 1.423 106.1 114 103.2 2.60 234s 9 109 1.543 104.8 113 99.9 1.80 234s 10 108 1.699 103.6 112 99.1 1.35 234s 11 102 1.299 98.2 106 98.6 2.25 234s 12 101 0.939 97.2 105 102.0 3.10 234s 13 102 0.731 98.7 106 104.5 3.01 234s 14 106 1.164 102.1 110 104.9 2.27 234s 15 112 1.896 107.3 117 105.4 2.20 234s 16 112 1.733 107.1 116 105.9 2.40 234s 17 113 2.316 107.4 118 102.1 2.02 234s 18 109 1.316 105.2 113 108.8 2.75 234s 19 111 1.497 106.8 115 111.9 3.73 234s 20 114 1.918 109.7 119 117.2 5.62 234s supply.lwr supply.upr 234s 1 86.2 106 234s 2 89.7 110 234s 3 89.7 110 234s 4 90.7 111 234s 5 89.0 109 234s 6 90.1 110 234s 7 91.8 112 234s 8 92.6 114 234s 9 89.7 110 234s 10 89.2 109 234s 11 88.2 109 234s 12 91.0 113 234s 13 93.6 115 234s 14 94.5 115 234s 15 95.0 116 234s 16 95.4 116 234s 17 91.9 112 234s 18 98.1 119 234s 19 100.4 123 234s 20 103.6 131 234s > print( predict( fitsuri2w$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 234s + level = 0.9, newdata = predictData ) ) 234s fit se.fit lwr upr 234s 1 96.1 1.37 86.2 106 234s 2 99.7 1.69 89.7 110 234s 3 99.8 1.61 89.7 110 234s 4 100.8 1.76 90.7 111 234s 5 99.2 2.00 89.0 109 234s 6 100.3 1.94 90.1 110 234s 7 102.1 2.12 91.8 112 234s 8 103.2 2.60 92.6 114 234s 9 99.9 1.80 89.7 110 234s 10 99.1 1.35 89.2 109 234s 11 98.6 2.25 88.2 109 234s 12 102.0 3.10 91.0 113 234s 13 104.5 3.01 93.6 115 234s 14 104.9 2.27 94.5 115 234s 15 105.4 2.20 95.0 116 234s 16 105.9 2.40 95.4 116 234s 17 102.1 2.02 91.9 112 234s 18 108.8 2.75 98.1 119 234s 19 111.9 3.73 100.4 123 234s 20 117.2 5.62 103.6 131 234s > 234s > print( predict( fitsuri3e, interval = "prediction", level = 0.925 ) ) 234s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 234s 1 97.4 93.5 101.2 93.4 82.5 104 234s 2 99.2 95.4 103.0 96.7 86.0 107 234s 3 99.3 95.5 103.0 96.7 86.0 107 234s 4 99.3 95.5 103.1 97.7 87.0 108 234s 5 102.5 98.7 106.2 96.1 85.1 107 234s 6 102.1 98.4 105.9 97.2 86.3 108 234s 7 102.4 98.6 106.2 98.8 88.1 110 234s 8 102.5 98.7 106.3 99.8 88.9 111 234s 9 102.0 98.2 105.8 96.9 85.9 108 234s 10 101.5 97.6 105.4 96.4 85.5 107 234s 11 96.1 92.1 100.1 96.3 84.9 108 234s 12 94.4 90.4 98.4 99.6 87.9 111 234s 13 95.4 91.4 99.3 101.9 90.4 113 234s 14 99.1 95.3 102.8 102.0 91.1 113 234s 15 104.7 100.8 108.6 102.2 91.4 113 234s 16 104.1 100.3 107.9 102.6 91.8 113 234s 17 105.9 101.6 110.2 99.1 88.1 110 234s 18 101.6 97.9 105.4 105.5 94.6 116 234s 19 103.1 99.2 106.9 108.4 97.1 120 234s 20 105.5 101.3 109.8 113.1 100.7 126 234s > print( predict( fitsuri3e$eq[[ 1 ]], interval = "prediction", level = 0.925 ) ) 234s fit lwr upr 234s 1 97.4 93.5 101.2 234s 2 99.2 95.4 103.0 234s 3 99.3 95.5 103.0 234s 4 99.3 95.5 103.1 234s 5 102.5 98.7 106.2 234s 6 102.1 98.4 105.9 234s 7 102.4 98.6 106.2 234s 8 102.5 98.7 106.3 234s 9 102.0 98.2 105.8 234s 10 101.5 97.6 105.4 234s 11 96.1 92.1 100.1 234s 12 94.4 90.4 98.4 234s 13 95.4 91.4 99.3 234s 14 99.1 95.3 102.8 234s 15 104.7 100.8 108.6 234s 16 104.1 100.3 107.9 234s 17 105.9 101.6 110.2 234s 18 101.6 97.9 105.4 234s 19 103.1 99.2 106.9 234s 20 105.5 101.3 109.8 234s > 234s > print( predict( fitsurio4, interval = "confidence", newdata = predictData ) ) 234s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 234s 1 102.7 100.8 105 95.5 93.6 97.4 234s 2 105.5 103.8 107 97.0 95.5 98.5 234s 3 105.3 103.6 107 97.2 95.6 98.8 234s 4 105.6 104.0 107 97.5 96.0 99.0 234s 5 107.5 105.0 110 99.1 96.5 101.6 234s 6 107.5 105.1 110 99.2 96.9 101.5 234s 7 108.1 105.9 110 99.3 97.2 101.4 234s 8 108.9 107.1 111 101.5 99.7 103.2 234s 9 106.7 104.0 109 99.5 96.7 102.3 234s 10 105.1 101.8 108 96.7 93.4 100.1 234s 11 99.8 97.2 102 93.1 90.4 95.9 234s 12 99.3 97.4 101 92.1 90.1 94.1 234s 13 101.1 99.7 103 93.9 92.3 95.5 234s 14 104.1 101.9 106 95.6 93.5 97.7 234s 15 109.3 106.2 112 99.7 96.7 102.7 234s 16 109.3 106.6 112 101.4 98.8 104.0 234s 17 108.7 104.5 113 100.0 95.5 104.5 234s 18 107.9 106.0 110 100.6 98.9 102.3 234s 19 109.8 107.9 112 100.7 99.2 102.2 234s 20 114.0 112.3 116 103.7 102.5 104.9 234s > print( predict( fitsurio4$eq[[ 2 ]], interval = "confidence", 234s + newdata = predictData ) ) 234s fit lwr upr 234s 1 95.5 93.6 97.4 234s 2 97.0 95.5 98.5 234s 3 97.2 95.6 98.8 234s 4 97.5 96.0 99.0 234s 5 99.1 96.5 101.6 234s 6 99.2 96.9 101.5 234s 7 99.3 97.2 101.4 234s 8 101.5 99.7 103.2 234s 9 99.5 96.7 102.3 234s 10 96.7 93.4 100.1 234s 11 93.1 90.4 95.9 234s 12 92.1 90.1 94.1 234s 13 93.9 92.3 95.5 234s 14 95.6 93.5 97.7 234s 15 99.7 96.7 102.7 234s 16 101.4 98.8 104.0 234s 17 100.0 95.5 104.5 234s 18 100.6 98.9 102.3 234s 19 100.7 99.2 102.2 234s 20 103.7 102.5 104.9 234s > print( predict( fitsuri4, interval = "confidence", newdata = predictData ) ) 234s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 234s 1 103.1 101.3 105 96.6 93.9 99.3 234s 2 105.5 103.7 107 99.4 96.2 102.5 234s 3 105.4 103.5 107 99.4 96.4 102.5 234s 4 105.6 103.8 107 100.3 97.1 103.5 234s 5 107.7 105.0 110 98.9 94.9 102.9 234s 6 107.6 105.0 110 99.8 96.1 103.5 234s 7 108.1 105.5 111 101.2 97.6 104.9 234s 8 108.7 106.1 111 102.0 97.7 106.4 234s 9 107.0 104.3 110 99.6 96.0 103.2 234s 10 105.7 102.7 109 99.3 96.6 102.0 234s 11 100.7 98.3 103 99.3 95.0 103.5 234s 12 99.9 98.2 102 102.1 95.8 108.4 234s 13 101.5 100.2 103 104.0 97.9 110.1 234s 14 104.5 102.4 107 104.1 99.8 108.4 234s 15 109.5 106.1 113 104.2 100.8 107.5 234s 16 109.4 106.3 112 104.5 100.9 108.2 234s 17 109.3 105.3 113 101.7 97.7 105.6 234s 18 107.8 105.4 110 107.0 103.1 110.9 234s 19 109.5 106.7 112 109.5 104.4 114.6 234s 20 113.0 109.4 117 113.4 106.3 120.6 234s > print( predict( fitsuri4$eq[[ 2 ]], interval = "confidence", 234s + newdata = predictData ) ) 234s fit lwr upr 234s 1 96.6 93.9 99.3 234s 2 99.4 96.2 102.5 234s 3 99.4 96.4 102.5 234s 4 100.3 97.1 103.5 234s 5 98.9 94.9 102.9 234s 6 99.8 96.1 103.5 234s 7 101.2 97.6 104.9 234s 8 102.0 97.7 106.4 234s 9 99.6 96.0 103.2 234s 10 99.3 96.6 102.0 234s 11 99.3 95.0 103.5 234s 12 102.1 95.8 108.4 234s 13 104.0 97.9 110.1 234s 14 104.1 99.8 108.4 234s 15 104.2 100.8 107.5 234s 16 104.5 100.9 108.2 234s 17 101.7 97.7 105.6 234s 18 107.0 103.1 110.9 234s 19 109.5 104.4 114.6 234s 20 113.4 106.3 120.6 234s > 234s > print( predict( fitsurio5r2 ) ) 234s demand.pred supply.pred 234s 1 97.8 98.5 234s 2 100.6 100.7 234s 3 100.4 100.6 234s 4 100.8 101.2 234s 5 101.7 101.3 234s 6 101.8 101.7 234s 7 102.5 102.2 234s 8 103.7 104.9 234s 9 100.8 101.4 234s 10 98.9 97.7 234s 11 94.6 94.8 234s 12 94.8 95.0 234s 13 96.8 97.6 234s 14 98.9 98.2 234s 15 102.9 101.3 234s 16 103.3 103.6 234s 17 101.4 99.8 234s 18 102.7 104.0 234s 19 104.5 104.4 234s 20 108.9 108.9 234s > print( predict( fitsurio5r2$eq[[ 1 ]] ) ) 234s fit 234s 1 97.8 234s 2 100.6 234s 3 100.4 234s 4 100.8 234s 5 101.7 234s 6 101.8 234s 7 102.5 234s 8 103.7 234s 9 100.8 234s 10 98.9 234s 11 94.6 234s 12 94.8 234s 13 96.8 234s 14 98.9 234s 15 102.9 234s 16 103.3 234s 17 101.4 234s 18 102.7 234s 19 104.5 234s 20 108.9 234s > print( predict( fitsuri5r2 ) ) 234s demand.pred supply.pred 234s 1 97.8 94.6 234s 2 99.8 97.1 234s 3 99.7 97.2 234s 4 99.9 98.0 234s 5 102.1 96.5 234s 6 101.9 97.4 234s 7 102.3 98.8 234s 8 102.7 99.5 234s 9 101.6 97.3 234s 10 100.6 97.2 234s 11 96.0 97.5 234s 12 95.0 100.3 234s 13 96.2 102.0 234s 14 99.1 102.0 234s 15 103.9 101.7 234s 16 103.6 102.0 234s 17 104.2 99.4 234s 18 101.9 104.6 234s 19 103.3 106.9 234s 20 106.2 110.4 234s > print( predict( fitsuri5r2$eq[[ 1 ]] ) ) 234s fit 234s 1 97.8 234s 2 99.8 234s 3 99.7 234s 4 99.9 234s 5 102.1 234s 6 101.9 234s 7 102.3 234s 8 102.7 234s 9 101.6 234s 10 100.6 234s 11 96.0 234s 12 95.0 234s 13 96.2 234s 14 99.1 234s 15 103.9 234s 16 103.6 234s 17 104.2 234s 18 101.9 234s 19 103.3 234s 20 106.2 234s > 234s > # predict just one observation 234s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 234s + trend = 25 ) 234s > 234s > print( predict( fitsur1e2, newdata = smallData ) ) 234s demand.pred supply.pred 234s 1 108 115 234s > print( predict( fitsur1e2$eq[[ 1 ]], newdata = smallData ) ) 234s fit 234s 1 108 234s > 234s > print( predict( fitsur2e, se.fit = TRUE, level = 0.9, 234s + newdata = smallData ) ) 234s demand.pred demand.se.fit supply.pred supply.se.fit 234s 1 108 2.21 113 3 234s > print( predict( fitsur2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 234s + newdata = smallData ) ) 234s fit se.pred 234s 1 108 3.03 234s > 234s > print( predict( fitsur3, interval = "prediction", level = 0.975, 234s + newdata = smallData ) ) 234s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 234s 1 108 100 115 113 103 123 234s > print( predict( fitsur3$eq[[ 1 ]], interval = "confidence", level = 0.8, 234s + newdata = smallData ) ) 234s fit lwr upr 234s 1 108 105 111 234s > 234s > print( predict( fitsur4r3, se.fit = TRUE, interval = "confidence", 234s + level = 0.999, newdata = smallData ) ) 234s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 234s 1 111 2.06 103 118 119 2.22 234s supply.lwr supply.upr 234s 1 111 127 234s > print( predict( fitsur4r3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 234s + level = 0.75, newdata = smallData ) ) 234s fit se.pred lwr upr 234s 1 119 3.41 115 123 234s > 234s > print( predict( fitsur5, se.fit = TRUE, interval = "prediction", 234s + newdata = smallData ) ) 234s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 234s 1 110 2.15 104 116 118 2.29 234s supply.lwr supply.upr 234s 1 111 125 234s > print( predict( fitsur5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 234s + newdata = smallData ) ) 234s fit se.pred lwr upr 234s 1 110 2.9 105 114 234s > 234s > print( predict( fitsurio5r2, se.fit = TRUE, se.pred = TRUE, 234s + interval = "prediction", level = 0.5, newdata = smallData ) ) 234s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 234s 1 115 1.98 3.09 113 117 123 234s supply.se.fit supply.se.pred supply.lwr supply.upr 234s 1 2.17 3.82 121 126 234s > print( predict( fitsurio5r2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 234s + interval = "confidence", level = 0.25, newdata = smallData ) ) 234s fit se.fit se.pred lwr upr 234s 1 115 1.98 3.09 114 115 234s > print( predict( fitsuri5r2, se.fit = TRUE, se.pred = TRUE, 234s + interval = "prediction", level = 0.5, newdata = smallData ) ) 234s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 234s 1 109 2.35 3.06 107 111 113 234s supply.se.fit supply.se.pred supply.lwr supply.upr 234s 1 3.91 6.87 108 117 234s > print( predict( fitsuri5r2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 234s + interval = "confidence", level = 0.25, newdata = smallData ) ) 234s fit se.fit se.pred lwr upr 234s 1 109 2.35 3.06 108 109 234s > 234s > print( predict( fitsuri5wr2, se.fit = TRUE, se.pred = TRUE, 234s + interval = "prediction", level = 0.5, newdata = smallData ) ) 234s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 234s 1 109 2.35 3.06 107 111 113 234s supply.se.fit supply.se.pred supply.lwr supply.upr 234s 1 3.91 6.87 108 117 234s > print( predict( fitsuri5wr2$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 234s + interval = "confidence", level = 0.25, newdata = smallData ) ) 234s fit se.fit se.pred lwr upr 234s 1 109 2.35 3.06 108 109 234s > 234s > 234s > ## ************ correlation of predicted values *************** 234s > print( correlation.systemfit( fitsur1e2, 2, 1 ) ) 234s [,1] 234s [1,] 0.849 234s [2,] 0.856 234s [3,] 0.864 234s [4,] 0.882 234s [5,] 0.844 234s [6,] 0.861 234s [7,] 0.875 234s [8,] 0.877 234s [9,] 0.884 234s [10,] 0.918 234s [11,] 0.903 234s [12,] 0.884 234s [13,] 0.880 234s [14,] 0.863 234s [15,] 0.896 234s [16,] 0.897 234s [17,] 0.914 234s [18,] 0.839 234s [19,] 0.867 234s [20,] 0.902 234s > 234s > print( correlation.systemfit( fitsur2e, 1, 2 ) ) 234s [,1] 234s [1,] 0.942 234s [2,] 0.944 234s [3,] 0.942 234s [4,] 0.941 234s [5,] 0.902 234s [6,] 0.909 234s [7,] 0.917 234s [8,] 0.903 234s [9,] 0.910 234s [10,] 0.941 234s [11,] 0.923 234s [12,] 0.902 234s [13,] 0.901 234s [14,] 0.893 234s [15,] 0.925 234s [16,] 0.952 234s [17,] 0.944 234s [18,] 0.935 234s [19,] 0.930 234s [20,] 0.938 234s > 234s > print( correlation.systemfit( fitsur3, 2, 1 ) ) 234s [,1] 234s [1,] 0.939 234s [2,] 0.943 234s [3,] 0.941 234s [4,] 0.940 234s [5,] 0.902 234s [6,] 0.909 234s [7,] 0.918 234s [8,] 0.903 234s [9,] 0.910 234s [10,] 0.941 234s [11,] 0.922 234s [12,] 0.900 234s [13,] 0.899 234s [14,] 0.892 234s [15,] 0.923 234s [16,] 0.952 234s [17,] 0.943 234s [18,] 0.936 234s [19,] 0.929 234s [20,] 0.937 234s > 234s > print( correlation.systemfit( fitsur3w, 2, 1 ) ) 234s [,1] 234s [1,] 0.940 234s [2,] 0.946 234s [3,] 0.944 234s [4,] 0.944 234s [5,] 0.908 234s [6,] 0.914 234s [7,] 0.922 234s [8,] 0.907 234s [9,] 0.914 234s [10,] 0.944 234s [11,] 0.926 234s [12,] 0.904 234s [13,] 0.903 234s [14,] 0.897 234s [15,] 0.926 234s [16,] 0.954 234s [17,] 0.946 234s [18,] 0.940 234s [19,] 0.932 234s [20,] 0.940 234s > 234s > print( correlation.systemfit( fitsur4r3, 1, 2 ) ) 234s [,1] 234s [1,] 0.963 234s [2,] 0.971 234s [3,] 0.971 234s [4,] 0.973 234s [5,] 0.940 234s [6,] 0.944 234s [7,] 0.947 234s [8,] 0.942 234s [9,] 0.947 234s [10,] 0.973 234s [11,] 0.910 234s [12,] 0.858 234s [13,] 0.914 234s [14,] 0.923 234s [15,] 0.977 234s [16,] 0.964 234s [17,] 0.978 234s [18,] 0.969 234s [19,] 0.946 234s [20,] 0.941 234s > 234s > print( correlation.systemfit( fitsur5, 2, 1 ) ) 234s [,1] 234s [1,] 0.938 234s [2,] 0.948 234s [3,] 0.948 234s [4,] 0.951 234s [5,] 0.892 234s [6,] 0.897 234s [7,] 0.903 234s [8,] 0.900 234s [9,] 0.907 234s [10,] 0.952 234s [11,] 0.853 234s [12,] 0.784 234s [13,] 0.858 234s [14,] 0.867 234s [15,] 0.961 234s [16,] 0.935 234s [17,] 0.961 234s [18,] 0.944 234s [19,] 0.907 234s [20,] 0.904 234s > 234s > print( correlation.systemfit( fitsuri1r3, 1, 2 ) ) 234s [,1] 234s [1,] -0.662 234s [2,] -0.656 234s [3,] -0.664 234s [4,] -0.689 234s [5,] -0.629 234s [6,] -0.664 234s [7,] -0.696 234s [8,] -0.675 234s [9,] -0.722 234s [10,] -0.757 234s [11,] -0.759 234s [12,] -0.732 234s [13,] -0.710 234s [14,] -0.669 234s [15,] -0.728 234s [16,] -0.737 234s [17,] -0.741 234s [18,] -0.583 234s [19,] -0.684 234s [20,] -0.746 234s > 234s > print( correlation.systemfit( fitsuri2, 2, 1 ) ) 234s [,1] 234s [1,] 0.360 234s [2,] 0.337 234s [3,] 0.337 234s [4,] 0.336 234s [5,] 0.286 234s [6,] 0.299 234s [7,] 0.317 234s [8,] 0.275 234s [9,] 0.322 234s [10,] 0.318 234s [11,] 0.334 234s [12,] 0.334 234s [13,] 0.318 234s [14,] 0.286 234s [15,] 0.358 234s [16,] 0.432 234s [17,] 0.367 234s [18,] 0.362 234s [19,] 0.333 234s [20,] 0.335 234s > 234s > print( correlation.systemfit( fitsuri2w, 1, 2 ) ) 234s [,1] 234s [1,] 0.360 234s [2,] 0.337 234s [3,] 0.337 234s [4,] 0.336 234s [5,] 0.286 234s [6,] 0.299 234s [7,] 0.317 234s [8,] 0.275 234s [9,] 0.322 234s [10,] 0.318 234s [11,] 0.334 234s [12,] 0.334 234s [13,] 0.318 234s [14,] 0.286 234s [15,] 0.358 234s [16,] 0.432 234s [17,] 0.367 234s [18,] 0.362 234s [19,] 0.333 234s [20,] 0.335 234s > 234s > print( correlation.systemfit( fitsuri3e, 1, 2 ) ) 234s [,1] 234s [1,] 0.368 234s [2,] 0.345 234s [3,] 0.344 234s [4,] 0.344 234s [5,] 0.292 234s [6,] 0.305 234s [7,] 0.323 234s [8,] 0.280 234s [9,] 0.329 234s [10,] 0.325 234s [11,] 0.340 234s [12,] 0.340 234s [13,] 0.324 234s [14,] 0.291 234s [15,] 0.366 234s [16,] 0.441 234s [17,] 0.375 234s [18,] 0.369 234s [19,] 0.340 234s [20,] 0.342 234s > 234s > print( correlation.systemfit( fitsurio4, 2, 1 ) ) 234s [,1] 234s [1,] 0.961 234s [2,] 0.971 234s [3,] 0.971 234s [4,] 0.973 234s [5,] 0.940 234s [6,] 0.944 234s [7,] 0.947 234s [8,] 0.939 234s [9,] 0.947 234s [10,] 0.972 234s [11,] 0.904 234s [12,] 0.861 234s [13,] 0.917 234s [14,] 0.922 234s [15,] 0.976 234s [16,] 0.964 234s [17,] 0.978 234s [18,] 0.967 234s [19,] 0.942 234s [20,] 0.934 234s > print( correlation.systemfit( fitsuri4, 2, 1 ) ) 234s [,1] 234s [1,] 0.0384 234s [2,] 0.1213 234s [3,] 0.0975 234s [4,] 0.1381 234s [5,] 0.1295 234s [6,] 0.0937 234s [7,] 0.0630 234s [8,] 0.1056 234s [9,] 0.2180 234s [10,] 0.4042 234s [11,] 0.1074 234s [12,] 0.0337 234s [13,] 0.0760 234s [14,] 0.0701 234s [15,] 0.0680 234s [16,] 0.1263 234s [17,] 0.3859 234s [18,] 0.2715 234s [19,] 0.2850 234s [20,] 0.3967 234s > 234s > print( correlation.systemfit( fitsurio5r2, 1, 2 ) ) 234s [,1] 234s [1,] 0.986 234s [2,] 0.991 234s [3,] 0.991 234s [4,] 0.991 234s [5,] 0.981 234s [6,] 0.983 234s [7,] 0.984 234s [8,] 0.980 234s [9,] 0.982 234s [10,] 0.991 234s [11,] 0.968 234s [12,] 0.947 234s [13,] 0.970 234s [14,] 0.975 234s [15,] 0.991 234s [16,] 0.989 234s [17,] 0.992 234s [18,] 0.990 234s [19,] 0.982 234s [20,] 0.978 234s > print( correlation.systemfit( fitsuri5r2, 1, 2 ) ) 234s [,1] 234s [1,] 0.0440 234s [2,] 0.1279 234s [3,] 0.1045 234s [4,] 0.1451 234s [5,] 0.1375 234s [6,] 0.1021 234s [7,] 0.0719 234s [8,] 0.1124 234s [9,] 0.2252 234s [10,] 0.4097 234s [11,] 0.1145 234s [12,] 0.0410 234s [13,] 0.0834 234s [14,] 0.0778 234s [15,] 0.0750 234s [16,] 0.1344 234s [17,] 0.3900 234s [18,] 0.2789 234s [19,] 0.2897 234s [20,] 0.4005 234s > 234s > 234s > ## ************ Log-Likelihood values *************** 234s > print( logLik( fitsur1e2 ) ) 234s 'log Lik.' -50.9 (df=10) 234s > print( logLik( fitsur1e2, residCovDiag = TRUE ) ) 234s 'log Lik.' -85.4 (df=10) 234s > 234s > print( logLik( fitsur2e ) ) 234s 'log Lik.' -52 (df=9) 234s > print( logLik( fitsur2e, residCovDiag = TRUE ) ) 234s 'log Lik.' -86.5 (df=9) 234s > 234s > print( logLik( fitsur3 ) ) 234s 'log Lik.' -52.2 (df=9) 234s > print( logLik( fitsur3, residCovDiag = TRUE ) ) 234s 'log Lik.' -86.4 (df=9) 234s > 234s > print( logLik( fitsur4r3 ) ) 234s 'log Lik.' -58.4 (df=8) 234s > print( logLik( fitsur4r3, residCovDiag = TRUE ) ) 234s 'log Lik.' -85.5 (df=8) 234s > 234s > print( logLik( fitsur5 ) ) 234s 'log Lik.' -58.5 (df=8) 234s > print( logLik( fitsur5, residCovDiag = TRUE ) ) 234s 'log Lik.' -84.6 (df=8) 234s > 234s > print( logLik( fitsur5w ) ) 234s 'log Lik.' -58.5 (df=8) 234s > print( logLik( fitsur5w, residCovDiag = TRUE ) ) 234s 'log Lik.' -84.7 (df=8) 234s > 234s > print( logLik( fitsuri1r3 ) ) 234s 'log Lik.' -67.8 (df=10) 234s > print( logLik( fitsuri1r3, residCovDiag = TRUE ) ) 234s 'log Lik.' -76.2 (df=10) 234s > 234s > print( logLik( fitsuri2 ) ) 234s 'log Lik.' -99.9 (df=9) 234s > print( logLik( fitsuri2, residCovDiag = TRUE ) ) 234s 'log Lik.' -101 (df=9) 234s > 234s > print( logLik( fitsuri3e ) ) 234s 'log Lik.' -99.9 (df=9) 234s > print( logLik( fitsuri3e, residCovDiag = TRUE ) ) 234s 'log Lik.' -102 (df=9) 234s > 234s > print( logLik( fitsurio4 ) ) 234s 'log Lik.' -58.5 (df=8) 234s > print( logLik( fitsurio4, residCovDiag = TRUE ) ) 234s 'log Lik.' -85.9 (df=8) 234s > 234s > print( logLik( fitsuri4 ) ) 234s 'log Lik.' -101 (df=8) 234s > print( logLik( fitsuri4, residCovDiag = TRUE ) ) 234s 'log Lik.' -101 (df=8) 234s > 234s > print( logLik( fitsuri4w ) ) 234s 'log Lik.' -101 (df=8) 234s > print( logLik( fitsuri4w, residCovDiag = TRUE ) ) 234s 'log Lik.' -101 (df=8) 234s > 234s > print( logLik( fitsurio5r2 ) ) 234s 'log Lik.' -59.8 (df=8) 234s > print( logLik( fitsurio5r2, residCovDiag = TRUE ) ) 234s 'log Lik.' -93.1 (df=8) 234s > 234s > print( logLik( fitsuri5r2 ) ) 234s 'log Lik.' -101 (df=8) 234s > print( logLik( fitsuri5r2, residCovDiag = TRUE ) ) 234s 'log Lik.' -101 (df=8) 234s > 234s > 234s > ## *********** likelihood ratio tests ************* 234s > # testing first restriction 234s > # non-iterating, methodResidCov = 1 234s > print( lrtest( fitsur2, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur2 234s Model 2: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -52.2 234s 2 10 -51.6 1 1.19 0.28 234s > print( lrtest( fitsur3, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur3 234s Model 2: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -52.2 234s 2 10 -51.6 1 1.19 0.28 234s > # non-iterating, methodResidCov = 0 234s > print( lrtest( fitsur2e, fitsur1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur2e 234s Model 2: fitsur1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -52.0 234s 2 10 -51.6 1 0.7 0.4 234s > print( lrtest( fitsur3e, fitsur1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur3e 234s Model 2: fitsur1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -52.0 234s 2 10 -51.6 1 0.7 0.4 234s > # iterating, methodResidCov = 1 234s > print( lrtest( fitsuri2, fitsuri1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri2 234s Model 2: fitsuri1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 10 -67.8 1 64.3 1.1e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsuri3, fitsuri1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri3 234s Model 2: fitsuri1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 10 -67.8 1 64.3 1.1e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # iterating, methodResidCov = 0 234s > print( lrtest( fitsuri2e, fitsuri1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri2e 234s Model 2: fitsuri1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 10 -67.8 1 64.3 1.1e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsuri3e, fitsuri1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri3e 234s Model 2: fitsuri1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 10 -67.8 1 64.3 1.1e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # non-iterating, methodResidCov = 1, WSUR 234s > print( lrtest( fitsur3w, fitsur1w ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur3w 234s Model 2: fitsur1w 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -52.1 234s 2 10 -51.6 1 0.87 0.35 234s > 234s > # testing second restriction 234s > # non-iterating, methodResidCov = 1 234s > print( lrtest( fitsur4, fitsur2 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4 234s Model 2: fitsur2 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.7 0.00037 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur4, fitsur3 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4 234s Model 2: fitsur3 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.7 0.00037 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur5, fitsur2 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5 234s Model 2: fitsur2 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.7 0.00037 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur5, fitsur3 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5 234s Model 2: fitsur3 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.7 0.00037 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # non-iterating, methodResidCov = 0 234s > print( lrtest( fitsur4e, fitsur2e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4e 234s Model 2: fitsur2e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.6 234s 2 9 -52.0 1 13.2 0.00028 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur4e, fitsur3e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4e 234s Model 2: fitsur3e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.6 234s 2 9 -52.0 1 13.2 0.00028 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur5e, fitsur2e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5e 234s Model 2: fitsur2e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.6 234s 2 9 -52.0 1 13.2 0.00028 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur5e, fitsur3e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5e 234s Model 2: fitsur3e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.6 234s 2 9 -52.0 1 13.2 0.00028 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # iterating, methodResidCov = 1 234s > print( lrtest( fitsurio4, fitsuri2 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio4 234s Model 2: fitsuri2 234s Warning message: 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -99.9 1 82.9 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s In lrtest.systemfit(fitsurio4, fitsuri2) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s > print( lrtest( fitsurio4, fitsuri3 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio4 234s Model 2: fitsuri3 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -99.9 1 82.9 <2e-16 *** 234s Warning message: 234s In lrtest.systemfit(fitsurio4, fitsuri3) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsurio5, fitsuri2 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio5 234s Model 2: fitsuri2 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -99.9 1 82.9 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s Warning message: 234s In lrtest.systemfit(fitsurio5, fitsuri2) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s > print( lrtest( fitsurio5, fitsuri3 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio5 234s Model 2: fitsuri3 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -99.9 1 82.9 <2e-16 *** 234s Warning message: 234s In lrtest.systemfit(fitsurio5, fitsuri3) :--- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # corrected 234s > print( lrtest( fitsuri2, fitsuri4 ) ) 234s 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s Likelihood ratio test 234s 234s Model 1: fitsuri2 234s Model 2: fitsuri4 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > print( lrtest( fitsuri3, fitsuri4 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri3 234s Model 2: fitsuri4 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > print( lrtest( fitsuri2, fitsuri5 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri2 234s Model 2: fitsuri5 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > print( lrtest( fitsuri3, fitsuri5 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri3 234s Model 2: fitsuri5 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > 234s > # iterating, methodResidCov = 0 234s > print( lrtest( fitsurio4e, fitsuri2e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio4e 234s Model 2: fitsuri2e 234s Warning message: 234s In lrtest.systemfit(fitsurio4e, fitsuri2e) : #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.4 234s 2 9 -99.9 1 83 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s > print( lrtest( fitsurio4e, fitsuri3e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio4e 234s Model 2: fitsuri3e 234s Warning message: 234s In lrtest.systemfit(fitsurio4e, fitsuri3e) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.4 234s 2 9 -99.9 1 83 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsurio5e, fitsuri2e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio5e 234s Model 2: fitsuri2e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.4 234s 2 9 -99.9 1 83 <2e-16 *** 234s Warning message: 234s In lrtest.systemfit(fitsurio5e, fitsuri2e) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsurio5e, fitsuri3e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio5e 234s Model 2: fitsuri3e 234s Warning message: 234s In lrtest.systemfit(fitsurio5e, fitsuri3e) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.4 234s 2 9 -99.9 1 83 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # corrected 234s > print( lrtest( fitsuri2e, fitsuri4e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri2e 234s Model 2: fitsuri4e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > print( lrtest( fitsuri3e, fitsuri4e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri3e 234s Model 2: fitsuri4e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > print( lrtest( fitsuri2e, fitsuri5e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri2e 234s Model 2: fitsuri5e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > print( lrtest( fitsuri3e, fitsuri5e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri3e 234s Model 2: fitsuri5e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > 234s > # non-iterating, methodResidCov = 0, WSUR 234s > print( lrtest( fitsur4we, fitsur2we ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4we 234s Model 2: fitsur2we 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.6 234s 2 9 -51.8 1 13.5 0.00024 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > # iterating, methodResidCov = 1, WSUR 234s > print( lrtest( fitsuri2w, fitsuri4w ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri2w 234s Model 2: fitsuri4w 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 9 -99.9 234s 2 8 -100.9 -1 1.9 0.17 234s > 234s > # testing both of the restrictions 234s > # non-iterating, methodResidCov = 1 234s > print( lrtest( fitsur4, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4 234s Model 2: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 10 -51.6 2 13.8 0.00098 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur5, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5 234s Model 2: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 10 -51.6 2 13.8 0.00098 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # non-iterating, methodResidCov = 0 234s > print( lrtest( fitsur4e, fitsur1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4e 234s Model 2: fitsur1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.6 234s 2 10 -51.6 2 13.9 0.00095 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur5e, fitsur1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5e 234s Model 2: fitsur1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.6 234s 2 10 -51.6 2 13.9 0.00095 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # iterating, methodResidCov = 1 234s > print( lrtest( fitsurio4, fitsuri1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio4 234s Model 2: fitsuri1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 10 -67.8 2 18.6 9e-05 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsurio5, fitsuri1 ) ) 234s Warning message: 234s In lrtest.systemfit(fitsurio4, fitsuri1) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s Likelihood ratio test 234s 234s Model 1: fitsurio5 234s Model 2: fitsuri1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 10 -67.8 2 18.6 9e-05 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # corrected 234s > print( lrtest( fitsuri1, fitsuri4 ) ) 234s Warning message: 234s In lrtest.systemfit(fitsurio5, fitsuri1) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s Likelihood ratio test 234s 234s Model 1: fitsuri1 234s Model 2: fitsuri4 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 10 -67.8 234s 2 8 -100.9 -2 66.2 4.2e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsuri1, fitsuri5 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri1 234s Model 2: fitsuri5 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 10 -67.8 234s 2 8 -100.9 -2 66.2 4.2e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # iterating, methodResidCov = 0 234s > print( lrtest( fitsurio4e, fitsuri1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsurio4e 234s Model 2: fitsuri1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.4 234s 2 10 -67.8 2 18.7 8.9e-05 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsurio5e, fitsuri1e ) ) 234s Warning message: 234s In lrtest.systemfit(fitsurio4e, fitsuri1e) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s Likelihood ratio test 234s 234s Model 1: fitsurio5e 234s Model 2: fitsuri1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.4 234s 2 10 -67.8 2 18.7 8.9e-05 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s Warning message: 234s In lrtest.systemfit(fitsurio5e, fitsuri1e) : 234s model '2' has a smaller log-likelihood value than the more restricted model '1' 234s > # corrected 234s > print( lrtest( fitsuri1e, fitsuri4e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri1e 234s Model 2: fitsuri4e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 10 -67.8 234s 2 8 -100.9 -2 66.2 4.2e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsuri1e, fitsuri5e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri1e 234s Model 2: fitsuri5e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 10 -67.8 234s 2 8 -100.9 -2 66.2 4.2e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # non-iterating, methodResidCov = 1, WSUR 234s > print( lrtest( fitsur5w, fitsur1w ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5w 234s Model 2: fitsur1w 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 10 -51.6 2 13.8 0.001 ** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > # testing the two restrictions with one call 234s > # non-iterating, methodResidCov = 1 234s > print( lrtest( fitsur4, fitsur2, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur4 234s Model 2: fitsur2 234s Model 3: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.66 0.00037 *** 234s 3 10 -51.6 1 1.19 0.27520 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur5, fitsur3, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5 234s Model 2: fitsur3 234s Model 3: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.66 0.00037 *** 234s 3 10 -51.6 1 1.19 0.27520 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur1, fitsur3, fitsur5 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur1 234s Model 2: fitsur3 234s Model 3: fitsur5 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 10 -51.6 234s 2 9 -52.2 -1 1.19 0.27520 234s 3 8 -58.5 -1 12.66 0.00037 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( object = fitsur5, fitsur3, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5 234s Model 2: fitsur3 234s Model 3: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.66 0.00037 *** 234s 3 10 -51.6 1 1.19 0.27520 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur3, object = fitsur5, fitsur1 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5 234s Model 2: fitsur3 234s Model 3: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.66 0.00037 *** 234s 3 10 -51.6 1 1.19 0.27520 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsur3, fitsur1, object = fitsur5 ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsur5 234s Model 2: fitsur3 234s Model 3: fitsur1 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -58.5 234s 2 9 -52.2 1 12.66 0.00037 *** 234s 3 10 -51.6 1 1.19 0.27520 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > # iterating, methodResidCov = 0 234s > print( lrtest( fitsuri4e, fitsuri2e, fitsuri1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri4e 234s Model 2: fitsuri2e 234s Model 3: fitsuri1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -100.9 234s 2 9 -99.9 1 1.9 0.17 234s 3 10 -67.8 1 64.3 1.1e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > print( lrtest( fitsuri5e, fitsuri3e, fitsuri1e ) ) 234s Likelihood ratio test 234s 234s Model 1: fitsuri5e 234s Model 2: fitsuri3e 234s Model 3: fitsuri1e 234s #Df LogLik Df Chisq Pr(>Chisq) 234s 1 8 -100.9 234s 2 9 -99.9 1 1.9 0.17 234s 3 10 -67.8 1 64.3 1.1e-15 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > ## ************** F tests **************** 234s > # testing first restriction 234s > print( linearHypothesis( fitsur1, restrm ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 1.24 0.27 234s > linearHypothesis( fitsur1, restrict ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 1.24 0.27 234s > 234s > print( linearHypothesis( fitsur1r2, restrm ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1r2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 1.65 0.21 234s > linearHypothesis( fitsur1r2, restrict ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1r2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 1.65 0.21 234s > 234s > print( linearHypothesis( fitsuri1e2, restrm ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1e2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 140 2.1e-13 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1e2, restrict ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1e2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 140 2.1e-13 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsuri1r3, restrm ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1r3 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 141 1.9e-13 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1r3, restrict ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1r3 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 141 1.9e-13 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsur1we2, restrm ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1we2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 1.65 0.21 234s > linearHypothesis( fitsur1we2, restrict ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1we2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 1.65 0.21 234s > 234s > print( linearHypothesis( fitsuri1wr3, restrm ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1wr3 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 141 1.9e-13 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1wr3, restrict ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1wr3 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 141 1.9e-13 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > # testing second restriction 234s > restrOnly2m <- matrix(0,1,7) 234s > restrOnly2q <- 0.5 234s > restrOnly2m[1,2] <- -1 234s > restrOnly2m[1,5] <- 1 234s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 234s > restrictOnly2i <- "- demand_price + supply_income = 0.5" 234s > # first restriction not imposed 234s > print( linearHypothesis( fitsur1e2, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1e2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 2.36 0.13 234s > linearHypothesis( fitsur1e2, restrictOnly2 ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1e2 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 2.36 0.13 234s > 234s > print( linearHypothesis( fitsuri1, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 12.2 0.0014 ** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1, restrictOnly2i ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1 234s 234s Res.Df Df F Pr(>F) 234s 1 34 234s 2 33 1 12.2 0.0014 ** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > # first restriction imposed 234s > print( linearHypothesis( fitsur2, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur2 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 5.5 0.025 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsur2, restrictOnly2 ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur2 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 5.5 0.025 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsur3, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur3 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 5.5 0.025 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsur3, restrictOnly2 ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur3 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 5.5 0.025 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsuri2e, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri2e 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 2.35 0.13 234s > linearHypothesis( fitsuri2e, restrictOnly2i ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri2e 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 2.35 0.13 234s > 234s > print( linearHypothesis( fitsuri3e, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri3e 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 2.35 0.13 234s > linearHypothesis( fitsuri3e, restrictOnly2i ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri3e 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 2.35 0.13 234s > 234s > print( linearHypothesis( fitsur2we, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur2we 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 6.26 0.017 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsur2we, restrictOnly2 ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur2we 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 6.26 0.017 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsuri3we, restrOnly2m, restrOnly2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri3we 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 2.35 0.13 234s > linearHypothesis( fitsuri3we, restrictOnly2i ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri3we 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 34 1 2.35 0.13 234s > 234s > # testing both of the restrictions 234s > print( linearHypothesis( fitsur1r3, restr2m, restr2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1r3 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 2.6 0.089 . 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsur1r3, restrict2 ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1r3 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 2.6 0.089 . 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsuri1e2, restr2m, restr2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1e2 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 89.1 5e-14 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1e2, restrict2i ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1e2 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 89.1 5e-14 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsur1w, restr2m, restr2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1w 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 1.8 0.18 234s > linearHypothesis( fitsur1w, restrict2 ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1w 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 1.8 0.18 234s > 234s > print( linearHypothesis( fitsuri1wr3, restr2m, restr2q ) ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1wr3 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 89.6 4.6e-14 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1wr3, restrict2i ) 234s Linear hypothesis test (Theil's F test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1wr3 234s 234s Res.Df Df F Pr(>F) 234s 1 35 234s 2 33 2 89.6 4.6e-14 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > 234s > ## ************** Wald tests **************** 234s > # testing first restriction 234s > print( linearHypothesis( fitsur1, restrm, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 0.81 0.37 234s > linearHypothesis( fitsur1, restrict, test = "Chisq" ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 0.81 0.37 234s > 234s > print( linearHypothesis( fitsur1r2, restrm, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1r2 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 1.12 0.29 234s > linearHypothesis( fitsur1r2, restrict, test = "Chisq" ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1r2 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 1.12 0.29 234s > 234s > print( linearHypothesis( fitsuri1e2, restrm, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1e2 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 147 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1e2, restrict, test = "Chisq" ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1e2 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 147 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsuri1r3, restrm, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1r3 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 147 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1r3, restrict, test = "Chisq" ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsuri1r3 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 147 <2e-16 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > print( linearHypothesis( fitsur1w, restrm, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1w 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 0.81 0.37 234s > linearHypothesis( fitsur1w, restrict, test = "Chisq" ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s demand_income - supply_trend = 0 234s 234s Model 1: restricted model 234s Model 2: fitsur1w 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 0.81 0.37 234s > 234s > # testing second restriction 234s > # first restriction not imposed 234s > print( linearHypothesis( fitsur1e2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1e2 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 1.6 0.21 234s > linearHypothesis( fitsur1e2, restrictOnly2, test = "Chisq" ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur1e2 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 1.6 0.21 234s > 234s > print( linearHypothesis( fitsuri1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 12.2 0.00047 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsuri1, restrictOnly2i, test = "Chisq" ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s - demand_price + supply_income = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsuri1 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 34 234s 2 33 1 12.2 0.00047 *** 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > 234s > # first restriction imposed 234s > print( linearHypothesis( fitsur2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 234s Linear hypothesis test (Chi^2 statistic of a Wald test) 234s 234s Hypothesis: 234s - demand_price + supply_price = 0.5 234s 234s Model 1: restricted model 234s Model 2: fitsur2 234s 234s Res.Df Df Chisq Pr(>Chisq) 234s 1 35 234s 2 34 1 3.95 0.047 * 234s --- 234s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 234s > linearHypothesis( fitsur2, restrictOnly2, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur2 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 3.95 0.047 * 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > 235s > print( linearHypothesis( fitsur3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur3 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 3.95 0.047 * 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > linearHypothesis( fitsur3, restrictOnly2, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur3 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 3.95 0.047 * 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > 235s > print( linearHypothesis( fitsuri2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri2e 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 2.76 0.096 . 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > linearHypothesis( fitsuri2e, restrictOnly2i, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri2e 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 2.76 0.096 . 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > 235s > print( linearHypothesis( fitsuri3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri3e 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 2.76 0.096 . 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > linearHypothesis( fitsuri3e, restrictOnly2i, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri3e 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 2.76 0.096 . 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > 235s > print( linearHypothesis( fitsuri2w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri2w 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 2.2 0.14 235s > linearHypothesis( fitsuri2w, restrictOnly2i, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri2w 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 2.2 0.14 235s > 235s > print( linearHypothesis( fitsur3w, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur3w 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 4.26 0.039 * 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > linearHypothesis( fitsur3w, restrictOnly2, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur3w 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 34 1 4.26 0.039 * 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > 235s > 235s > # testing both of the restrictions 235s > print( linearHypothesis( fitsur1r3, restr2m, restr2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur1r3 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 3.51 0.17 235s > linearHypothesis( fitsur1r3, restrict2, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur1r3 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 3.51 0.17 235s > 235s > print( linearHypothesis( fitsuri1e2, restr2m, restr2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri1e2 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 188 <2e-16 *** 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > linearHypothesis( fitsuri1e2, restrict2i, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri1e2 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 188 <2e-16 *** 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > 235s > print( linearHypothesis( fitsur1we2, restr2m, restr2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur1we2 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 3.66 0.16 235s > linearHypothesis( fitsur1we2, restrict2, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_price = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsur1we2 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 3.66 0.16 235s > 235s > print( linearHypothesis( fitsuri1wr3, restr2m, restr2q, test = "Chisq" ) ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri1wr3 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 187 <2e-16 *** 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > linearHypothesis( fitsuri1wr3, restrict2i, test = "Chisq" ) 235s Linear hypothesis test (Chi^2 statistic of a Wald test) 235s 235s Hypothesis: 235s demand_income - supply_trend = 0 235s - demand_price + supply_income = 0.5 235s 235s Model 1: restricted model 235s Model 2: fitsuri1wr3 235s 235s Res.Df Df Chisq Pr(>Chisq) 235s 1 35 235s 2 33 2 187 <2e-16 *** 235s --- 235s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 235s > 235s > 235s > ## ****************** model frame ************************** 235s > print( mf <- model.frame( fitsur1e2 ) ) 235s consump price income farmPrice trend 235s 1 98.5 100.3 87.4 98.0 1 235s 2 99.2 104.3 97.6 99.1 2 235s 3 102.2 103.4 96.7 99.1 3 235s 4 101.5 104.5 98.2 98.1 4 235s 5 104.2 98.0 99.8 110.8 5 235s 6 103.2 99.5 100.5 108.2 6 235s 7 104.0 101.1 103.2 105.6 7 235s 8 99.9 104.8 107.8 109.8 8 235s 9 100.3 96.4 96.6 108.7 9 235s 10 102.8 91.2 88.9 100.6 10 235s 11 95.4 93.1 75.1 81.0 11 235s 12 92.4 98.8 76.9 68.6 12 235s 13 94.5 102.9 84.6 70.9 13 235s 14 98.8 98.8 90.6 81.4 14 235s 15 105.8 95.1 103.1 102.3 15 235s 16 100.2 98.5 105.1 105.0 16 235s 17 103.5 86.5 96.4 110.5 17 235s 18 99.9 104.0 104.4 92.5 18 235s 19 105.2 105.8 110.7 89.3 19 235s 20 106.2 113.5 127.1 93.0 20 235s > print( mf1 <- model.frame( fitsur1e2$eq[[ 1 ]] ) ) 235s consump price income 235s 1 98.5 100.3 87.4 235s 2 99.2 104.3 97.6 235s 3 102.2 103.4 96.7 235s 4 101.5 104.5 98.2 235s 5 104.2 98.0 99.8 235s 6 103.2 99.5 100.5 235s 7 104.0 101.1 103.2 235s 8 99.9 104.8 107.8 235s 9 100.3 96.4 96.6 235s 10 102.8 91.2 88.9 235s 11 95.4 93.1 75.1 235s 12 92.4 98.8 76.9 235s 13 94.5 102.9 84.6 235s 14 98.8 98.8 90.6 235s 15 105.8 95.1 103.1 235s 16 100.2 98.5 105.1 235s 17 103.5 86.5 96.4 235s 18 99.9 104.0 104.4 235s 19 105.2 105.8 110.7 235s 20 106.2 113.5 127.1 235s > print( attributes( mf1 )$terms ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > print( mf2 <- model.frame( fitsur1e2$eq[[ 2 ]] ) ) 235s consump price farmPrice trend 235s 1 98.5 100.3 98.0 1 235s 2 99.2 104.3 99.1 2 235s 3 102.2 103.4 99.1 3 235s 4 101.5 104.5 98.1 4 235s 5 104.2 98.0 110.8 5 235s 6 103.2 99.5 108.2 6 235s 7 104.0 101.1 105.6 7 235s 8 99.9 104.8 109.8 8 235s 9 100.3 96.4 108.7 9 235s 10 102.8 91.2 100.6 10 235s 11 95.4 93.1 81.0 11 235s 12 92.4 98.8 68.6 12 235s 13 94.5 102.9 70.9 13 235s 14 98.8 98.8 81.4 14 235s 15 105.8 95.1 102.3 15 235s 16 100.2 98.5 105.0 16 235s 17 103.5 86.5 110.5 17 235s 18 99.9 104.0 92.5 18 235s 19 105.2 105.8 89.3 19 235s 20 106.2 113.5 93.0 20 235s > print( attributes( mf2 )$terms ) 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > 235s > print( all.equal( mf, model.frame( fitsur1w ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsur1w$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsur2e ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsur2e$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsur3 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf2, model.frame( fitsur3$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsur4r3 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsur4r3$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsur4we ) ) ) 235s [1] TRUE 235s > print( all.equal( mf2, model.frame( fitsur4we$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsur5 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf2, model.frame( fitsur5$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsuri1r3 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsuri1r3$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsuri2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsuri2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsuri3e ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsuri3e$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsurio4 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf2, model.frame( fitsurio4$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mf, model.frame( fitsuri4 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsuri4$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsurio5r2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsurio5r2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mf, model.frame( fitsuri5r2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsuri5r2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > print( all.equal( mf, model.frame( fitsuri5wr2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mf1, model.frame( fitsuri5wr2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > 235s > ## **************** model matrix ************************ 235s > # with x (returnModelMatrix) = TRUE 235s > print( !is.null( fitsur1e2$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( mm <- model.matrix( fitsur1e2 ) ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s demand_1 1 100.3 87.4 0 235s demand_2 1 104.3 97.6 0 235s demand_3 1 103.4 96.7 0 235s demand_4 1 104.5 98.2 0 235s demand_5 1 98.0 99.8 0 235s demand_6 1 99.5 100.5 0 235s demand_7 1 101.1 103.2 0 235s demand_8 1 104.8 107.8 0 235s demand_9 1 96.4 96.6 0 235s demand_10 1 91.2 88.9 0 235s demand_11 1 93.1 75.1 0 235s demand_12 1 98.8 76.9 0 235s demand_13 1 102.9 84.6 0 235s demand_14 1 98.8 90.6 0 235s demand_15 1 95.1 103.1 0 235s demand_16 1 98.5 105.1 0 235s demand_17 1 86.5 96.4 0 235s demand_18 1 104.0 104.4 0 235s demand_19 1 105.8 110.7 0 235s demand_20 1 113.5 127.1 0 235s supply_1 0 0.0 0.0 1 235s supply_2 0 0.0 0.0 1 235s supply_3 0 0.0 0.0 1 235s supply_4 0 0.0 0.0 1 235s supply_5 0 0.0 0.0 1 235s supply_6 0 0.0 0.0 1 235s supply_7 0 0.0 0.0 1 235s supply_8 0 0.0 0.0 1 235s supply_9 0 0.0 0.0 1 235s supply_10 0 0.0 0.0 1 235s supply_11 0 0.0 0.0 1 235s supply_12 0 0.0 0.0 1 235s supply_13 0 0.0 0.0 1 235s supply_14 0 0.0 0.0 1 235s supply_15 0 0.0 0.0 1 235s supply_16 0 0.0 0.0 1 235s supply_17 0 0.0 0.0 1 235s supply_18 0 0.0 0.0 1 235s supply_19 0 0.0 0.0 1 235s supply_20 0 0.0 0.0 1 235s supply_price supply_farmPrice supply_trend 235s demand_1 0.0 0.0 0 235s demand_2 0.0 0.0 0 235s demand_3 0.0 0.0 0 235s demand_4 0.0 0.0 0 235s demand_5 0.0 0.0 0 235s demand_6 0.0 0.0 0 235s demand_7 0.0 0.0 0 235s demand_8 0.0 0.0 0 235s demand_9 0.0 0.0 0 235s demand_10 0.0 0.0 0 235s demand_11 0.0 0.0 0 235s demand_12 0.0 0.0 0 235s demand_13 0.0 0.0 0 235s demand_14 0.0 0.0 0 235s demand_15 0.0 0.0 0 235s demand_16 0.0 0.0 0 235s demand_17 0.0 0.0 0 235s demand_18 0.0 0.0 0 235s demand_19 0.0 0.0 0 235s demand_20 0.0 0.0 0 235s supply_1 100.3 98.0 1 235s supply_2 104.3 99.1 2 235s supply_3 103.4 99.1 3 235s supply_4 104.5 98.1 4 235s supply_5 98.0 110.8 5 235s supply_6 99.5 108.2 6 235s supply_7 101.1 105.6 7 235s supply_8 104.8 109.8 8 235s supply_9 96.4 108.7 9 235s supply_10 91.2 100.6 10 235s supply_11 93.1 81.0 11 235s supply_12 98.8 68.6 12 235s supply_13 102.9 70.9 13 235s supply_14 98.8 81.4 14 235s supply_15 95.1 102.3 15 235s supply_16 98.5 105.0 16 235s supply_17 86.5 110.5 17 235s supply_18 104.0 92.5 18 235s supply_19 105.8 89.3 19 235s supply_20 113.5 93.0 20 235s > print( mm1 <- model.matrix( fitsur1e2$eq[[ 1 ]] ) ) 235s (Intercept) price income 235s 1 1 100.3 87.4 235s 2 1 104.3 97.6 235s 3 1 103.4 96.7 235s 4 1 104.5 98.2 235s 5 1 98.0 99.8 235s 6 1 99.5 100.5 235s 7 1 101.1 103.2 235s 8 1 104.8 107.8 235s 9 1 96.4 96.6 235s 10 1 91.2 88.9 235s 11 1 93.1 75.1 235s 12 1 98.8 76.9 235s 13 1 102.9 84.6 235s 14 1 98.8 90.6 235s 15 1 95.1 103.1 235s 16 1 98.5 105.1 235s 17 1 86.5 96.4 235s 18 1 104.0 104.4 235s 19 1 105.8 110.7 235s 20 1 113.5 127.1 235s attr(,"assign") 235s [1] 0 1 2 235s > print( mm2 <- model.matrix( fitsur1e2$eq[[ 2 ]] ) ) 235s (Intercept) price farmPrice trend 235s 1 1 100.3 98.0 1 235s 2 1 104.3 99.1 2 235s 3 1 103.4 99.1 3 235s 4 1 104.5 98.1 4 235s 5 1 98.0 110.8 5 235s 6 1 99.5 108.2 6 235s 7 1 101.1 105.6 7 235s 8 1 104.8 109.8 8 235s 9 1 96.4 108.7 9 235s 10 1 91.2 100.6 10 235s 11 1 93.1 81.0 11 235s 12 1 98.8 68.6 12 235s 13 1 102.9 70.9 13 235s 14 1 98.8 81.4 14 235s 15 1 95.1 102.3 15 235s 16 1 98.5 105.0 16 235s 17 1 86.5 110.5 17 235s 18 1 104.0 92.5 18 235s 19 1 105.8 89.3 19 235s 20 1 113.5 93.0 20 235s attr(,"assign") 235s [1] 0 1 2 3 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsur1r2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur1r2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur1r2$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > print( !is.null( fitsur1r2$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > 235s > # with x (returnModelMatrix) = TRUE 235s > print( !is.null( fitsur2e$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( all.equal( mm, model.matrix( fitsur2e ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur2e$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur2e$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsur2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur2$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > print( !is.null( fitsur2$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > 235s > # with x (returnModelMatrix) = TRUE 235s > print( !is.null( fitsur2we$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( all.equal( mm, model.matrix( fitsur2we ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur2we$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur2we$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsur2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur2$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > print( !is.null( fitsuri2$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > 235s > # with x (returnModelMatrix) = TRUE 235s > print( !is.null( fitsur3e$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( all.equal( mm, model.matrix( fitsur3e ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur3e$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur3e$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsur3 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur3$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur3$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > print( !is.null( fitsur3$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > 235s > # with x (returnModelMatrix) = TRUE 235s > print( !is.null( fitsur3w$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( all.equal( mm, model.matrix( fitsur3w ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur3w$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur3w$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsur3 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur3$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur3$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > print( !is.null( fitsuri3$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > 235s > # with x (returnModelMatrix) = TRUE 235s > print( !is.null( fitsur4r3$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( all.equal( mm, model.matrix( fitsur4r3 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur4r3$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur4r3$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsur4we ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur4we$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm2, model.matrix( fitsur4we$eq[[ 2 ]] ) ) ) 235s [1] TRUE 235s > print( !is.null( fitsur4we$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > 235s > # with x (returnModelMatrix) = TRUE 235s > print( !is.null( fitsurio5r2$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( !is.null( fitsur5$eq[[ 1 ]]$x ) ) 235s [1] TRUE 235s > print( all.equal( mm, model.matrix( fitsurio5r2 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsurio5r2$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > print( all.equal( mm, model.matrix( fitsur5 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur5$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > #print( all.equal( mm2, model.matrix( fitsuri5r2$eq[[ 2 ]] ) ) ) 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsurio5 ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsurio5$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > 235s > # with x (returnModelMatrix) = FALSE 235s > print( all.equal( mm, model.matrix( fitsur5w ) ) ) 235s [1] TRUE 235s > print( all.equal( mm1, model.matrix( fitsur5w$eq[[ 1 ]] ) ) ) 235s [1] TRUE 235s > #print( all.equal( mm2, model.matrix( fitsuri5r2$eq[[ 1 ]] ) ) ) 235s > print( !is.null( fitsurio5$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > print( !is.null( fitsur5w$eq[[ 1 ]]$x ) ) 235s [1] FALSE 235s > 235s > 235s > ## **************** formulas ************************ 235s > formula( fitsur1e2 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsur1e2$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s > 235s > formula( fitsur2e ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsur2e$eq[[ 1 ]] ) 235s consump ~ price + income 235s > 235s > formula( fitsur2we ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsur2we$eq[[ 1 ]] ) 235s consump ~ price + income 235s > 235s > formula( fitsur3 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsur3$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s > 235s > formula( fitsur4r3 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsur4r3$eq[[ 1 ]] ) 235s consump ~ price + income 235s > 235s > formula( fitsur5 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsur5$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s > 235s > formula( fitsuri1r3 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s price ~ income + farmPrice + trend 235s 235s > formula( fitsuri1r3$eq[[ 1 ]] ) 235s consump ~ price + income 235s > 235s > formula( fitsuri2 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s price ~ income + farmPrice + trend 235s 235s > formula( fitsuri2$eq[[ 2 ]] ) 235s price ~ income + farmPrice + trend 235s > 235s > formula( fitsuri3e ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s price ~ income + farmPrice + trend 235s 235s > formula( fitsuri3e$eq[[ 1 ]] ) 235s consump ~ price + income 235s > 235s > formula( fitsurio4 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsurio4$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s > formula( fitsuri4 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s price ~ income + farmPrice + trend 235s 235s > formula( fitsuri4$eq[[ 2 ]] ) 235s price ~ income + farmPrice + trend 235s > 235s > formula( fitsurio5r2 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s 235s > formula( fitsurio5r2$eq[[ 1 ]] ) 235s consump ~ price + income 235s > formula( fitsuri5r2 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s price ~ income + farmPrice + trend 235s 235s > formula( fitsuri5r2$eq[[ 1 ]] ) 235s consump ~ price + income 235s > 235s > formula( fitsuri5wr2 ) 235s $demand 235s consump ~ price + income 235s 235s $supply 235s price ~ income + farmPrice + trend 235s 235s > formula( fitsuri5wr2$eq[[ 1 ]] ) 235s consump ~ price + income 235s > 235s > 235s > ## **************** model terms ******************* 235s > terms( fitsur1e2 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsur1e2$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > 235s > terms( fitsur2e ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsur2e$eq[[ 1 ]] ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > 235s > terms( fitsur3 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsur3$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > 235s > terms( fitsur3w ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsur3w$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > 235s > terms( fitsur4r3 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsur4r3$eq[[ 1 ]] ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > 235s > terms( fitsur4we ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsur4we$eq[[ 1 ]] ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > 235s > terms( fitsur5 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsur5$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > 235s > terms( fitsuri1r3 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s price ~ income + farmPrice + trend 235s attr(,"variables") 235s list(price, income, farmPrice, trend) 235s attr(,"factors") 235s income farmPrice trend 235s price 0 0 0 235s income 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "income" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(price, income, farmPrice, trend) 235s attr(,"dataClasses") 235s price income farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsuri1r3$eq[[ 1 ]] ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > 235s > terms( fitsuri2 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s price ~ income + farmPrice + trend 235s attr(,"variables") 235s list(price, income, farmPrice, trend) 235s attr(,"factors") 235s income farmPrice trend 235s price 0 0 0 235s income 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "income" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(price, income, farmPrice, trend) 235s attr(,"dataClasses") 235s price income farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsuri2$eq[[ 2 ]] ) 235s price ~ income + farmPrice + trend 235s attr(,"variables") 235s list(price, income, farmPrice, trend) 235s attr(,"factors") 235s income farmPrice trend 235s price 0 0 0 235s income 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "income" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(price, income, farmPrice, trend) 235s attr(,"dataClasses") 235s price income farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > 235s > terms( fitsuri3e ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s price ~ income + farmPrice + trend 235s attr(,"variables") 235s list(price, income, farmPrice, trend) 235s attr(,"factors") 235s income farmPrice trend 235s price 0 0 0 235s income 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "income" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(price, income, farmPrice, trend) 235s attr(,"dataClasses") 235s price income farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsuri3e$eq[[ 1 ]] ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > 235s > terms( fitsurio4 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsurio4$eq[[ 2 ]] ) 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > terms( fitsuri4 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s price ~ income + farmPrice + trend 235s attr(,"variables") 235s list(price, income, farmPrice, trend) 235s attr(,"factors") 235s income farmPrice trend 235s price 0 0 0 235s income 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "income" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(price, income, farmPrice, trend) 235s attr(,"dataClasses") 235s price income farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsuri4$eq[[ 2 ]] ) 235s price ~ income + farmPrice + trend 235s attr(,"variables") 235s list(price, income, farmPrice, trend) 235s attr(,"factors") 235s income farmPrice trend 235s price 0 0 0 235s income 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "income" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(price, income, farmPrice, trend) 235s attr(,"dataClasses") 235s price income farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s > 235s > terms( fitsurio5r2 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s consump ~ price + farmPrice + trend 235s attr(,"variables") 235s list(consump, price, farmPrice, trend) 235s attr(,"factors") 235s price farmPrice trend 235s consump 0 0 0 235s price 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "price" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, farmPrice, trend) 235s attr(,"dataClasses") 235s consump price farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsurio5r2$eq[[ 1 ]] ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > terms( fitsuri5r2 ) 235s $demand 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s 235s $supply 235s price ~ income + farmPrice + trend 235s attr(,"variables") 235s list(price, income, farmPrice, trend) 235s attr(,"factors") 235s income farmPrice trend 235s price 0 0 0 235s income 1 0 0 235s farmPrice 0 1 0 235s trend 0 0 1 235s attr(,"term.labels") 235s [1] "income" "farmPrice" "trend" 235s attr(,"order") 235s [1] 1 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(price, income, farmPrice, trend) 235s attr(,"dataClasses") 235s price income farmPrice trend 235s "numeric" "numeric" "numeric" "numeric" 235s 235s > terms( fitsuri5r2$eq[[ 1 ]] ) 235s consump ~ price + income 235s attr(,"variables") 235s list(consump, price, income) 235s attr(,"factors") 235s price income 235s consump 0 0 235s price 1 0 235s income 0 1 235s attr(,"term.labels") 235s [1] "price" "income" 235s attr(,"order") 235s [1] 1 1 235s attr(,"intercept") 235s [1] 1 235s attr(,"response") 235s [1] 1 235s attr(,".Environment") 235s 235s attr(,"predvars") 235s list(consump, price, income) 235s attr(,"dataClasses") 235s consump price income 235s "numeric" "numeric" "numeric" 235s > 235s > 235s > ## **************** estfun ************************ 235s > library( "sandwich" ) 235s > 235s > estfun( fitsur1 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s demand_1 0.9083 91.12 79.38 -0.6496 235s demand_2 -0.7320 -76.32 -71.44 0.5235 235s demand_3 3.2023 331.23 309.66 -2.2902 235s demand_4 2.1435 224.00 210.49 -1.5330 235s demand_5 2.7516 269.66 274.61 -1.9679 235s demand_6 1.7015 169.22 171.00 -1.2169 235s demand_7 2.2068 223.03 227.74 -1.5783 235s demand_8 -3.5946 -376.58 -387.50 2.5708 235s demand_9 -1.6348 -157.67 -157.92 1.1692 235s demand_10 2.7103 247.26 240.95 -1.9384 235s demand_11 -0.8810 -82.01 -66.16 0.6301 235s demand_12 -3.4554 -341.39 -265.72 2.4712 235s demand_13 -2.2246 -228.93 -188.20 1.5910 235s demand_14 -0.5461 -53.93 -49.48 0.3906 235s demand_15 2.4619 234.17 253.82 -1.7607 235s demand_16 -4.3873 -431.94 -461.11 3.1378 235s demand_17 -0.9942 -85.99 -95.84 0.7110 235s demand_18 -2.5012 -260.17 -261.13 1.7888 235s demand_19 2.5805 272.93 285.66 -1.8455 235s demand_20 0.2846 32.30 36.17 -0.2036 235s supply_1 -0.4396 -44.11 -38.42 0.3959 235s supply_2 -0.0184 -1.92 -1.79 0.0166 235s supply_3 -2.5916 -268.06 -250.60 2.3337 235s supply_4 -1.7132 -179.04 -168.24 1.5428 235s supply_5 -2.3049 -225.88 -230.03 2.0756 235s supply_6 -1.3780 -137.06 -138.49 1.2410 235s supply_7 -2.0596 -208.16 -212.55 1.8547 235s supply_8 3.4200 358.29 368.68 -3.0798 235s supply_9 1.9576 188.80 189.10 -1.7628 235s supply_10 -2.3620 -215.48 -209.98 2.1270 235s supply_11 1.1852 110.32 89.01 -1.0673 235s supply_12 2.6183 258.69 201.34 -2.3578 235s supply_13 1.9874 204.52 168.14 -1.7897 235s supply_14 -0.1072 -10.59 -9.72 0.0966 235s supply_15 -2.6839 -255.29 -276.71 2.4169 235s supply_16 3.8259 376.66 402.10 -3.4452 235s supply_17 0.5270 45.59 50.80 -0.4746 235s supply_18 3.0021 312.27 313.42 -2.7035 235s supply_19 -2.0184 -213.48 -223.44 1.8176 235s supply_20 -0.8466 -96.08 -107.60 0.7623 235s supply_price supply_farmPrice supply_trend 235s demand_1 -65.17 -63.66 -0.6496 235s demand_2 54.58 51.88 1.0470 235s demand_3 -236.89 -226.96 -6.8707 235s demand_4 -160.20 -150.38 -6.1319 235s demand_5 -192.86 -218.05 -9.8397 235s demand_6 -121.02 -131.66 -7.3012 235s demand_7 -159.51 -166.67 -11.0480 235s demand_8 269.33 282.28 20.5665 235s demand_9 112.76 127.09 10.5227 235s demand_10 -176.84 -195.00 -19.3840 235s demand_11 58.65 51.04 6.9309 235s demand_12 244.16 169.53 29.6547 235s demand_13 163.73 112.80 20.6833 235s demand_14 38.57 31.79 5.4681 235s demand_15 -167.48 -180.12 -26.4104 235s demand_16 308.92 329.47 50.2044 235s demand_17 61.50 78.57 12.0871 235s demand_18 186.07 165.47 32.1991 235s demand_19 -195.20 -164.81 -35.0650 235s demand_20 -23.10 -18.93 -4.0710 235s supply_1 39.72 38.80 0.3959 235s supply_2 1.73 1.64 0.0331 235s supply_3 241.39 231.27 7.0012 235s supply_4 161.23 151.34 6.1710 235s supply_5 203.41 229.98 10.3781 235s supply_6 123.42 134.27 7.4457 235s supply_7 187.45 195.86 12.9829 235s supply_8 -322.64 -338.16 -24.6380 235s supply_9 -170.02 -191.62 -15.8653 235s supply_10 194.04 213.98 21.2699 235s supply_11 -99.35 -86.45 -11.7402 235s supply_12 -232.95 -161.74 -28.2933 235s supply_13 -184.18 -126.89 -23.2663 235s supply_14 9.54 7.86 1.3521 235s supply_15 229.90 247.25 36.2539 235s supply_16 -339.19 -361.75 -55.1237 235s supply_17 -41.05 -52.44 -8.0678 235s supply_18 -281.20 -250.07 -48.6623 235s supply_19 192.24 162.31 34.5341 235s supply_20 86.52 70.90 15.2466 235s > round( colSums( estfun( fitsur1 ) ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s 0 0 0 0 235s supply_price supply_farmPrice supply_trend 235s 0 0 0 235s > 235s > estfun( fitsur1e2 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s demand_1 1.09034 109.386 95.295 -0.80605 235s demand_2 -1.05992 -110.511 -103.448 0.78356 235s demand_3 4.28760 443.488 414.611 -3.16968 235s demand_4 2.85253 298.107 280.119 -2.10878 235s demand_5 3.80226 372.625 379.466 -2.81088 235s demand_6 2.36197 234.912 237.378 -1.74612 235s demand_7 3.06088 309.351 315.883 -2.26280 235s demand_8 -4.81806 -504.754 -519.386 3.56182 235s demand_9 -2.17915 -210.170 -210.506 1.61097 235s demand_10 3.70159 337.689 329.071 -2.73646 235s demand_11 -1.39799 -130.132 -104.989 1.03349 235s demand_12 -4.96091 -490.143 -381.494 3.66743 235s demand_13 -3.24623 -334.063 -274.631 2.39983 235s demand_14 -0.81794 -80.776 -74.105 0.60467 235s demand_15 3.49861 332.784 360.707 -2.58640 235s demand_16 -5.83443 -574.406 -613.199 4.31320 235s demand_17 -1.15650 -100.035 -111.487 0.85496 235s demand_18 -3.36717 -350.239 -351.532 2.48923 235s demand_19 3.59870 380.631 398.376 -2.66040 235s demand_20 0.58382 66.257 74.203 -0.43160 235s supply_1 -0.54811 -54.988 -47.905 0.47751 235s supply_2 0.00819 0.854 0.799 -0.00713 235s supply_3 -3.61236 -373.644 -349.315 3.14703 235s supply_4 -2.38151 -248.882 -233.865 2.07474 235s supply_5 -3.32295 -325.653 -331.631 2.89490 235s supply_6 -2.00948 -199.855 -201.953 1.75063 235s supply_7 -2.95622 -298.773 -305.081 2.57541 235s supply_8 4.67628 489.901 504.103 -4.07390 235s supply_9 2.65680 256.238 256.647 -2.31456 235s supply_10 -3.31875 -302.763 -295.037 2.89124 235s supply_11 1.84429 171.676 138.506 -1.60672 235s supply_12 3.95003 390.267 303.757 -3.44120 235s supply_13 3.01568 310.338 255.127 -2.62722 235s supply_14 -0.02452 -2.421 -2.221 0.02136 235s supply_15 -3.84791 -366.010 -396.720 3.35224 235s supply_16 5.24831 516.701 551.597 -4.57224 235s supply_17 0.59732 51.667 57.582 -0.52037 235s supply_18 4.17631 434.404 436.007 -3.63834 235s supply_19 -2.86060 -302.562 -316.668 2.49211 235s supply_20 -1.29079 -146.492 -164.060 1.12452 235s supply_price supply_farmPrice supply_trend 235s demand_1 -80.865 -78.993 -0.8060 235s demand_2 81.697 77.651 1.5671 235s demand_3 -327.856 -314.115 -9.5090 235s demand_4 -220.380 -206.871 -8.4351 235s demand_5 -275.469 -311.446 -14.0544 235s demand_6 -173.662 -188.931 -10.4767 235s demand_7 -228.692 -238.952 -15.8396 235s demand_8 373.147 391.088 28.4946 235s demand_9 155.372 175.113 14.4987 235s demand_10 -249.642 -275.288 -27.3646 235s demand_11 96.202 83.712 11.3683 235s demand_12 362.346 251.586 44.0092 235s demand_13 246.962 170.148 31.1978 235s demand_14 59.715 49.220 8.4654 235s demand_15 -246.016 -264.589 -38.7961 235s demand_16 424.638 452.886 69.0111 235s demand_17 73.953 94.473 14.5344 235s demand_18 258.920 230.254 44.8061 235s demand_19 -281.388 -237.573 -50.5475 235s demand_20 -48.982 -40.138 -8.6319 235s supply_1 47.905 46.796 0.4775 235s supply_2 -0.744 -0.707 -0.0143 235s supply_3 325.513 311.871 9.4411 235s supply_4 216.822 203.532 8.2989 235s supply_5 283.704 320.755 14.4745 235s supply_6 174.111 189.418 10.5038 235s supply_7 260.286 271.963 18.0279 235s supply_8 -426.794 -447.314 -32.5912 235s supply_9 -223.230 -251.593 -20.8310 235s supply_10 263.762 290.859 28.9124 235s supply_11 -149.561 -130.144 -17.6739 235s supply_12 -339.994 -236.066 -41.2944 235s supply_13 -270.361 -186.270 -34.1538 235s supply_14 2.109 1.739 0.2990 235s supply_15 318.862 342.934 50.2836 235s supply_16 -450.142 -480.085 -73.1559 235s supply_17 -45.011 -57.501 -8.8464 235s supply_18 -378.445 -336.546 -65.4901 235s supply_19 263.588 222.545 47.3500 235s supply_20 127.621 104.580 22.4903 235s > round( colSums( estfun( fitsur1e2 ) ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s 0 0 0 0 235s supply_price supply_farmPrice supply_trend 235s 0 0 0 235s > 235s > estfun( fitsur1r3 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s demand_1 1.07229 107.575 93.718 -0.79049 235s demand_2 -1.02096 -106.450 -99.646 0.75265 235s demand_3 4.16424 430.729 402.682 -3.06988 235s demand_4 2.77231 289.723 272.240 -2.04374 235s demand_5 3.68037 360.680 367.301 -2.71316 235s demand_6 2.28513 227.270 229.656 -1.68460 235s demand_7 2.96157 299.314 305.634 -2.18327 235s demand_8 -4.67889 -490.175 -504.385 3.44927 235s demand_9 -2.11749 -204.223 -204.549 1.56101 235s demand_10 3.58740 327.271 318.920 -2.64463 235s demand_11 -1.33464 -124.235 -100.231 0.98389 235s demand_12 -4.78276 -472.541 -367.794 3.52584 235s demand_13 -3.12449 -321.535 -264.332 2.30337 235s demand_14 -0.78522 -77.545 -71.141 0.57886 235s demand_15 3.37652 321.171 348.119 -2.48917 235s demand_16 -5.67080 -558.296 -596.001 4.18051 235s demand_17 -1.14172 -98.757 -110.062 0.84168 235s demand_18 -3.26836 -339.962 -341.217 2.40943 235s demand_19 3.47995 368.071 385.231 -2.56542 235s demand_20 0.54555 61.914 69.339 -0.40218 235s supply_1 -0.53834 -54.008 -47.051 0.47031 235s supply_2 0.00335 0.349 0.327 -0.00293 235s supply_3 -3.49682 -361.694 -338.143 3.05492 235s supply_4 -2.30621 -241.013 -226.470 2.01477 235s supply_5 -3.20507 -314.100 -319.866 2.80004 235s supply_6 -1.93606 -192.553 -194.574 1.69139 235s supply_7 -2.85248 -288.289 -294.376 2.49200 235s supply_8 4.53460 475.059 488.830 -3.96155 235s supply_9 2.57840 248.676 249.073 -2.25256 235s supply_10 -3.20906 -292.756 -285.286 2.80352 235s supply_11 1.76494 164.289 132.547 -1.54190 235s supply_12 3.79168 374.622 291.580 -3.31251 235s supply_13 2.89330 297.744 244.773 -2.52766 235s supply_14 -0.03625 -3.580 -3.284 0.03167 235s supply_15 -3.71220 -353.101 -382.728 3.24307 235s supply_16 5.08854 500.972 534.805 -4.44548 235s supply_17 0.59312 51.303 57.176 -0.51816 235s supply_18 4.04346 420.584 422.137 -3.53247 235s supply_19 -2.76240 -292.176 -305.797 2.41330 235s supply_20 -1.23648 -140.329 -157.157 1.08023 235s supply_price supply_farmPrice supply_trend 235s demand_1 -79.304 -77.47 -0.79049 235s demand_2 78.475 74.59 1.50531 235s demand_3 -317.533 -304.22 -9.20963 235s demand_4 -213.583 -200.49 -8.17496 235s demand_5 -265.893 -300.62 -13.56581 235s demand_6 -167.543 -182.27 -10.10759 235s demand_7 -220.654 -230.55 -15.28289 235s demand_8 361.356 378.73 27.59420 235s demand_9 150.553 169.68 14.04907 235s demand_10 -241.264 -266.05 -26.44627 235s demand_11 91.586 79.70 10.82281 235s demand_12 348.357 241.87 42.31014 235s demand_13 237.035 163.31 29.94383 235s demand_14 57.166 47.12 8.10410 235s demand_15 -236.767 -254.64 -37.33751 235s demand_16 411.575 438.95 66.88809 235s demand_17 72.803 93.01 14.30850 235s demand_18 250.619 222.87 43.36977 235s demand_19 -271.341 -229.09 -48.74290 235s demand_20 -45.643 -37.40 -8.04353 235s supply_1 47.183 46.09 0.47031 235s supply_2 -0.305 -0.29 -0.00585 235s supply_3 315.985 302.74 9.16476 235s supply_4 210.555 197.65 8.05908 235s supply_5 274.406 310.24 14.00018 235s supply_6 168.219 183.01 10.14835 235s supply_7 251.857 263.16 17.44401 235s supply_8 -415.024 -434.98 -31.69241 235s supply_9 -217.250 -244.85 -20.27300 235s supply_10 255.760 282.03 28.03523 235s supply_11 -143.528 -124.89 -16.96088 235s supply_12 -327.279 -227.24 -39.75013 235s supply_13 -260.117 -179.21 -32.85963 235s supply_14 3.128 2.58 0.44339 235s supply_15 308.478 331.77 48.64611 235s supply_16 -437.662 -466.78 -71.12773 235s supply_17 -44.820 -57.26 -8.80876 235s supply_18 -367.434 -326.75 -63.58452 235s supply_19 255.253 215.51 45.85274 235s supply_20 122.595 100.46 21.60450 235s > round( colSums( estfun( fitsur1r3 ) ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s 0 0 0 0 235s supply_price supply_farmPrice supply_trend 235s 0 0 0 235s > 235s > estfun( fitsur1w ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s demand_1 0.9083 91.12 79.38 -0.6496 235s demand_2 -0.7320 -76.32 -71.44 0.5235 235s demand_3 3.2023 331.23 309.66 -2.2902 235s demand_4 2.1435 224.00 210.49 -1.5330 235s demand_5 2.7516 269.66 274.61 -1.9679 235s demand_6 1.7015 169.22 171.00 -1.2169 235s demand_7 2.2068 223.03 227.74 -1.5783 235s demand_8 -3.5946 -376.58 -387.50 2.5708 235s demand_9 -1.6348 -157.67 -157.92 1.1692 235s demand_10 2.7103 247.26 240.95 -1.9384 235s demand_11 -0.8810 -82.01 -66.16 0.6301 235s demand_12 -3.4554 -341.39 -265.72 2.4712 235s demand_13 -2.2246 -228.93 -188.20 1.5910 235s demand_14 -0.5461 -53.93 -49.48 0.3906 235s demand_15 2.4619 234.17 253.82 -1.7607 235s demand_16 -4.3873 -431.94 -461.11 3.1378 235s demand_17 -0.9942 -85.99 -95.84 0.7110 235s demand_18 -2.5012 -260.17 -261.13 1.7888 235s demand_19 2.5805 272.93 285.66 -1.8455 235s demand_20 0.2846 32.30 36.17 -0.2036 235s supply_1 -0.4396 -44.11 -38.42 0.3959 235s supply_2 -0.0184 -1.92 -1.79 0.0166 235s supply_3 -2.5916 -268.06 -250.60 2.3337 235s supply_4 -1.7132 -179.04 -168.24 1.5428 235s supply_5 -2.3049 -225.88 -230.03 2.0756 235s supply_6 -1.3780 -137.06 -138.49 1.2410 235s supply_7 -2.0596 -208.16 -212.55 1.8547 235s supply_8 3.4200 358.29 368.68 -3.0798 235s supply_9 1.9576 188.80 189.10 -1.7628 235s supply_10 -2.3620 -215.48 -209.98 2.1270 235s supply_11 1.1852 110.32 89.01 -1.0673 235s supply_12 2.6183 258.69 201.34 -2.3578 235s supply_13 1.9874 204.52 168.14 -1.7897 235s supply_14 -0.1072 -10.59 -9.72 0.0966 235s supply_15 -2.6839 -255.29 -276.71 2.4169 235s supply_16 3.8259 376.66 402.10 -3.4452 235s supply_17 0.5270 45.59 50.80 -0.4746 235s supply_18 3.0021 312.27 313.42 -2.7035 235s supply_19 -2.0184 -213.48 -223.44 1.8176 235s supply_20 -0.8466 -96.08 -107.60 0.7623 235s supply_price supply_farmPrice supply_trend 235s demand_1 -65.17 -63.66 -0.6496 235s demand_2 54.58 51.88 1.0470 235s demand_3 -236.89 -226.96 -6.8707 235s demand_4 -160.20 -150.38 -6.1319 235s demand_5 -192.86 -218.05 -9.8397 235s demand_6 -121.02 -131.66 -7.3012 235s demand_7 -159.51 -166.67 -11.0480 235s demand_8 269.33 282.28 20.5665 235s demand_9 112.76 127.09 10.5227 235s demand_10 -176.84 -195.00 -19.3840 235s demand_11 58.65 51.04 6.9309 235s demand_12 244.16 169.53 29.6547 235s demand_13 163.73 112.80 20.6833 235s demand_14 38.57 31.79 5.4681 235s demand_15 -167.48 -180.12 -26.4104 235s demand_16 308.92 329.47 50.2044 235s demand_17 61.50 78.57 12.0871 235s demand_18 186.07 165.47 32.1991 235s demand_19 -195.20 -164.81 -35.0650 235s demand_20 -23.10 -18.93 -4.0710 235s supply_1 39.72 38.80 0.3959 235s supply_2 1.73 1.64 0.0331 235s supply_3 241.39 231.27 7.0012 235s supply_4 161.23 151.34 6.1710 235s supply_5 203.41 229.98 10.3781 235s supply_6 123.42 134.27 7.4457 235s supply_7 187.45 195.86 12.9829 235s supply_8 -322.64 -338.16 -24.6380 235s supply_9 -170.02 -191.62 -15.8653 235s supply_10 194.04 213.98 21.2699 235s supply_11 -99.35 -86.45 -11.7402 235s supply_12 -232.95 -161.74 -28.2933 235s supply_13 -184.18 -126.89 -23.2663 235s supply_14 9.54 7.86 1.3521 235s supply_15 229.90 247.25 36.2539 235s supply_16 -339.19 -361.75 -55.1237 235s supply_17 -41.05 -52.44 -8.0678 235s supply_18 -281.20 -250.07 -48.6623 235s supply_19 192.24 162.31 34.5341 235s supply_20 86.52 70.90 15.2466 235s > round( colSums( estfun( fitsur1w ) ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s 0 0 0 0 235s supply_price supply_farmPrice supply_trend 235s 0 0 0 235s > 235s > estfun( fitsuri1e ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s demand_1 0.5467 54.84 47.78 0.5219 235s demand_2 -0.5182 -54.03 -50.58 -0.4947 235s demand_3 1.5799 163.41 152.77 1.5082 235s demand_4 0.9787 102.28 96.11 0.9343 235s demand_5 1.4899 146.02 148.70 1.4224 235s demand_6 0.8875 88.27 89.19 0.8472 235s demand_7 1.0809 109.24 111.55 1.0319 235s demand_8 -2.1165 -221.73 -228.15 -2.0205 235s demand_9 -0.7383 -71.21 -71.32 -0.7049 235s demand_10 1.7668 161.19 157.07 1.6867 235s demand_11 -0.0682 -6.35 -5.12 -0.0651 235s demand_12 -1.6133 -159.40 -124.07 -1.5402 235s demand_13 -1.1570 -119.06 -97.88 -1.1045 235s demand_14 -0.1925 -19.01 -17.44 -0.1838 235s demand_15 1.4026 133.41 144.61 1.3390 235s demand_16 -2.3128 -227.70 -243.08 -2.2080 235s demand_17 -0.0876 -7.58 -8.44 -0.0836 235s demand_18 -1.4924 -155.23 -155.81 -1.4247 235s demand_19 1.0702 113.20 118.47 1.0217 235s demand_20 -0.5064 -57.47 -64.36 -0.4834 235s supply_1 0.1054 10.57 9.21 0.1789 235s supply_2 -0.8882 -92.60 -86.68 -1.5080 235s supply_3 -0.5218 -53.97 -50.46 -0.8859 235s supply_4 -0.2644 -27.63 -25.96 -0.4489 235s supply_5 -0.7666 -75.13 -76.51 -1.3016 235s supply_6 -0.4056 -40.34 -40.77 -0.6887 235s supply_7 -0.8114 -82.00 -83.74 -1.3777 235s supply_8 1.4243 149.22 153.54 2.4183 235s supply_9 1.0270 99.05 99.21 1.7438 235s supply_10 -1.0278 -93.77 -91.37 -1.7451 235s supply_11 0.6336 58.98 47.58 1.0758 235s supply_12 0.2724 26.92 20.95 0.4626 235s supply_13 0.8434 86.79 71.35 1.4319 235s supply_14 -0.7107 -70.19 -64.39 -1.2067 235s supply_15 -1.5343 -145.94 -158.18 -2.6050 235s supply_16 1.1276 111.01 118.51 1.9145 235s supply_17 -0.6907 -59.75 -66.58 -1.1727 235s supply_18 2.2394 232.94 233.79 3.8022 235s supply_19 0.1792 18.96 19.84 0.3043 235s supply_20 -0.2309 -26.21 -29.35 -0.3921 235s supply_income supply_farmPrice supply_trend 235s demand_1 45.61 51.15 0.522 235s demand_2 -48.28 -49.03 -0.989 235s demand_3 145.85 149.47 4.525 235s demand_4 91.75 91.66 3.737 235s demand_5 141.95 157.60 7.112 235s demand_6 85.15 91.67 5.083 235s demand_7 106.49 108.97 7.223 235s demand_8 -217.81 -221.85 -16.164 235s demand_9 -68.09 -76.62 -6.344 235s demand_10 149.95 169.69 16.867 235s demand_11 -4.89 -5.28 -0.717 235s demand_12 -118.44 -105.66 -18.482 235s demand_13 -93.44 -78.31 -14.359 235s demand_14 -16.65 -14.96 -2.573 235s demand_15 138.05 136.98 20.085 235s demand_16 -232.06 -231.84 -35.327 235s demand_17 -8.06 -9.24 -1.421 235s demand_18 -148.74 -131.79 -25.645 235s demand_19 113.10 91.24 19.412 235s demand_20 -61.44 -44.96 -9.668 235s supply_1 15.64 17.53 0.179 235s supply_2 -147.18 -149.44 -3.016 235s supply_3 -85.67 -87.79 -2.658 235s supply_4 -44.08 -44.04 -1.796 235s supply_5 -129.90 -144.21 -6.508 235s supply_6 -69.22 -74.52 -4.132 235s supply_7 -142.17 -145.48 -9.644 235s supply_8 260.69 265.53 19.346 235s supply_9 168.45 189.55 15.694 235s supply_10 -155.14 -175.56 -17.451 235s supply_11 80.79 87.14 11.833 235s supply_12 35.57 31.73 5.551 235s supply_13 121.14 101.52 18.615 235s supply_14 -109.33 -98.23 -16.894 235s supply_15 -268.57 -266.49 -39.075 235s supply_16 201.22 201.03 30.633 235s supply_17 -113.05 -129.59 -19.937 235s supply_18 396.95 351.71 68.440 235s supply_19 33.69 27.18 5.782 235s supply_20 -49.83 -36.46 -7.841 235s > round( colSums( estfun( fitsuri1e ) ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s 0 0 0 0 235s supply_income supply_farmPrice supply_trend 235s 0 0 0 235s > 235s > estfun( fitsuri1wr3 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s demand_1 0.5102 51.19 44.59 0.4867 235s demand_2 -0.4886 -50.94 -47.68 -0.4661 235s demand_3 1.4782 152.90 142.94 1.4102 235s demand_4 0.9143 95.55 89.79 0.8722 235s demand_5 1.3982 137.03 139.54 1.3339 235s demand_6 0.8327 82.82 83.69 0.7944 235s demand_7 1.0134 102.42 104.59 0.9668 235s demand_8 -1.9849 -207.94 -213.97 -1.8935 235s demand_9 -0.6897 -66.52 -66.63 -0.6580 235s demand_10 1.6602 151.46 147.60 1.5838 235s demand_11 -0.0636 -5.92 -4.77 -0.0606 235s demand_12 -1.5152 -149.71 -116.52 -1.4455 235s demand_13 -1.0888 -112.05 -92.11 -1.0387 235s demand_14 -0.1809 -17.86 -16.39 -0.1726 235s demand_15 1.3190 125.46 135.99 1.2583 235s demand_16 -2.1651 -213.16 -227.55 -2.0655 235s demand_17 -0.0731 -6.33 -7.05 -0.0698 235s demand_18 -1.4001 -145.63 -146.17 -1.3357 235s demand_19 1.0017 105.95 110.89 0.9556 235s demand_20 -0.4780 -54.25 -60.76 -0.4560 235s supply_1 0.0755 7.57 6.60 0.1193 235s supply_2 -0.8526 -88.90 -83.22 -1.3478 235s supply_3 -0.5074 -52.48 -49.07 -0.8021 235s supply_4 -0.2631 -27.49 -25.83 -0.4159 235s supply_5 -0.7425 -72.77 -74.10 -1.1737 235s supply_6 -0.3998 -39.77 -40.18 -0.6320 235s supply_7 -0.7750 -78.33 -79.98 -1.2251 235s supply_8 1.3178 138.06 142.06 2.0831 235s supply_9 0.9476 91.39 91.54 1.4979 235s supply_10 -0.9683 -88.34 -86.08 -1.5306 235s supply_11 0.6060 56.40 45.51 0.9578 235s supply_12 0.2813 27.79 21.63 0.4446 235s supply_13 0.8170 84.07 69.12 1.2914 235s supply_14 -0.6451 -63.71 -58.44 -1.0197 235s supply_15 -1.4315 -136.17 -147.59 -2.2629 235s supply_16 1.0615 104.50 111.56 1.6779 235s supply_17 -0.6453 -55.82 -62.21 -1.0200 235s supply_18 2.1183 220.33 221.15 3.3484 235s supply_19 0.1946 20.58 21.54 0.3076 235s supply_20 -0.1888 -21.42 -23.99 -0.2984 235s supply_income supply_farmPrice supply_trend 235s demand_1 42.54 47.70 0.487 235s demand_2 -45.49 -46.19 -0.932 235s demand_3 136.37 139.75 4.231 235s demand_4 85.65 85.57 3.489 235s demand_5 133.12 147.79 6.669 235s demand_6 79.84 85.95 4.766 235s demand_7 99.77 102.09 6.768 235s demand_8 -204.12 -207.91 -15.148 235s demand_9 -63.56 -71.52 -5.922 235s demand_10 140.80 159.34 15.838 235s demand_11 -4.55 -4.91 -0.667 235s demand_12 -111.16 -99.16 -17.346 235s demand_13 -87.88 -73.64 -13.503 235s demand_14 -15.63 -14.05 -2.416 235s demand_15 129.73 128.72 18.874 235s demand_16 -217.08 -216.88 -33.048 235s demand_17 -6.73 -7.71 -1.186 235s demand_18 -139.45 -123.55 -24.042 235s demand_19 105.78 85.33 18.156 235s demand_20 -57.96 -42.41 -9.120 235s supply_1 10.43 11.69 0.119 235s supply_2 -131.54 -133.56 -2.696 235s supply_3 -77.56 -79.49 -2.406 235s supply_4 -40.84 -40.80 -1.663 235s supply_5 -117.13 -130.04 -5.868 235s supply_6 -63.52 -68.39 -3.792 235s supply_7 -126.43 -129.37 -8.575 235s supply_8 224.56 228.72 16.665 235s supply_9 144.70 162.82 13.481 235s supply_10 -136.07 -153.98 -15.306 235s supply_11 71.93 77.58 10.536 235s supply_12 34.19 30.50 5.335 235s supply_13 109.25 91.56 16.788 235s supply_14 -92.38 -83.00 -14.276 235s supply_15 -233.30 -231.49 -33.943 235s supply_16 176.34 176.17 26.846 235s supply_17 -98.33 -112.71 -17.341 235s supply_18 349.57 309.73 60.271 235s supply_19 34.05 27.47 5.845 235s supply_20 -37.92 -27.75 -5.967 235s > round( colSums( estfun( fitsuri1wr3 ) ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s 0 0 0 0 235s supply_income supply_farmPrice supply_trend 235s 0 0 0 235s > 235s > estfun( fitsurS1 ) 235s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 235s eq1_1 7.162 0.02160 2.127 0.0216 235s eq1_2 15.562 0.04659 4.621 0.0932 235s eq1_3 6.026 0.01752 1.789 0.0525 235s eq1_4 10.524 0.03079 3.125 0.1232 235s eq1_5 -14.099 -0.04017 -4.187 -0.2008 235s eq1_6 -7.426 -0.02136 -2.205 -0.1282 235s eq1_7 -5.141 -0.01468 -1.527 -0.1028 235s eq1_8 15.138 0.04500 4.495 0.3600 235s eq1_9 -7.596 -0.02248 -2.256 -0.2023 235s eq1_10 -28.217 -0.08150 -8.379 -0.8150 235s eq1_11 -3.498 -0.01088 -1.039 -0.1197 235s eq1_12 17.457 0.05609 5.184 0.6731 235s eq1_13 22.800 0.07162 6.771 0.9311 235s eq1_14 2.479 0.00746 0.736 0.1044 235s eq1_15 -26.446 -0.07423 -7.853 -1.1135 235s eq1_16 -2.054 -0.00609 -0.610 -0.0974 235s eq1_17 -42.973 -0.12327 -12.761 -2.0956 235s eq1_18 13.132 0.03902 3.900 0.7024 235s eq1_19 4.307 0.01216 1.279 0.2310 235s eq1_20 22.866 0.06392 6.790 1.2784 235s eq2_1 -1.322 -0.02928 -2.884 -0.0293 235s eq2_2 -0.971 -0.02136 -2.118 -0.0427 235s eq2_3 -5.293 -0.11298 -11.542 -0.3389 235s eq2_4 -4.273 -0.09180 -9.318 -0.3672 235s eq2_5 1.836 0.03840 4.003 0.1920 235s eq2_6 2.119 0.04477 4.622 0.2686 235s eq2_7 -0.532 -0.01115 -1.160 -0.0781 235s eq2_8 10.068 0.21978 21.956 1.7582 235s eq2_9 9.192 0.19974 20.044 1.7977 235s eq2_10 -0.465 -0.00986 -1.014 -0.0986 235s eq2_11 -2.679 -0.06122 -5.843 -0.6735 235s eq2_12 -6.257 -0.14762 -13.644 -1.7715 235s eq2_13 -7.360 -0.16978 -16.050 -2.2072 235s eq2_14 -5.865 -0.12951 -12.790 -1.8131 235s eq2_15 -0.730 -0.01505 -1.593 -0.2258 235s eq2_16 11.188 0.24342 24.396 3.8947 235s eq2_17 11.047 0.23271 24.091 3.9561 235s eq2_18 3.346 0.07302 7.297 1.3144 235s eq2_19 -7.478 -0.15498 -16.307 -2.9445 235s eq2_20 -5.570 -0.11434 -12.146 -2.2868 235s > round( colSums( estfun( fitsurS1 ) ), digits = 7 ) 235s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 235s 0 0 0 0 235s > 235s > estfun( fitsurS2 ) 235s eq1_price eq2_trend 235s eq1_1 -5.42871 -0.000114 235s eq1_2 -13.14782 -0.000531 235s eq1_3 -4.34907 -0.000266 235s eq1_4 -8.39779 -0.000677 235s eq1_5 12.19030 0.001310 235s eq1_6 6.97176 0.000886 235s eq1_7 5.14513 0.000750 235s eq1_8 -12.72321 -0.002046 235s eq1_9 7.04895 0.001385 235s eq1_10 22.20478 0.005126 235s eq1_11 3.65437 0.000909 235s eq1_12 -15.21951 -0.003893 235s eq1_13 -20.44077 -0.005438 235s eq1_14 -1.31641 -0.000393 235s eq1_15 21.18383 0.007035 235s eq1_16 2.54257 0.000870 235s eq1_17 31.47441 0.013026 235s eq1_18 -10.84129 -0.003951 235s eq1_19 -2.78655 -0.001054 235s eq1_20 -19.91341 -0.007390 235s eq2_1 0.42448 0.037215 235s eq2_2 0.40866 0.068949 235s eq2_3 0.38411 0.097989 235s eq2_4 0.34891 0.117463 235s eq2_5 0.30591 0.137281 235s eq2_6 0.27161 0.144126 235s eq2_7 0.24474 0.149098 235s eq2_8 0.19771 0.132796 235s eq2_9 0.15083 0.123801 235s eq2_10 0.12174 0.117373 235s eq2_11 0.06024 0.062610 235s eq2_12 0.01611 0.017205 235s eq2_13 -0.00856 -0.009507 235s eq2_14 -0.02284 -0.028474 235s eq2_15 -0.02363 -0.032773 235s eq2_16 -0.08383 -0.119831 235s eq2_17 -0.09018 -0.155889 235s eq2_18 -0.16161 -0.245985 235s eq2_19 -0.17473 -0.276076 235s eq2_20 -0.22123 -0.342915 235s > round( colSums( estfun( fitsurS2 ) ), digits = 7 ) 235s eq1_price eq2_trend 235s 0 0 235s > 235s > estfun( fitsurS3 ) 235s eq1_trend eq2_trend 235s eq1_1 2.069 -2.039 235s eq1_2 3.833 -3.777 235s eq1_3 5.448 -5.369 235s eq1_4 6.531 -6.436 235s eq1_5 7.634 -7.523 235s eq1_6 8.015 -7.899 235s eq1_7 8.293 -8.173 235s eq1_8 7.389 -7.281 235s eq1_9 6.890 -6.790 235s eq1_10 6.535 -6.440 235s eq1_11 3.493 -3.443 235s eq1_12 0.972 -0.958 235s eq1_13 -0.510 0.503 235s eq1_14 -1.562 1.539 235s eq1_15 -1.798 1.772 235s eq1_16 -6.634 6.537 235s eq1_17 -8.634 8.509 235s eq1_18 -13.639 13.441 235s eq1_19 -15.308 15.085 235s eq1_20 -19.019 18.743 235s eq2_1 -2.082 2.089 235s eq2_2 -4.012 4.027 235s eq2_3 -5.472 5.491 235s eq2_4 -6.736 6.760 235s eq2_5 -6.873 6.897 235s eq2_6 -7.460 7.486 235s eq2_7 -7.809 7.837 235s eq2_8 -8.276 8.305 235s eq2_9 -6.161 6.182 235s eq2_10 -4.039 4.053 235s eq2_11 -3.098 3.109 235s eq2_12 -2.949 2.960 235s eq2_13 -2.261 2.269 235s eq2_14 1.160 -1.164 235s eq2_15 4.921 -4.939 235s eq2_16 6.677 -6.701 235s eq2_17 14.428 -14.479 235s eq2_18 11.167 -11.207 235s eq2_19 14.155 -14.205 235s eq2_20 14.719 -14.771 235s > round( colSums( estfun( fitsurS3 ) ), digits = 7 ) 235s eq1_trend eq2_trend 235s 0 0 235s > 235s > try( estfun( fitsurS4 ) ) 235s Error in estfun.systemfit(fitsurS4) : 235s returning the estimation function for models with restrictions has not yet been impleme> 235s > estfun( fitsurS5 ) 235s nted. 235s eq1_(Intercept) eq2_(Intercept) 235s eq1_1 -0.17267 0.01074 235s eq1_2 -0.12244 0.00761 235s eq1_3 0.09050 -0.00563 235s eq1_4 0.04335 -0.00270 235s eq1_5 0.23912 -0.01487 235s eq1_6 0.16778 -0.01043 235s eq1_7 0.22144 -0.01377 235s eq1_8 -0.07143 0.00444 235s eq1_9 -0.03923 0.00244 235s eq1_10 0.13751 -0.00855 235s eq1_11 -0.39091 0.02431 235s eq1_12 -0.60636 0.03770 235s eq1_13 -0.45531 0.02831 235s eq1_14 -0.15321 0.00953 235s eq1_15 0.35053 -0.02180 235s eq1_16 -0.04817 0.00300 235s eq1_17 0.18774 -0.01167 235s eq1_18 -0.06935 0.00431 235s eq1_19 0.30946 -0.01924 235s eq1_20 0.38165 -0.02373 235s eq2_1 -0.00135 0.00874 235s eq2_2 -0.01889 0.12205 235s eq2_3 -0.01520 0.09821 235s eq2_4 -0.01996 0.12901 235s eq2_5 0.00898 -0.05802 235s eq2_6 0.00251 -0.01619 235s eq2_7 -0.00466 0.03010 235s eq2_8 -0.02111 0.13640 235s eq2_9 0.01590 -0.10273 235s eq2_10 0.03911 -0.25276 235s eq2_11 0.03085 -0.19937 235s eq2_12 0.00542 -0.03502 235s eq2_13 -0.01285 0.08306 235s eq2_14 0.00562 -0.03631 235s eq2_15 0.02180 -0.14088 235s eq2_16 0.00698 -0.04508 235s eq2_17 0.06016 -0.38875 235s eq2_18 -0.01778 0.11492 235s eq2_19 -0.02558 0.16532 235s eq2_20 -0.05994 0.38731 235s > round( colSums( estfun( fitsurS5 ) ), digits = 7 ) 235s eq1_(Intercept) eq2_(Intercept) 235s 0 0 235s > 235s > 235s > ## **************** bread ************************ 235s > round( bread( fitsur1 ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s [1,] 2258.680 -23.5779 1.0971 2354.23 235s [2,] -23.578 0.3134 -0.0796 -15.01 235s [3,] 1.097 -0.0796 0.0704 -8.66 235s [4,] 2354.232 -15.0109 -8.6593 4911.36 235s [5,] -24.454 0.2225 0.0225 -38.45 235s [6,] 0.887 -0.0644 0.0569 -9.51 235s [7,] 1.348 -0.0978 0.0864 -12.94 235s supply_price supply_farmPrice supply_trend 235s [1,] -24.4536 0.8871 1.3477 235s [2,] 0.2225 -0.0644 -0.0978 235s [3,] 0.0225 0.0569 0.0864 235s [4,] -38.4456 -9.5077 -12.9352 235s [5,] 0.3567 0.0252 0.0320 235s [6,] 0.0252 0.0636 0.0807 235s [7,] 0.0320 0.0807 0.1845 235s > 235s > round( bread( fitsur1e2 ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s [1,] 2257.61 -23.5004 1.0286 2442.20 235s [2,] -23.50 0.3077 -0.0746 -16.15 235s [3,] 1.03 -0.0746 0.0660 -8.39 235s [4,] 2442.20 -16.1480 -8.3922 4816.72 235s [5,] -25.30 0.2317 0.0218 -38.19 235s [6,] 0.86 -0.0624 0.0552 -8.86 235s [7,] 1.31 -0.0948 0.0838 -12.35 235s supply_price supply_farmPrice supply_trend 235s [1,] -25.2995 0.8598 1.3061 235s [2,] 0.2317 -0.0624 -0.0948 235s [3,] 0.0218 0.0552 0.0838 235s [4,] -38.1886 -8.8582 -12.3470 235s [5,] 0.3560 0.0234 0.0309 235s [6,] 0.0234 0.0590 0.0780 235s [7,] 0.0309 0.0780 0.1640 235s > 235s > round( bread( fitsur1r3 ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s [1,] 2257.728 -23.5088 1.0361 2434.43 235s [2,] -23.509 0.3083 -0.0752 -16.03 235s [3,] 1.036 -0.0752 0.0665 -8.43 235s [4,] 2434.429 -16.0346 -8.4292 4826.83 235s [5,] -25.226 0.2308 0.0219 -38.22 235s [6,] 0.864 -0.0627 0.0554 -8.93 235s [7,] 1.312 -0.0952 0.0842 -12.42 235s supply_price supply_farmPrice supply_trend 235s [1,] -25.2264 0.8636 1.3118 235s [2,] 0.2308 -0.0627 -0.0952 235s [3,] 0.0219 0.0554 0.0842 235s [4,] -38.2158 -8.9270 -12.4169 235s [5,] 0.3561 0.0235 0.0310 235s [6,] 0.0235 0.0595 0.0784 235s [7,] 0.0310 0.0784 0.1660 235s > 235s > round( bread( fitsur1w ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s [1,] 2258.680 -23.5779 1.0971 2354.23 235s [2,] -23.578 0.3134 -0.0796 -15.01 235s [3,] 1.097 -0.0796 0.0704 -8.66 235s [4,] 2354.232 -15.0109 -8.6593 4911.36 235s [5,] -24.454 0.2225 0.0225 -38.45 235s [6,] 0.887 -0.0644 0.0569 -9.51 235s [7,] 1.348 -0.0978 0.0864 -12.94 235s supply_price supply_farmPrice supply_trend 235s [1,] -24.4536 0.8871 1.3477 235s [2,] 0.2225 -0.0644 -0.0978 235s [3,] 0.0225 0.0569 0.0864 235s [4,] -38.4456 -9.5077 -12.9352 235s [5,] 0.3567 0.0252 0.0320 235s [6,] 0.0252 0.0636 0.0807 235s [7,] 0.0320 0.0807 0.1845 235s > 235s > round( bread( fitsuri1e ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s [1,] 1876.862 -19.2519 0.5677 -81.89 235s [2,] -19.252 0.2661 -0.0755 -2.81 235s [3,] 0.568 -0.0755 0.0716 3.68 235s [4,] -81.887 -2.8102 3.6811 363.96 235s [5,] 7.186 -0.0595 -0.0127 -1.84 235s [6,] -5.538 0.0766 -0.0217 -1.67 235s [7,] -8.357 0.1155 -0.0328 -1.82 235s supply_income supply_farmPrice supply_trend 235s [1,] 7.1857 -5.5385 -8.3572 235s [2,] -0.0595 0.0766 0.1155 235s [3,] -0.0127 -0.0217 -0.0328 235s [4,] -1.8380 -1.6714 -1.8169 235s [5,] 0.0569 -0.0327 -0.0527 235s [6,] -0.0327 0.0441 0.0571 235s [7,] -0.0527 0.0571 0.1367 235s > 235s > round( bread( fitsuri1wr3 ), digits = 7 ) 235s demand_(Intercept) demand_price demand_income supply_(Intercept) 235s [1,] 2182.020 -22.2793 0.5557 -108.13 235s [2,] -22.279 0.3080 -0.0874 -3.49 235s [3,] 0.556 -0.0874 0.0839 4.64 235s [4,] -108.127 -3.4932 4.6397 458.64 235s [5,] 8.996 -0.0739 -0.0164 -2.35 235s [6,] -6.884 0.0952 -0.0270 -2.07 235s [7,] -10.388 0.1436 -0.0408 -2.31 235s supply_income supply_farmPrice supply_trend 235s [1,] 8.9961 -6.8844 -10.3882 235s [2,] -0.0739 0.0952 0.1436 235s [3,] -0.0164 -0.0270 -0.0408 235s [4,] -2.3500 -2.0691 -2.3134 235s [5,] 0.0715 -0.0407 -0.0653 235s [6,] -0.0407 0.0547 0.0717 235s [7,] -0.0653 0.0717 0.1662 235s > 235s > round( bread( fitsurS1 ), digits = 7 ) 235s eq1_consump eq2_(Intercept) eq2_consump eq2_trend 235s [1,] 0.00876 0.0 -4.02e-03 0.000 235s [2,] 0.00000 91218.4 -9.08e+02 48.892 235s [3,] -0.00402 -908.0 9.09e+00 -0.866 235s [4,] 0.00000 48.9 -8.66e-01 3.664 235s > 235s > round( bread( fitsurS2 ), digits = 7 ) 235s eq1_price eq2_trend 235s [1,] 0.00903 -0.00752 235s [2,] -0.00752 34.11430 235s > 235s > round( bread( fitsurS3 ), digits = 7 ) 235s eq1_trend eq2_trend 235s [1,] 34.1 34.0 235s [2,] 34.0 34.5 235s > 235s > try( bread( fitsurS4 ) ) 235s > 235s Error in bread.systemfit(fitsurS4) : 235s returning the 'bread' for models with restrictions has not yet been implemented. 235s BEGIN TEST test_w2sls.R 235s 235s R version 4.3.2 (2023-10-31) -- "Eye Holes" 235s Copyright (C) 2023 The R Foundation for Statistical Computing 235s Platform: aarch64-unknown-linux-gnu (64-bit) 235s 235s R is free software and comes with ABSOLUTELY NO WARRANTY. 235s You are welcome to redistribute it under certain conditions. 235s Type 'license()' or 'licence()' for distribution details. 235s 235s R is a collaborative project with many contributors. 235s Type 'contributors()' for more information and 235s 'citation()' on how to cite R or R packages in publications. 235s 235s Type 'demo()' for some demos, 'help()' for on-line help, or 235s 'help.start()' for an HTML browser interface to help. 235s Type 'q()' to quit R. 235s 235s > library( systemfit ) 235s Loading required package: Matrix 236s Loading required package: car 236s Loading required package: carData 236s Loading required package: lmtest 236s Loading required package: zoo 236s 236s Attaching package: ‘zoo’ 236s 236s The following objects are masked from ‘package:base’: 236s 236s as.Date, as.Date.numeric 236s 236s 236s Please cite the 'systemfit' package as: 236s 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/. 236s 236s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 236s https://r-forge.r-project.org/projects/systemfit/ 236s > options( digits = 3 ) 236s > 236s > data( "Kmenta" ) 236s > useMatrix <- FALSE 236s > 236s > demand <- consump ~ price + income 236s > supply <- consump ~ price + farmPrice + trend 236s > inst <- ~ income + farmPrice + trend 236s > inst1 <- ~ income + farmPrice 236s > instlist <- list( inst1, inst ) 236s > system <- list( demand = demand, supply = supply ) 236s > restrm <- matrix(0,1,7) # restriction matrix "R" 236s > restrm[1,3] <- 1 236s > restrm[1,7] <- -1 236s > restrict <- "demand_income - supply_trend = 0" 236s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 236s > restr2m[1,3] <- 1 236s > restr2m[1,7] <- -1 236s > restr2m[2,2] <- -1 236s > restr2m[2,5] <- 1 236s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 236s > restrict2 <- c( "demand_income - supply_trend = 0", 236s + "- demand_price + supply_price = 0.5" ) 236s > tc <- matrix(0,7,6) 236s > tc[1,1] <- 1 236s > tc[2,2] <- 1 236s > tc[3,3] <- 1 236s > tc[4,4] <- 1 236s > tc[5,5] <- 1 236s > tc[6,6] <- 1 236s > tc[7,3] <- 1 236s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 236s > restr3m[1,2] <- -1 236s > restr3m[1,5] <- 1 236s > restr3q <- c( 0.5 ) # restriction vector "q" 2 236s > restrict3 <- "- C2 + C5 = 0.5" 236s > 236s > 236s > ## ********************* W2SLS ***************** 236s > fitw2sls1 <- systemfit( system, "W2SLS", data = Kmenta, inst = inst, 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2sls1 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 33 162 4.36 0.697 0.548 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.7 3.87 1.97 0.755 0.726 236s supply 20 16 96.6 6.04 2.46 0.640 0.572 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.87 0.00 236s supply 0.00 6.04 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.87 4.36 236s supply 4.36 6.04 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.902 236s supply 0.902 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 94.6333 7.9208 11.95 1.1e-09 *** 236s price -0.2436 0.0965 -2.52 0.022 * 236s income 0.3140 0.0469 6.69 3.8e-06 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.966 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 236s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 236s price 0.2401 0.0999 2.40 0.0288 * 236s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 236s trend 0.2529 0.0997 2.54 0.0219 * 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.458 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 236s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 236s 236s > 236s > ## ********************* W2SLS (EViews-like) ***************** 236s > fitw2sls1e <- systemfit( system, "W2SLS", data = Kmenta, inst = inst, 236s + methodResidCov = "noDfCor", x = TRUE, 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2sls1e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 33 162 2.97 0.697 0.525 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.7 3.87 1.97 0.755 0.726 236s supply 20 16 96.6 6.04 2.46 0.640 0.572 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.29 0.00 236s supply 0.00 4.83 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.29 3.59 236s supply 3.59 4.83 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.902 236s supply 0.902 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 94.6333 7.3027 12.96 1.7e-14 *** 236s price -0.2436 0.0890 -2.74 0.0099 ** 236s income 0.3140 0.0433 7.25 2.5e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.966 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 236s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 236s price 0.2401 0.0894 2.69 0.0112 * 236s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 236s trend 0.2529 0.0891 2.84 0.0077 ** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.458 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 236s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 236s 236s > 236s > ## ********************* W2SLS with restriction ******************* 236s > fitw2sls2 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 236s + inst = inst, useMatrix = useMatrix ) 236s > print( summary( fitw2sls2 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 165 3.41 0.692 0.565 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 66.8 3.93 1.98 0.751 0.721 236s supply 20 16 98.4 6.15 2.48 0.633 0.564 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.97 0.00 236s supply 0.00 6.13 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.93 4.56 236s supply 4.56 6.15 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.927 236s supply 0.927 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 236s price -0.2302 0.0946 -2.43 0.02 * 236s income 0.3028 0.0430 7.05 3.9e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.983 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 66.838 MSE: 3.932 Root MSE: 1.983 236s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 48.0494 11.8001 4.07 0.00026 *** 236s price 0.2430 0.1006 2.42 0.02122 * 236s farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 236s trend 0.3028 0.0430 7.05 3.9e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.48 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 98.445 MSE: 6.153 Root MSE: 2.48 236s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 236s 236s > # the same with symbolically specified restrictions 236s > fitw2sls2Sym <- systemfit( system, "W2SLS", data = Kmenta, 236s + restrict.matrix = restrict, inst = inst, useMatrix = useMatrix ) 236s > all.equal( fitw2sls2, fitw2sls2Sym ) 236s [1] "Component “call”: target, current do not match when deparsed" 236s > 236s > ## ********************* W2SLS with restriction (EViews-like) ************** 236s > fitw2sls2e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 236s + inst = inst, methodResidCov = "noDfCor", x = TRUE, 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2sls2e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 165 2.33 0.692 0.535 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 66.9 3.94 1.98 0.750 0.721 236s supply 20 16 98.4 6.15 2.48 0.633 0.564 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.37 0.00 236s supply 0.00 4.91 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.35 3.76 236s supply 3.76 4.92 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.926 236s supply 0.926 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 94.3706 7.3834 12.78 1.6e-14 *** 236s price -0.2295 0.0871 -2.63 0.013 * 236s income 0.3022 0.0394 7.67 6.4e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.984 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 66.906 MSE: 3.936 Root MSE: 1.984 236s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 48.0661 10.5574 4.55 6.5e-05 *** 236s price 0.2430 0.0900 2.70 0.011 * 236s farmPrice 0.2624 0.0411 6.39 2.7e-07 *** 236s trend 0.3022 0.0394 7.67 6.4e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.48 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 98.408 MSE: 6.15 Root MSE: 2.48 236s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 236s 236s > nobs( fitw2sls2e ) 236s [1] 40 236s > 236s > ## ********************* W2SLS with restriction via restrict.regMat ******************* 236s > fitw2sls3 <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 236s + inst = inst, x = TRUE, useMatrix = useMatrix ) 236s > print( summary( fitw2sls3 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 165 3.41 0.692 0.565 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 66.8 3.93 1.98 0.751 0.721 236s supply 20 16 98.4 6.15 2.48 0.633 0.564 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.97 0.00 236s supply 0.00 6.13 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.93 4.56 236s supply 4.56 6.15 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.927 236s supply 0.927 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 236s price -0.2302 0.0946 -2.43 0.02 * 236s income 0.3028 0.0430 7.05 3.9e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.983 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 66.838 MSE: 3.932 Root MSE: 1.983 236s Multiple R-Squared: 0.751 Adjusted R-Squared: 0.721 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 48.0494 11.8001 4.07 0.00026 *** 236s price 0.2430 0.1006 2.42 0.02122 * 236s farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 236s trend 0.3028 0.0430 7.05 3.9e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.48 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 98.445 MSE: 6.153 Root MSE: 2.48 236s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 236s 236s > 236s > ## ********************* W2SLS with restriction via restrict.regMat (EViews-like) ************** 236s > fitw2sls3e <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 236s + inst = inst, methodResidCov = "noDfCor", useMatrix = useMatrix ) 236s > print( summary( fitw2sls3e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 165 2.33 0.692 0.535 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 66.9 3.94 1.98 0.750 0.721 236s supply 20 16 98.4 6.15 2.48 0.633 0.564 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.37 0.00 236s supply 0.00 4.91 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.35 3.76 236s supply 3.76 4.92 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.926 236s supply 0.926 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 94.3706 7.3834 12.78 1.6e-14 *** 236s price -0.2295 0.0871 -2.63 0.013 * 236s income 0.3022 0.0394 7.67 6.4e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.984 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 66.906 MSE: 3.936 Root MSE: 1.984 236s Multiple R-Squared: 0.75 Adjusted R-Squared: 0.721 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 48.0661 10.5574 4.55 6.5e-05 *** 236s price 0.2430 0.0900 2.70 0.011 * 236s farmPrice 0.2624 0.0411 6.39 2.7e-07 *** 236s trend 0.3022 0.0394 7.67 6.4e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.48 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 98.408 MSE: 6.15 Root MSE: 2.48 236s Multiple R-Squared: 0.633 Adjusted R-Squared: 0.564 236s 236s > 236s > ## ***************** W2SLS with 2 restrictions ******************** 236s > fitw2sls4 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr2m, 236s + restrict.rhs = restr2q, inst = inst, x = TRUE, 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2sls4 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 35 166 3.57 0.69 0.575 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.9 3.88 1.97 0.754 0.725 236s supply 20 16 100.3 6.27 2.50 0.626 0.556 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.89 0.00 236s supply 0.00 6.25 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.88 4.55 236s supply 4.55 6.27 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.924 236s supply 0.924 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 95.3043 6.3056 15.11 < 2e-16 *** 236s price -0.2428 0.0684 -3.55 0.0011 ** 236s income 0.3063 0.0394 7.78 3.9e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.969 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 236s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 46.4229 8.3296 5.57 2.8e-06 *** 236s price 0.2572 0.0684 3.76 0.00062 *** 236s farmPrice 0.2642 0.0455 5.80 1.4e-06 *** 236s trend 0.3063 0.0394 7.78 3.9e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.503 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 236s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 236s 236s > # the same with symbolically specified restrictions 236s > fitw2sls4Sym <- systemfit( system, "W2SLS", data = Kmenta, 236s + restrict.matrix = restrict2, inst = inst, x = TRUE, 236s + useMatrix = useMatrix ) 236s > all.equal( fitw2sls4, fitw2sls4Sym ) 236s [1] "Component “call”: target, current do not match when deparsed" 236s > 236s > ## ***************** W2SLS with 2 restrictions (EViews-like) ************** 236s > fitw2sls4e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr2m, 236s + restrict.rhs = restr2q, inst = inst, methodResidCov = "noDfCor", 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2sls4e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 35 166 2.44 0.69 0.546 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.9 3.88 1.97 0.754 0.725 236s supply 20 16 100.2 6.26 2.50 0.626 0.556 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.3 0 236s supply 0.0 5 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.30 3.75 236s supply 3.75 5.01 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.923 236s supply 0.923 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 236s price -0.2428 0.0621 -3.91 0.00041 *** 236s income 0.3059 0.0360 8.49 5.1e-10 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.97 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 236s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 236s price 0.2572 0.0621 4.14 0.00021 *** 236s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 236s trend 0.3059 0.0360 8.49 5.1e-10 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.503 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 236s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 236s 236s > 236s > ## ***************** W2SLS with 2 restrictions via R and restrict.regMat ****************** 236s > fitw2sls5 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr3m, 236s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 236s + x = TRUE, useMatrix = useMatrix ) 236s > print( summary( fitw2sls5 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 35 166 3.57 0.69 0.575 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.9 3.88 1.97 0.754 0.725 236s supply 20 16 100.3 6.27 2.50 0.626 0.556 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.89 0.00 236s supply 0.00 6.25 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.88 4.55 236s supply 4.55 6.27 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.924 236s supply 0.924 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 95.3043 6.3056 15.11 < 2e-16 *** 236s price -0.2428 0.0684 -3.55 0.0011 ** 236s income 0.3063 0.0394 7.78 3.9e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.969 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 236s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 46.4229 8.3296 5.57 2.8e-06 *** 236s price 0.2572 0.0684 3.76 0.00062 *** 236s farmPrice 0.2642 0.0455 5.80 1.4e-06 *** 236s trend 0.3063 0.0394 7.78 3.9e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.503 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 236s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 236s 236s > # the same with symbolically specified restrictions 236s > fitw2sls5Sym <- systemfit( system, "W2SLS", data = Kmenta, 236s + restrict.matrix = restrict3, restrict.regMat = tc, inst = inst, 236s + x = TRUE, useMatrix = useMatrix ) 236s > all.equal( fitw2sls5, fitw2sls5Sym ) 236s [1] "Component “call”: target, current do not match when deparsed" 236s > 236s > ## ***************** W2SLS with 2 restrictions via R and restrict.regMat (EViews-like) ************** 236s > fitw2sls5e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restr3m, 236s + restrict.rhs = restr3q, restrict.regMat = tc, inst = inst, 236s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 236s > print( summary( fitw2sls5e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 35 166 2.44 0.69 0.546 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.9 3.88 1.97 0.754 0.725 236s supply 20 16 100.2 6.26 2.50 0.626 0.556 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.3 0 236s supply 0.0 5 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.30 3.75 236s supply 3.75 5.01 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.923 236s supply 0.923 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 236s price -0.2428 0.0621 -3.91 0.00041 *** 236s income 0.3059 0.0360 8.49 5.1e-10 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.97 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 236s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 236s price 0.2572 0.0621 4.14 0.00021 *** 236s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 236s trend 0.3059 0.0360 8.49 5.1e-10 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.503 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 236s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 236s 236s > 236s > ## ****** 2SLS estimation with different instruments ********************** 236s > fitw2slsd1 <- systemfit( system, "W2SLS", data = Kmenta, inst = instlist, 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2slsd1 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 33 164 9.25 0.694 0.512 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 67.4 3.97 1.99 0.748 0.719 236s supply 20 16 96.6 6.04 2.46 0.640 0.572 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.97 0.00 236s supply 0.00 6.04 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.97 3.84 236s supply 3.84 6.04 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.784 236s supply 0.784 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 106.7894 11.1435 9.58 2.9e-08 *** 236s price -0.4116 0.1448 -2.84 0.011 * 236s income 0.3617 0.0564 6.41 6.4e-06 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.992 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 236s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 49.5324 12.0105 4.12 0.0008 *** 236s price 0.2401 0.0999 2.40 0.0288 * 236s farmPrice 0.2556 0.0473 5.41 5.8e-05 *** 236s trend 0.2529 0.0997 2.54 0.0219 * 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.458 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 236s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 236s 236s > 236s > ## ****** 2SLS estimation with different instruments (EViews-like)****************** 236s > fitw2slsd1e <- systemfit( system, "W2SLS", data = Kmenta, inst = instlist, 236s + methodResidCov = "noDfCor", x = TRUE, 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2slsd1e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 33 164 6.29 0.694 0.5 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 67.4 3.97 1.99 0.748 0.719 236s supply 20 16 96.6 6.04 2.46 0.640 0.572 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.37 0.00 236s supply 0.00 4.83 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.37 3.16 236s supply 3.16 4.83 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.784 236s supply 0.784 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 106.789 10.274 10.39 6.1e-12 *** 236s price -0.412 0.134 -3.08 0.0041 ** 236s income 0.362 0.052 6.95 6.0e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.992 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 67.447 MSE: 3.967 Root MSE: 1.992 236s Multiple R-Squared: 0.748 Adjusted R-Squared: 0.719 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 49.5324 10.7425 4.61 5.8e-05 *** 236s price 0.2401 0.0894 2.69 0.0112 * 236s farmPrice 0.2556 0.0423 6.05 8.4e-07 *** 236s trend 0.2529 0.0891 2.84 0.0077 ** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.458 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 236s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 236s 236s > 236s > ## **** W2SLS estimation with different instruments and restriction ******** 236s > fitw2slsd2 <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 236s + inst = instlist, useMatrix = useMatrix ) 236s > print( summary( fitw2slsd2 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 166 5.11 0.69 0.557 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 64.8 3.81 1.95 0.758 0.730 236s supply 20 16 101.4 6.34 2.52 0.622 0.551 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.79 0.00 236s supply 0.00 6.27 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.81 4.36 236s supply 4.36 6.34 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.888 236s supply 0.888 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 104.5695 10.6344 9.83 1.8e-11 *** 236s price -0.3653 0.1327 -2.75 0.0094 ** 236s income 0.3369 0.0485 6.95 5.1e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.952 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 64.776 MSE: 3.81 Root MSE: 1.952 236s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 47.0356 11.9466 3.94 0.00039 *** 236s price 0.2450 0.1017 2.41 0.02156 * 236s farmPrice 0.2672 0.0465 5.74 1.9e-06 *** 236s trend 0.3369 0.0485 6.95 5.1e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.518 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 101.426 MSE: 6.339 Root MSE: 2.518 236s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 236s 236s > 236s > ## **** W2SLS estimation with different instruments and restriction (EViews-like)* 236s > fitw2slsd2e <- systemfit( system, "W2SLS", data = Kmenta, restrict.matrix = restrm, 236s + inst = instlist, methodResidCov = "noDfCor", x = TRUE, 236s + useMatrix = useMatrix ) 236s > print( summary( fitw2slsd2e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 166 3.45 0.69 0.535 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 64.7 3.81 1.95 0.759 0.730 236s supply 20 16 101.3 6.33 2.52 0.622 0.551 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.22 0.00 236s supply 0.00 5.02 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.24 3.60 236s supply 3.60 5.06 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.888 236s supply 0.888 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 236s price -0.3630 0.1220 -2.98 0.0053 ** 236s income 0.3357 0.0444 7.57 8.6e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.951 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 64.715 MSE: 3.807 Root MSE: 1.951 236s Multiple R-Squared: 0.759 Adjusted R-Squared: 0.73 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 47.0706 10.6890 4.40 0.0001 *** 236s price 0.2449 0.0910 2.69 0.0109 * 236s farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 236s trend 0.3357 0.0444 7.57 8.6e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.516 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 101.299 MSE: 6.331 Root MSE: 2.516 236s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 236s 236s > 236s > ## ** W2SLS estimation with different instruments and restriction via restrict.regMat **** 236s > fitw2slsd3 <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 236s + inst = instlist, x = TRUE, useMatrix = useMatrix ) 236s > print( summary( fitw2slsd3 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 166 5.11 0.69 0.557 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 64.8 3.81 1.95 0.758 0.730 236s supply 20 16 101.4 6.34 2.52 0.622 0.551 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.79 0.00 236s supply 0.00 6.27 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.81 4.36 236s supply 4.36 6.34 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.888 236s supply 0.888 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 104.5695 10.6344 9.83 1.8e-11 *** 236s price -0.3653 0.1327 -2.75 0.0094 ** 236s income 0.3369 0.0485 6.95 5.1e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.952 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 64.776 MSE: 3.81 Root MSE: 1.952 236s Multiple R-Squared: 0.758 Adjusted R-Squared: 0.73 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 47.0356 11.9466 3.94 0.00039 *** 236s price 0.2450 0.1017 2.41 0.02156 * 236s farmPrice 0.2672 0.0465 5.74 1.9e-06 *** 236s trend 0.3369 0.0485 6.95 5.1e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.518 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 101.426 MSE: 6.339 Root MSE: 2.518 236s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 236s 236s > 236s > ## W2SLS estimation with different instruments and restriction via restrict.regMat (EViews-like) 236s > fitw2slsd3e <- systemfit( system, "W2SLS", data = Kmenta, restrict.regMat = tc, 236s + inst = instlist, methodResidCov = "noDfCor", useMatrix = useMatrix ) 236s > print( summary( fitw2slsd3e, useDfSys = TRUE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 166 3.45 0.69 0.535 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 64.7 3.81 1.95 0.759 0.730 236s supply 20 16 101.3 6.33 2.52 0.622 0.551 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.22 0.00 236s supply 0.00 5.02 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.24 3.60 236s supply 3.60 5.06 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.888 236s supply 0.888 1.000 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 236s price -0.3630 0.1220 -2.98 0.0053 ** 236s income 0.3357 0.0444 7.57 8.6e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.951 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 64.715 MSE: 3.807 Root MSE: 1.951 236s Multiple R-Squared: 0.759 Adjusted R-Squared: 0.73 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 47.0706 10.6890 4.40 0.0001 *** 236s price 0.2449 0.0910 2.69 0.0109 * 236s farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 236s trend 0.3357 0.0444 7.57 8.6e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.516 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 101.299 MSE: 6.331 Root MSE: 2.516 236s Multiple R-Squared: 0.622 Adjusted R-Squared: 0.551 236s 236s > 236s > 236s > ## *********** estimations with a single regressor ************ 236s > fitw2slsS1 <- systemfit( 236s + list( consump ~ price - 1, price ~ consump + trend ), "W2SLS", 236s + data = Kmenta, inst = ~ farmPrice + trend + income, useMatrix = useMatrix ) 236s > print( summary( fitw2slsS1 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 36 1544 179 -0.65 0.852 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s eq1 20 19 861 45.3 6.73 -2.213 -2.213 236s eq2 20 17 682 40.1 6.33 -0.022 -0.143 236s 236s The covariance matrix of the residuals used for estimation 236s eq1 eq2 236s eq1 45.3 0.0 236s eq2 0.0 40.1 236s 236s The covariance matrix of the residuals 236s eq1 eq2 236s eq1 45.3 -40.5 236s eq2 -40.5 40.1 236s 236s The correlations of the residuals 236s eq1 eq2 236s eq1 1.00 -0.95 236s eq2 -0.95 1.00 236s 236s 236s W2SLS estimates for 'eq1' (equation 1) 236s Model Formula: consump ~ price - 1 236s Instruments: ~farmPrice + trend + income 236s 236s Estimate Std. Error t value Pr(>|t|) 236s price 1.006 0.015 66.9 <2e-16 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 6.734 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 861.48 MSE: 45.341 Root MSE: 6.734 236s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 236s 236s 236s W2SLS estimates for 'eq2' (equation 2) 236s Model Formula: price ~ consump + trend 236s Instruments: ~farmPrice + trend + income 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 55.5365 46.2668 1.20 0.25 236s consump 0.4453 0.4622 0.96 0.35 236s trend -0.0426 0.2496 -0.17 0.87 236s 236s Residual standard error: 6.335 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 682.257 MSE: 40.133 Root MSE: 6.335 236s Multiple R-Squared: -0.022 Adjusted R-Squared: -0.143 236s 236s > fitw2slsS2 <- systemfit( 236s + list( consump ~ price - 1, consump ~ trend - 1 ), "W2SLS", 236s + data = Kmenta, inst = ~ farmPrice + price + income, useMatrix = useMatrix ) 236s > print( summary( fitw2slsS2 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 38 47456 111148 -87.5 -5.28 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s eq1 20 19 861 45.3 6.73 -2.21 -2.21 236s eq2 20 19 46595 2452.3 49.52 -172.79 -172.79 236s 236s The covariance matrix of the residuals used for estimation 236s eq1 eq2 236s eq1 45.3 0 236s eq2 0.0 2452 236s 236s The covariance matrix of the residuals 236s eq1 eq2 236s eq1 45.34 -6.33 236s eq2 -6.33 2452.34 236s 236s The correlations of the residuals 236s eq1 eq2 236s eq1 1.0000 -0.0448 236s eq2 -0.0448 1.0000 236s 236s 236s W2SLS estimates for 'eq1' (equation 1) 236s Model Formula: consump ~ price - 1 236s Instruments: ~farmPrice + price + income 236s 236s Estimate Std. Error t value Pr(>|t|) 236s price 1.006 0.015 66.9 <2e-16 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 6.733 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 236s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 236s 236s 236s W2SLS estimates for 'eq2' (equation 2) 236s Model Formula: consump ~ trend - 1 236s Instruments: ~farmPrice + price + income 236s 236s Estimate Std. Error t value Pr(>|t|) 236s trend 7.578 0.934 8.11 1.4e-07 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 49.521 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 46594.549 MSE: 2452.345 Root MSE: 49.521 236s Multiple R-Squared: -172.786 Adjusted R-Squared: -172.786 236s 236s > fitw2slsS3 <- systemfit( 236s + list( consump ~ trend - 1, price ~ trend - 1 ), "W2SLS", 236s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 236s > print( summary( fitw2slsS3 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 38 97978 687515 -104 -10.6 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s eq1 20 19 50950 2682 51.8 -189.0 -189.0 236s eq2 20 19 47028 2475 49.8 -69.5 -69.5 236s 236s The covariance matrix of the residuals used for estimation 236s eq1 eq2 236s eq1 2682 0 236s eq2 0 2475 236s 236s The covariance matrix of the residuals 236s eq1 eq2 236s eq1 2682 2439 236s eq2 2439 2475 236s 236s The correlations of the residuals 236s eq1 eq2 236s eq1 1.000 0.989 236s eq2 0.989 1.000 236s 236s 236s W2SLS estimates for 'eq1' (equation 1) 236s Model Formula: consump ~ trend - 1 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s trend 8.65 1.05 8.27 1e-07 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 51.784 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 50949.985 MSE: 2681.578 Root MSE: 51.784 236s Multiple R-Squared: -189.031 Adjusted R-Squared: -189.031 236s 236s 236s W2SLS estimates for 'eq2' (equation 2) 236s Model Formula: price ~ trend - 1 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s trend 7.318 0.929 7.88 2.1e-07 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 49.751 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 236s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 236s 236s > fitw2slsS4 <- systemfit( 236s + list( consump ~ trend - 1, price ~ trend - 1 ), "W2SLS", 236s + data = Kmenta, inst = ~ farmPrice + trend + income, 236s + restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), useMatrix = useMatrix ) 236s > print( summary( fitw2slsS4 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 39 93548 111736 -99 -1.03 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s eq1 20 19 46514 2448 49.5 -172.5 -172.5 236s eq2 20 19 47034 2475 49.8 -69.5 -69.5 236s 236s The covariance matrix of the residuals used for estimation 236s eq1 eq2 236s eq1 2448 0 236s eq2 0 2475 236s 236s The covariance matrix of the residuals 236s eq1 eq2 236s eq1 2448 2439 236s eq2 2439 2475 236s 236s The correlations of the residuals 236s eq1 eq2 236s eq1 1.000 0.988 236s eq2 0.988 1.000 236s 236s 236s W2SLS estimates for 'eq1' (equation 1) 236s Model Formula: consump ~ trend - 1 236s Instruments: ~farmPrice + trend + income 236s 236s Estimate Std. Error t value Pr(>|t|) 236s trend 7.362 0.655 11.2 8.4e-14 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 49.478 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 46514.224 MSE: 2448.117 Root MSE: 49.478 236s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 236s 236s 236s W2SLS estimates for 'eq2' (equation 2) 236s Model Formula: price ~ trend - 1 236s Instruments: ~farmPrice + trend + income 236s 236s Estimate Std. Error t value Pr(>|t|) 236s trend 7.362 0.655 11.2 8.4e-14 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 49.754 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 47033.528 MSE: 2475.449 Root MSE: 49.754 236s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 236s 236s > fitw2slsS5 <- systemfit( 236s + list( consump ~ 1, price ~ 1 ), "W2SLS", 236s + data = Kmenta, inst = instlist, useMatrix = useMatrix ) 236s > print( summary( fitw2slsS5 ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 38 935 491 0 0 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s eq1 20 19 268 14.1 3.76 0 0 236s eq2 20 19 667 35.1 5.93 0 0 236s 236s The covariance matrix of the residuals used for estimation 236s eq1 eq2 236s eq1 14.1 0.0 236s eq2 0.0 35.1 236s 236s The covariance matrix of the residuals 236s eq1 eq2 236s eq1 14.11 2.18 236s eq2 2.18 35.12 236s 236s The correlations of the residuals 236s eq1 eq2 236s eq1 1.0000 0.0981 236s eq2 0.0981 1.0000 236s 236s 236s W2SLS estimates for 'eq1' (equation 1) 236s Model Formula: consump ~ 1 236s Instruments: ~income + farmPrice 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 100.90 0.84 120 <2e-16 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 3.756 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 236s Multiple R-Squared: 0 Adjusted R-Squared: 0 236s 236s 236s W2SLS estimates for 'eq2' (equation 2) 236s Model Formula: price ~ 1 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 100.02 1.33 75.5 <2e-16 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 5.926 on 19 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 19 236s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 236s Multiple R-Squared: 0 Adjusted R-Squared: 0 236s 236s > 236s > 236s > ## **************** shorter summaries ********************** 236s > print( summary( fitw2sls1e, residCov = FALSE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 33 162 2.97 0.697 0.525 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.7 3.87 1.97 0.755 0.726 236s supply 20 16 96.6 6.04 2.46 0.640 0.572 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 94.6333 7.3027 12.96 3.1e-10 *** 236s price -0.2436 0.0890 -2.74 0.014 * 236s income 0.3140 0.0433 7.25 1.3e-06 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.966 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.729 MSE: 3.866 Root MSE: 1.966 236s Multiple R-Squared: 0.755 Adjusted R-Squared: 0.726 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 49.5324 10.7425 4.61 0.00029 *** 236s price 0.2401 0.0894 2.69 0.01623 * 236s farmPrice 0.2556 0.0423 6.05 1.7e-05 *** 236s trend 0.2529 0.0891 2.84 0.01188 * 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.458 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 96.633 MSE: 6.04 Root MSE: 2.458 236s Multiple R-Squared: 0.64 Adjusted R-Squared: 0.572 236s 236s > 236s > print( summary( fitw2sls2, residCov = FALSE, equations = FALSE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 165 3.41 0.692 0.565 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 66.8 3.93 1.98 0.751 0.721 236s supply 20 16 98.4 6.15 2.48 0.633 0.564 236s 236s 236s Coefficients: 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 94.3832 8.0090 11.78 1.5e-13 *** 236s demand_price -0.2302 0.0946 -2.43 0.02042 * 236s demand_income 0.3028 0.0430 7.05 3.9e-08 *** 236s supply_(Intercept) 48.0494 11.8001 4.07 0.00026 *** 236s supply_price 0.2430 0.1006 2.42 0.02122 * 236s supply_farmPrice 0.2625 0.0459 5.72 2.0e-06 *** 236s supply_trend 0.3028 0.0430 7.05 3.9e-08 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s > 236s > print( summary( fitw2sls3, useDfSys = FALSE ), equations = FALSE ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 165 3.41 0.692 0.565 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 66.8 3.93 1.98 0.751 0.721 236s supply 20 16 98.4 6.15 2.48 0.633 0.564 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.97 0.00 236s supply 0.00 6.13 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.93 4.56 236s supply 4.56 6.15 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.927 236s supply 0.927 1.000 236s 236s 236s Coefficients: 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 94.3832 8.0090 11.78 1.3e-09 *** 236s demand_price -0.2302 0.0946 -2.43 0.02634 * 236s demand_income 0.3028 0.0430 7.05 2.0e-06 *** 236s supply_(Intercept) 48.0494 11.8001 4.07 0.00089 *** 236s supply_price 0.2430 0.1006 2.42 0.02802 * 236s supply_farmPrice 0.2625 0.0459 5.72 3.2e-05 *** 236s supply_trend 0.3028 0.0430 7.05 2.8e-06 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s > 236s > print( summary( fitw2sls4e ), residCov = FALSE ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 35 166 2.44 0.69 0.546 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.9 3.88 1.97 0.754 0.725 236s supply 20 16 100.2 6.26 2.50 0.626 0.556 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 95.3470 5.7579 16.56 < 2e-16 *** 236s price -0.2428 0.0621 -3.91 0.00041 *** 236s income 0.3059 0.0360 8.49 5.1e-10 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.97 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.945 MSE: 3.879 Root MSE: 1.97 236s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 46.4366 7.5360 6.16 4.7e-07 *** 236s price 0.2572 0.0621 4.14 0.00021 *** 236s farmPrice 0.2642 0.0407 6.48 1.8e-07 *** 236s trend 0.3059 0.0360 8.49 5.1e-10 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.503 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 100.225 MSE: 6.264 Root MSE: 2.503 236s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 236s 236s > 236s > print( summary( fitw2sls5, useDfSys = FALSE, residCov = FALSE ) ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 35 166 3.57 0.69 0.575 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 65.9 3.88 1.97 0.754 0.725 236s supply 20 16 100.3 6.27 2.50 0.626 0.556 236s 236s 236s W2SLS estimates for 'demand' (equation 1) 236s Model Formula: consump ~ price + income 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 95.3043 6.3056 15.11 2.7e-11 *** 236s price -0.2428 0.0684 -3.55 0.0025 ** 236s income 0.3063 0.0394 7.78 5.4e-07 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 1.969 on 17 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 17 236s SSR: 65.931 MSE: 3.878 Root MSE: 1.969 236s Multiple R-Squared: 0.754 Adjusted R-Squared: 0.725 236s 236s 236s W2SLS estimates for 'supply' (equation 2) 236s Model Formula: consump ~ price + farmPrice + trend 236s Instruments: ~income + farmPrice + trend 236s 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 46.4229 8.3296 5.57 4.2e-05 *** 236s price 0.2572 0.0684 3.76 0.0017 ** 236s farmPrice 0.2642 0.0455 5.80 2.7e-05 *** 236s trend 0.3063 0.0394 7.78 8.0e-07 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s 236s Residual standard error: 2.503 on 16 degrees of freedom 236s Number of observations: 20 Degrees of Freedom: 16 236s SSR: 100.255 MSE: 6.266 Root MSE: 2.503 236s Multiple R-Squared: 0.626 Adjusted R-Squared: 0.556 236s 236s > 236s > print( summary( fitw2slsd1, useDfSys = TRUE ), residCov = FALSE, 236s + equations = FALSE ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 33 164 9.25 0.694 0.512 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 67.4 3.97 1.99 0.748 0.719 236s supply 20 16 96.6 6.04 2.46 0.640 0.572 236s 236s 236s Coefficients: 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 106.7894 11.1435 9.58 4.7e-11 *** 236s demand_price -0.4116 0.1448 -2.84 0.00764 ** 236s demand_income 0.3617 0.0564 6.41 2.9e-07 *** 236s supply_(Intercept) 49.5324 12.0105 4.12 0.00024 *** 236s supply_price 0.2401 0.0999 2.40 0.02208 * 236s supply_farmPrice 0.2556 0.0473 5.41 5.5e-06 *** 236s supply_trend 0.2529 0.0997 2.54 0.01605 * 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s > 236s > print( summary( fitw2slsd2e, equations = TRUE ), equations = FALSE ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 166 3.45 0.69 0.535 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 64.7 3.81 1.95 0.759 0.730 236s supply 20 16 101.3 6.33 2.52 0.622 0.551 236s 236s The covariance matrix of the residuals used for estimation 236s demand supply 236s demand 3.22 0.00 236s supply 0.00 5.02 236s 236s The covariance matrix of the residuals 236s demand supply 236s demand 3.24 3.60 236s supply 3.60 5.06 236s 236s The correlations of the residuals 236s demand supply 236s demand 1.000 0.888 236s supply 0.888 1.000 236s 236s 236s Coefficients: 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 236s demand_price -0.3630 0.1220 -2.98 0.0053 ** 236s demand_income 0.3357 0.0444 7.57 8.6e-09 *** 236s supply_(Intercept) 47.0706 10.6890 4.40 0.0001 *** 236s supply_price 0.2449 0.0910 2.69 0.0109 * 236s supply_farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 236s supply_trend 0.3357 0.0444 7.57 8.6e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s > 236s > print( summary( fitw2slsd3e, equations = FALSE ), residCov = FALSE ) 236s 236s systemfit results 236s method: W2SLS 236s 236s N DF SSR detRCov OLS-R2 McElroy-R2 236s system 40 34 166 3.45 0.69 0.535 236s 236s N DF SSR MSE RMSE R2 Adj R2 236s demand 20 17 64.7 3.81 1.95 0.759 0.730 236s supply 20 16 101.3 6.33 2.52 0.622 0.551 236s 236s 236s Coefficients: 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 104.4638 9.7929 10.67 2.2e-12 *** 236s demand_price -0.3630 0.1220 -2.98 0.0053 ** 236s demand_income 0.3357 0.0444 7.57 8.6e-09 *** 236s supply_(Intercept) 47.0706 10.6890 4.40 0.0001 *** 236s supply_price 0.2449 0.0910 2.69 0.0109 * 236s supply_farmPrice 0.2671 0.0416 6.41 2.5e-07 *** 236s supply_trend 0.3357 0.0444 7.57 8.6e-09 *** 236s --- 236s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 236s > 236s > 236s > ## ****************** residuals ************************** 236s > print( residuals( fitw2sls1e ) ) 236s demand supply 236s 1 0.843 -0.4348 236s 2 -0.698 -1.2131 236s 3 2.359 1.7090 236s 4 1.490 0.7956 236s 5 2.139 1.5942 236s 6 1.277 0.6595 236s 7 1.571 1.4346 236s 8 -3.066 -4.8724 236s 9 -1.125 -2.3975 236s 10 2.492 3.1427 236s 11 -0.108 0.0689 236s 12 -2.292 -1.3978 236s 13 -1.598 -1.1136 236s 14 -0.271 1.1684 236s 15 1.958 3.4865 236s 16 -3.430 -3.8285 236s 17 -0.313 0.6793 236s 18 -2.151 -2.7713 236s 19 1.592 2.6668 236s 20 -0.668 0.6235 236s > print( residuals( fitw2sls1e$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 236s 0.843 -0.698 2.359 1.490 2.139 1.277 1.571 -3.066 -1.125 2.492 -0.108 236s 12 13 14 15 16 17 18 19 20 236s -2.292 -1.598 -0.271 1.958 -3.430 -0.313 -2.151 1.592 -0.668 236s > 236s > print( residuals( fitw2sls2 ) ) 236s demand supply 236s 1 0.726 0.0287 236s 2 -0.754 -0.8185 236s 3 2.304 2.0561 236s 4 1.437 1.0966 236s 5 2.191 1.7764 236s 6 1.317 0.8056 236s 7 1.620 1.5441 236s 8 -3.015 -4.8526 236s 9 -1.087 -2.3957 236s 10 2.513 3.1658 236s 11 -0.265 0.1722 236s 12 -2.506 -1.2753 236s 13 -1.781 -1.0688 236s 14 -0.332 1.1028 236s 15 2.086 3.2370 236s 16 -3.325 -4.1563 236s 17 -0.144 0.2984 236s 18 -2.128 -3.1286 236s 19 1.662 2.2767 236s 20 -0.518 0.1355 236s > print( residuals( fitw2sls2$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 236s 0.0287 -0.8185 2.0561 1.0966 1.7764 0.8056 1.5441 -4.8526 -2.3957 3.1658 236s 11 12 13 14 15 16 17 18 19 20 236s 0.1722 -1.2753 -1.0688 1.1028 3.2370 -4.1563 0.2984 -3.1286 2.2767 0.1355 236s > 236s > print( residuals( fitw2sls3 ) ) 236s demand supply 236s 1 0.726 0.0287 236s 2 -0.754 -0.8185 236s 3 2.304 2.0561 236s 4 1.437 1.0966 236s 5 2.191 1.7764 236s 6 1.317 0.8056 236s 7 1.620 1.5441 236s 8 -3.015 -4.8526 236s 9 -1.087 -2.3957 236s 10 2.513 3.1658 236s 11 -0.265 0.1722 236s 12 -2.506 -1.2753 236s 13 -1.781 -1.0688 236s 14 -0.332 1.1028 236s 15 2.086 3.2370 236s 16 -3.325 -4.1563 236s 17 -0.144 0.2984 236s 18 -2.128 -3.1286 236s 19 1.662 2.2767 236s 20 -0.518 0.1355 236s > print( residuals( fitw2sls3$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 236s 0.726 -0.754 2.304 1.437 2.191 1.317 1.620 -3.015 -1.087 2.513 -0.265 236s 12 13 14 15 16 17 18 19 20 236s -2.506 -1.781 -0.332 2.086 -3.325 -0.144 -2.128 1.662 -0.518 236s > 236s > print( residuals( fitw2sls4e ) ) 236s demand supply 236s 1 0.761 0.0514 236s 2 -0.700 -0.8567 236s 3 2.350 2.0266 236s 4 1.492 1.0504 236s 5 2.159 1.7988 236s 6 1.301 0.8085 236s 7 1.616 1.5253 236s 8 -2.986 -4.9339 236s 9 -1.130 -2.3600 236s 10 2.429 3.2858 236s 11 -0.284 0.2948 236s 12 -2.458 -1.2168 236s 13 -1.705 -1.0756 236s 14 -0.327 1.1348 236s 15 2.007 3.2835 236s 16 -3.368 -4.1646 236s 17 -0.312 0.4480 236s 18 -2.099 -3.2018 236s 19 1.694 2.1807 236s 20 -0.439 -0.0794 236s > print( residuals( fitw2sls4e$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 236s 0.0514 -0.8567 2.0266 1.0504 1.7988 0.8085 1.5253 -4.9339 -2.3600 3.2858 236s 11 12 13 14 15 16 17 18 19 20 236s 0.2948 -1.2168 -1.0756 1.1348 3.2835 -4.1646 0.4480 -3.2018 2.1807 -0.0794 236s > 236s > print( residuals( fitw2sls5 ) ) 236s demand supply 236s 1 0.765 0.0551 236s 2 -0.701 -0.8537 236s 3 2.350 2.0293 236s 4 1.491 1.0527 236s 5 2.158 1.8003 236s 6 1.300 0.8097 236s 7 1.614 1.5262 236s 8 -2.991 -4.9339 236s 9 -1.129 -2.3600 236s 10 2.433 3.2862 236s 11 -0.275 0.2958 236s 12 -2.450 -1.2157 236s 13 -1.700 -1.0752 236s 14 -0.324 1.1344 236s 15 2.005 3.2816 236s 16 -3.371 -4.1672 236s 17 -0.311 0.4452 236s 18 -2.102 -3.2047 236s 19 1.688 2.1776 236s 20 -0.451 -0.0835 236s > print( residuals( fitw2sls5$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 236s 0.765 -0.701 2.350 1.491 2.158 1.300 1.614 -2.991 -1.129 2.433 -0.275 236s 12 13 14 15 16 17 18 19 20 236s -2.450 -1.700 -0.324 2.005 -3.371 -0.311 -2.102 1.688 -0.451 236s > 236s > print( residuals( fitw2slsd1 ) ) 236s demand supply 236s 1 1.3775 -0.4348 236s 2 0.0125 -1.2131 236s 3 2.9728 1.7090 236s 4 2.2121 0.7956 236s 5 1.6920 1.5942 236s 6 1.0407 0.6595 236s 7 1.4768 1.4346 236s 8 -2.7583 -4.8724 236s 9 -1.6807 -2.3975 236s 10 1.4265 3.1427 236s 11 -0.2029 0.0689 236s 12 -1.5123 -1.3978 236s 13 -0.4958 -1.1136 236s 14 -0.1528 1.1684 236s 15 0.8692 3.4865 236s 16 -4.0547 -3.8285 236s 17 -2.5309 0.6793 236s 18 -1.8070 -2.7713 236s 19 1.9299 2.6668 236s 20 0.1853 0.6235 236s > print( residuals( fitw2slsd1$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 236s -0.4348 -1.2131 1.7090 0.7956 1.5942 0.6595 1.4346 -4.8724 -2.3975 3.1427 236s 11 12 13 14 15 16 17 18 19 20 236s 0.0689 -1.3978 -1.1136 1.1684 3.4865 -3.8285 0.6793 -2.7713 2.6668 0.6235 236s > 236s > print( residuals( fitw2slsd2e ) ) 236s demand supply 236s 1 1.100 0.3346 236s 2 -0.192 -0.5581 236s 3 2.785 2.2852 236s 4 2.012 1.2953 236s 5 1.849 1.8966 236s 6 1.145 0.9020 236s 7 1.573 1.6164 236s 8 -2.722 -4.8395 236s 9 -1.531 -2.3946 236s 10 1.629 3.1810 236s 11 -0.448 0.2403 236s 12 -1.988 -1.1944 236s 13 -0.972 -1.0393 236s 14 -0.271 1.0594 236s 15 1.251 3.0723 236s 16 -3.782 -4.3726 236s 17 -1.904 0.0471 236s 18 -1.823 -3.3644 236s 19 1.992 2.0193 236s 20 0.298 -0.1866 236s > print( residuals( fitw2slsd2e$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 236s 1.100 -0.192 2.785 2.012 1.849 1.145 1.573 -2.722 -1.531 1.629 -0.448 236s 12 13 14 15 16 17 18 19 20 236s -1.988 -0.972 -0.271 1.251 -3.782 -1.904 -1.823 1.992 0.298 236s > 236s > print( residuals( fitw2slsd3e ) ) 236s demand supply 236s 1 1.100 0.3346 236s 2 -0.192 -0.5581 236s 3 2.785 2.2852 236s 4 2.012 1.2953 236s 5 1.849 1.8966 236s 6 1.145 0.9020 236s 7 1.573 1.6164 236s 8 -2.722 -4.8395 236s 9 -1.531 -2.3946 236s 10 1.629 3.1810 236s 11 -0.448 0.2403 236s 12 -1.988 -1.1944 236s 13 -0.972 -1.0393 236s 14 -0.271 1.0594 236s 15 1.251 3.0723 236s 16 -3.782 -4.3726 236s 17 -1.904 0.0471 236s 18 -1.823 -3.3644 236s 19 1.992 2.0193 236s 20 0.298 -0.1866 236s > print( residuals( fitw2slsd3e$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 236s 0.3346 -0.5581 2.2852 1.2953 1.8966 0.9020 1.6164 -4.8395 -2.3946 3.1810 236s 11 12 13 14 15 16 17 18 19 20 236s 0.2403 -1.1944 -1.0393 1.0594 3.0723 -4.3726 0.0471 -3.3644 2.0193 -0.1866 236s > 236s > 236s > ## *************** coefficients ********************* 236s > print( round( coef( fitw2sls1e ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income supply_(Intercept) 236s 94.633 -0.244 0.314 49.532 236s supply_price supply_farmPrice supply_trend 236s 0.240 0.256 0.253 236s > print( round( coef( fitw2sls1e$eq[[ 2 ]] ), digits = 6 ) ) 236s (Intercept) price farmPrice trend 236s 49.532 0.240 0.256 0.253 236s > 236s > print( round( coef( fitw2slsd2e ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income supply_(Intercept) 236s 104.464 -0.363 0.336 47.071 236s supply_price supply_farmPrice supply_trend 236s 0.245 0.267 0.336 236s > print( round( coef( fitw2slsd2e$eq[[ 1 ]] ), digits = 6 ) ) 236s (Intercept) price income 236s 104.464 -0.363 0.336 236s > 236s > print( round( coef( fitw2slsd3e ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income supply_(Intercept) 236s 104.464 -0.363 0.336 47.071 236s supply_price supply_farmPrice supply_trend 236s 0.245 0.267 0.336 236s > print( round( coef( fitw2slsd3e, modified.regMat = TRUE ), digits = 6 ) ) 236s C1 C2 C3 C4 C5 C6 236s 104.464 -0.363 0.336 47.071 0.245 0.267 236s > print( round( coef( fitw2slsd3e$eq[[ 2 ]] ), digits = 6 ) ) 236s (Intercept) price farmPrice trend 236s 47.071 0.245 0.267 0.336 236s > 236s > print( round( coef( fitw2sls4 ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income supply_(Intercept) 236s 95.304 -0.243 0.306 46.423 236s supply_price supply_farmPrice supply_trend 236s 0.257 0.264 0.306 236s > print( round( coef( fitw2sls4$eq[[ 1 ]] ), digits = 6 ) ) 236s (Intercept) price income 236s 95.304 -0.243 0.306 236s > 236s > print( round( coef( fitw2sls5 ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income supply_(Intercept) 236s 95.304 -0.243 0.306 46.423 236s supply_price supply_farmPrice supply_trend 236s 0.257 0.264 0.306 236s > print( round( coef( fitw2sls5, modified.regMat = TRUE ), digits = 6 ) ) 236s C1 C2 C3 C4 C5 C6 236s 95.304 -0.243 0.306 46.423 0.257 0.264 236s > print( round( coef( fitw2sls5$eq[[ 2 ]] ), digits = 6 ) ) 236s (Intercept) price farmPrice trend 236s 46.423 0.257 0.264 0.306 236s > 236s > 236s > ## *************** coefficients with stats ********************* 236s > print( round( coef( summary( fitw2sls1e, useDfSys = FALSE ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 94.633 7.3027 12.96 0.000000 236s demand_price -0.244 0.0890 -2.74 0.014016 236s demand_income 0.314 0.0433 7.25 0.000001 236s supply_(Intercept) 49.532 10.7425 4.61 0.000289 236s supply_price 0.240 0.0894 2.69 0.016234 236s supply_farmPrice 0.256 0.0423 6.05 0.000017 236s supply_trend 0.253 0.0891 2.84 0.011883 236s > print( round( coef( summary( fitw2sls1e$eq[[ 2 ]], useDfSys = FALSE ) ), 236s + digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 49.532 10.7425 4.61 0.000289 236s price 0.240 0.0894 2.69 0.016234 236s farmPrice 0.256 0.0423 6.05 0.000017 236s trend 0.253 0.0891 2.84 0.011883 236s > 236s > print( round( coef( summary( fitw2slsd2e ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 104.464 9.7929 10.67 0.00000 236s demand_price -0.363 0.1220 -2.98 0.00534 236s demand_income 0.336 0.0444 7.57 0.00000 236s supply_(Intercept) 47.071 10.6890 4.40 0.00010 236s supply_price 0.245 0.0910 2.69 0.01093 236s supply_farmPrice 0.267 0.0416 6.41 0.00000 236s supply_trend 0.336 0.0444 7.57 0.00000 236s > print( round( coef( summary( fitw2slsd2e$eq[[ 1 ]] ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 104.464 9.7929 10.67 0.00000 236s price -0.363 0.1220 -2.98 0.00534 236s income 0.336 0.0444 7.57 0.00000 236s > 236s > print( round( coef( summary( fitw2slsd3e, useDfSys = FALSE ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 104.464 9.7929 10.67 0.000000 236s demand_price -0.363 0.1220 -2.98 0.008475 236s demand_income 0.336 0.0444 7.57 0.000001 236s supply_(Intercept) 47.071 10.6890 4.40 0.000444 236s supply_price 0.245 0.0910 2.69 0.016014 236s supply_farmPrice 0.267 0.0416 6.41 0.000009 236s supply_trend 0.336 0.0444 7.57 0.000001 236s > print( round( coef( summary( fitw2slsd3e, useDfSys = FALSE ), 236s + modified.regMat = TRUE ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s C1 104.464 9.7929 10.67 NA 236s C2 -0.363 0.1220 -2.98 NA 236s C3 0.336 0.0444 7.57 NA 236s C4 47.071 10.6890 4.40 NA 236s C5 0.245 0.0910 2.69 NA 236s C6 0.267 0.0416 6.41 NA 236s > print( round( coef( summary( fitw2slsd3e$eq[[ 2 ]], useDfSys = FALSE ) ), 236s + digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 47.071 10.6890 4.40 0.000444 236s price 0.245 0.0910 2.69 0.016014 236s farmPrice 0.267 0.0416 6.41 0.000009 236s trend 0.336 0.0444 7.57 0.000001 236s > 236s > print( round( coef( summary( fitw2sls4 ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 95.304 6.3056 15.11 0.000000 236s demand_price -0.243 0.0684 -3.55 0.001128 236s demand_income 0.306 0.0394 7.78 0.000000 236s supply_(Intercept) 46.423 8.3296 5.57 0.000003 236s supply_price 0.257 0.0684 3.76 0.000622 236s supply_farmPrice 0.264 0.0455 5.80 0.000001 236s supply_trend 0.306 0.0394 7.78 0.000000 236s > print( round( coef( summary( fitw2sls4$eq[[ 1 ]] ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 95.304 6.3056 15.11 0.00000 236s price -0.243 0.0684 -3.55 0.00113 236s income 0.306 0.0394 7.78 0.00000 236s > 236s > print( round( coef( summary( fitw2sls5 ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s demand_(Intercept) 95.304 6.3056 15.11 0.000000 236s demand_price -0.243 0.0684 -3.55 0.001128 236s demand_income 0.306 0.0394 7.78 0.000000 236s supply_(Intercept) 46.423 8.3296 5.57 0.000003 236s supply_price 0.257 0.0684 3.76 0.000622 236s supply_farmPrice 0.264 0.0455 5.80 0.000001 236s supply_trend 0.306 0.0394 7.78 0.000000 236s > print( round( coef( summary( fitw2sls5 ), modified.regMat = TRUE ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s C1 95.304 6.3056 15.11 0.000000 236s C2 -0.243 0.0684 -3.55 0.001128 236s C3 0.306 0.0394 7.78 0.000000 236s C4 46.423 8.3296 5.57 0.000003 236s C5 0.257 0.0684 3.76 0.000622 236s C6 0.264 0.0455 5.80 0.000001 236s > print( round( coef( summary( fitw2sls5$eq[[ 2 ]] ) ), digits = 6 ) ) 236s Estimate Std. Error t value Pr(>|t|) 236s (Intercept) 46.423 8.3296 5.57 0.000003 236s price 0.257 0.0684 3.76 0.000622 236s farmPrice 0.264 0.0455 5.80 0.000001 236s trend 0.306 0.0394 7.78 0.000000 236s > 236s > 236s > ## *********** variance covariance matrix of the coefficients ******* 236s > print( round( vcov( fitw2sls1e ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 53.3287 -0.57241 0.04191 236s demand_price -0.5724 0.00791 -0.00225 236s demand_income 0.0419 -0.00225 0.00187 236s supply_(Intercept) 0.0000 0.00000 0.00000 236s supply_price 0.0000 0.00000 0.00000 236s supply_farmPrice 0.0000 0.00000 0.00000 236s supply_trend 0.0000 0.00000 0.00000 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) 0.000 0.000000 0.000000 236s demand_price 0.000 0.000000 0.000000 236s demand_income 0.000 0.000000 0.000000 236s supply_(Intercept) 115.402 -0.876328 -0.259055 236s supply_price -0.876 0.007989 0.000749 236s supply_farmPrice -0.259 0.000749 0.001786 236s supply_trend -0.236 0.000463 0.001101 236s supply_trend 236s demand_(Intercept) 0.000000 236s demand_price 0.000000 236s demand_income 0.000000 236s supply_(Intercept) -0.236183 236s supply_price 0.000463 236s supply_farmPrice 0.001101 236s supply_trend 0.007945 236s > print( round( vcov( fitw2sls1e$eq[[ 2 ]] ), digits = 6 ) ) 236s (Intercept) price farmPrice trend 236s (Intercept) 115.402 -0.876328 -0.259055 -0.236183 236s price -0.876 0.007989 0.000749 0.000463 236s farmPrice -0.259 0.000749 0.001786 0.001101 236s trend -0.236 0.000463 0.001101 0.007945 236s > 236s > print( round( vcov( fitw2sls2 ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 64.14482 -0.679629 0.041312 236s demand_price -0.67963 0.008954 -0.002214 236s demand_income 0.04131 -0.002214 0.001847 236s supply_(Intercept) -1.22810 0.065809 -0.054894 236s supply_price 0.00241 -0.000129 0.000108 236s supply_farmPrice 0.00573 -0.000307 0.000256 236s supply_trend 0.04131 -0.002214 0.001847 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) -1.2281 0.002409 0.005727 236s demand_price 0.0658 -0.000129 -0.000307 236s demand_income -0.0549 0.000108 0.000256 236s supply_(Intercept) 139.2416 -1.098376 -0.294954 236s supply_price -1.0984 0.010116 0.000884 236s supply_farmPrice -0.2950 0.000884 0.002109 236s supply_trend -0.0549 0.000108 0.000256 236s supply_trend 236s demand_(Intercept) 0.041312 236s demand_price -0.002214 236s demand_income 0.001847 236s supply_(Intercept) -0.054894 236s supply_price 0.000108 236s supply_farmPrice 0.000256 236s supply_trend 0.001847 236s > print( round( vcov( fitw2sls2$eq[[ 1 ]] ), digits = 6 ) ) 236s (Intercept) price income 236s (Intercept) 64.1448 -0.67963 0.04131 236s price -0.6796 0.00895 -0.00221 236s income 0.0413 -0.00221 0.00185 236s > 236s > print( round( vcov( fitw2sls3e ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 54.51421 -0.577209 0.034718 236s demand_price -0.57721 0.007585 -0.001860 236s demand_income 0.03472 -0.001860 0.001552 236s supply_(Intercept) -1.03208 0.055305 -0.046132 236s supply_price 0.00202 -0.000108 0.000090 236s supply_farmPrice 0.00481 -0.000258 0.000215 236s supply_trend 0.03472 -0.001860 0.001552 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) -1.0321 0.002024 0.004813 236s demand_price 0.0553 -0.000108 -0.000258 236s demand_income -0.0461 0.000090 0.000215 236s supply_(Intercept) 111.4592 -0.878830 -0.236271 236s supply_price -0.8788 0.008093 0.000708 236s supply_farmPrice -0.2363 0.000708 0.001689 236s supply_trend -0.0461 0.000090 0.000215 236s supply_trend 236s demand_(Intercept) 0.034718 236s demand_price -0.001860 236s demand_income 0.001552 236s supply_(Intercept) -0.046132 236s supply_price 0.000090 236s supply_farmPrice 0.000215 236s supply_trend 0.001552 236s > print( round( vcov( fitw2sls3e, modified.regMat = TRUE ), digits = 6 ) ) 236s C1 C2 C3 C4 C5 C6 236s C1 54.51421 -0.577209 0.034718 -1.0321 0.002024 0.004813 236s C2 -0.57721 0.007585 -0.001860 0.0553 -0.000108 -0.000258 236s C3 0.03472 -0.001860 0.001552 -0.0461 0.000090 0.000215 236s C4 -1.03208 0.055305 -0.046132 111.4592 -0.878830 -0.236271 236s C5 0.00202 -0.000108 0.000090 -0.8788 0.008093 0.000708 236s C6 0.00481 -0.000258 0.000215 -0.2363 0.000708 0.001689 236s > print( round( vcov( fitw2sls3e$eq[[ 2 ]] ), digits = 6 ) ) 236s (Intercept) price farmPrice trend 236s (Intercept) 111.4592 -0.878830 -0.236271 -0.046132 236s price -0.8788 0.008093 0.000708 0.000090 236s farmPrice -0.2363 0.000708 0.001689 0.000215 236s trend -0.0461 0.000090 0.000215 0.001552 236s > 236s > print( round( vcov( fitw2sls4 ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 39.7610 -0.358128 -0.03842 236s demand_price -0.3581 0.004681 -0.00113 236s demand_income -0.0384 -0.001129 0.00155 236s supply_(Intercept) 39.6949 -0.480685 0.08595 236s supply_price -0.3581 0.004681 -0.00113 236s supply_farmPrice -0.0359 0.000252 0.00011 236s supply_trend -0.0384 -0.001129 0.00155 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) 39.6949 -0.358128 -0.035932 236s demand_price -0.4807 0.004681 0.000252 236s demand_income 0.0859 -0.001129 0.000110 236s supply_(Intercept) 69.3817 -0.480685 -0.226588 236s supply_price -0.4807 0.004681 0.000252 236s supply_farmPrice -0.2266 0.000252 0.002072 236s supply_trend 0.0859 -0.001129 0.000110 236s supply_trend 236s demand_(Intercept) -0.03842 236s demand_price -0.00113 236s demand_income 0.00155 236s supply_(Intercept) 0.08595 236s supply_price -0.00113 236s supply_farmPrice 0.00011 236s supply_trend 0.00155 236s > print( round( vcov( fitw2sls4$eq[[ 1 ]] ), digits = 6 ) ) 236s (Intercept) price income 236s (Intercept) 39.7610 -0.35813 -0.03842 236s price -0.3581 0.00468 -0.00113 236s income -0.0384 -0.00113 0.00155 236s > 236s > print( round( vcov( fitw2sls5 ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 39.7610 -0.358128 -0.03842 236s demand_price -0.3581 0.004681 -0.00113 236s demand_income -0.0384 -0.001129 0.00155 236s supply_(Intercept) 39.6949 -0.480685 0.08595 236s supply_price -0.3581 0.004681 -0.00113 236s supply_farmPrice -0.0359 0.000252 0.00011 236s supply_trend -0.0384 -0.001129 0.00155 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) 39.6949 -0.358128 -0.035932 236s demand_price -0.4807 0.004681 0.000252 236s demand_income 0.0859 -0.001129 0.000110 236s supply_(Intercept) 69.3817 -0.480685 -0.226588 236s supply_price -0.4807 0.004681 0.000252 236s supply_farmPrice -0.2266 0.000252 0.002072 236s supply_trend 0.0859 -0.001129 0.000110 236s supply_trend 236s demand_(Intercept) -0.03842 236s demand_price -0.00113 236s demand_income 0.00155 236s supply_(Intercept) 0.08595 236s supply_price -0.00113 236s supply_farmPrice 0.00011 236s supply_trend 0.00155 236s > print( round( vcov( fitw2sls5, modified.regMat = TRUE ), digits = 6 ) ) 236s C1 C2 C3 C4 C5 C6 236s C1 39.7610 -0.358128 -0.03842 39.6949 -0.358128 -0.035932 236s C2 -0.3581 0.004681 -0.00113 -0.4807 0.004681 0.000252 236s C3 -0.0384 -0.001129 0.00155 0.0859 -0.001129 0.000110 236s C4 39.6949 -0.480685 0.08595 69.3817 -0.480685 -0.226588 236s C5 -0.3581 0.004681 -0.00113 -0.4807 0.004681 0.000252 236s C6 -0.0359 0.000252 0.00011 -0.2266 0.000252 0.002072 236s > print( round( vcov( fitw2sls5$eq[[ 2 ]] ), digits = 6 ) ) 236s (Intercept) price farmPrice trend 236s (Intercept) 69.3817 -0.480685 -0.226588 0.08595 236s price -0.4807 0.004681 0.000252 -0.00113 236s farmPrice -0.2266 0.000252 0.002072 0.00011 236s trend 0.0859 -0.001129 0.000110 0.00155 236s > 236s > print( round( vcov( fitw2slsd1 ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 124.179 -1.51767 0.28519 236s demand_price -1.518 0.02098 -0.00595 236s demand_income 0.285 -0.00595 0.00318 236s supply_(Intercept) 0.000 0.00000 0.00000 236s supply_price 0.000 0.00000 0.00000 236s supply_farmPrice 0.000 0.00000 0.00000 236s supply_trend 0.000 0.00000 0.00000 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) 0.000 0.000000 0.000000 236s demand_price 0.000 0.000000 0.000000 236s demand_income 0.000 0.000000 0.000000 236s supply_(Intercept) 144.253 -1.095410 -0.323818 236s supply_price -1.095 0.009987 0.000936 236s supply_farmPrice -0.324 0.000936 0.002233 236s supply_trend -0.295 0.000579 0.001377 236s supply_trend 236s demand_(Intercept) 0.000000 236s demand_price 0.000000 236s demand_income 0.000000 236s supply_(Intercept) -0.295229 236s supply_price 0.000579 236s supply_farmPrice 0.001377 236s supply_trend 0.009931 236s > print( round( vcov( fitw2slsd1$eq[[ 1 ]] ), digits = 6 ) ) 236s (Intercept) price income 236s (Intercept) 124.179 -1.51767 0.28519 236s price -1.518 0.02098 -0.00595 236s income 0.285 -0.00595 0.00318 236s > 236s > print( round( vcov( fitw2slsd2e ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 95.9017 -1.129212 0.176368 236s demand_price -1.1292 0.014881 -0.003682 236s demand_income 0.1764 -0.003682 0.001968 236s supply_(Intercept) -5.2430 0.109460 -0.058492 236s supply_price 0.0103 -0.000215 0.000115 236s supply_farmPrice 0.0245 -0.000510 0.000273 236s supply_trend 0.1764 -0.003682 0.001968 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) -5.2430 0.010284 0.024451 236s demand_price 0.1095 -0.000215 -0.000510 236s demand_income -0.0585 0.000115 0.000273 236s supply_(Intercept) 114.2555 -0.898881 -0.243056 236s supply_price -0.8989 0.008273 0.000727 236s supply_farmPrice -0.2431 0.000727 0.001733 236s supply_trend -0.0585 0.000115 0.000273 236s supply_trend 236s demand_(Intercept) 0.176368 236s demand_price -0.003682 236s demand_income 0.001968 236s supply_(Intercept) -0.058492 236s supply_price 0.000115 236s supply_farmPrice 0.000273 236s supply_trend 0.001968 236s > print( round( vcov( fitw2slsd2e$eq[[ 2 ]] ), digits = 6 ) ) 236s (Intercept) price farmPrice trend 236s (Intercept) 114.2555 -0.898881 -0.243056 -0.058492 236s price -0.8989 0.008273 0.000727 0.000115 236s farmPrice -0.2431 0.000727 0.001733 0.000273 236s trend -0.0585 0.000115 0.000273 0.001968 236s > 236s > print( round( vcov( fitw2slsd3 ), digits = 6 ) ) 236s demand_(Intercept) demand_price demand_income 236s demand_(Intercept) 113.0903 -1.334011 0.210445 236s demand_price -1.3340 0.017622 -0.004394 236s demand_income 0.2104 -0.004394 0.002348 236s supply_(Intercept) -6.2560 0.130609 -0.069794 236s supply_price 0.0123 -0.000256 0.000137 236s supply_farmPrice 0.0292 -0.000609 0.000325 236s supply_trend 0.2104 -0.004394 0.002348 236s supply_(Intercept) supply_price supply_farmPrice 236s demand_(Intercept) -6.2560 0.012271 0.029175 236s demand_price 0.1306 -0.000256 -0.000609 236s demand_income -0.0698 0.000137 0.000325 236s supply_(Intercept) 142.7207 -1.123408 -0.303360 236s supply_price -1.1234 0.010341 0.000908 236s supply_farmPrice -0.3034 0.000908 0.002165 236s supply_trend -0.0698 0.000137 0.000325 236s supply_trend 236s demand_(Intercept) 0.210445 236s demand_price -0.004394 236s demand_income 0.002348 236s supply_(Intercept) -0.069794 236s supply_price 0.000137 236s supply_farmPrice 0.000325 236s supply_trend 0.002348 236s > print( round( vcov( fitw2slsd3, modified.regMat = TRUE ), digits = 6 ) ) 236s C1 C2 C3 C4 C5 C6 236s C1 113.0903 -1.334011 0.210445 -6.2560 0.012271 0.029175 236s C2 -1.3340 0.017622 -0.004394 0.1306 -0.000256 -0.000609 236s C3 0.2104 -0.004394 0.002348 -0.0698 0.000137 0.000325 236s C4 -6.2560 0.130609 -0.069794 142.7207 -1.123408 -0.303360 236s C5 0.0123 -0.000256 0.000137 -1.1234 0.010341 0.000908 236s C6 0.0292 -0.000609 0.000325 -0.3034 0.000908 0.002165 236s > print( round( vcov( fitw2slsd3$eq[[ 1 ]] ), digits = 6 ) ) 236s (Intercept) price income 236s (Intercept) 113.09 -1.33401 0.21044 236s price -1.33 0.01762 -0.00439 236s income 0.21 -0.00439 0.00235 236s > 236s > 236s > ## *********** confidence intervals of coefficients ************* 236s > print( confint( fitw2sls1e, useDfSys = TRUE ) ) 236s 2.5 % 97.5 % 236s demand_(Intercept) 79.776 109.491 236s demand_price -0.425 -0.063 236s demand_income 0.226 0.402 236s supply_(Intercept) 27.677 71.388 236s supply_price 0.058 0.422 236s supply_farmPrice 0.170 0.342 236s supply_trend 0.072 0.434 236s > print( confint( fitw2sls1e$eq[[ 1 ]], level = 0.9, useDfSys = TRUE ) ) 236s 5 % 95 % 236s (Intercept) 82.275 106.992 236s price -0.394 -0.093 236s income 0.241 0.387 236s > 236s > print( confint( fitw2sls2, level = 0.9 ) ) 236s 5 % 95 % 236s demand_(Intercept) 78.107 110.660 236s demand_price -0.422 -0.038 236s demand_income 0.215 0.390 236s supply_(Intercept) 24.069 72.030 236s supply_price 0.039 0.447 236s supply_farmPrice 0.169 0.356 236s supply_trend 0.215 0.390 236s > print( confint( fitw2sls2$eq[[ 2 ]], level = 0.99 ) ) 236s 0.5 % 99.5 % 236s (Intercept) 15.854 80.245 236s price -0.031 0.517 236s farmPrice 0.137 0.388 236s trend 0.186 0.420 236s > 236s > print( confint( fitw2sls3, level = 0.99 ) ) 236s 0.5 % 99.5 % 236s demand_(Intercept) 78.107 110.660 236s demand_price -0.422 -0.038 236s demand_income 0.215 0.390 236s supply_(Intercept) 24.069 72.030 236s supply_price 0.039 0.447 236s supply_farmPrice 0.169 0.356 236s supply_trend 0.215 0.390 236s > print( confint( fitw2sls3$eq[[ 1 ]], level = 0.5 ) ) 236s 25 % 75 % 236s (Intercept) 88.923 99.844 236s price -0.295 -0.166 236s income 0.274 0.332 236s > 236s > print( confint( fitw2sls4e, level = 0.5, useDfSys = TRUE ) ) 236s 25 % 75 % 236s demand_(Intercept) 83.658 107.036 236s demand_price -0.369 -0.117 236s demand_income 0.233 0.379 236s supply_(Intercept) 31.138 61.736 236s supply_price 0.131 0.383 236s supply_farmPrice 0.181 0.347 236s supply_trend 0.233 0.379 236s > print( confint( fitw2sls4e$eq[[ 2 ]], level = 0.25, useDfSys = TRUE ) ) 236s 37.5 % 62.5 % 236s (Intercept) 44.016 48.857 236s price 0.237 0.277 236s farmPrice 0.251 0.277 236s trend 0.294 0.317 236s > 236s > print( confint( fitw2sls5, level = 0.25 ) ) 236s 37.5 % 62.5 % 236s demand_(Intercept) 82.503 108.105 236s demand_price -0.382 -0.104 236s demand_income 0.226 0.386 236s supply_(Intercept) 29.513 63.333 236s supply_price 0.118 0.396 236s supply_farmPrice 0.172 0.357 236s supply_trend 0.226 0.386 236s > print( confint( fitw2sls5$eq[[ 1 ]], level = 0.975 ) ) 236s 1.3 % 98.8 % 236s (Intercept) 80.537 110.072 236s price -0.403 -0.083 236s income 0.214 0.399 236s > 236s > print( confint( fitw2slsd1, level = 0.975 ) ) 236s 1.3 % 98.8 % 236s demand_(Intercept) 83.279 130.300 236s demand_price -0.717 -0.106 236s demand_income 0.243 0.481 236s supply_(Intercept) 24.071 74.994 236s supply_price 0.028 0.452 236s supply_farmPrice 0.155 0.356 236s supply_trend 0.042 0.464 236s > print( confint( fitw2slsd1$eq[[ 2 ]], level = 0.999 ) ) 236s 0.1 % 100 % 236s (Intercept) 1.310 97.755 236s price -0.161 0.641 236s farmPrice 0.066 0.445 236s trend -0.147 0.653 236s > 236s > print( confint( fitw2slsd2e, level = 0.999, useDfSys = TRUE ) ) 236s 0.1 % 100 % 236s demand_(Intercept) 84.562 124.365 236s demand_price -0.611 -0.115 236s demand_income 0.246 0.426 236s supply_(Intercept) 25.348 68.793 236s supply_price 0.060 0.430 236s supply_farmPrice 0.182 0.352 236s supply_trend 0.246 0.426 236s > print( confint( fitw2slsd2e$eq[[ 1 ]], level = 0.01, useDfSys = TRUE ) ) 236s 49.5 % 50.5 % 236s (Intercept) 104.340 104.587 236s price -0.365 -0.362 236s income 0.335 0.336 236s > 236s > print( confint( fitw2slsd3e, level = 0.01, useDfSys = TRUE ) ) 236s 49.5 % 50.5 % 236s demand_(Intercept) 84.562 124.365 236s demand_price -0.611 -0.115 236s demand_income 0.246 0.426 236s supply_(Intercept) 25.348 68.793 236s supply_price 0.060 0.430 236s supply_farmPrice 0.182 0.352 236s supply_trend 0.246 0.426 236s > print( confint( fitw2slsd3e$eq[[ 2 ]], useDfSys = TRUE ) ) 236s 2.5 % 97.5 % 236s (Intercept) 25.348 68.793 236s price 0.060 0.430 236s farmPrice 0.182 0.352 236s trend 0.246 0.426 236s > 236s > 236s > ## *********** fitted values ************* 236s > print( fitted( fitw2sls1e ) ) 236s demand supply 236s 1 97.6 98.9 236s 2 99.9 100.4 236s 3 99.8 100.5 236s 4 100.0 100.7 236s 5 102.1 102.6 236s 6 102.0 102.6 236s 7 102.4 102.6 236s 8 103.0 104.8 236s 9 101.5 102.7 236s 10 100.3 99.7 236s 11 95.5 95.4 236s 12 94.7 93.8 236s 13 96.1 95.6 236s 14 99.0 97.6 236s 15 103.8 102.3 236s 16 103.7 104.1 236s 17 103.8 102.8 236s 18 102.1 102.7 236s 19 103.6 102.6 236s 20 106.9 105.6 236s > print( fitted( fitw2sls1e$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 97.6 99.9 99.8 100.0 102.1 102.0 102.4 103.0 101.5 100.3 95.5 94.7 96.1 236s 14 15 16 17 18 19 20 236s 99.0 103.8 103.7 103.8 102.1 103.6 106.9 236s > 236s > print( fitted( fitw2sls2 ) ) 236s demand supply 236s 1 97.8 98.5 236s 2 99.9 100.0 236s 3 99.9 100.1 236s 4 100.1 100.4 236s 5 102.0 102.5 236s 6 101.9 102.4 236s 7 102.4 102.4 236s 8 102.9 104.8 236s 9 101.4 102.7 236s 10 100.3 99.7 236s 11 95.7 95.3 236s 12 94.9 93.7 236s 13 96.3 95.6 236s 14 99.1 97.7 236s 15 103.7 102.6 236s 16 103.5 104.4 236s 17 103.7 103.2 236s 18 102.1 103.1 236s 19 103.6 102.9 236s 20 106.8 106.1 236s > print( fitted( fitw2sls2$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 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 236s 14 15 16 17 18 19 20 236s 97.7 102.6 104.4 103.2 103.1 102.9 106.1 236s > 236s > print( fitted( fitw2sls3 ) ) 236s demand supply 236s 1 97.8 98.5 236s 2 99.9 100.0 236s 3 99.9 100.1 236s 4 100.1 100.4 236s 5 102.0 102.5 236s 6 101.9 102.4 236s 7 102.4 102.4 236s 8 102.9 104.8 236s 9 101.4 102.7 236s 10 100.3 99.7 236s 11 95.7 95.3 236s 12 94.9 93.7 236s 13 96.3 95.6 236s 14 99.1 97.7 236s 15 103.7 102.6 236s 16 103.5 104.4 236s 17 103.7 103.2 236s 18 102.1 103.1 236s 19 103.6 102.9 236s 20 106.8 106.1 236s > print( fitted( fitw2sls3$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 97.8 99.9 99.9 100.1 102.0 101.9 102.4 102.9 101.4 100.3 95.7 94.9 96.3 236s 14 15 16 17 18 19 20 236s 99.1 103.7 103.5 103.7 102.1 103.6 106.8 236s > 236s > print( fitted( fitw2sls4e ) ) 236s demand supply 236s 1 97.7 98.4 236s 2 99.9 100.0 236s 3 99.8 100.1 236s 4 100.0 100.5 236s 5 102.1 102.4 236s 6 101.9 102.4 236s 7 102.4 102.5 236s 8 102.9 104.8 236s 9 101.5 102.7 236s 10 100.4 99.5 236s 11 95.7 95.1 236s 12 94.9 93.6 236s 13 96.2 95.6 236s 14 99.1 97.6 236s 15 103.8 102.5 236s 16 103.6 104.4 236s 17 103.8 103.1 236s 18 102.0 103.1 236s 19 103.5 103.0 236s 20 106.7 106.3 236s > print( fitted( fitw2sls4e$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 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 236s 14 15 16 17 18 19 20 236s 97.6 102.5 104.4 103.1 103.1 103.0 106.3 236s > 236s > print( fitted( fitw2sls5 ) ) 236s demand supply 236s 1 97.7 98.4 236s 2 99.9 100.0 236s 3 99.8 100.1 236s 4 100.0 100.5 236s 5 102.1 102.4 236s 6 101.9 102.4 236s 7 102.4 102.5 236s 8 102.9 104.8 236s 9 101.5 102.7 236s 10 100.4 99.5 236s 11 95.7 95.1 236s 12 94.9 93.6 236s 13 96.2 95.6 236s 14 99.1 97.6 236s 15 103.8 102.5 236s 16 103.6 104.4 236s 17 103.8 103.1 236s 18 102.0 103.1 236s 19 103.5 103.0 236s 20 106.7 106.3 236s > print( fitted( fitw2sls5$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 97.7 99.9 99.8 100.0 102.1 101.9 102.4 102.9 101.5 100.4 95.7 94.9 96.2 236s 14 15 16 17 18 19 20 236s 99.1 103.8 103.6 103.8 102.0 103.5 106.7 236s > 236s > print( fitted( fitw2slsd1 ) ) 236s demand supply 236s 1 97.1 98.9 236s 2 99.2 100.4 236s 3 99.2 100.5 236s 4 99.3 100.7 236s 5 102.5 102.6 236s 6 102.2 102.6 236s 7 102.5 102.6 236s 8 102.7 104.8 236s 9 102.0 102.7 236s 10 101.4 99.7 236s 11 95.6 95.4 236s 12 93.9 93.8 236s 13 95.0 95.6 236s 14 98.9 97.6 236s 15 104.9 102.3 236s 16 104.3 104.1 236s 17 106.1 102.8 236s 18 101.7 102.7 236s 19 103.3 102.6 236s 20 106.0 105.6 236s > print( fitted( fitw2slsd1$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 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 236s 14 15 16 17 18 19 20 236s 97.6 102.3 104.1 102.8 102.7 102.6 105.6 236s > 236s > print( fitted( fitw2slsd2e ) ) 236s demand supply 236s 1 97.4 98.2 236s 2 99.4 99.7 236s 3 99.4 99.9 236s 4 99.5 100.2 236s 5 102.4 102.3 236s 6 102.1 102.3 236s 7 102.4 102.4 236s 8 102.6 104.7 236s 9 101.9 102.7 236s 10 101.2 99.6 236s 11 95.9 95.2 236s 12 94.4 93.6 236s 13 95.5 95.6 236s 14 99.0 97.7 236s 15 104.5 102.7 236s 16 104.0 104.6 236s 17 105.4 103.5 236s 18 101.8 103.3 236s 19 103.2 103.2 236s 20 105.9 106.4 236s > print( fitted( fitw2slsd2e$eq[[ 1 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 97.4 99.4 99.4 99.5 102.4 102.1 102.4 102.6 101.9 101.2 95.9 94.4 95.5 236s 14 15 16 17 18 19 20 236s 99.0 104.5 104.0 105.4 101.8 103.2 105.9 236s > 236s > print( fitted( fitw2slsd3e ) ) 236s demand supply 236s 1 97.4 98.2 236s 2 99.4 99.7 236s 3 99.4 99.9 236s 4 99.5 100.2 236s 5 102.4 102.3 236s 6 102.1 102.3 236s 7 102.4 102.4 236s 8 102.6 104.7 236s 9 101.9 102.7 236s 10 101.2 99.6 236s 11 95.9 95.2 236s 12 94.4 93.6 236s 13 95.5 95.6 236s 14 99.0 97.7 236s 15 104.5 102.7 236s 16 104.0 104.6 236s 17 105.4 103.5 236s 18 101.8 103.3 236s 19 103.2 103.2 236s 20 105.9 106.4 236s > print( fitted( fitw2slsd3e$eq[[ 2 ]] ) ) 236s 1 2 3 4 5 6 7 8 9 10 11 12 13 236s 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 236s 14 15 16 17 18 19 20 236s 97.7 102.7 104.6 103.5 103.3 103.2 106.4 236s > 236s > 236s > ## *********** predicted values ************* 236s > predictData <- Kmenta 236s > predictData$consump <- NULL 236s > predictData$price <- Kmenta$price * 0.9 236s > predictData$income <- Kmenta$income * 1.1 236s > 236s > print( predict( fitw2sls1e, se.fit = TRUE, interval = "prediction", 236s + useDfSys = TRUE ) ) 236s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 236s 1 97.6 0.609 93.5 101.8 98.9 0.965 236s 2 99.9 0.553 95.7 104.0 100.4 0.952 236s 3 99.8 0.520 95.7 103.9 100.5 0.861 236s 4 100.0 0.558 95.9 104.2 100.7 0.839 236s 5 102.1 0.476 98.0 106.2 102.6 0.818 236s 6 102.0 0.437 97.9 106.1 102.6 0.723 236s 7 102.4 0.454 98.3 106.5 102.6 0.658 236s 8 103.0 0.567 98.8 107.1 104.8 0.889 236s 9 101.5 0.502 97.3 105.6 102.7 0.723 236s 10 100.3 0.758 96.0 104.6 99.7 0.915 236s 11 95.5 0.888 91.2 99.9 95.4 1.098 236s 12 94.7 0.928 90.3 99.1 93.8 1.277 236s 13 96.1 0.844 91.8 100.5 95.6 1.137 236s 14 99.0 0.477 94.9 103.1 97.6 0.820 236s 15 103.8 0.731 99.6 108.1 102.3 0.804 236s 16 103.7 0.587 99.5 107.8 104.1 0.837 236s 17 103.8 1.243 99.1 108.6 102.8 1.489 236s 18 102.1 0.506 97.9 106.2 102.7 0.884 236s 19 103.6 0.641 99.4 107.8 102.6 1.010 236s 20 106.9 1.204 102.2 111.6 105.6 1.550 236s supply.lwr supply.upr 236s 1 93.5 104.3 236s 2 95.0 105.8 236s 3 95.2 105.8 236s 4 95.4 106.0 236s 5 97.4 107.9 236s 6 97.4 107.8 236s 7 97.4 107.7 236s 8 99.5 110.1 236s 9 97.5 108.0 236s 10 94.3 105.0 236s 11 89.9 100.8 236s 12 88.2 99.5 236s 13 90.1 101.2 236s 14 92.3 102.9 236s 15 97.1 107.6 236s 16 98.8 109.3 236s 17 97.0 108.7 236s 18 97.4 108.0 236s 19 97.2 108.0 236s 20 99.7 111.5 236s > print( predict( fitw2sls1e$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 236s + useDfSys = TRUE ) ) 236s fit se.fit lwr upr 236s 1 97.6 0.609 93.5 101.8 236s 2 99.9 0.553 95.7 104.0 236s 3 99.8 0.520 95.7 103.9 236s 4 100.0 0.558 95.9 104.2 236s 5 102.1 0.476 98.0 106.2 236s 6 102.0 0.437 97.9 106.1 236s 7 102.4 0.454 98.3 106.5 236s 8 103.0 0.567 98.8 107.1 236s 9 101.5 0.502 97.3 105.6 236s 10 100.3 0.758 96.0 104.6 236s 11 95.5 0.888 91.2 99.9 236s 12 94.7 0.928 90.3 99.1 236s 13 96.1 0.844 91.8 100.5 236s 14 99.0 0.477 94.9 103.1 236s 15 103.8 0.731 99.6 108.1 236s 16 103.7 0.587 99.5 107.8 236s 17 103.8 1.243 99.1 108.6 236s 18 102.1 0.506 97.9 106.2 236s 19 103.6 0.641 99.4 107.8 236s 20 106.9 1.204 102.2 111.6 236s > 236s > print( predict( fitw2sls2, se.pred = TRUE, interval = "confidence", 236s + level = 0.999, newdata = predictData ) ) 236s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 236s 1 102.7 2.22 99.1 106 96.0 2.75 236s 2 105.3 2.22 101.7 109 97.5 2.64 236s 3 105.2 2.23 101.5 109 97.6 2.65 236s 4 105.4 2.22 101.9 109 97.9 2.62 236s 5 107.3 2.51 101.8 113 100.1 2.83 236s 6 107.3 2.46 102.0 112 100.0 2.77 236s 7 107.8 2.44 102.7 113 100.0 2.71 236s 8 108.6 2.40 103.7 113 102.2 2.65 236s 9 106.6 2.52 101.0 112 100.4 2.87 236s 10 105.1 2.65 98.8 111 97.4 3.10 236s 11 100.1 2.41 95.2 105 93.0 3.18 236s 12 99.5 2.21 96.0 103 91.3 3.15 236s 13 101.2 2.12 98.5 104 93.1 2.95 236s 14 104.1 2.31 99.8 108 95.3 2.91 236s 15 109.0 2.73 102.3 116 100.2 2.92 236s 16 109.0 2.61 102.9 115 102.0 2.80 236s 17 108.6 3.08 100.1 117 101.1 3.37 236s 18 107.6 2.35 103.0 112 100.5 2.65 236s 19 109.3 2.44 104.2 114 100.4 2.64 236s 20 113.2 2.66 106.8 120 103.3 2.58 236s supply.lwr supply.upr 236s 1 91.7 100.3 236s 2 94.2 100.7 236s 3 94.2 101.0 236s 4 94.8 101.0 236s 5 95.1 105.0 236s 6 95.6 104.4 236s 7 96.1 103.9 236s 8 98.8 105.6 236s 9 95.2 105.6 236s 10 90.7 104.1 236s 11 85.9 100.1 236s 12 84.3 98.3 236s 13 87.3 98.9 236s 14 89.7 100.8 236s 15 94.7 105.8 236s 16 97.3 106.6 236s 17 92.9 109.4 236s 18 97.1 103.9 236s 19 97.1 103.6 236s 20 100.7 105.9 236s > print( predict( fitw2sls2$eq[[ 2 ]], se.pred = TRUE, interval = "confidence", 236s + level = 0.999, newdata = predictData ) ) 236s fit se.pred lwr upr 236s 1 96.0 2.75 91.7 100.3 236s 2 97.5 2.64 94.2 100.7 236s 3 97.6 2.65 94.2 101.0 236s 4 97.9 2.62 94.8 101.0 236s 5 100.1 2.83 95.1 105.0 236s 6 100.0 2.77 95.6 104.4 236s 7 100.0 2.71 96.1 103.9 236s 8 102.2 2.65 98.8 105.6 236s 9 100.4 2.87 95.2 105.6 236s 10 97.4 3.10 90.7 104.1 236s 11 93.0 3.18 85.9 100.1 236s 12 91.3 3.15 84.3 98.3 236s 13 93.1 2.95 87.3 98.9 236s 14 95.3 2.91 89.7 100.8 236s 15 100.2 2.92 94.7 105.8 236s 16 102.0 2.80 97.3 106.6 236s 17 101.1 3.37 92.9 109.4 236s 18 100.5 2.65 97.1 103.9 236s 19 100.4 2.64 97.1 103.6 236s 20 103.3 2.58 100.7 105.9 236s > 236s > print( predict( fitw2sls3, se.pred = TRUE, interval = "prediction", 236s + level = 0.975 ) ) 236s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 236s 1 97.8 2.08 92.9 103 98.5 2.57 236s 2 99.9 2.07 95.1 105 100.0 2.61 236s 3 99.9 2.06 95.0 105 100.1 2.59 236s 4 100.1 2.07 95.2 105 100.4 2.60 236s 5 102.0 2.05 97.2 107 102.5 2.63 236s 6 101.9 2.04 97.1 107 102.4 2.60 236s 7 102.4 2.04 97.6 107 102.4 2.58 236s 8 102.9 2.08 98.0 108 104.8 2.68 236s 9 101.4 2.06 96.6 106 102.7 2.61 236s 10 100.3 2.15 95.3 105 99.7 2.69 236s 11 95.7 2.19 90.6 101 95.3 2.77 236s 12 94.9 2.20 89.8 100 93.7 2.86 236s 13 96.3 2.16 91.2 101 95.6 2.79 236s 14 99.1 2.05 94.3 104 97.7 2.64 236s 15 103.7 2.13 98.7 109 102.6 2.60 236s 16 103.5 2.08 98.7 108 104.4 2.59 236s 17 103.7 2.39 98.1 109 103.2 2.91 236s 18 102.1 2.06 97.2 107 103.1 2.59 236s 19 103.6 2.10 98.6 108 102.9 2.64 236s 20 106.8 2.37 101.2 112 106.1 2.90 236s supply.lwr supply.upr 236s 1 92.4 104 236s 2 93.9 106 236s 3 94.0 106 236s 4 94.3 106 236s 5 96.3 109 236s 6 96.3 109 236s 7 96.4 109 236s 8 98.5 111 236s 9 96.6 109 236s 10 93.4 106 236s 11 88.8 102 236s 12 87.0 100 236s 13 89.1 102 236s 14 91.5 104 236s 15 96.5 109 236s 16 98.3 110 236s 17 96.4 110 236s 18 97.0 109 236s 19 96.8 109 236s 20 99.3 113 236s > print( predict( fitw2sls3$eq[[ 1 ]], se.pred = TRUE, interval = "prediction", 236s + level = 0.975 ) ) 236s fit se.pred lwr upr 236s 1 97.8 2.08 92.9 103 236s 2 99.9 2.07 95.1 105 236s 3 99.9 2.06 95.0 105 236s 4 100.1 2.07 95.2 105 236s 5 102.0 2.05 97.2 107 236s 6 101.9 2.04 97.1 107 236s 7 102.4 2.04 97.6 107 236s 8 102.9 2.08 98.0 108 236s 9 101.4 2.06 96.6 106 236s 10 100.3 2.15 95.3 105 236s 11 95.7 2.19 90.6 101 236s 12 94.9 2.20 89.8 100 236s 13 96.3 2.16 91.2 101 236s 14 99.1 2.05 94.3 104 236s 15 103.7 2.13 98.7 109 236s 16 103.5 2.08 98.7 108 236s 17 103.7 2.39 98.1 109 236s 18 102.1 2.06 97.2 107 236s 19 103.6 2.10 98.6 108 236s 20 106.8 2.37 101.2 112 236s > 236s > print( predict( fitw2sls4e, se.fit = TRUE, interval = "confidence", 236s + level = 0.25, useDfSys = TRUE ) ) 236s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 236s 1 97.7 0.552 97.5 97.9 98.4 0.611 236s 2 99.9 0.484 99.7 100.0 100.0 0.700 236s 3 99.8 0.465 99.7 100.0 100.1 0.652 236s 4 100.0 0.488 99.9 100.2 100.5 0.664 236s 5 102.1 0.443 101.9 102.2 102.4 0.769 236s 6 101.9 0.425 101.8 102.1 102.4 0.695 236s 7 102.4 0.447 102.2 102.5 102.5 0.639 236s 8 102.9 0.547 102.7 103.1 104.8 0.821 236s 9 101.5 0.458 101.3 101.6 102.7 0.716 236s 10 100.4 0.648 100.2 100.6 99.5 0.743 236s 11 95.7 0.847 95.4 96.0 95.1 0.944 236s 12 94.9 0.823 94.6 95.1 93.6 1.254 236s 13 96.2 0.695 96.0 96.5 95.6 1.154 236s 14 99.1 0.467 98.9 99.2 97.6 0.814 236s 15 103.8 0.590 103.6 104.0 102.5 0.675 236s 16 103.6 0.520 103.4 103.8 104.4 0.659 236s 17 103.8 0.919 103.5 104.1 103.1 1.196 236s 18 102.0 0.487 101.9 102.2 103.1 0.587 236s 19 103.5 0.615 103.3 103.7 103.0 0.664 236s 20 106.7 1.126 106.3 107.0 106.3 0.909 236s supply.lwr supply.upr 236s 1 98.2 98.6 236s 2 99.8 100.3 236s 3 99.9 100.3 236s 4 100.2 100.7 236s 5 102.2 102.7 236s 6 102.2 102.7 236s 7 102.3 102.7 236s 8 104.6 105.1 236s 9 102.5 102.9 236s 10 99.3 99.8 236s 11 94.8 95.4 236s 12 93.2 94.0 236s 13 95.2 96.0 236s 14 97.4 97.9 236s 15 102.3 102.7 236s 16 104.2 104.6 236s 17 102.7 103.5 236s 18 102.9 103.3 236s 19 102.8 103.3 236s 20 106.0 106.6 236s > print( predict( fitw2sls4e$eq[[ 2 ]], se.fit = TRUE, interval = "confidence", 236s + level = 0.25, useDfSys = TRUE ) ) 236s fit se.fit lwr upr 236s 1 98.4 0.611 98.2 98.6 236s 2 100.0 0.700 99.8 100.3 236s 3 100.1 0.652 99.9 100.3 236s 4 100.5 0.664 100.2 100.7 236s 5 102.4 0.769 102.2 102.7 236s 6 102.4 0.695 102.2 102.7 236s 7 102.5 0.639 102.3 102.7 236s 8 104.8 0.821 104.6 105.1 236s 9 102.7 0.716 102.5 102.9 236s 10 99.5 0.743 99.3 99.8 236s 11 95.1 0.944 94.8 95.4 236s 12 93.6 1.254 93.2 94.0 236s 13 95.6 1.154 95.2 96.0 236s 14 97.6 0.814 97.4 97.9 236s 15 102.5 0.675 102.3 102.7 236s 16 104.4 0.659 104.2 104.6 236s 17 103.1 1.196 102.7 103.5 236s 18 103.1 0.587 102.9 103.3 236s 19 103.0 0.664 102.8 103.3 236s 20 106.3 0.909 106.0 106.6 236s > 236s > print( predict( fitw2sls5, se.fit = TRUE, se.pred = TRUE, 236s + interval = "prediction", level = 0.5, newdata = predictData ) ) 236s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 236s 1 102.8 0.781 2.12 101.4 104 95.8 236s 2 105.4 0.812 2.13 104.0 107 97.4 236s 3 105.3 0.824 2.13 103.8 107 97.5 236s 4 105.6 0.820 2.13 104.1 107 97.8 236s 5 107.5 1.186 2.30 106.0 109 99.9 236s 6 107.4 1.133 2.27 105.9 109 99.9 236s 7 108.0 1.141 2.28 106.4 110 99.9 236s 8 108.7 1.143 2.28 107.2 110 102.1 236s 9 106.8 1.179 2.30 105.2 108 100.2 236s 10 105.3 1.307 2.36 103.7 107 97.2 236s 11 100.3 1.108 2.26 98.7 102 92.7 236s 12 99.6 0.841 2.14 98.2 101 91.1 236s 13 101.3 0.638 2.07 99.9 103 93.0 236s 14 104.3 0.914 2.17 102.8 106 95.1 236s 15 109.3 1.440 2.44 107.6 111 100.1 236s 16 109.2 1.333 2.38 107.6 111 101.9 236s 17 108.9 1.742 2.63 107.1 111 100.9 236s 18 107.8 1.049 2.23 106.2 109 100.5 236s 19 109.5 1.216 2.31 107.9 111 100.3 236s 20 113.3 1.669 2.58 111.6 115 103.4 236s supply.se.fit supply.se.pred supply.lwr supply.upr 236s 1 0.825 2.64 94.1 97.6 236s 2 0.696 2.60 95.6 99.1 236s 3 0.712 2.60 95.7 99.2 236s 4 0.674 2.59 96.0 99.5 236s 5 1.087 2.73 98.1 101.8 236s 6 0.979 2.69 98.0 101.7 236s 7 0.874 2.65 98.1 101.7 236s 8 0.871 2.65 100.3 103.9 236s 9 1.143 2.75 98.4 102.1 236s 10 1.338 2.84 95.3 99.1 236s 11 1.483 2.91 90.8 94.7 236s 12 1.645 3.00 89.1 93.1 236s 13 1.440 2.89 91.0 94.9 236s 14 1.247 2.80 93.2 97.0 236s 15 1.222 2.79 98.2 102.0 236s 16 1.104 2.74 100.0 103.7 236s 17 1.808 3.09 98.7 103.0 236s 18 0.861 2.65 98.7 102.3 236s 19 0.861 2.65 98.5 102.1 236s 20 0.666 2.59 101.6 105.2 236s > print( predict( fitw2sls5$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 236s + interval = "prediction", level = 0.5, newdata = predictData ) ) 236s fit se.fit se.pred lwr upr 236s 1 102.8 0.781 2.12 101.4 104 236s 2 105.4 0.812 2.13 104.0 107 236s 3 105.3 0.824 2.13 103.8 107 236s 4 105.6 0.820 2.13 104.1 107 236s 5 107.5 1.186 2.30 106.0 109 236s 6 107.4 1.133 2.27 105.9 109 236s 7 108.0 1.141 2.28 106.4 110 236s 8 108.7 1.143 2.28 107.2 110 236s 9 106.8 1.179 2.30 105.2 108 236s 10 105.3 1.307 2.36 103.7 107 236s 11 100.3 1.108 2.26 98.7 102 236s 12 99.6 0.841 2.14 98.2 101 236s 13 101.3 0.638 2.07 99.9 103 236s 14 104.3 0.914 2.17 102.8 106 236s 15 109.3 1.440 2.44 107.6 111 236s 16 109.2 1.333 2.38 107.6 111 236s 17 108.9 1.742 2.63 107.1 111 236s 18 107.8 1.049 2.23 106.2 109 236s 19 109.5 1.216 2.31 107.9 111 236s 20 113.3 1.669 2.58 111.6 115 236s > 236s > print( predict( fitw2slsd1, se.fit = TRUE, se.pred = TRUE, 236s + interval = "confidence", level = 0.99 ) ) 236s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 236s 1 97.1 0.751 2.13 94.9 99.3 98.9 236s 2 99.2 0.757 2.13 97.0 101.4 100.4 236s 3 99.2 0.692 2.11 97.2 101.2 100.5 236s 4 99.3 0.766 2.13 97.1 101.5 100.7 236s 5 102.5 0.595 2.08 100.8 104.3 102.6 236s 6 102.2 0.503 2.05 100.7 103.7 102.6 236s 7 102.5 0.503 2.05 101.1 104.0 102.6 236s 8 102.7 0.653 2.10 100.8 104.5 104.8 236s 9 102.0 0.655 2.10 100.1 103.9 102.7 236s 10 101.4 1.074 2.26 98.3 104.5 99.7 236s 11 95.6 0.978 2.22 92.8 98.5 95.4 236s 12 93.9 1.134 2.29 90.7 97.2 93.8 236s 13 95.0 1.162 2.31 91.7 98.4 95.6 236s 14 98.9 0.530 2.06 97.4 100.4 97.6 236s 15 104.9 1.061 2.26 101.9 108.0 102.3 236s 16 104.3 0.757 2.13 102.1 106.5 104.1 236s 17 106.1 1.963 2.80 100.4 111.7 102.8 236s 18 101.7 0.597 2.08 100.0 103.5 102.7 236s 19 103.3 0.736 2.12 101.2 105.4 102.6 236s 20 106.0 1.430 2.45 101.9 110.2 105.6 236s supply.se.fit supply.se.pred supply.lwr supply.upr 236s 1 1.079 2.68 95.8 102.1 236s 2 1.064 2.68 97.3 103.5 236s 3 0.962 2.64 97.6 103.3 236s 4 0.938 2.63 98.0 103.4 236s 5 0.914 2.62 100.0 105.3 236s 6 0.808 2.59 100.2 104.9 236s 7 0.736 2.57 100.4 104.7 236s 8 0.994 2.65 101.9 107.7 236s 9 0.808 2.59 100.4 105.1 236s 10 1.023 2.66 96.7 102.7 236s 11 1.228 2.75 91.8 99.0 236s 12 1.428 2.84 89.7 98.0 236s 13 1.272 2.77 91.9 99.4 236s 14 0.917 2.62 94.9 100.3 236s 15 0.899 2.62 99.7 104.9 236s 16 0.936 2.63 101.3 106.8 236s 17 1.665 2.97 98.0 107.7 236s 18 0.988 2.65 99.8 105.6 236s 19 1.129 2.70 99.3 105.9 236s 20 1.733 3.01 100.5 110.7 236s > print( predict( fitw2slsd1$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 236s + interval = "confidence", level = 0.99 ) ) 236s fit se.fit se.pred lwr upr 236s 1 98.9 1.079 2.68 95.8 102.1 236s 2 100.4 1.064 2.68 97.3 103.5 236s 3 100.5 0.962 2.64 97.6 103.3 236s 4 100.7 0.938 2.63 98.0 103.4 236s 5 102.6 0.914 2.62 100.0 105.3 236s 6 102.6 0.808 2.59 100.2 104.9 236s 7 102.6 0.736 2.57 100.4 104.7 236s 8 104.8 0.994 2.65 101.9 107.7 236s 9 102.7 0.808 2.59 100.4 105.1 236s 10 99.7 1.023 2.66 96.7 102.7 236s 11 95.4 1.228 2.75 91.8 99.0 236s 12 93.8 1.428 2.84 89.7 98.0 236s 13 95.6 1.272 2.77 91.9 99.4 236s 14 97.6 0.917 2.62 94.9 100.3 236s 15 102.3 0.899 2.62 99.7 104.9 236s 16 104.1 0.936 2.63 101.3 106.8 236s 17 102.8 1.665 2.97 98.0 107.7 236s 18 102.7 0.988 2.65 99.8 105.6 236s 19 102.6 1.129 2.70 99.3 105.9 236s 20 105.6 1.733 3.01 100.5 110.7 236s > 236s > print( predict( fitw2slsd2e, se.fit = TRUE, interval = "prediction", 236s + level = 0.9, newdata = predictData, useDfSys = TRUE ) ) 236s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 236s 1 104 1.214 100.1 108 95.7 1.100 236s 2 106 1.169 102.6 110 97.2 0.835 236s 3 106 1.216 102.5 110 97.3 0.864 236s 4 107 1.169 102.7 110 97.6 0.789 236s 5 109 1.897 104.7 114 99.9 1.242 236s 6 109 1.773 104.6 114 99.9 1.115 236s 7 110 1.718 105.2 114 99.9 0.983 236s 8 110 1.552 105.8 114 102.2 0.843 236s 9 109 1.939 104.0 113 100.4 1.310 236s 10 107 2.229 102.5 112 97.4 1.683 236s 11 102 1.655 97.5 106 92.9 1.794 236s 12 101 1.125 96.8 104 91.2 1.750 236s 13 102 0.879 98.5 106 93.1 1.449 236s 14 106 1.480 101.5 110 95.3 1.383 236s 15 111 2.331 106.3 117 100.4 1.395 236s 16 111 2.064 106.3 116 102.2 1.175 236s 17 112 3.001 105.7 118 101.4 2.074 236s 18 109 1.475 104.9 113 100.7 0.861 236s 19 111 1.589 106.5 115 100.6 0.829 236s 20 114 1.756 109.9 119 103.6 0.680 236s supply.lwr supply.upr 236s 1 91.1 100.3 236s 2 92.7 101.7 236s 3 92.8 101.8 236s 4 93.2 102.1 236s 5 95.2 104.7 236s 6 95.3 104.6 236s 7 95.3 104.5 236s 8 97.7 106.7 236s 9 95.6 105.2 236s 10 92.3 102.5 236s 11 87.7 98.1 236s 12 86.0 96.4 236s 13 88.1 98.0 236s 14 90.4 100.1 236s 15 95.5 105.3 236s 16 97.5 106.9 236s 17 95.8 106.9 236s 18 96.2 105.2 236s 19 96.1 105.1 236s 20 99.2 108.0 236s > print( predict( fitw2slsd2e$eq[[ 1 ]], se.fit = TRUE, interval = "prediction", 236s + level = 0.9, newdata = predictData, useDfSys = TRUE ) ) 236s fit se.fit lwr upr 236s 1 104 1.214 100.1 108 236s 2 106 1.169 102.6 110 236s 3 106 1.216 102.5 110 236s 4 107 1.169 102.7 110 236s 5 109 1.897 104.7 114 236s 6 109 1.773 104.6 114 236s 7 110 1.718 105.2 114 236s 8 110 1.552 105.8 114 236s 9 109 1.939 104.0 113 236s 10 107 2.229 102.5 112 236s 11 102 1.655 97.5 106 236s 12 101 1.125 96.8 104 236s 13 102 0.879 98.5 106 236s 14 106 1.480 101.5 110 236s 15 111 2.331 106.3 117 236s 16 111 2.064 106.3 116 236s 17 112 3.001 105.7 118 236s 18 109 1.475 104.9 113 236s 19 111 1.589 106.5 115 236s 20 114 1.756 109.9 119 236s > 236s > print( predict( fitw2slsd3e, se.fit = TRUE, se.pred = TRUE, 236s + interval = "prediction", level = 0.01, useDfSys = TRUE ) ) 236s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 236s 1 97.4 0.622 2.05 97.4 97.4 98.2 236s 2 99.4 0.654 2.06 99.4 99.4 99.7 236s 3 99.4 0.598 2.04 99.4 99.4 99.9 236s 4 99.5 0.663 2.06 99.5 99.5 100.2 236s 5 102.4 0.515 2.02 102.4 102.4 102.3 236s 6 102.1 0.442 2.00 102.1 102.1 102.3 236s 7 102.4 0.444 2.00 102.4 102.4 102.4 236s 8 102.6 0.587 2.04 102.6 102.6 104.7 236s 9 101.9 0.573 2.03 101.9 101.9 102.7 236s 10 101.2 0.948 2.17 101.2 101.2 99.6 236s 11 95.9 0.849 2.13 95.9 95.9 95.2 236s 12 94.4 0.914 2.15 94.4 94.4 93.6 236s 13 95.5 0.943 2.17 95.5 95.5 95.6 236s 14 99.0 0.464 2.01 99.0 99.1 97.7 236s 15 104.5 0.883 2.14 104.5 104.6 102.7 236s 16 104.0 0.631 2.05 104.0 104.0 104.6 236s 17 105.4 1.665 2.56 105.4 105.5 103.5 236s 18 101.8 0.538 2.02 101.7 101.8 103.3 236s 19 103.2 0.661 2.06 103.2 103.3 103.2 236s 20 105.9 1.284 2.34 105.9 106.0 106.4 236s supply.se.fit supply.se.pred supply.lwr supply.upr 236s 1 0.652 2.60 98.1 98.2 236s 2 0.740 2.62 99.7 99.8 236s 3 0.682 2.61 99.8 99.9 236s 4 0.708 2.61 100.2 100.2 236s 5 0.782 2.63 102.3 102.4 236s 6 0.699 2.61 102.3 102.4 236s 7 0.648 2.60 102.3 102.4 236s 8 0.906 2.67 104.7 104.8 236s 9 0.736 2.62 102.7 102.8 236s 10 0.931 2.68 99.6 99.7 236s 11 1.107 2.75 95.2 95.2 236s 12 1.287 2.83 93.6 93.7 236s 13 1.157 2.77 95.5 95.6 236s 14 0.829 2.65 97.7 97.7 236s 15 0.717 2.62 102.7 102.8 236s 16 0.676 2.61 104.6 104.6 236s 17 1.392 2.88 103.4 103.5 236s 18 0.699 2.61 103.3 103.3 236s 19 0.822 2.65 103.2 103.2 236s 20 1.376 2.87 106.4 106.5 236s > print( predict( fitw2slsd3e$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 236s + interval = "prediction", level = 0.01, useDfSys = TRUE ) ) 236s fit se.fit se.pred lwr upr 236s 1 98.2 0.652 2.60 98.1 98.2 236s 2 99.7 0.740 2.62 99.7 99.8 236s 3 99.9 0.682 2.61 99.8 99.9 236s 4 100.2 0.708 2.61 100.2 100.2 236s 5 102.3 0.782 2.63 102.3 102.4 236s 6 102.3 0.699 2.61 102.3 102.4 236s 7 102.4 0.648 2.60 102.3 102.4 236s 8 104.7 0.906 2.67 104.7 104.8 236s 9 102.7 0.736 2.62 102.7 102.8 236s 10 99.6 0.931 2.68 99.6 99.7 236s 11 95.2 1.107 2.75 95.2 95.2 236s 12 93.6 1.287 2.83 93.6 93.7 236s 13 95.6 1.157 2.77 95.5 95.6 236s 14 97.7 0.829 2.65 97.7 97.7 236s 15 102.7 0.717 2.62 102.7 102.8 236s 16 104.6 0.676 2.61 104.6 104.6 236s 17 103.5 1.392 2.88 103.4 103.5 236s 18 103.3 0.699 2.61 103.3 103.3 236s 19 103.2 0.822 2.65 103.2 103.2 236s 20 106.4 1.376 2.87 106.4 106.5 236s > 236s > # predict just one observation 236s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 236s + trend = 25 ) 236s > 236s > print( predict( fitw2sls1e, newdata = smallData ) ) 236s demand.pred supply.pred 236s 1 110 118 236s > print( predict( fitw2sls1e$eq[[ 1 ]], newdata = smallData ) ) 236s fit 236s 1 110 236s > 236s > print( predict( fitw2sls2, se.fit = TRUE, level = 0.9, 236s + newdata = smallData ) ) 236s demand.pred demand.se.fit supply.pred supply.se.fit 236s 1 110 2.52 119 3.53 236s > print( predict( fitw2sls2$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 236s + newdata = smallData ) ) 236s fit se.pred 236s 1 110 3.21 236s > 236s > print( predict( fitw2sls3, interval = "prediction", level = 0.975, 236s + newdata = smallData ) ) 236s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 236s 1 110 102 117 119 109 129 236s > print( predict( fitw2sls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 236s + newdata = smallData ) ) 236s fit lwr upr 236s 1 110 107 113 236s > 236s > print( predict( fitw2sls4e, se.fit = TRUE, interval = "confidence", 236s + level = 0.999, newdata = smallData ) ) 236s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 236s 1 110 2.08 102 117 119 2.11 236s supply.lwr supply.upr 236s 1 112 127 236s > print( predict( fitw2sls4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 236s + level = 0.75, newdata = smallData ) ) 236s fit se.pred lwr upr 236s 1 119 3.27 115 123 236s > 236s > print( predict( fitw2sls5, se.fit = TRUE, interval = "prediction", 236s + newdata = smallData ) ) 236s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 236s 1 110 2.26 104 116 119 2.33 236s supply.lwr supply.upr 236s 1 112 126 236s > print( predict( fitw2sls5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 236s + newdata = smallData ) ) 236s fit se.pred lwr upr 236s 1 110 3 105 114 236s > 236s > print( predict( fitw2slsd2e, se.fit = TRUE, se.pred = TRUE, 236s + interval = "prediction", level = 0.5, newdata = smallData ) ) 236s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 236s 1 108 2.71 3.34 105 110 119 236s supply.se.fit supply.se.pred supply.lwr supply.upr 236s 1 3.22 4.08 117 122 236s > print( predict( fitw2slsd2e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 236s + interval = "confidence", level = 0.25, newdata = smallData ) ) 236s fit se.fit se.pred lwr upr 236s 1 108 2.71 3.34 107 109 236s > 236s > 236s > ## ************ correlation of predicted values *************** 236s > print( correlation.systemfit( fitw2sls1e, 1, 2 ) ) 236s [,1] 236s [1,] 0 236s [2,] 0 236s [3,] 0 236s [4,] 0 236s [5,] 0 236s [6,] 0 236s [7,] 0 236s [8,] 0 236s [9,] 0 236s [10,] 0 236s [11,] 0 236s [12,] 0 236s [13,] 0 236s [14,] 0 236s [15,] 0 236s [16,] 0 236s [17,] 0 236s [18,] 0 236s [19,] 0 236s [20,] 0 236s > 236s > print( correlation.systemfit( fitw2sls2, 2, 1 ) ) 236s [,1] 236s [1,] 0.413453 236s [2,] 0.153759 236s [3,] 0.152962 236s [4,] 0.112671 236s [5,] -0.071442 236s [6,] -0.053943 236s [7,] -0.050961 236s [8,] -0.005442 236s [9,] -0.000476 236s [10,] -0.001894 236s [11,] 0.047351 236s [12,] 0.064973 236s [13,] 0.024591 236s [14,] -0.028036 236s [15,] 0.175326 236s [16,] 0.254878 236s [17,] 0.104540 236s [18,] 0.065579 236s [19,] 0.147008 236s [20,] 0.124593 236s > 236s > print( correlation.systemfit( fitw2sls3, 1, 2 ) ) 236s [,1] 236s [1,] 0.413453 236s [2,] 0.153759 236s [3,] 0.152962 236s [4,] 0.112671 236s [5,] -0.071442 236s [6,] -0.053943 236s [7,] -0.050961 236s [8,] -0.005442 236s [9,] -0.000476 236s [10,] -0.001894 236s [11,] 0.047351 236s [12,] 0.064973 236s [13,] 0.024591 236s [14,] -0.028036 236s [15,] 0.175326 236s [16,] 0.254878 236s [17,] 0.104540 236s [18,] 0.065579 236s [19,] 0.147008 236s [20,] 0.124593 236s > 236s > print( correlation.systemfit( fitw2sls4e, 2, 1 ) ) 236s [,1] 236s [1,] 0.38438 236s [2,] 0.30697 236s [3,] 0.26690 236s [4,] 0.30163 236s [5,] -0.02768 236s [6,] -0.05086 236s [7,] -0.05895 236s [8,] 0.10102 236s [9,] 0.10072 236s [10,] 0.45547 236s [11,] 0.10817 236s [12,] 0.00552 236s [13,] 0.04219 236s [14,] -0.04054 236s [15,] 0.42100 236s [16,] 0.24974 236s [17,] 0.65722 236s [18,] 0.24286 236s [19,] 0.34336 236s [20,] 0.54717 236s > 236s > print( correlation.systemfit( fitw2sls5, 1, 2 ) ) 236s [,1] 236s [1,] 0.38030 236s [2,] 0.30892 236s [3,] 0.26808 236s [4,] 0.30325 236s [5,] -0.02730 236s [6,] -0.05035 236s [7,] -0.05831 236s [8,] 0.10036 236s [9,] 0.10045 236s [10,] 0.45492 236s [11,] 0.10525 236s [12,] 0.00394 236s [13,] 0.04171 236s [14,] -0.04037 236s [15,] 0.41958 236s [16,] 0.24706 236s [17,] 0.65619 236s [18,] 0.23872 236s [19,] 0.33729 236s [20,] 0.54239 236s > 236s > print( correlation.systemfit( fitw2slsd1, 2, 1 ) ) 236s [,1] 236s [1,] 0 236s [2,] 0 236s [3,] 0 236s [4,] 0 236s [5,] 0 236s [6,] 0 236s [7,] 0 236s [8,] 0 236s [9,] 0 236s [10,] 0 236s [11,] 0 236s [12,] 0 236s [13,] 0 236s [14,] 0 236s [15,] 0 236s [16,] 0 236s [17,] 0 236s [18,] 0 236s [19,] 0 236s [20,] 0 236s > 236s > print( correlation.systemfit( fitw2slsd2e, 1, 2 ) ) 236s [,1] 236s [1,] 0.482214 236s [2,] 0.253368 236s [3,] 0.242824 236s [4,] 0.195411 236s [5,] -0.107828 236s [6,] -0.074958 236s [7,] -0.055696 236s [8,] -0.002037 236s [9,] -0.000921 236s [10,] -0.008040 236s [11,] 0.040999 236s [12,] 0.075418 236s [13,] 0.029702 236s [14,] -0.030775 236s [15,] 0.229063 236s [16,] 0.318607 236s [17,] 0.156734 236s [18,] -0.023016 236s [19,] 0.068128 236s [20,] 0.047481 236s > 236s > print( correlation.systemfit( fitw2slsd3e, 2, 1 ) ) 236s [,1] 236s [1,] 0.482214 236s [2,] 0.253368 236s [3,] 0.242824 236s [4,] 0.195411 236s [5,] -0.107828 236s [6,] -0.074958 236s [7,] -0.055696 236s [8,] -0.002037 236s [9,] -0.000921 236s [10,] -0.008040 236s [11,] 0.040999 236s [12,] 0.075418 236s [13,] 0.029702 236s [14,] -0.030775 236s [15,] 0.229063 236s [16,] 0.318607 236s [17,] 0.156734 236s [18,] -0.023016 236s [19,] 0.068128 236s [20,] 0.047481 236s > 236s > 236s > ## ************ LOG-Likelihood values *************** 236s > print( logLik( fitw2sls1e ) ) 236s 'log Lik.' -67.6 (df=9) 236s > print( logLik( fitw2sls1e, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.4 (df=9) 236s > 236s > print( logLik( fitw2sls2 ) ) 236s 'log Lik.' -65.2 (df=8) 236s > print( logLik( fitw2sls2, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.8 (df=8) 236s > 236s > print( logLik( fitw2sls3 ) ) 236s 'log Lik.' -65.2 (df=8) 236s > print( logLik( fitw2sls3, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.8 (df=8) 236s > 236s > print( logLik( fitw2sls4e ) ) 236s 'log Lik.' -65.7 (df=7) 236s > print( logLik( fitw2sls4e, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.8 (df=7) 236s > 236s > print( logLik( fitw2sls5 ) ) 236s 'log Lik.' -65.6 (df=7) 236s > print( logLik( fitw2sls5, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.8 (df=7) 236s > 236s > print( logLik( fitw2slsd1 ) ) 236s 'log Lik.' -75.1 (df=9) 236s > print( logLik( fitw2slsd1, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.7 (df=9) 236s > 236s > print( logLik( fitw2slsd2e ) ) 236s 'log Lik.' -69.1 (df=8) 236s > print( logLik( fitw2slsd2e, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.7 (df=8) 236s > 236s > print( logLik( fitw2slsd3e ) ) 236s 'log Lik.' -69.1 (df=8) 236s > print( logLik( fitw2slsd3e, residCovDiag = TRUE ) ) 236s 'log Lik.' -84.7 (df=8) 236s > 236s > 236s > ## ************** F tests **************** 236s > # testing first restriction 236s > print( linearHypothesis( fitw2sls1, restrm ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.31 0.58 236s > linearHypothesis( fitw2sls1, restrict ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.31 0.58 236s > 236s > print( linearHypothesis( fitw2slsd1e, restrm ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1e 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.92 0.35 236s > linearHypothesis( fitw2slsd1e, restrict ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1e 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.92 0.35 236s > 236s > # testing second restriction 236s > restrOnly2m <- matrix(0,1,7) 236s > restrOnly2q <- 0.5 236s > restrOnly2m[1,2] <- -1 236s > restrOnly2m[1,5] <- 1 236s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 236s > # first restriction not imposed 236s > print( linearHypothesis( fitw2sls1e, restrOnly2m, restrOnly2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.01 0.91 236s > linearHypothesis( fitw2sls1e, restrictOnly2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.01 0.91 236s > 236s > print( linearHypothesis( fitw2slsd1, restrOnly2m, restrOnly2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.74 0.39 236s > linearHypothesis( fitw2slsd1, restrictOnly2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df F Pr(>F) 236s 1 34 236s 2 33 1 0.74 0.39 236s > 236s > # first restriction imposed 236s > print( linearHypothesis( fitw2sls2, restrOnly2m, restrOnly2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls2 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.04 0.85 236s > linearHypothesis( fitw2sls2, restrictOnly2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls2 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.04 0.85 236s > 236s > print( linearHypothesis( fitw2sls3, restrOnly2m, restrOnly2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls3 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.04 0.85 236s > linearHypothesis( fitw2sls3, restrictOnly2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls3 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.04 0.85 236s > 236s > print( linearHypothesis( fitw2slsd2e, restrOnly2m, restrOnly2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd2e 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.42 0.52 236s > linearHypothesis( fitw2slsd2e, restrictOnly2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd2e 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.42 0.52 236s > 236s > print( linearHypothesis( fitw2slsd3e, restrOnly2m, restrOnly2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd3e 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.42 0.52 236s > linearHypothesis( fitw2slsd3e, restrictOnly2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd3e 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 34 1 0.42 0.52 236s > 236s > # testing both of the restrictions 236s > print( linearHypothesis( fitw2sls1e, restr2m, restr2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 33 2 0.18 0.84 236s > linearHypothesis( fitw2sls1e, restrict2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 33 2 0.18 0.84 236s > 236s > print( linearHypothesis( fitw2slsd1, restr2m, restr2q ) ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 33 2 0.65 0.53 236s > linearHypothesis( fitw2slsd1, restrict2 ) 236s Linear hypothesis test (Theil's F test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df F Pr(>F) 236s 1 35 236s 2 33 2 0.65 0.53 236s > 236s > 236s > ## ************** Wald tests **************** 236s > # testing first restriction 236s > print( linearHypothesis( fitw2sls1, restrm, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 0.31 0.58 236s > linearHypothesis( fitw2sls1, restrict, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 0.31 0.58 236s > 236s > print( linearHypothesis( fitw2slsd1e, restrm, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 1.11 0.29 236s > linearHypothesis( fitw2slsd1e, restrict, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 1.11 0.29 236s > 236s > # testing second restriction 236s > # first restriction not imposed 236s > print( linearHypothesis( fitw2sls1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 0.02 0.9 236s > linearHypothesis( fitw2sls1e, restrictOnly2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 0.02 0.9 236s > 236s > print( linearHypothesis( fitw2slsd1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 0.74 0.39 236s > linearHypothesis( fitw2slsd1, restrictOnly2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 34 236s 2 33 1 0.74 0.39 236s > # first restriction imposed 236s > print( linearHypothesis( fitw2sls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls2 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.04 0.85 236s > linearHypothesis( fitw2sls2, restrictOnly2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls2 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.04 0.85 236s > 236s > print( linearHypothesis( fitw2sls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls3 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.04 0.85 236s > linearHypothesis( fitw2sls3, restrictOnly2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls3 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.04 0.85 236s > 236s > print( linearHypothesis( fitw2slsd2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd2e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.49 0.48 236s > linearHypothesis( fitw2slsd2e, restrictOnly2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd2e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.49 0.48 236s > 236s > print( linearHypothesis( fitw2slsd3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd3e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.49 0.48 236s > linearHypothesis( fitw2slsd3e, restrictOnly2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd3e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 34 1 0.49 0.48 236s > 236s > # testing both of the restrictions 236s > print( linearHypothesis( fitw2sls1e, restr2m, restr2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 33 2 0.43 0.81 236s > linearHypothesis( fitw2sls1e, restrict2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2sls1e 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 33 2 0.43 0.81 236s > 236s > print( linearHypothesis( fitw2slsd1, restr2m, restr2q, test = "Chisq" ) ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 33 2 1.3 0.52 236s > linearHypothesis( fitw2slsd1, restrict2, test = "Chisq" ) 236s Linear hypothesis test (Chi^2 statistic of a Wald test) 236s 236s Hypothesis: 236s demand_income - supply_trend = 0 236s - demand_price + supply_price = 0.5 236s 236s Model 1: restricted model 236s Model 2: fitw2slsd1 236s 236s Res.Df Df Chisq Pr(>Chisq) 236s 1 35 236s 2 33 2 1.3 0.52 236s > 236s > 236s > ## ****************** model frame ************************** 236s > print( mf <- model.frame( fitw2sls1e ) ) 236s consump price income farmPrice trend 236s 1 98.5 100.3 87.4 98.0 1 236s 2 99.2 104.3 97.6 99.1 2 236s 3 102.2 103.4 96.7 99.1 3 236s 4 101.5 104.5 98.2 98.1 4 236s 5 104.2 98.0 99.8 110.8 5 236s 6 103.2 99.5 100.5 108.2 6 236s 7 104.0 101.1 103.2 105.6 7 236s 8 99.9 104.8 107.8 109.8 8 236s 9 100.3 96.4 96.6 108.7 9 236s 10 102.8 91.2 88.9 100.6 10 236s 11 95.4 93.1 75.1 81.0 11 236s 12 92.4 98.8 76.9 68.6 12 236s 13 94.5 102.9 84.6 70.9 13 236s 14 98.8 98.8 90.6 81.4 14 236s 15 105.8 95.1 103.1 102.3 15 236s 16 100.2 98.5 105.1 105.0 16 236s 17 103.5 86.5 96.4 110.5 17 236s 18 99.9 104.0 104.4 92.5 18 236s 19 105.2 105.8 110.7 89.3 19 236s 20 106.2 113.5 127.1 93.0 20 236s > print( mf1 <- model.frame( fitw2sls1e$eq[[ 1 ]] ) ) 236s consump price income 236s 1 98.5 100.3 87.4 236s 2 99.2 104.3 97.6 236s 3 102.2 103.4 96.7 236s 4 101.5 104.5 98.2 236s 5 104.2 98.0 99.8 236s 6 103.2 99.5 100.5 236s 7 104.0 101.1 103.2 236s 8 99.9 104.8 107.8 236s 9 100.3 96.4 96.6 236s 10 102.8 91.2 88.9 236s 11 95.4 93.1 75.1 236s 12 92.4 98.8 76.9 236s 13 94.5 102.9 84.6 236s 14 98.8 98.8 90.6 236s 15 105.8 95.1 103.1 236s 16 100.2 98.5 105.1 236s 17 103.5 86.5 96.4 236s 18 99.9 104.0 104.4 236s 19 105.2 105.8 110.7 236s 20 106.2 113.5 127.1 236s > print( attributes( mf1 )$terms ) 236s consump ~ price + income 236s attr(,"variables") 236s list(consump, price, income) 236s attr(,"factors") 236s price income 236s consump 0 0 236s price 1 0 236s income 0 1 236s attr(,"term.labels") 236s [1] "price" "income" 236s attr(,"order") 236s [1] 1 1 236s attr(,"intercept") 236s [1] 1 236s attr(,"response") 236s [1] 1 236s attr(,".Environment") 236s 236s attr(,"predvars") 236s list(consump, price, income) 236s attr(,"dataClasses") 236s consump price income 236s "numeric" "numeric" "numeric" 236s > print( mf2 <- model.frame( fitw2sls1e$eq[[ 2 ]] ) ) 236s consump price farmPrice trend 236s 1 98.5 100.3 98.0 1 236s 2 99.2 104.3 99.1 2 236s 3 102.2 103.4 99.1 3 236s 4 101.5 104.5 98.1 4 236s 5 104.2 98.0 110.8 5 236s 6 103.2 99.5 108.2 6 236s 7 104.0 101.1 105.6 7 236s 8 99.9 104.8 109.8 8 236s 9 100.3 96.4 108.7 9 236s 10 102.8 91.2 100.6 10 236s 11 95.4 93.1 81.0 11 236s 12 92.4 98.8 68.6 12 236s 13 94.5 102.9 70.9 13 236s 14 98.8 98.8 81.4 14 236s 15 105.8 95.1 102.3 15 236s 16 100.2 98.5 105.0 16 236s 17 103.5 86.5 110.5 17 236s 18 99.9 104.0 92.5 18 236s 19 105.2 105.8 89.3 19 236s 20 106.2 113.5 93.0 20 236s > print( attributes( mf2 )$terms ) 236s consump ~ price + farmPrice + trend 236s attr(,"variables") 236s list(consump, price, farmPrice, trend) 236s attr(,"factors") 236s price farmPrice trend 236s consump 0 0 0 236s price 1 0 0 236s farmPrice 0 1 0 236s trend 0 0 1 236s attr(,"term.labels") 236s [1] "price" "farmPrice" "trend" 236s attr(,"order") 236s [1] 1 1 1 236s attr(,"intercept") 236s [1] 1 236s attr(,"response") 236s [1] 1 236s attr(,".Environment") 236s 236s attr(,"predvars") 236s list(consump, price, farmPrice, trend) 236s attr(,"dataClasses") 236s consump price farmPrice trend 236s "numeric" "numeric" "numeric" "numeric" 236s > 236s > print( all.equal( mf, model.frame( fitw2sls2 ) ) ) 236s [1] TRUE 236s > print( all.equal( mf2, model.frame( fitw2sls2$eq[[ 2 ]] ) ) ) 236s [1] TRUE 236s > 236s > print( all.equal( mf, model.frame( fitw2sls3 ) ) ) 236s [1] TRUE 236s > print( all.equal( mf1, model.frame( fitw2sls3$eq[[ 1 ]] ) ) ) 236s [1] TRUE 236s > 236s > print( all.equal( mf, model.frame( fitw2sls4e ) ) ) 236s [1] TRUE 236s > print( all.equal( mf2, model.frame( fitw2sls4e$eq[[ 2 ]] ) ) ) 236s [1] TRUE 236s > 236s > print( all.equal( mf, model.frame( fitw2sls5 ) ) ) 236s [1] TRUE 236s > print( all.equal( mf1, model.frame( fitw2sls5$eq[[ 1 ]] ) ) ) 236s [1] TRUE 236s > 236s > print( all.equal( mf, model.frame( fitw2slsd1 ) ) ) 236s [1] TRUE 236s > print( all.equal( mf2, model.frame( fitw2slsd1$eq[[ 2 ]] ) ) ) 236s [1] TRUE 236s > 236s > print( all.equal( mf, model.frame( fitw2slsd2e ) ) ) 236s [1] TRUE 236s > print( all.equal( mf1, model.frame( fitw2slsd2e$eq[[ 1 ]] ) ) ) 236s [1] TRUE 236s > 236s > print( all.equal( mf, model.frame( fitw2slsd3e ) ) ) 236s [1] TRUE 236s > print( all.equal( mf2, model.frame( fitw2slsd3e$eq[[ 2 ]] ) ) ) 236s [1] TRUE 236s > 236s > fitw2sls1e$eq[[ 1 ]]$modelInst 236s income farmPrice trend 236s 1 87.4 98.0 1 236s 2 97.6 99.1 2 236s 3 96.7 99.1 3 236s 4 98.2 98.1 4 236s 5 99.8 110.8 5 236s 6 100.5 108.2 6 236s 7 103.2 105.6 7 236s 8 107.8 109.8 8 236s 9 96.6 108.7 9 236s 10 88.9 100.6 10 236s 11 75.1 81.0 11 236s 12 76.9 68.6 12 236s 13 84.6 70.9 13 236s 14 90.6 81.4 14 236s 15 103.1 102.3 15 236s 16 105.1 105.0 16 236s 17 96.4 110.5 17 236s 18 104.4 92.5 18 236s 19 110.7 89.3 19 236s 20 127.1 93.0 20 236s > fitw2sls1e$eq[[ 2 ]]$modelInst 236s income farmPrice trend 236s 1 87.4 98.0 1 236s 2 97.6 99.1 2 236s 3 96.7 99.1 3 236s 4 98.2 98.1 4 236s 5 99.8 110.8 5 236s 6 100.5 108.2 6 236s 7 103.2 105.6 7 236s 8 107.8 109.8 8 236s 9 96.6 108.7 9 236s 10 88.9 100.6 10 236s 11 75.1 81.0 11 236s 12 76.9 68.6 12 236s 13 84.6 70.9 13 236s 14 90.6 81.4 14 236s 15 103.1 102.3 15 236s 16 105.1 105.0 16 236s 17 96.4 110.5 17 236s 18 104.4 92.5 18 236s 19 110.7 89.3 19 236s 20 127.1 93.0 20 236s > 236s > fitw2sls4Sym$eq[[ 1 ]]$modelInst 236s income farmPrice trend 236s 1 87.4 98.0 1 236s 2 97.6 99.1 2 236s 3 96.7 99.1 3 236s 4 98.2 98.1 4 236s 5 99.8 110.8 5 236s 6 100.5 108.2 6 236s 7 103.2 105.6 7 236s 8 107.8 109.8 8 236s 9 96.6 108.7 9 236s 10 88.9 100.6 10 236s 11 75.1 81.0 11 236s 12 76.9 68.6 12 236s 13 84.6 70.9 13 236s 14 90.6 81.4 14 236s 15 103.1 102.3 15 236s 16 105.1 105.0 16 236s 17 96.4 110.5 17 236s 18 104.4 92.5 18 236s 19 110.7 89.3 19 236s 20 127.1 93.0 20 236s > fitw2sls4Sym$eq[[ 2 ]]$modelInst 236s income farmPrice trend 236s 1 87.4 98.0 1 236s 2 97.6 99.1 2 236s 3 96.7 99.1 3 236s 4 98.2 98.1 4 236s 5 99.8 110.8 5 236s 6 100.5 108.2 6 236s 7 103.2 105.6 7 236s 8 107.8 109.8 8 236s 9 96.6 108.7 9 236s 10 88.9 100.6 10 236s 11 75.1 81.0 11 236s 12 76.9 68.6 12 236s 13 84.6 70.9 13 236s 14 90.6 81.4 14 236s 15 103.1 102.3 15 236s 16 105.1 105.0 16 236s 17 96.4 110.5 17 236s 18 104.4 92.5 18 236s 19 110.7 89.3 19 236s 20 127.1 93.0 20 236s > 236s > fitw2sls5$eq[[ 1 ]]$modelInst 236s income farmPrice trend 236s 1 87.4 98.0 1 236s 2 97.6 99.1 2 236s 3 96.7 99.1 3 236s 4 98.2 98.1 4 236s 5 99.8 110.8 5 236s 6 100.5 108.2 6 236s 7 103.2 105.6 7 236s 8 107.8 109.8 8 236s 9 96.6 108.7 9 236s 10 88.9 100.6 10 236s 11 75.1 81.0 11 236s 12 76.9 68.6 12 236s 13 84.6 70.9 13 236s 14 90.6 81.4 14 236s 15 103.1 102.3 15 236s 16 105.1 105.0 16 236s 17 96.4 110.5 17 236s 18 104.4 92.5 18 236s 19 110.7 89.3 19 236s 20 127.1 93.0 20 236s > fitw2sls5$eq[[ 2 ]]$modelInst 236s income farmPrice trend 236s 1 87.4 98.0 1 236s 2 97.6 99.1 2 236s 3 96.7 99.1 3 236s 4 98.2 98.1 4 236s 5 99.8 110.8 5 236s 6 100.5 108.2 6 236s 7 103.2 105.6 7 236s 8 107.8 109.8 8 236s 9 96.6 108.7 9 236s 10 88.9 100.6 10 236s 11 75.1 81.0 11 236s 12 76.9 68.6 12 236s 13 84.6 70.9 13 236s 14 90.6 81.4 14 236s 15 103.1 102.3 15 236s 16 105.1 105.0 16 236s 17 96.4 110.5 17 236s 18 104.4 92.5 18 236s 19 110.7 89.3 19 236s 20 127.1 93.0 20 236s > 236s > 236s > ## **************** model matrix ************************ 236s > # with x (returnModelMatrix) = TRUE 236s > print( !is.null( fitw2sls1e$eq[[ 1 ]]$x ) ) 236s [1] TRUE 236s > print( mm <- model.matrix( fitw2sls1e ) ) 236s demand_(Intercept) demand_price demand_income supply_(Intercept) 236s demand_1 1 100.3 87.4 0 236s demand_2 1 104.3 97.6 0 236s demand_3 1 103.4 96.7 0 236s demand_4 1 104.5 98.2 0 236s demand_5 1 98.0 99.8 0 236s demand_6 1 99.5 100.5 0 236s demand_7 1 101.1 103.2 0 236s demand_8 1 104.8 107.8 0 236s demand_9 1 96.4 96.6 0 236s demand_10 1 91.2 88.9 0 236s demand_11 1 93.1 75.1 0 236s demand_12 1 98.8 76.9 0 236s demand_13 1 102.9 84.6 0 236s demand_14 1 98.8 90.6 0 236s demand_15 1 95.1 103.1 0 236s demand_16 1 98.5 105.1 0 236s demand_17 1 86.5 96.4 0 236s demand_18 1 104.0 104.4 0 236s demand_19 1 105.8 110.7 0 236s demand_20 1 113.5 127.1 0 236s supply_1 0 0.0 0.0 1 236s supply_2 0 0.0 0.0 1 236s supply_3 0 0.0 0.0 1 236s supply_4 0 0.0 0.0 1 236s supply_5 0 0.0 0.0 1 236s supply_6 0 0.0 0.0 1 236s supply_7 0 0.0 0.0 1 236s supply_8 0 0.0 0.0 1 236s supply_9 0 0.0 0.0 1 236s supply_10 0 0.0 0.0 1 236s supply_11 0 0.0 0.0 1 236s supply_12 0 0.0 0.0 1 236s supply_13 0 0.0 0.0 1 236s supply_14 0 0.0 0.0 1 236s supply_15 0 0.0 0.0 1 236s supply_16 0 0.0 0.0 1 236s supply_17 0 0.0 0.0 1 236s supply_18 0 0.0 0.0 1 236s supply_19 0 0.0 0.0 1 236s supply_20 0 0.0 0.0 1 236s supply_price supply_farmPrice supply_trend 236s demand_1 0.0 0.0 0 236s demand_2 0.0 0.0 0 236s demand_3 0.0 0.0 0 236s demand_4 0.0 0.0 0 236s demand_5 0.0 0.0 0 236s demand_6 0.0 0.0 0 236s demand_7 0.0 0.0 0 236s demand_8 0.0 0.0 0 236s demand_9 0.0 0.0 0 236s demand_10 0.0 0.0 0 236s demand_11 0.0 0.0 0 236s demand_12 0.0 0.0 0 236s demand_13 0.0 0.0 0 236s demand_14 0.0 0.0 0 236s demand_15 0.0 0.0 0 236s demand_16 0.0 0.0 0 236s demand_17 0.0 0.0 0 236s demand_18 0.0 0.0 0 236s demand_19 0.0 0.0 0 236s demand_20 0.0 0.0 0 236s supply_1 100.3 98.0 1 236s supply_2 104.3 99.1 2 236s supply_3 103.4 99.1 3 236s supply_4 104.5 98.1 4 236s supply_5 98.0 110.8 5 236s supply_6 99.5 108.2 6 236s supply_7 101.1 105.6 7 236s supply_8 104.8 109.8 8 236s supply_9 96.4 108.7 9 236s supply_10 91.2 100.6 10 236s supply_11 93.1 81.0 11 236s supply_12 98.8 68.6 12 236s supply_13 102.9 70.9 13 236s supply_14 98.8 81.4 14 236s supply_15 95.1 102.3 15 236s supply_16 98.5 105.0 16 236s supply_17 86.5 110.5 17 236s supply_18 104.0 92.5 18 236s supply_19 105.8 89.3 19 236s supply_20 113.5 93.0 20 236s > print( mm1 <- model.matrix( fitw2sls1e$eq[[ 1 ]] ) ) 236s (Intercept) price income 236s 1 1 100.3 87.4 236s 2 1 104.3 97.6 236s 3 1 103.4 96.7 236s 4 1 104.5 98.2 237s 5 1 98.0 99.8 237s 6 1 99.5 100.5 237s 7 1 101.1 103.2 237s 8 1 104.8 107.8 237s 9 1 96.4 96.6 237s 10 1 91.2 88.9 237s 11 1 93.1 75.1 237s 12 1 98.8 76.9 237s 13 1 102.9 84.6 237s 14 1 98.8 90.6 237s 15 1 95.1 103.1 237s 16 1 98.5 105.1 237s 17 1 86.5 96.4 237s 18 1 104.0 104.4 237s 19 1 105.8 110.7 237s 20 1 113.5 127.1 237s attr(,"assign") 237s [1] 0 1 2 237s > print( mm2 <- model.matrix( fitw2sls1e$eq[[ 2 ]] ) ) 237s (Intercept) price farmPrice trend 237s 1 1 100.3 98.0 1 237s 2 1 104.3 99.1 2 237s 3 1 103.4 99.1 3 237s 4 1 104.5 98.1 4 237s 5 1 98.0 110.8 5 237s 6 1 99.5 108.2 6 237s 7 1 101.1 105.6 7 237s 8 1 104.8 109.8 8 237s 9 1 96.4 108.7 9 237s 10 1 91.2 100.6 10 237s 11 1 93.1 81.0 11 237s 12 1 98.8 68.6 12 237s 13 1 102.9 70.9 13 237s 14 1 98.8 81.4 14 237s 15 1 95.1 102.3 15 237s 16 1 98.5 105.0 16 237s 17 1 86.5 110.5 17 237s 18 1 104.0 92.5 18 237s 19 1 105.8 89.3 19 237s 20 1 113.5 93.0 20 237s attr(,"assign") 237s [1] 0 1 2 3 237s > 237s > # with x (returnModelMatrix) = FALSE 237s > print( all.equal( mm, model.matrix( fitw2sls1 ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2sls1$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2sls1$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > print( !is.null( fitw2sls1$eq[[ 1 ]]$x ) ) 237s [1] FALSE 237s > 237s > # with x (returnModelMatrix) = TRUE 237s > print( !is.null( fitw2sls2e$eq[[ 1 ]]$x ) ) 237s [1] TRUE 237s > print( all.equal( mm, model.matrix( fitw2sls2e ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2sls2e$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2sls2e$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > 237s > # with x (returnModelMatrix) = FALSE 237s > print( all.equal( mm, model.matrix( fitw2sls2Sym ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2sls2Sym$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2sls2Sym$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > print( !is.null( fitw2sls2Sym$eq[[ 1 ]]$x ) ) 237s [1] FALSE 237s > 237s > # with x (returnModelMatrix) = TRUE 237s > print( !is.null( fitw2slsd3$eq[[ 1 ]]$x ) ) 237s [1] TRUE 237s > print( all.equal( mm, model.matrix( fitw2slsd3 ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2slsd3$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2slsd3$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > 237s > # with x (returnModelMatrix) = FALSE 237s > print( all.equal( mm, model.matrix( fitw2slsd3e ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2slsd3e$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2slsd3e$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > print( !is.null( fitw2slsd3e$eq[[ 1 ]]$x ) ) 237s [1] FALSE 237s > 237s > # with x (returnModelMatrix) = TRUE 237s > print( !is.null( fitw2sls4$eq[[ 1 ]]$x ) ) 237s [1] TRUE 237s > print( all.equal( mm, model.matrix( fitw2sls4 ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2sls4$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2sls4$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > 237s > # with x (returnModelMatrix) = FALSE 237s > print( all.equal( mm, model.matrix( fitw2sls4e ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2sls4e$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2sls4e$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > print( !is.null( fitw2sls4e$eq[[ 1 ]]$x ) ) 237s [1] FALSE 237s > 237s > # with x (returnModelMatrix) = TRUE 237s > print( !is.null( fitw2sls5$eq[[ 1 ]]$x ) ) 237s [1] TRUE 237s > print( all.equal( mm, model.matrix( fitw2sls5 ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2sls5$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2sls5$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > 237s > # with x (returnModelMatrix) = FALSE 237s > print( all.equal( mm, model.matrix( fitw2sls5e ) ) ) 237s [1] TRUE 237s > print( all.equal( mm1, model.matrix( fitw2sls5e$eq[[ 1 ]] ) ) ) 237s [1] TRUE 237s > print( all.equal( mm2, model.matrix( fitw2sls5e$eq[[ 2 ]] ) ) ) 237s [1] TRUE 237s > print( !is.null( fitw2sls5e$eq[[ 1 ]]$x ) ) 237s [1] FALSE 237s > 237s > # matrices of instrumental variables 237s > model.matrix( fitw2sls1, which = "z" ) 237s demand_(Intercept) demand_income demand_farmPrice demand_trend 237s demand_1 1 87.4 98.0 1 237s demand_2 1 97.6 99.1 2 237s demand_3 1 96.7 99.1 3 237s demand_4 1 98.2 98.1 4 237s demand_5 1 99.8 110.8 5 237s demand_6 1 100.5 108.2 6 237s demand_7 1 103.2 105.6 7 237s demand_8 1 107.8 109.8 8 237s demand_9 1 96.6 108.7 9 237s demand_10 1 88.9 100.6 10 237s demand_11 1 75.1 81.0 11 237s demand_12 1 76.9 68.6 12 237s demand_13 1 84.6 70.9 13 237s demand_14 1 90.6 81.4 14 237s demand_15 1 103.1 102.3 15 237s demand_16 1 105.1 105.0 16 237s demand_17 1 96.4 110.5 17 237s demand_18 1 104.4 92.5 18 237s demand_19 1 110.7 89.3 19 237s demand_20 1 127.1 93.0 20 237s supply_1 0 0.0 0.0 0 237s supply_2 0 0.0 0.0 0 237s supply_3 0 0.0 0.0 0 237s supply_4 0 0.0 0.0 0 237s supply_5 0 0.0 0.0 0 237s supply_6 0 0.0 0.0 0 237s supply_7 0 0.0 0.0 0 237s supply_8 0 0.0 0.0 0 237s supply_9 0 0.0 0.0 0 237s supply_10 0 0.0 0.0 0 237s supply_11 0 0.0 0.0 0 237s supply_12 0 0.0 0.0 0 237s supply_13 0 0.0 0.0 0 237s supply_14 0 0.0 0.0 0 237s supply_15 0 0.0 0.0 0 237s supply_16 0 0.0 0.0 0 237s supply_17 0 0.0 0.0 0 237s supply_18 0 0.0 0.0 0 237s supply_19 0 0.0 0.0 0 237s supply_20 0 0.0 0.0 0 237s supply_(Intercept) supply_income supply_farmPrice supply_trend 237s demand_1 0 0.0 0.0 0 237s demand_2 0 0.0 0.0 0 237s demand_3 0 0.0 0.0 0 237s demand_4 0 0.0 0.0 0 237s demand_5 0 0.0 0.0 0 237s demand_6 0 0.0 0.0 0 237s demand_7 0 0.0 0.0 0 237s demand_8 0 0.0 0.0 0 237s demand_9 0 0.0 0.0 0 237s demand_10 0 0.0 0.0 0 237s demand_11 0 0.0 0.0 0 237s demand_12 0 0.0 0.0 0 237s demand_13 0 0.0 0.0 0 237s demand_14 0 0.0 0.0 0 237s demand_15 0 0.0 0.0 0 237s demand_16 0 0.0 0.0 0 237s demand_17 0 0.0 0.0 0 237s demand_18 0 0.0 0.0 0 237s demand_19 0 0.0 0.0 0 237s demand_20 0 0.0 0.0 0 237s supply_1 1 87.4 98.0 1 237s supply_2 1 97.6 99.1 2 237s supply_3 1 96.7 99.1 3 237s supply_4 1 98.2 98.1 4 237s supply_5 1 99.8 110.8 5 237s supply_6 1 100.5 108.2 6 237s supply_7 1 103.2 105.6 7 237s supply_8 1 107.8 109.8 8 237s supply_9 1 96.6 108.7 9 237s supply_10 1 88.9 100.6 10 237s supply_11 1 75.1 81.0 11 237s supply_12 1 76.9 68.6 12 237s supply_13 1 84.6 70.9 13 237s supply_14 1 90.6 81.4 14 237s supply_15 1 103.1 102.3 15 237s supply_16 1 105.1 105.0 16 237s supply_17 1 96.4 110.5 17 237s supply_18 1 104.4 92.5 18 237s supply_19 1 110.7 89.3 19 237s supply_20 1 127.1 93.0 20 237s > model.matrix( fitw2sls1$eq[[ 1 ]], which = "z" ) 237s (Intercept) income farmPrice trend 237s 1 1 87.4 98.0 1 237s 2 1 97.6 99.1 2 237s 3 1 96.7 99.1 3 237s 4 1 98.2 98.1 4 237s 5 1 99.8 110.8 5 237s 6 1 100.5 108.2 6 237s 7 1 103.2 105.6 7 237s 8 1 107.8 109.8 8 237s 9 1 96.6 108.7 9 237s 10 1 88.9 100.6 10 237s 11 1 75.1 81.0 11 237s 12 1 76.9 68.6 12 237s 13 1 84.6 70.9 13 237s 14 1 90.6 81.4 14 237s 15 1 103.1 102.3 15 237s 16 1 105.1 105.0 16 237s 17 1 96.4 110.5 17 237s 18 1 104.4 92.5 18 237s 19 1 110.7 89.3 19 237s 20 1 127.1 93.0 20 237s attr(,"assign") 237s [1] 0 1 2 3 237s > model.matrix( fitw2sls1$eq[[ 2 ]], which = "z" ) 237s (Intercept) income farmPrice trend 237s 1 1 87.4 98.0 1 237s 2 1 97.6 99.1 2 237s 3 1 96.7 99.1 3 237s 4 1 98.2 98.1 4 237s 5 1 99.8 110.8 5 237s 6 1 100.5 108.2 6 237s 7 1 103.2 105.6 7 237s 8 1 107.8 109.8 8 237s 9 1 96.6 108.7 9 237s 10 1 88.9 100.6 10 237s 11 1 75.1 81.0 11 237s 12 1 76.9 68.6 12 237s 13 1 84.6 70.9 13 237s 14 1 90.6 81.4 14 237s 15 1 103.1 102.3 15 237s 16 1 105.1 105.0 16 237s 17 1 96.4 110.5 17 237s 18 1 104.4 92.5 18 237s 19 1 110.7 89.3 19 237s 20 1 127.1 93.0 20 237s attr(,"assign") 237s [1] 0 1 2 3 237s > 237s > # matrices of fitted regressors 237s > model.matrix( fitw2sls5e, which = "xHat" ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s demand_1 1 99.6 87.4 0 237s demand_2 1 105.1 97.6 0 237s demand_3 1 103.8 96.7 0 237s demand_4 1 104.5 98.2 0 237s demand_5 1 98.7 99.8 0 237s demand_6 1 99.6 100.5 0 237s demand_7 1 102.0 103.2 0 237s demand_8 1 102.2 107.8 0 237s demand_9 1 94.6 96.6 0 237s demand_10 1 92.7 88.9 0 237s demand_11 1 92.4 75.1 0 237s demand_12 1 98.9 76.9 0 237s demand_13 1 102.2 84.6 0 237s demand_14 1 100.3 90.6 0 237s demand_15 1 97.6 103.1 0 237s demand_16 1 96.9 105.1 0 237s demand_17 1 87.7 96.4 0 237s demand_18 1 101.1 104.4 0 237s demand_19 1 106.1 110.7 0 237s demand_20 1 114.4 127.1 0 237s supply_1 0 0.0 0.0 1 237s supply_2 0 0.0 0.0 1 237s supply_3 0 0.0 0.0 1 237s supply_4 0 0.0 0.0 1 237s supply_5 0 0.0 0.0 1 237s supply_6 0 0.0 0.0 1 237s supply_7 0 0.0 0.0 1 237s supply_8 0 0.0 0.0 1 237s supply_9 0 0.0 0.0 1 237s supply_10 0 0.0 0.0 1 237s supply_11 0 0.0 0.0 1 237s supply_12 0 0.0 0.0 1 237s supply_13 0 0.0 0.0 1 237s supply_14 0 0.0 0.0 1 237s supply_15 0 0.0 0.0 1 237s supply_16 0 0.0 0.0 1 237s supply_17 0 0.0 0.0 1 237s supply_18 0 0.0 0.0 1 237s supply_19 0 0.0 0.0 1 237s supply_20 0 0.0 0.0 1 237s supply_price supply_farmPrice supply_trend 237s demand_1 0.0 0.0 0 237s demand_2 0.0 0.0 0 237s demand_3 0.0 0.0 0 237s demand_4 0.0 0.0 0 237s demand_5 0.0 0.0 0 237s demand_6 0.0 0.0 0 237s demand_7 0.0 0.0 0 237s demand_8 0.0 0.0 0 237s demand_9 0.0 0.0 0 237s demand_10 0.0 0.0 0 237s demand_11 0.0 0.0 0 237s demand_12 0.0 0.0 0 237s demand_13 0.0 0.0 0 237s demand_14 0.0 0.0 0 237s demand_15 0.0 0.0 0 237s demand_16 0.0 0.0 0 237s demand_17 0.0 0.0 0 237s demand_18 0.0 0.0 0 237s demand_19 0.0 0.0 0 237s demand_20 0.0 0.0 0 237s supply_1 99.6 98.0 1 237s supply_2 105.1 99.1 2 237s supply_3 103.8 99.1 3 237s supply_4 104.5 98.1 4 237s supply_5 98.7 110.8 5 237s supply_6 99.6 108.2 6 237s supply_7 102.0 105.6 7 237s supply_8 102.2 109.8 8 237s supply_9 94.6 108.7 9 237s supply_10 92.7 100.6 10 237s supply_11 92.4 81.0 11 237s supply_12 98.9 68.6 12 237s supply_13 102.2 70.9 13 237s supply_14 100.3 81.4 14 237s supply_15 97.6 102.3 15 237s supply_16 96.9 105.0 16 237s supply_17 87.7 110.5 17 237s supply_18 101.1 92.5 18 237s supply_19 106.1 89.3 19 237s supply_20 114.4 93.0 20 237s > model.matrix( fitw2sls5e$eq[[ 1 ]], which = "xHat" ) 237s (Intercept) price income 237s 1 1 99.6 87.4 237s 2 1 105.1 97.6 237s 3 1 103.8 96.7 237s 4 1 104.5 98.2 237s 5 1 98.7 99.8 237s 6 1 99.6 100.5 237s 7 1 102.0 103.2 237s 8 1 102.2 107.8 237s 9 1 94.6 96.6 237s 10 1 92.7 88.9 237s 11 1 92.4 75.1 237s 12 1 98.9 76.9 237s 13 1 102.2 84.6 237s 14 1 100.3 90.6 237s 15 1 97.6 103.1 237s 16 1 96.9 105.1 237s 17 1 87.7 96.4 237s 18 1 101.1 104.4 237s 19 1 106.1 110.7 237s 20 1 114.4 127.1 237s > model.matrix( fitw2sls5e$eq[[ 2 ]], which = "xHat" ) 237s (Intercept) price farmPrice trend 237s 1 1 99.6 98.0 1 237s 2 1 105.1 99.1 2 237s 3 1 103.8 99.1 3 237s 4 1 104.5 98.1 4 237s 5 1 98.7 110.8 5 237s 6 1 99.6 108.2 6 237s 7 1 102.0 105.6 7 237s 8 1 102.2 109.8 8 237s 9 1 94.6 108.7 9 237s 10 1 92.7 100.6 10 237s 11 1 92.4 81.0 11 237s 12 1 98.9 68.6 12 237s 13 1 102.2 70.9 13 237s 14 1 100.3 81.4 14 237s 15 1 97.6 102.3 15 237s 16 1 96.9 105.0 16 237s 17 1 87.7 110.5 17 237s 18 1 101.1 92.5 18 237s 19 1 106.1 89.3 19 237s 20 1 114.4 93.0 20 237s > 237s > 237s > ## **************** formulas ************************ 237s > formula( fitw2sls1e ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2sls1e$eq[[ 1 ]] ) 237s consump ~ price + income 237s > 237s > formula( fitw2sls2 ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2sls2$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s > 237s > formula( fitw2sls3 ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2sls3$eq[[ 1 ]] ) 237s consump ~ price + income 237s > 237s > formula( fitw2sls4e ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2sls4e$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s > 237s > formula( fitw2sls5 ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2sls5$eq[[ 1 ]] ) 237s consump ~ price + income 237s > 237s > formula( fitw2slsd1 ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2slsd1$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s > 237s > formula( fitw2slsd2e ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2slsd2e$eq[[ 1 ]] ) 237s consump ~ price + income 237s > 237s > formula( fitw2slsd3e ) 237s $demand 237s consump ~ price + income 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s 237s > formula( fitw2slsd3e$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s > 237s > 237s > ## **************** model terms ******************* 237s > terms( fitw2sls1e ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2sls1e$eq[[ 1 ]] ) 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s > 237s > terms( fitw2sls2 ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2sls2$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s > 237s > terms( fitw2sls3 ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2sls3$eq[[ 1 ]] ) 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s > 237s > terms( fitw2sls4e ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2sls4e$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s > 237s > terms( fitw2sls5 ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2sls5$eq[[ 1 ]] ) 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s > 237s > terms( fitw2slsd1 ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2slsd1$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s > 237s > terms( fitw2slsd2e ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2slsd2e$eq[[ 1 ]] ) 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s > 237s > terms( fitw2slsd3e ) 237s $demand 237s consump ~ price + income 237s attr(,"variables") 237s list(consump, price, income) 237s attr(,"factors") 237s price income 237s consump 0 0 237s price 1 0 237s income 0 1 237s attr(,"term.labels") 237s [1] "price" "income" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, income) 237s attr(,"dataClasses") 237s consump price income 237s "numeric" "numeric" "numeric" 237s 237s $supply 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s 237s > terms( fitw2slsd3e$eq[[ 2 ]] ) 237s consump ~ price + farmPrice + trend 237s attr(,"variables") 237s list(consump, price, farmPrice, trend) 237s attr(,"factors") 237s price farmPrice trend 237s consump 0 0 0 237s price 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "price" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 1 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(consump, price, farmPrice, trend) 237s attr(,"dataClasses") 237s consump price farmPrice trend 237s "numeric" "numeric" "numeric" "numeric" 237s > 237s > 237s > ## **************** terms of instruments ******************* 237s > fitw2sls1e$eq[[ 1 ]]$termsInst 237s ~income + farmPrice + trend 237s attr(,"variables") 237s list(income, farmPrice, trend) 237s attr(,"factors") 237s income farmPrice trend 237s income 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice, trend) 237s attr(,"dataClasses") 237s income farmPrice trend 237s "numeric" "numeric" "numeric" 237s > 237s > fitw2sls2$eq[[ 2 ]]$termsInst 237s ~income + farmPrice + trend 237s attr(,"variables") 237s list(income, farmPrice, trend) 237s attr(,"factors") 237s income farmPrice trend 237s income 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice, trend) 237s attr(,"dataClasses") 237s income farmPrice trend 237s "numeric" "numeric" "numeric" 237s > 237s > fitw2sls3$eq[[ 1 ]]$termsInst 237s ~income + farmPrice + trend 237s attr(,"variables") 237s list(income, farmPrice, trend) 237s attr(,"factors") 237s income farmPrice trend 237s income 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice, trend) 237s attr(,"dataClasses") 237s income farmPrice trend 237s "numeric" "numeric" "numeric" 237s > 237s > fitw2sls4e$eq[[ 2 ]]$termsInst 237s ~income + farmPrice + trend 237s attr(,"variables") 237s list(income, farmPrice, trend) 237s attr(,"factors") 237s income farmPrice trend 237s income 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice, trend) 237s attr(,"dataClasses") 237s income farmPrice trend 237s "numeric" "numeric" "numeric" 237s > 237s > fitw2sls5$eq[[ 1 ]]$termsInst 237s ~income + farmPrice + trend 237s attr(,"variables") 237s list(income, farmPrice, trend) 237s attr(,"factors") 237s income farmPrice trend 237s income 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice, trend) 237s attr(,"dataClasses") 237s income farmPrice trend 237s "numeric" "numeric" "numeric" 237s > 237s > fitw2slsd1$eq[[ 2 ]]$termsInst 237s ~income + farmPrice + trend 237s attr(,"variables") 237s list(income, farmPrice, trend) 237s attr(,"factors") 237s income farmPrice trend 237s income 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice, trend) 237s attr(,"dataClasses") 237s income farmPrice trend 237s "numeric" "numeric" "numeric" 237s > 237s > fitw2slsd2e$eq[[ 1 ]]$termsInst 237s ~income + farmPrice 237s attr(,"variables") 237s list(income, farmPrice) 237s attr(,"factors") 237s income farmPrice 237s income 1 0 237s farmPrice 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" 237s attr(,"order") 237s [1] 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice) 237s attr(,"dataClasses") 237s income farmPrice 237s "numeric" "numeric" 237s > 237s > fitw2slsd3e$eq[[ 2 ]]$termsInst 237s ~income + farmPrice + trend 237s attr(,"variables") 237s list(income, farmPrice, trend) 237s attr(,"factors") 237s income farmPrice trend 237s income 1 0 0 237s farmPrice 0 1 0 237s trend 0 0 1 237s attr(,"term.labels") 237s [1] "income" "farmPrice" "trend" 237s attr(,"order") 237s [1] 1 1 1 237s attr(,"intercept") 237s [1] 1 237s attr(,"response") 237s [1] 0 237s attr(,".Environment") 237s 237s attr(,"predvars") 237s list(income, farmPrice, trend) 237s attr(,"dataClasses") 237s income farmPrice trend 237s "numeric" "numeric" "numeric" 237s > 237s > 237s > ## **************** estfun ************************ 237s > library( "sandwich" ) 237s > 237s > estfun( fitw2sls1 ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s demand_1 0.17426 17.362 15.231 0.0000 237s demand_2 -0.12666 -13.314 -12.362 0.0000 237s demand_3 0.63211 65.603 61.125 0.0000 237s demand_4 0.38686 40.439 37.990 0.0000 237s demand_5 0.59421 58.619 59.302 0.0000 237s demand_6 0.34231 34.111 34.403 0.0000 237s demand_7 0.46340 47.253 47.822 0.0000 237s demand_8 -0.95225 -97.353 -102.653 0.0000 237s demand_9 -0.40681 -38.486 -39.297 0.0000 237s demand_10 0.73846 68.469 65.649 0.0000 237s demand_11 -0.07078 -6.540 -5.315 0.0000 237s demand_12 -0.58541 -57.907 -45.018 0.0000 237s demand_13 -0.46025 -47.020 -38.937 0.0000 237s demand_14 0.02562 2.569 2.322 0.0000 237s demand_15 0.66403 64.824 68.462 0.0000 237s demand_16 -0.98546 -95.483 -103.572 0.0000 237s demand_17 -0.00533 -0.468 -0.514 0.0000 237s demand_18 -0.74266 -75.053 -77.534 0.0000 237s demand_19 0.43017 45.625 47.620 0.0000 237s demand_20 -0.11583 -13.250 -14.722 0.0000 237s supply_1 0.00000 0.000 0.000 -0.0444 237s supply_2 0.00000 0.000 0.000 -0.2348 237s supply_3 0.00000 0.000 0.000 0.2691 237s supply_4 0.00000 0.000 0.000 0.1308 237s supply_5 0.00000 0.000 0.000 0.2381 237s supply_6 0.00000 0.000 0.000 0.1015 237s supply_7 0.00000 0.000 0.000 0.2015 237s supply_8 0.00000 0.000 0.000 -0.7062 237s supply_9 0.00000 0.000 0.000 -0.3238 237s supply_10 0.00000 0.000 0.000 0.4611 237s supply_11 0.00000 0.000 0.000 0.0385 237s supply_12 0.00000 0.000 0.000 -0.2360 237s supply_13 0.00000 0.000 0.000 -0.1548 237s supply_14 0.00000 0.000 0.000 0.1330 237s supply_15 0.00000 0.000 0.000 0.4778 237s supply_16 0.00000 0.000 0.000 -0.5719 237s supply_17 0.00000 0.000 0.000 0.0648 237s supply_18 0.00000 0.000 0.000 -0.3413 237s supply_19 0.00000 0.000 0.000 0.4299 237s supply_20 0.00000 0.000 0.000 0.0672 237s supply_price supply_farmPrice supply_trend 237s demand_1 0.00 0.00 0.0000 237s demand_2 0.00 0.00 0.0000 237s demand_3 0.00 0.00 0.0000 237s demand_4 0.00 0.00 0.0000 237s demand_5 0.00 0.00 0.0000 237s demand_6 0.00 0.00 0.0000 237s demand_7 0.00 0.00 0.0000 237s demand_8 0.00 0.00 0.0000 237s demand_9 0.00 0.00 0.0000 237s demand_10 0.00 0.00 0.0000 237s demand_11 0.00 0.00 0.0000 237s demand_12 0.00 0.00 0.0000 237s demand_13 0.00 0.00 0.0000 237s demand_14 0.00 0.00 0.0000 237s demand_15 0.00 0.00 0.0000 237s demand_16 0.00 0.00 0.0000 237s demand_17 0.00 0.00 0.0000 237s demand_18 0.00 0.00 0.0000 237s demand_19 0.00 0.00 0.0000 237s demand_20 0.00 0.00 0.0000 237s supply_1 -4.42 -4.35 -0.0444 237s supply_2 -24.68 -23.27 -0.4696 237s supply_3 27.93 26.67 0.8073 237s supply_4 13.67 12.83 0.5230 237s supply_5 23.49 26.38 1.1905 237s supply_6 10.12 10.99 0.6093 237s supply_7 20.55 21.28 1.4107 237s supply_8 -72.20 -77.54 -5.6498 237s supply_9 -30.64 -35.20 -2.9145 237s supply_10 42.75 46.39 4.6109 237s supply_11 3.56 3.12 0.4235 237s supply_12 -23.35 -16.19 -2.8326 237s supply_13 -15.81 -10.97 -2.0121 237s supply_14 13.34 10.83 1.8621 237s supply_15 46.64 48.88 7.1671 237s supply_16 -55.42 -60.05 -9.1508 237s supply_17 5.68 7.16 1.1011 237s supply_18 -34.49 -31.57 -6.1438 237s supply_19 45.59 38.39 8.1674 237s supply_20 7.69 6.25 1.3448 237s > round( colSums( estfun( fitw2sls1 ) ), digits = 7 ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s 0 0 0 0 237s supply_price supply_farmPrice supply_trend 237s 0 0 0 237s > 237s > estfun( fitw2sls1e ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s demand_1 0.20502 20.43 17.918 0.0000 237s demand_2 -0.14901 -15.66 -14.543 0.0000 237s demand_3 0.74366 77.18 71.912 0.0000 237s demand_4 0.45513 47.57 44.694 0.0000 237s demand_5 0.69907 68.96 69.767 0.0000 237s demand_6 0.40272 40.13 40.474 0.0000 237s demand_7 0.54517 55.59 56.262 0.0000 237s demand_8 -1.12030 -114.53 -120.768 0.0000 237s demand_9 -0.47860 -45.28 -46.232 0.0000 237s demand_10 0.86877 80.55 77.234 0.0000 237s demand_11 -0.08327 -7.69 -6.253 0.0000 237s demand_12 -0.68871 -68.13 -52.962 0.0000 237s demand_13 -0.54147 -55.32 -45.808 0.0000 237s demand_14 0.03015 3.02 2.731 0.0000 237s demand_15 0.78121 76.26 80.543 0.0000 237s demand_16 -1.15937 -112.33 -121.850 0.0000 237s demand_17 -0.00627 -0.55 -0.605 0.0000 237s demand_18 -0.87372 -88.30 -91.217 0.0000 237s demand_19 0.50608 53.68 56.023 0.0000 237s demand_20 -0.13627 -15.59 -17.320 0.0000 237s supply_1 0.00000 0.00 0.000 -0.0554 237s supply_2 0.00000 0.00 0.000 -0.2935 237s supply_3 0.00000 0.00 0.000 0.3364 237s supply_4 0.00000 0.00 0.000 0.1634 237s supply_5 0.00000 0.00 0.000 0.2976 237s supply_6 0.00000 0.00 0.000 0.1269 237s supply_7 0.00000 0.00 0.000 0.2519 237s supply_8 0.00000 0.00 0.000 -0.8828 237s supply_9 0.00000 0.00 0.000 -0.4048 237s supply_10 0.00000 0.00 0.000 0.5764 237s supply_11 0.00000 0.00 0.000 0.0481 237s supply_12 0.00000 0.00 0.000 -0.2951 237s supply_13 0.00000 0.00 0.000 -0.1935 237s supply_14 0.00000 0.00 0.000 0.1663 237s supply_15 0.00000 0.00 0.000 0.5973 237s supply_16 0.00000 0.00 0.000 -0.7149 237s supply_17 0.00000 0.00 0.000 0.0810 237s supply_18 0.00000 0.00 0.000 -0.4267 237s supply_19 0.00000 0.00 0.000 0.5373 237s supply_20 0.00000 0.00 0.000 0.0841 237s supply_price supply_farmPrice supply_trend 237s demand_1 0.00 0.00 0.0000 237s demand_2 0.00 0.00 0.0000 237s demand_3 0.00 0.00 0.0000 237s demand_4 0.00 0.00 0.0000 237s demand_5 0.00 0.00 0.0000 237s demand_6 0.00 0.00 0.0000 237s demand_7 0.00 0.00 0.0000 237s demand_8 0.00 0.00 0.0000 237s demand_9 0.00 0.00 0.0000 237s demand_10 0.00 0.00 0.0000 237s demand_11 0.00 0.00 0.0000 237s demand_12 0.00 0.00 0.0000 237s demand_13 0.00 0.00 0.0000 237s demand_14 0.00 0.00 0.0000 237s demand_15 0.00 0.00 0.0000 237s demand_16 0.00 0.00 0.0000 237s demand_17 0.00 0.00 0.0000 237s demand_18 0.00 0.00 0.0000 237s demand_19 0.00 0.00 0.0000 237s demand_20 0.00 0.00 0.0000 237s supply_1 -5.52 -5.43 -0.0554 237s supply_2 -30.85 -29.09 -0.5870 237s supply_3 34.91 33.33 1.0091 237s supply_4 17.09 16.03 0.6538 237s supply_5 29.36 32.98 1.4882 237s supply_6 12.65 13.73 0.7616 237s supply_7 25.69 26.60 1.7633 237s supply_8 -90.25 -96.93 -7.0623 237s supply_9 -38.30 -44.00 -3.6431 237s supply_10 53.44 57.98 5.7636 237s supply_11 4.45 3.90 0.5294 237s supply_12 -29.19 -20.24 -3.5407 237s supply_13 -19.77 -13.72 -2.5151 237s supply_14 16.67 13.53 2.3277 237s supply_15 58.30 61.10 8.9588 237s supply_16 -69.27 -75.07 -11.4386 237s supply_17 7.10 8.95 1.3763 237s supply_18 -43.12 -39.47 -7.6797 237s supply_19 56.99 47.98 10.2092 237s supply_20 9.62 7.82 1.6810 237s > round( colSums( estfun( fitw2sls1e ) ), digits = 7 ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s 0 0 0 0 237s supply_price supply_farmPrice supply_trend 237s 0 0 0 237s > 237s > estfun( fitw2slsd1e ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s demand_1 -0.2141 -20.39 -18.71 0.0000 237s demand_2 -0.5971 -59.32 -58.28 0.0000 237s demand_3 0.3342 33.06 32.31 0.0000 237s demand_4 0.0923 9.21 9.06 0.0000 237s demand_5 0.3748 36.34 37.40 0.0000 237s demand_6 0.1317 12.91 13.23 0.0000 237s demand_7 0.2982 29.80 30.78 0.0000 237s demand_8 -1.3110 -132.05 -141.32 0.0000 237s demand_9 -0.5322 -51.18 -51.41 0.0000 237s demand_10 0.8995 85.57 79.97 0.0000 237s demand_11 0.1399 13.25 10.51 0.0000 237s demand_12 -0.4189 -41.49 -32.21 0.0000 237s demand_13 -0.2903 -29.54 -24.56 0.0000 237s demand_14 0.2709 27.46 24.55 0.0000 237s demand_15 0.9535 96.13 98.30 0.0000 237s demand_16 -0.9012 -90.95 -94.71 0.0000 237s demand_17 0.3566 34.08 34.37 0.0000 237s demand_18 -0.5159 -53.75 -53.86 0.0000 237s demand_19 0.8239 88.84 91.20 0.0000 237s demand_20 0.1054 12.00 13.39 0.0000 237s supply_1 0.0000 0.00 0.00 -0.0554 237s supply_2 0.0000 0.00 0.00 -0.2935 237s supply_3 0.0000 0.00 0.00 0.3364 237s supply_4 0.0000 0.00 0.00 0.1634 237s supply_5 0.0000 0.00 0.00 0.2976 237s supply_6 0.0000 0.00 0.00 0.1269 237s supply_7 0.0000 0.00 0.00 0.2519 237s supply_8 0.0000 0.00 0.00 -0.8828 237s supply_9 0.0000 0.00 0.00 -0.4048 237s supply_10 0.0000 0.00 0.00 0.5764 237s supply_11 0.0000 0.00 0.00 0.0481 237s supply_12 0.0000 0.00 0.00 -0.2951 237s supply_13 0.0000 0.00 0.00 -0.1935 237s supply_14 0.0000 0.00 0.00 0.1663 237s supply_15 0.0000 0.00 0.00 0.5973 237s supply_16 0.0000 0.00 0.00 -0.7149 237s supply_17 0.0000 0.00 0.00 0.0810 237s supply_18 0.0000 0.00 0.00 -0.4267 237s supply_19 0.0000 0.00 0.00 0.5373 237s supply_20 0.0000 0.00 0.00 0.0841 237s supply_price supply_farmPrice supply_trend 237s demand_1 0.00 0.00 0.0000 237s demand_2 0.00 0.00 0.0000 237s demand_3 0.00 0.00 0.0000 237s demand_4 0.00 0.00 0.0000 237s demand_5 0.00 0.00 0.0000 237s demand_6 0.00 0.00 0.0000 237s demand_7 0.00 0.00 0.0000 237s demand_8 0.00 0.00 0.0000 237s demand_9 0.00 0.00 0.0000 237s demand_10 0.00 0.00 0.0000 237s demand_11 0.00 0.00 0.0000 237s demand_12 0.00 0.00 0.0000 237s demand_13 0.00 0.00 0.0000 237s demand_14 0.00 0.00 0.0000 237s demand_15 0.00 0.00 0.0000 237s demand_16 0.00 0.00 0.0000 237s demand_17 0.00 0.00 0.0000 237s demand_18 0.00 0.00 0.0000 237s demand_19 0.00 0.00 0.0000 237s demand_20 0.00 0.00 0.0000 237s supply_1 -5.52 -5.43 -0.0554 237s supply_2 -30.85 -29.09 -0.5870 237s supply_3 34.91 33.33 1.0091 237s supply_4 17.09 16.03 0.6538 237s supply_5 29.36 32.98 1.4882 237s supply_6 12.65 13.73 0.7616 237s supply_7 25.69 26.60 1.7633 237s supply_8 -90.25 -96.93 -7.0623 237s supply_9 -38.30 -44.00 -3.6431 237s supply_10 53.44 57.98 5.7636 237s supply_11 4.45 3.90 0.5294 237s supply_12 -29.19 -20.24 -3.5407 237s supply_13 -19.77 -13.72 -2.5151 237s supply_14 16.67 13.53 2.3277 237s supply_15 58.30 61.10 8.9588 237s supply_16 -69.27 -75.07 -11.4386 237s supply_17 7.10 8.95 1.3763 237s supply_18 -43.12 -39.47 -7.6797 237s supply_19 56.99 47.98 10.2092 237s supply_20 9.62 7.82 1.6810 237s > round( colSums( estfun( fitw2slsd1e ) ), digits = 7 ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s 0 0 0 0 237s supply_price supply_farmPrice supply_trend 237s 0 0 0 237s > 237s > 237s > ## **************** bread ************************ 237s > bread( fitw2sls1 ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s [1,] 2509.59 -26.937 1.9721 0.0 237s [2,] -26.94 0.372 -0.1057 0.0 237s [3,] 1.97 -0.106 0.0881 0.0 237s [4,] 0.00 0.000 0.0000 5770.1 237s [5,] 0.00 0.000 0.0000 -43.8 237s [6,] 0.00 0.000 0.0000 -13.0 237s [7,] 0.00 0.000 0.0000 -11.8 237s supply_price supply_farmPrice supply_trend 237s [1,] 0.0000 0.0000 0.0000 237s [2,] 0.0000 0.0000 0.0000 237s [3,] 0.0000 0.0000 0.0000 237s [4,] -43.8164 -12.9527 -11.8092 237s [5,] 0.3995 0.0374 0.0232 237s [6,] 0.0374 0.0893 0.0551 237s [7,] 0.0232 0.0551 0.3972 237s > 237s > bread( fitw2sls1e ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s [1,] 2133.15 -22.8963 1.6763 0.00 237s [2,] -22.90 0.3165 -0.0898 0.00 237s [3,] 1.68 -0.0898 0.0749 0.00 237s [4,] 0.00 0.0000 0.0000 4616.09 237s [5,] 0.00 0.0000 0.0000 -35.05 237s [6,] 0.00 0.0000 0.0000 -10.36 237s [7,] 0.00 0.0000 0.0000 -9.45 237s supply_price supply_farmPrice supply_trend 237s [1,] 0.0000 0.0000 0.0000 237s [2,] 0.0000 0.0000 0.0000 237s [3,] 0.0000 0.0000 0.0000 237s [4,] -35.0531 -10.3622 -9.4473 237s [5,] 0.3196 0.0300 0.0185 237s [6,] 0.0300 0.0714 0.0441 237s [7,] 0.0185 0.0441 0.3178 237s > 237s > bread( fitw2slsd1e ) 237s demand_(Intercept) demand_price demand_income supply_(Intercept) 237s [1,] 4222.1 -51.601 9.696 0.00 237s [2,] -51.6 0.713 -0.202 0.00 237s [3,] 9.7 -0.202 0.108 0.00 237s [4,] 0.0 0.000 0.000 4616.09 237s [5,] 0.0 0.000 0.000 -35.05 237s [6,] 0.0 0.000 0.000 -10.36 237s [7,] 0.0 0.000 0.000 -9.45 237s supply_price supply_farmPrice supply_trend 237s [1,] 0.0000 0.0000 0.0000 237s [2,] 0.0000 0.0000 0.0000 237s [3,] 0.0000 0.0000 0.0000 237s [4,] -35.0531 -10.3622 -9.4473 237s [5,] 0.3196 0.0300 0.0185 237s [6,] 0.0300 0.0714 0.0441 237s [7,] 0.0185 0.0441 0.3178 237s > 237s BEGIN TEST test_wls.R 237s 237s R version 4.3.2 (2023-10-31) -- "Eye Holes" 237s Copyright (C) 2023 The R Foundation for Statistical Computing 237s Platform: aarch64-unknown-linux-gnu (64-bit) 237s 237s R is free software and comes with ABSOLUTELY NO WARRANTY. 237s You are welcome to redistribute it under certain conditions. 237s Type 'license()' or 'licence()' for distribution details. 237s 237s R is a collaborative project with many contributors. 237s Type 'contributors()' for more information and 237s 'citation()' on how to cite R or R packages in publications. 237s 237s Type 'demo()' for some demos, 'help()' for on-line help, or 237s 'help.start()' for an HTML browser interface to help. 237s Type 'q()' to quit R. 237s 237s > library( systemfit ) 237s Loading required package: Matrix 238s Loading required package: car 238s Loading required package: carData 238s Loading required package: lmtest 238s Loading required package: zoo 238s 238s Attaching package: ‘zoo’ 238s 238s The following objects are masked from ‘package:base’: 238s 238s as.Date, as.Date.numeric 238s 238s 238s Please cite the 'systemfit' package as: 238s 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/. 238s 238s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 238s https://r-forge.r-project.org/projects/systemfit/ 238s > options( digits = 3 ) 238s > 238s > data( "Kmenta" ) 238s > useMatrix <- FALSE 238s > 238s > demand <- consump ~ price + income 238s > supply <- consump ~ price + farmPrice + trend 238s > system <- list( demand = demand, supply = supply ) 238s > restrm <- matrix(0,1,7) # restriction matrix "R" 238s > restrm[1,3] <- 1 238s > restrm[1,7] <- -1 238s > restrict <- "demand_income - supply_trend = 0" 238s > restr2m <- matrix(0,2,7) # restriction matrix "R" 2 238s > restr2m[1,3] <- 1 238s > restr2m[1,7] <- -1 238s > restr2m[2,2] <- -1 238s > restr2m[2,5] <- 1 238s > restr2q <- c( 0, 0.5 ) # restriction vector "q" 2 238s > restrict2 <- c( "demand_income - supply_trend = 0", 238s + "- demand_price + supply_price = 0.5" ) 238s > tc <- matrix(0,7,6) 238s > tc[1,1] <- 1 238s > tc[2,2] <- 1 238s > tc[3,3] <- 1 238s > tc[4,4] <- 1 238s > tc[5,5] <- 1 238s > tc[6,6] <- 1 238s > tc[7,3] <- 1 238s > restr3m <- matrix(0,1,6) # restriction matrix "R" 2 238s > restr3m[1,2] <- -1 238s > restr3m[1,5] <- 1 238s > restr3q <- c( 0.5 ) # restriction vector "q" 2 238s > restrict3 <- "- C2 + C5 = 0.5" 238s > 238s > 238s > ## ******* single-equation OLS estimations ********************* 238s > lmDemand <- lm( demand, data = Kmenta ) 238s > lmSupply <- lm( supply, data = Kmenta ) 238s > 238s > ## *************** WLS estimation ************************ 238s > fitwls1 <- systemfit( system, "WLS", data = Kmenta, useMatrix = useMatrix ) 238s > print( summary( fitwls1 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 33 156 4.43 0.709 0.558 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.3 3.73 1.93 0.764 0.736 238s supply 20 16 92.6 5.78 2.40 0.655 0.590 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.73 0.00 238s supply 0.00 5.78 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.73 4.14 238s supply 4.14 5.78 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.891 238s supply 0.891 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 238s price -0.3163 0.0907 -3.49 0.0028 ** 238s income 0.3346 0.0454 7.37 1.1e-06 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.93 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 238s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 58.2754 11.4629 5.08 0.00011 *** 238s price 0.1604 0.0949 1.69 0.11039 238s farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 238s trend 0.2483 0.0975 2.55 0.02157 * 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.405 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 238s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 238s 238s > all.equal( coef( fitwls1 ), c( coef( lmDemand ), coef( lmSupply ) ), 238s + check.attributes = FALSE ) 238s [1] TRUE 238s > all.equal( coef( summary( fitwls1 ) ), 238s + rbind( coef( summary( lmDemand ) ), coef( summary( lmSupply ) ) ), 238s + check.attributes = FALSE ) 238s [1] TRUE 238s > all.equal( vcov( fitwls1 ), 238s + as.matrix( bdiag( vcov( lmDemand ), vcov( lmSupply ) ) ), 238s + check.attributes = FALSE ) 238s [1] TRUE 238s > 238s > ## *************** WLS estimation (EViews-like) ************************ 238s > fitwls1e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 238s + x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwls1e, useDfSys = TRUE ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 33 156 3.02 0.709 0.537 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.3 3.73 1.93 0.764 0.736 238s supply 20 16 92.6 5.78 2.40 0.655 0.590 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.17 0.00 238s supply 0.00 4.63 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.17 3.41 238s supply 3.41 4.63 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.891 238s supply 0.891 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 238s price -0.3163 0.0836 -3.78 0.00062 *** 238s income 0.3346 0.0419 7.99 3.2e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.93 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 238s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 238s price 0.1604 0.0849 1.89 0.0676 . 238s farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 238s trend 0.2483 0.0872 2.85 0.0075 ** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.405 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 238s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 238s 238s > all.equal( coef( fitwls1e ), c( coef( lmDemand ), coef( lmSupply ) ), 238s + check.attributes = FALSE ) 238s [1] TRUE 238s > 238s > ## ************** WLS with cross-equation restriction *************** 238s > fitwls2 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 238s + x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwls2 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 2.35 0.703 0.622 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.98 2.44 0.643 0.576 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.78 0.00 238s supply 0.00 5.94 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.75 4.48 238s supply 4.48 5.98 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 238s price -0.2991 0.0887 -3.37 0.0019 ** 238s income 0.3194 0.0415 7.70 6.0e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.936 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 238s price 0.1643 0.0960 1.71 0.096 . 238s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 238s trend 0.3194 0.0415 7.70 6.0e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.445 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 238s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 238s 238s > # the same with symbolically specified restrictions 238s > fitwls2Sym <- systemfit( system, "WLS", data = Kmenta, 238s + restrict.matrix = restrict, x = TRUE, 238s + useMatrix = useMatrix ) 238s > all.equal( fitwls2, fitwls2Sym ) 238s [1] "Component “call”: target, current do not match when deparsed" 238s > 238s > ## ************** WLS with cross-equation restriction (EViews-like) ******* 238s > fitwls2e <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 238s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 238s > print( summary( fitwls2e ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 1.61 0.703 0.589 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.97 2.44 0.644 0.577 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.21 0.00 238s supply 0.00 4.75 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.19 3.69 238s supply 3.69 4.78 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6461 6.9734 14.29 6.7e-16 *** 238s price -0.2982 0.0816 -3.65 0.00086 *** 238s income 0.3186 0.0381 8.37 8.9e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.937 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.794 MSE: 3.753 Root MSE: 1.937 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.2104 10.1248 5.55 3.3e-06 *** 238s price 0.1642 0.0859 1.91 0.064 . 238s farmPrice 0.2579 0.0404 6.38 2.7e-07 *** 238s trend 0.3186 0.0381 8.37 8.9e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.444 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.561 MSE: 5.973 Root MSE: 2.444 238s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 238s 238s > 238s > ## ******* WLS with cross-equation restriction via restrict.regMat ********** 238s > fitwls3 <- systemfit( system,"WLS", data = Kmenta, restrict.regMat = tc, 238s + x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwls3 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 2.35 0.703 0.622 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.98 2.44 0.643 0.576 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.78 0.00 238s supply 0.00 5.94 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.75 4.48 238s supply 4.48 5.98 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 238s price -0.2991 0.0887 -3.37 0.0019 ** 238s income 0.3194 0.0415 7.70 6.0e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.936 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 238s price 0.1643 0.0960 1.71 0.096 . 238s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 238s trend 0.3194 0.0415 7.70 6.0e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.445 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 238s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 238s 238s > 238s > ## ******* WLS with cross-equation restriction via restrict.regMat (EViews-like) ***** 238s > fitwls3e <- systemfit( system,"WLS", data = Kmenta, restrict.regMat = tc, 238s + methodResidCov = "noDfCor", useMatrix = useMatrix ) 238s > print( summary( fitwls3e ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 1.61 0.703 0.589 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.97 2.44 0.644 0.577 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.21 0.00 238s supply 0.00 4.75 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.19 3.69 238s supply 3.69 4.78 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6461 6.9734 14.29 6.7e-16 *** 238s price -0.2982 0.0816 -3.65 0.00086 *** 238s income 0.3186 0.0381 8.37 8.9e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.937 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.794 MSE: 3.753 Root MSE: 1.937 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.2104 10.1248 5.55 3.3e-06 *** 238s price 0.1642 0.0859 1.91 0.064 . 238s farmPrice 0.2579 0.0404 6.38 2.7e-07 *** 238s trend 0.3186 0.0381 8.37 8.9e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.444 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.561 MSE: 5.973 Root MSE: 2.444 238s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 238s 238s > 238s > ## ***** WLS with 2 cross-equation restrictions *************** 238s > fitwls4 <- systemfit( system,"WLS", data = Kmenta, restrict.matrix = restr2m, 238s + restrict.rhs = restr2q, useMatrix = useMatrix ) 238s > print( summary( fitwls4 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 2.51 0.702 0.619 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.6 3.74 1.94 0.763 0.735 238s supply 20 16 96.3 6.02 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.76 0.00 238s supply 0.00 5.99 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.74 4.47 238s supply 4.47 6.02 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.943 238s supply 0.943 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9138 6.0474 16.69 < 2e-16 *** 238s price -0.3160 0.0648 -4.87 2.3e-05 *** 238s income 0.3238 0.0385 8.42 6.3e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9416 7.9687 6.77 7.6e-08 *** 238s price 0.1840 0.0648 2.84 0.0075 ** 238s farmPrice 0.2603 0.0446 5.84 1.3e-06 *** 238s trend 0.3238 0.0385 8.42 6.3e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.453 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > # the same with symbolically specified restrictions 238s > fitwls4Sym <- systemfit( system, "WLS", data = Kmenta, 238s + restrict.matrix = restrict2, useMatrix = useMatrix ) 238s > all.equal( fitwls4, fitwls4Sym ) 238s [1] "Component “call”: target, current do not match when deparsed" 238s > 238s > ## ***** WLS with 2 cross-equation restrictions (EViews-like) ********** 238s > fitwls4e <- systemfit( system,"WLS", data = Kmenta, methodResidCov = "noDfCor", 238s + restrict.matrix = restr2m, restrict.rhs = restr2q, 238s + x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwls4e ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 1.72 0.702 0.586 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.763 0.735 238s supply 20 16 96.2 6.01 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.2 0.00 238s supply 0.0 4.79 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.18 3.69 238s supply 3.69 4.81 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.942 238s supply 0.942 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 238s price -0.3160 0.0589 -5.37 5.3e-06 *** 238s income 0.3233 0.0352 9.18 7.6e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.67 MSE: 3.745 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 238s price 0.1840 0.0589 3.13 0.0036 ** 238s farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 238s trend 0.3233 0.0352 9.18 7.6e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.452 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.215 MSE: 6.013 Root MSE: 2.452 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > ## *********** WLS with 2 cross-equation restrictions via R and restrict.regMat ****** 238s > fitwls5 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr3m, 238s + restrict.rhs = restr3q, restrict.regMat = tc, 238s + x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwls5 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 2.51 0.702 0.619 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.6 3.74 1.94 0.763 0.735 238s supply 20 16 96.3 6.02 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.76 0.00 238s supply 0.00 5.99 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.74 4.47 238s supply 4.47 6.02 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.943 238s supply 0.943 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9138 6.0474 16.69 < 2e-16 *** 238s price -0.3160 0.0648 -4.87 2.3e-05 *** 238s income 0.3238 0.0385 8.42 6.3e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9416 7.9687 6.77 7.6e-08 *** 238s price 0.1840 0.0648 2.84 0.0075 ** 238s farmPrice 0.2603 0.0446 5.84 1.3e-06 *** 238s trend 0.3238 0.0385 8.42 6.3e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.453 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > # the same with symbolically specified restrictions 238s > fitwls5Sym <- systemfit( system, "WLS", data = Kmenta, 238s + restrict.matrix = restrict3, restrict.regMat = tc, 238s + x = TRUE, useMatrix = useMatrix ) 238s > all.equal( fitwls5, fitwls5Sym ) 238s [1] "Component “call”: target, current do not match when deparsed" 238s > 238s > ## *********** WLS with 2 cross-equation restrictions via R and restrict.regMat (EViews-like) 238s > fitwls5e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 238s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 238s + useMatrix = useMatrix ) 238s > print( summary( fitwls5e ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 1.72 0.702 0.586 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.763 0.735 238s supply 20 16 96.2 6.01 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.2 0.00 238s supply 0.0 4.79 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.18 3.69 238s supply 3.69 4.81 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.942 238s supply 0.942 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 238s price -0.3160 0.0589 -5.37 5.3e-06 *** 238s income 0.3233 0.0352 9.18 7.6e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.67 MSE: 3.745 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 238s price 0.1840 0.0589 3.13 0.0036 ** 238s farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 238s trend 0.3233 0.0352 9.18 7.6e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.452 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.215 MSE: 6.013 Root MSE: 2.452 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > ## *************** iterated WLS estimation ********************* 238s > fitwlsi1 <- systemfit( system, "WLS", data = Kmenta, 238s + maxit = 100, useMatrix = useMatrix ) 238s > print( summary( fitwlsi1, useDfSys = TRUE ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 33 156 4.43 0.709 0.558 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.3 3.73 1.93 0.764 0.736 238s supply 20 16 92.6 5.78 2.40 0.655 0.590 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.73 0.00 238s supply 0.00 5.78 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.73 4.14 238s supply 4.14 5.78 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.891 238s supply 0.891 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.8954 7.5194 13.29 8.4e-15 *** 238s price -0.3163 0.0907 -3.49 0.0014 ** 238s income 0.3346 0.0454 7.37 1.8e-08 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.93 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 238s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 58.2754 11.4629 5.08 1.4e-05 *** 238s price 0.1604 0.0949 1.69 0.100 238s farmPrice 0.2481 0.0462 5.37 6.1e-06 *** 238s trend 0.2483 0.0975 2.55 0.016 * 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.405 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 238s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 238s 238s > 238s > ## *************** iterated WLS estimation (EViews-like) ************ 238s > fitwlsi1e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 238s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwlsi1e, useDfSys = TRUE ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 33 156 3.02 0.709 0.537 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.3 3.73 1.93 0.764 0.736 238s supply 20 16 92.6 5.78 2.40 0.655 0.590 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.17 0.00 238s supply 0.00 4.63 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.17 3.41 238s supply 3.41 4.63 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.891 238s supply 0.891 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 238s price -0.3163 0.0836 -3.78 0.00062 *** 238s income 0.3346 0.0419 7.99 3.2e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.93 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.332 MSE: 3.725 Root MSE: 1.93 238s Multiple R-Squared: 0.764 Adjusted R-Squared: 0.736 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 238s price 0.1604 0.0849 1.89 0.0676 . 238s farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 238s trend 0.2483 0.0872 2.85 0.0075 ** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.405 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 92.551 MSE: 5.784 Root MSE: 2.405 238s Multiple R-Squared: 0.655 Adjusted R-Squared: 0.59 238s 238s > 238s > ## ****** iterated WLS with cross-equation restriction *************** 238s > fitwlsi2 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 238s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwlsi2 ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 2.34 0.703 0.623 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.98 2.44 0.643 0.576 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.75 0.00 238s supply 0.00 5.98 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.75 4.48 238s supply 4.48 5.98 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 238s price -0.2993 0.0884 -3.39 0.0018 ** 238s income 0.3196 0.0414 7.72 5.6e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.936 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.741 MSE: 3.749 Root MSE: 1.936 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 238s price 0.1643 0.0963 1.71 0.097 . 238s farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 238s trend 0.3196 0.0414 7.72 5.6e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.445 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.641 MSE: 5.978 Root MSE: 2.445 238s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 238s 238s > 238s > ## ****** iterated WLS with cross-equation restriction (EViews-like) ******** 238s > fitwlsi2e <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restrm, 238s + methodResidCov = "noDfCor", maxit = 100, useMatrix = useMatrix ) 238s > print( summary( fitwlsi2e ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 1.6 0.703 0.589 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.97 2.44 0.644 0.577 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.19 0.00 238s supply 0.00 4.78 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.19 3.69 238s supply 3.69 4.78 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 238s price -0.2984 0.0814 -3.67 0.00083 *** 238s income 0.3188 0.0380 8.39 8.4e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.937 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.785 MSE: 3.752 Root MSE: 1.937 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 238s price 0.1642 0.0861 1.91 0.065 . 238s farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 238s trend 0.3188 0.0380 8.39 8.4e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.444 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.573 MSE: 5.973 Root MSE: 2.444 238s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 238s 238s > 238s > ## ******* iterated WLS with cross-equation restriction via restrict.regMat ********** 238s > fitwlsi3 <- systemfit( system, "WLS", data = Kmenta, restrict.regMat = tc, 238s + maxit = 100, x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwlsi3 ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 2.34 0.703 0.623 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.98 2.44 0.643 0.576 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.75 0.00 238s supply 0.00 5.98 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.75 4.48 238s supply 4.48 5.98 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 238s price -0.2993 0.0884 -3.39 0.0018 ** 238s income 0.3196 0.0414 7.72 5.6e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.936 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.741 MSE: 3.749 Root MSE: 1.936 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 238s price 0.1643 0.0963 1.71 0.097 . 238s farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 238s trend 0.3196 0.0414 7.72 5.6e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.445 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.641 MSE: 5.978 Root MSE: 2.445 238s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 238s 238s > 238s > ## ******* iterated WLS with cross-equation restriction via restrict.regMat (EViews-like) *** 238s > fitwlsi3e <- systemfit( system, "WLS", data = Kmenta, restrict.regMat = tc, 238s + methodResidCov = "noDfCor", maxit = 100, useMatrix = useMatrix ) 238s > print( summary( fitwlsi3e ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 1.6 0.703 0.589 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.97 2.44 0.644 0.577 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.19 0.00 238s supply 0.00 4.78 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.19 3.69 238s supply 3.69 4.78 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 238s price -0.2984 0.0814 -3.67 0.00083 *** 238s income 0.3188 0.0380 8.39 8.4e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.937 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.785 MSE: 3.752 Root MSE: 1.937 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 238s price 0.1642 0.0861 1.91 0.065 . 238s farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 238s trend 0.3188 0.0380 8.39 8.4e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.444 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.573 MSE: 5.973 Root MSE: 2.444 238s Multiple R-Squared: 0.644 Adjusted R-Squared: 0.577 238s 238s > nobs( fitwlsi3e ) 238s [1] 40 238s > 238s > ## ******* iterated WLS with 2 cross-equation restrictions *********** 238s > fitwlsi4 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr2m, 238s + restrict.rhs = restr2q, maxit = 100, useMatrix = useMatrix ) 238s > print( summary( fitwlsi4 ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 2.51 0.702 0.619 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.6 3.74 1.94 0.763 0.735 238s supply 20 16 96.3 6.02 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.74 0.00 238s supply 0.00 6.02 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.74 4.47 238s supply 4.47 6.02 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.943 238s supply 0.943 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 238s price -0.3159 0.0648 -4.88 2.3e-05 *** 238s income 0.3239 0.0384 8.43 6.0e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 238s price 0.1841 0.0648 2.84 0.0075 ** 238s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 238s trend 0.3239 0.0384 8.43 6.0e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.453 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > ## ******* iterated WLS with 2 cross-equation restrictions (EViews-like) ***** 238s > fitwlsi4e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 238s + restrict.matrix = restr2m, restrict.rhs = restr2q, maxit = 100, 238s + x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwlsi4e ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 1.72 0.702 0.586 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.763 0.735 238s supply 20 16 96.2 6.01 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.18 0.00 238s supply 0.00 4.81 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.18 3.69 238s supply 3.69 4.81 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.942 238s supply 0.942 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9662 5.5170 18.30 < 2e-16 *** 238s price -0.3160 0.0589 -5.37 5.2e-06 *** 238s income 0.3234 0.0352 9.20 7.3e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9595 7.2114 7.48 9.2e-09 *** 238s price 0.1840 0.0589 3.13 0.0036 ** 238s farmPrice 0.2602 0.0400 6.51 1.6e-07 *** 238s trend 0.3234 0.0352 9.20 7.3e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.452 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > ## ***** iterated WLS with 2 cross-equation restrictions via R and restrict.regMat ****** 238s > fitwlsi5 <- systemfit( system, "WLS", data = Kmenta, restrict.matrix = restr3m, 238s + restrict.rhs = restr3q, restrict.regMat = tc, maxit = 100, 238s + x = TRUE, useMatrix = useMatrix ) 238s > print( summary( fitwlsi5 ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 2.51 0.702 0.619 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.6 3.74 1.94 0.763 0.735 238s supply 20 16 96.3 6.02 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.74 0.00 238s supply 0.00 6.02 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.74 4.47 238s supply 4.47 6.02 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.943 238s supply 0.943 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 238s price -0.3159 0.0648 -4.88 2.3e-05 *** 238s income 0.3239 0.0384 8.43 6.0e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 238s price 0.1841 0.0648 2.84 0.0075 ** 238s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 238s trend 0.3239 0.0384 8.43 6.0e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.453 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > ## *** iterated WLS with 2 cross-equation restrictions via R and restrict.regMat (EViews-like) 238s > fitwlsi5e <- systemfit( system, "WLS", data = Kmenta, methodResidCov = "noDfCor", 238s + restrict.matrix = restr3m, restrict.rhs = restr3q, restrict.regMat = tc, 238s + maxit = 100, useMatrix = useMatrix ) 238s > print( summary( fitwlsi5e ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 1.72 0.702 0.586 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.763 0.735 238s supply 20 16 96.2 6.01 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.18 0.00 238s supply 0.00 4.81 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.18 3.69 238s supply 3.69 4.81 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.942 238s supply 0.942 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9662 5.5170 18.30 < 2e-16 *** 238s price -0.3160 0.0589 -5.37 5.2e-06 *** 238s income 0.3234 0.0352 9.20 7.3e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9595 7.2114 7.48 9.2e-09 *** 238s price 0.1840 0.0589 3.13 0.0036 ** 238s farmPrice 0.2602 0.0400 6.51 1.6e-07 *** 238s trend 0.3234 0.0352 9.20 7.3e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.452 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > 238s > ## *********** estimations with a single regressor ************ 238s > fitwlsS1 <- systemfit( 238s + list( consump ~ price - 1, consump ~ price + trend ), "WLS", 238s + data = Kmenta, useMatrix = useMatrix ) 238s > print( summary( fitwlsS1 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 36 1121 484 -1.09 -1.05 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s eq1 20 19 861 45.3 6.73 -2.213 -2.213 238s eq2 20 17 259 15.3 3.91 0.032 -0.082 238s 238s The covariance matrix of the residuals used for estimation 238s eq1 eq2 238s eq1 45.3 0.0 238s eq2 0.0 15.3 238s 238s The covariance matrix of the residuals 238s eq1 eq2 238s eq1 45.3 14.4 238s eq2 14.4 15.3 238s 238s The correlations of the residuals 238s eq1 eq2 238s eq1 1.000 0.549 238s eq2 0.549 1.000 238s 238s 238s WLS estimates for 'eq1' (equation 1) 238s Model Formula: consump ~ price - 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s price 1.006 0.015 66.9 <2e-16 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 6.733 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 238s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 238s 238s 238s WLS estimates for 'eq2' (equation 2) 238s Model Formula: consump ~ price + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 93.6767 15.2367 6.15 1.1e-05 *** 238s price 0.0622 0.1513 0.41 0.69 238s trend 0.0953 0.1515 0.63 0.54 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 3.907 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 259.497 MSE: 15.265 Root MSE: 3.907 238s Multiple R-Squared: 0.032 Adjusted R-Squared: -0.082 238s 238s > fitwlsS2 <- systemfit( 238s + list( consump ~ price - 1, consump ~ trend - 1 ), "WLS", 238s + data = Kmenta, useMatrix = useMatrix ) 238s > print( summary( fitwlsS2 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 38 47370 110957 -87.3 -5.28 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s eq1 20 19 861 45.3 6.73 -2.21 -2.21 238s eq2 20 19 46509 2447.8 49.48 -172.47 -172.47 238s 238s The covariance matrix of the residuals used for estimation 238s eq1 eq2 238s eq1 45.3 0 238s eq2 0.0 2448 238s 238s The covariance matrix of the residuals 238s eq1 eq2 238s eq1 45.34 -5.15 238s eq2 -5.15 2447.84 238s 238s The correlations of the residuals 238s eq1 eq2 238s eq1 1.0000 -0.0439 238s eq2 -0.0439 1.0000 238s 238s 238s WLS estimates for 'eq1' (equation 1) 238s Model Formula: consump ~ price - 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s price 1.006 0.015 66.9 <2e-16 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 6.733 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 861.449 MSE: 45.339 Root MSE: 6.733 238s Multiple R-Squared: -2.213 Adjusted R-Squared: -2.213 238s 238s 238s WLS estimates for 'eq2' (equation 2) 238s Model Formula: consump ~ trend - 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s trend 7.405 0.924 8.02 1.6e-07 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 49.476 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 238s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 238s 238s > fitwlsS3 <- systemfit( 238s + list( consump ~ trend - 1, price ~ trend - 1 ), "WLS", 238s + data = Kmenta, useMatrix = useMatrix ) 238s > print( summary( fitwlsS3 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 38 93537 108970 -99 -0.977 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s eq1 20 19 46509 2448 49.5 -172.5 -172.5 238s eq2 20 19 47028 2475 49.8 -69.5 -69.5 238s 238s The covariance matrix of the residuals used for estimation 238s eq1 eq2 238s eq1 2448 0 238s eq2 0 2475 238s 238s The covariance matrix of the residuals 238s eq1 eq2 238s eq1 2448 2439 238s eq2 2439 2475 238s 238s The correlations of the residuals 238s eq1 eq2 238s eq1 1.000 0.988 238s eq2 0.988 1.000 238s 238s 238s WLS estimates for 'eq1' (equation 1) 238s Model Formula: consump ~ trend - 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s trend 7.405 0.924 8.02 1.6e-07 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 49.476 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 46508.922 MSE: 2447.838 Root MSE: 49.476 238s Multiple R-Squared: -172.467 Adjusted R-Squared: -172.467 238s 238s 238s WLS estimates for 'eq2' (equation 2) 238s Model Formula: price ~ trend - 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s trend 7.318 0.929 7.88 2.1e-07 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 49.751 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 47028.107 MSE: 2475.164 Root MSE: 49.751 238s Multiple R-Squared: -69.48 Adjusted R-Squared: -69.48 238s 238s > fitwlsS4 <- systemfit( 238s + list( consump ~ trend - 1, price ~ trend - 1 ), "WLS", 238s + data = Kmenta, restrict.matrix = matrix( c( 1, -1 ), nrow = 1 ), 238s + useMatrix = useMatrix ) 238s > print( summary( fitwlsS4 ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 39 93548 111736 -99 -1.03 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s eq1 20 19 46514 2448 49.5 -172.5 -172.5 238s eq2 20 19 47034 2475 49.8 -69.5 -69.5 238s 238s The covariance matrix of the residuals used for estimation 238s eq1 eq2 238s eq1 2448 0 238s eq2 0 2475 238s 238s The covariance matrix of the residuals 238s eq1 eq2 238s eq1 2448 2439 238s eq2 2439 2475 238s 238s The correlations of the residuals 238s eq1 eq2 238s eq1 1.000 0.988 238s eq2 0.988 1.000 238s 238s 238s WLS estimates for 'eq1' (equation 1) 238s Model Formula: consump ~ trend - 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s trend 7.362 0.655 11.2 8.4e-14 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 49.478 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 46514.224 MSE: 2448.117 Root MSE: 49.478 238s Multiple R-Squared: -172.487 Adjusted R-Squared: -172.487 238s 238s 238s WLS estimates for 'eq2' (equation 2) 238s Model Formula: price ~ trend - 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s trend 7.362 0.655 11.2 8.4e-14 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 49.754 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 47033.528 MSE: 2475.449 Root MSE: 49.754 238s Multiple R-Squared: -69.488 Adjusted R-Squared: -69.488 238s 238s > fitwlsS5 <- systemfit( 238s + list( consump ~ 1, price ~ 1 ), "WLS", 238s + data = Kmenta, useMatrix = useMatrix ) 238s > print( summary( fitwlsS5) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 38 935 491 0 0 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s eq1 20 19 268 14.1 3.76 0 0 238s eq2 20 19 667 35.1 5.93 0 0 238s 238s The covariance matrix of the residuals used for estimation 238s eq1 eq2 238s eq1 14.1 0.0 238s eq2 0.0 35.1 238s 238s The covariance matrix of the residuals 238s eq1 eq2 238s eq1 14.11 2.18 238s eq2 2.18 35.12 238s 238s The correlations of the residuals 238s eq1 eq2 238s eq1 1.0000 0.0981 238s eq2 0.0981 1.0000 238s 238s 238s WLS estimates for 'eq1' (equation 1) 238s Model Formula: consump ~ 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.90 0.84 120 <2e-16 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 3.756 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 268.114 MSE: 14.111 Root MSE: 3.756 238s Multiple R-Squared: 0 Adjusted R-Squared: 0 238s 238s 238s WLS estimates for 'eq2' (equation 2) 238s Model Formula: price ~ 1 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.02 1.33 75.5 <2e-16 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 5.926 on 19 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 19 238s SSR: 667.251 MSE: 35.118 Root MSE: 5.926 238s Multiple R-Squared: 0 Adjusted R-Squared: 0 238s 238s > 238s > 238s > ## **************** shorter summaries ********************** 238s > print( summary( fitwls1 ), residCov = FALSE, equations = FALSE ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 33 156 4.43 0.709 0.558 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.3 3.73 1.93 0.764 0.736 238s supply 20 16 92.6 5.78 2.40 0.655 0.590 238s 238s 238s Coefficients: 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.8954 7.5194 13.29 2.1e-10 *** 238s demand_price -0.3163 0.0907 -3.49 0.00282 ** 238s demand_income 0.3346 0.0454 7.37 1.1e-06 *** 238s supply_(Intercept) 58.2754 11.4629 5.08 0.00011 *** 238s supply_price 0.1604 0.0949 1.69 0.11039 238s supply_farmPrice 0.2481 0.0462 5.37 6.2e-05 *** 238s supply_trend 0.2483 0.0975 2.55 0.02157 * 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s > 238s > print( summary( fitwls2e, useDfSys = FALSE, residCov = FALSE ), 238s + equations = FALSE ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 1.61 0.703 0.589 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.97 2.44 0.644 0.577 238s 238s 238s Coefficients: 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.6461 6.9734 14.29 6.7e-11 *** 238s demand_price -0.2982 0.0816 -3.65 0.002 ** 238s demand_income 0.3186 0.0381 8.37 2.0e-07 *** 238s supply_(Intercept) 56.2104 10.1248 5.55 4.4e-05 *** 238s supply_price 0.1642 0.0859 1.91 0.074 . 238s supply_farmPrice 0.2579 0.0404 6.38 9.1e-06 *** 238s supply_trend 0.3186 0.0381 8.37 3.1e-07 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s > 238s > print( summary( fitwls3 ), residCov = FALSE ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 2.35 0.703 0.622 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.98 2.44 0.643 0.576 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.6582 7.5640 13.18 6.4e-15 *** 238s price -0.2991 0.0887 -3.37 0.0019 ** 238s income 0.3194 0.0415 7.70 6.0e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.936 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.75 MSE: 3.75 Root MSE: 1.936 238s Multiple R-Squared: 0.762 Adjusted R-Squared: 0.734 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.1877 11.3165 4.97 1.9e-05 *** 238s price 0.1643 0.0960 1.71 0.096 . 238s farmPrice 0.2580 0.0451 5.71 2.0e-06 *** 238s trend 0.3194 0.0415 7.70 6.0e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.445 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 95.627 MSE: 5.977 Root MSE: 2.445 238s Multiple R-Squared: 0.643 Adjusted R-Squared: 0.576 238s 238s > 238s > print( summary( fitwls4e, residCov = FALSE, equations = FALSE ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 1.72 0.702 0.586 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.763 0.735 238s supply 20 16 96.2 6.01 2.45 0.641 0.574 238s 238s 238s Coefficients: 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 100.9762 5.5234 18.28 < 2e-16 *** 238s demand_price -0.3160 0.0589 -5.37 5.3e-06 *** 238s demand_income 0.3233 0.0352 9.18 7.6e-11 *** 238s supply_(Intercept) 53.9630 7.2089 7.49 9.1e-09 *** 238s supply_price 0.1840 0.0589 3.13 0.0036 ** 238s supply_farmPrice 0.2602 0.0399 6.53 1.6e-07 *** 238s supply_trend 0.3233 0.0352 9.18 7.6e-11 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s > 238s > print( summary( fitwls5, useDfSys = FALSE ), residCov = FALSE ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 2.51 0.702 0.619 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.6 3.74 1.94 0.763 0.735 238s supply 20 16 96.3 6.02 2.45 0.641 0.574 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9138 6.0474 16.69 5.6e-12 *** 238s price -0.3160 0.0648 -4.87 0.00014 *** 238s income 0.3238 0.0385 8.42 1.8e-07 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.636 MSE: 3.743 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9416 7.9687 6.77 4.5e-06 *** 238s price 0.1840 0.0648 2.84 0.012 * 238s farmPrice 0.2603 0.0446 5.84 2.5e-05 *** 238s trend 0.3238 0.0385 8.42 2.9e-07 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.453 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.268 MSE: 6.017 Root MSE: 2.453 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > print( summary( fitwlsi1e, useDfSys = TRUE, equations = FALSE ) ) 238s 238s systemfit results 238s method: WLS 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 33 156 3.02 0.709 0.537 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.3 3.73 1.93 0.764 0.736 238s supply 20 16 92.6 5.78 2.40 0.655 0.590 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.17 0.00 238s supply 0.00 4.63 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.17 3.41 238s supply 3.41 4.63 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.891 238s supply 0.891 1.000 238s 238s 238s Coefficients: 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.8954 6.9325 14.41 8.9e-16 *** 238s demand_price -0.3163 0.0836 -3.78 0.00062 *** 238s demand_income 0.3346 0.0419 7.99 3.2e-09 *** 238s supply_(Intercept) 58.2754 10.2527 5.68 2.4e-06 *** 238s supply_price 0.1604 0.0849 1.89 0.06762 . 238s supply_farmPrice 0.2481 0.0413 6.01 9.5e-07 *** 238s supply_trend 0.2483 0.0872 2.85 0.00754 ** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s > 238s > print( summary( fitwlsi2, equations = FALSE, residCov = FALSE ), 238s + residCov = TRUE ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 2.34 0.703 0.623 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.98 2.44 0.643 0.576 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.75 0.00 238s supply 0.00 5.98 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.75 4.48 238s supply 4.48 5.98 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.946 238s supply 0.946 1.000 238s 238s 238s Coefficients: 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.6607 7.5378 13.22 5.8e-15 *** 238s demand_price -0.2993 0.0884 -3.39 0.0018 ** 238s demand_income 0.3196 0.0414 7.72 5.6e-09 *** 238s supply_(Intercept) 56.1830 11.3487 4.95 2.0e-05 *** 238s supply_price 0.1643 0.0963 1.71 0.0972 . 238s supply_farmPrice 0.2580 0.0453 5.70 2.1e-06 *** 238s supply_trend 0.3196 0.0414 7.72 5.6e-09 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s > 238s > print( summary( fitwlsi3e ), equations = FALSE, residCov = FALSE ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 34 159 1.6 0.703 0.589 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.8 3.75 1.94 0.762 0.734 238s supply 20 16 95.6 5.97 2.44 0.644 0.577 238s 238s 238s Coefficients: 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.6484 6.9516 14.33 4.4e-16 *** 238s demand_price -0.2984 0.0814 -3.67 0.00083 *** 238s demand_income 0.3188 0.0380 8.39 8.4e-10 *** 238s supply_(Intercept) 56.2061 10.1500 5.54 3.4e-06 *** 238s supply_price 0.1642 0.0861 1.91 0.06502 . 238s supply_farmPrice 0.2579 0.0405 6.37 2.9e-07 *** 238s supply_trend 0.3188 0.0380 8.39 8.4e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s > 238s > print( summary( fitwlsi4, equations = FALSE ), equations = TRUE ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 2.51 0.702 0.619 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.6 3.74 1.94 0.763 0.735 238s supply 20 16 96.3 6.02 2.45 0.641 0.574 238s 238s The covariance matrix of the residuals used for estimation 238s demand supply 238s demand 3.74 0.00 238s supply 0.00 6.02 238s 238s The covariance matrix of the residuals 238s demand supply 238s demand 3.74 4.47 238s supply 4.47 6.02 238s 238s The correlations of the residuals 238s demand supply 238s demand 1.000 0.943 238s supply 0.943 1.000 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9031 6.0396 16.71 < 2e-16 *** 238s price -0.3159 0.0648 -4.88 2.3e-05 *** 238s income 0.3239 0.0384 8.43 6.0e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.63 MSE: 3.743 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9379 7.9718 6.77 7.7e-08 *** 238s price 0.1841 0.0648 2.84 0.0075 ** 238s farmPrice 0.2603 0.0447 5.83 1.3e-06 *** 238s trend 0.3239 0.0384 8.43 6.0e-10 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.453 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.277 MSE: 6.017 Root MSE: 2.453 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > print( summary( fitwlsi5e, useDfSys = FALSE, residCov = FALSE ) ) 238s 238s systemfit results 238s method: iterated WLS 238s 238s convergence achieved after 3 iterations 238s 238s N DF SSR detRCov OLS-R2 McElroy-R2 238s system 40 35 160 1.72 0.702 0.586 238s 238s N DF SSR MSE RMSE R2 Adj R2 238s demand 20 17 63.7 3.75 1.94 0.763 0.735 238s supply 20 16 96.2 6.01 2.45 0.641 0.574 238s 238s 238s WLS estimates for 'demand' (equation 1) 238s Model Formula: consump ~ price + income 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.9662 5.5170 18.30 1.3e-12 *** 238s price -0.3160 0.0589 -5.37 5.1e-05 *** 238s income 0.3234 0.0352 9.20 5.2e-08 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 1.935 on 17 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 17 238s SSR: 63.665 MSE: 3.745 Root MSE: 1.935 238s Multiple R-Squared: 0.763 Adjusted R-Squared: 0.735 238s 238s 238s WLS estimates for 'supply' (equation 2) 238s Model Formula: consump ~ price + farmPrice + trend 238s 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.9595 7.2114 7.48 1.3e-06 *** 238s price 0.1840 0.0589 3.13 0.0065 ** 238s farmPrice 0.2602 0.0400 6.51 7.2e-06 *** 238s trend 0.3234 0.0352 9.20 8.7e-08 *** 238s --- 238s Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 238s 238s Residual standard error: 2.452 on 16 degrees of freedom 238s Number of observations: 20 Degrees of Freedom: 16 238s SSR: 96.223 MSE: 6.014 Root MSE: 2.452 238s Multiple R-Squared: 0.641 Adjusted R-Squared: 0.574 238s 238s > 238s > 238s > ## ****************** residuals ************************** 238s > print( residuals( fitwls1 ) ) 238s demand supply 238s 1 1.074 -0.444 238s 2 -0.390 -0.896 238s 3 2.625 1.965 238s 4 1.802 1.134 238s 5 1.946 1.514 238s 6 1.175 0.680 238s 7 1.530 1.569 238s 8 -2.933 -4.407 238s 9 -1.365 -2.599 238s 10 2.031 2.469 238s 11 -0.149 -0.598 238s 12 -1.954 -1.697 238s 13 -1.121 -1.064 238s 14 -0.220 0.970 238s 15 1.487 3.159 238s 16 -3.701 -3.866 238s 17 -1.273 -0.265 238s 18 -2.002 -2.449 238s 19 1.738 3.110 238s 20 -0.299 1.714 238s > print( residuals( fitwls1$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 238s -0.444 -0.896 1.965 1.134 1.514 0.680 1.569 -4.407 -2.599 2.469 -0.598 238s 12 13 14 15 16 17 18 19 20 238s -1.697 -1.064 0.970 3.159 -3.866 -0.265 -2.449 3.110 1.714 238s > 238s > print( residuals( fitwls2e ) ) 238s demand supply 238s 1 0.9069 0.209 238s 2 -0.4660 -0.338 238s 3 2.5495 2.455 238s 4 1.7320 1.560 238s 5 2.0183 1.771 238s 6 1.2321 0.886 238s 7 1.6019 1.724 238s 8 -2.8544 -4.378 238s 9 -1.3158 -2.597 238s 10 2.0517 2.500 238s 11 -0.3823 -0.455 238s 12 -2.2623 -1.525 238s 13 -1.3801 -1.001 238s 14 -0.3081 0.877 238s 15 1.6643 2.806 238s 16 -3.5513 -4.328 238s 17 -1.0466 -0.805 238s 18 -1.9647 -2.952 238s 19 1.8446 2.561 238s 20 -0.0697 1.029 238s > print( residuals( fitwls2e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 238s 0.9069 -0.4660 2.5495 1.7320 2.0183 1.2321 1.6019 -2.8544 -1.3158 2.0517 238s 11 12 13 14 15 16 17 18 19 20 238s -0.3823 -2.2623 -1.3801 -0.3081 1.6643 -3.5513 -1.0466 -1.9647 1.8446 -0.0697 238s > 238s > print( residuals( fitwls3 ) ) 238s demand supply 238s 1 0.9150 0.217 238s 2 -0.4624 -0.332 238s 3 2.5532 2.461 238s 4 1.7354 1.564 238s 5 2.0148 1.773 238s 6 1.2293 0.889 238s 7 1.5984 1.725 238s 8 -2.8582 -4.378 238s 9 -1.3182 -2.597 238s 10 2.0507 2.500 238s 11 -0.3710 -0.453 238s 12 -2.2473 -1.524 238s 13 -1.3675 -1.000 238s 14 -0.3038 0.876 238s 15 1.6557 2.802 238s 16 -3.5586 -4.333 238s 17 -1.0576 -0.811 238s 18 -1.9666 -2.957 238s 19 1.8394 2.555 238s 20 -0.0808 1.022 238s > print( residuals( fitwls3$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 238s 0.217 -0.332 2.461 1.564 1.773 0.889 1.725 -4.378 -2.597 2.500 -0.453 238s 12 13 14 15 16 17 18 19 20 238s -1.524 -1.000 0.876 2.802 -4.333 -0.811 -2.957 2.555 1.022 238s > 238s > print( residuals( fitwls4e ) ) 238s demand supply 238s 1 0.9593 0.244 238s 2 -0.3907 -0.388 238s 3 2.6143 2.417 238s 4 1.8088 1.498 238s 5 1.9718 1.803 238s 6 1.2083 0.892 238s 7 1.5943 1.699 238s 8 -2.8174 -4.491 238s 9 -1.3751 -2.548 238s 10 1.9351 2.667 238s 11 -0.4019 -0.284 238s 12 -2.1883 -1.443 238s 13 -1.2686 -1.010 238s 14 -0.2984 0.921 238s 15 1.5512 2.869 238s 16 -3.6143 -4.342 238s 17 -1.2823 -0.600 238s 18 -1.9253 -3.056 238s 19 1.8860 2.425 238s 20 0.0333 0.728 238s > print( residuals( fitwls4e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 238s 0.9593 -0.3907 2.6143 1.8088 1.9718 1.2083 1.5943 -2.8174 -1.3751 1.9351 238s 11 12 13 14 15 16 17 18 19 20 238s -0.4019 -2.1883 -1.2686 -0.2984 1.5512 -3.6143 -1.2823 -1.9253 1.8860 0.0333 238s > 238s > print( residuals( fitwls5 ) ) 238s demand supply 238s 1 0.9649 0.249 238s 2 -0.3911 -0.384 238s 3 2.6145 2.421 238s 4 1.8081 1.501 238s 5 1.9707 1.805 238s 6 1.2067 0.893 238s 7 1.5910 1.700 238s 8 -2.8235 -4.491 238s 9 -1.3743 -2.548 238s 10 1.9406 2.667 238s 11 -0.3887 -0.282 238s 12 -2.1767 -1.442 238s 13 -1.2616 -1.009 238s 14 -0.2944 0.920 238s 15 1.5485 2.866 238s 16 -3.6185 -4.345 238s 17 -1.2806 -0.604 238s 18 -1.9295 -3.060 238s 19 1.8782 2.420 238s 20 0.0157 0.721 238s > print( residuals( fitwls5$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 238s 0.249 -0.384 2.421 1.501 1.805 0.893 1.700 -4.491 -2.548 2.667 -0.282 238s 12 13 14 15 16 17 18 19 20 238s -1.442 -1.009 0.920 2.866 -4.345 -0.604 -3.060 2.420 0.721 238s > 238s > print( residuals( fitwlsi1e ) ) 238s demand supply 238s 1 1.074 -0.444 238s 2 -0.390 -0.896 238s 3 2.625 1.965 238s 4 1.802 1.134 238s 5 1.946 1.514 238s 6 1.175 0.680 238s 7 1.530 1.569 238s 8 -2.933 -4.407 238s 9 -1.365 -2.599 238s 10 2.031 2.469 238s 11 -0.149 -0.598 238s 12 -1.954 -1.697 238s 13 -1.121 -1.064 238s 14 -0.220 0.970 238s 15 1.487 3.159 238s 16 -3.701 -3.866 238s 17 -1.273 -0.265 238s 18 -2.002 -2.449 238s 19 1.738 3.110 238s 20 -0.299 1.714 238s > print( residuals( fitwlsi1e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 238s 1.074 -0.390 2.625 1.802 1.946 1.175 1.530 -2.933 -1.365 2.031 -0.149 238s 12 13 14 15 16 17 18 19 20 238s -1.954 -1.121 -0.220 1.487 -3.701 -1.273 -2.002 1.738 -0.299 238s > 238s > print( residuals( fitwlsi2 ) ) 238s demand supply 238s 1 0.9167 0.218 238s 2 -0.4616 -0.331 238s 3 2.5539 2.462 238s 4 1.7361 1.565 238s 5 2.0140 1.774 238s 6 1.2288 0.889 238s 7 1.5977 1.726 238s 8 -2.8589 -4.378 238s 9 -1.3187 -2.597 238s 10 2.0505 2.500 238s 11 -0.3686 -0.453 238s 12 -2.2443 -1.523 238s 13 -1.3649 -1.000 238s 14 -0.3029 0.876 238s 15 1.6539 2.802 238s 16 -3.5601 -4.334 238s 17 -1.0599 -0.812 238s 18 -1.9669 -2.958 238s 19 1.8383 2.554 238s 20 -0.0831 1.020 238s > print( residuals( fitwlsi2$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 238s 0.218 -0.331 2.462 1.565 1.774 0.889 1.726 -4.378 -2.597 2.500 -0.453 238s 12 13 14 15 16 17 18 19 20 238s -1.523 -1.000 0.876 2.802 -4.334 -0.812 -2.958 2.554 1.020 238s > 238s > print( residuals( fitwlsi3e ) ) 238s demand supply 238s 1 0.9084 0.211 238s 2 -0.4653 -0.337 238s 3 2.5502 2.456 238s 4 1.7326 1.561 238s 5 2.0176 1.771 238s 6 1.2316 0.887 238s 7 1.6012 1.724 238s 8 -2.8551 -4.378 238s 9 -1.3162 -2.597 238s 10 2.0515 2.500 238s 11 -0.3801 -0.454 238s 12 -2.2594 -1.525 238s 13 -1.3777 -1.001 238s 14 -0.3073 0.877 238s 15 1.6627 2.806 238s 16 -3.5527 -4.329 238s 17 -1.0487 -0.806 238s 18 -1.9651 -2.953 238s 19 1.8436 2.560 238s 20 -0.0718 1.028 238s > print( residuals( fitwlsi3e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 238s 0.9084 -0.4653 2.5502 1.7326 2.0176 1.2316 1.6012 -2.8551 -1.3162 2.0515 238s 11 12 13 14 15 16 17 18 19 20 238s -0.3801 -2.2594 -1.3777 -0.3073 1.6627 -3.5527 -1.0487 -1.9651 1.8436 -0.0718 238s > 238s > print( residuals( fitwlsi4 ) ) 238s demand supply 238s 1 0.9659 0.250 238s 2 -0.3911 -0.383 238s 3 2.6145 2.421 238s 4 1.8080 1.502 238s 5 1.9705 1.805 238s 6 1.2064 0.893 238s 7 1.5905 1.700 238s 8 -2.8246 -4.491 238s 9 -1.3742 -2.547 238s 10 1.9415 2.667 238s 11 -0.3865 -0.282 238s 12 -2.1747 -1.442 238s 13 -1.2604 -1.009 238s 14 -0.2938 0.920 238s 15 1.5480 2.866 238s 16 -3.6192 -4.346 238s 17 -1.2804 -0.604 238s 18 -1.9302 -3.061 238s 19 1.8768 2.420 238s 20 0.0127 0.720 238s > print( residuals( fitwlsi4$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 238s 0.250 -0.383 2.421 1.502 1.805 0.893 1.700 -4.491 -2.547 2.667 -0.282 238s 12 13 14 15 16 17 18 19 20 238s -1.442 -1.009 0.920 2.866 -4.346 -0.604 -3.061 2.420 0.720 238s > 238s > print( residuals( fitwlsi5e ) ) 238s demand supply 238s 1 0.9602 0.245 238s 2 -0.3908 -0.388 238s 3 2.6143 2.418 238s 4 1.8087 1.498 238s 5 1.9716 1.803 238s 6 1.2081 0.892 238s 7 1.5938 1.699 238s 8 -2.8184 -4.491 238s 9 -1.3750 -2.548 238s 10 1.9360 2.667 238s 11 -0.3997 -0.284 238s 12 -2.1865 -1.443 238s 13 -1.2675 -1.010 238s 14 -0.2978 0.921 238s 15 1.5508 2.869 238s 16 -3.6150 -4.342 238s 17 -1.2820 -0.601 238s 18 -1.9260 -3.057 238s 19 1.8848 2.424 238s 20 0.0305 0.727 238s > print( residuals( fitwlsi5e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 238s 0.9602 -0.3908 2.6143 1.8087 1.9716 1.2081 1.5938 -2.8184 -1.3750 1.9360 238s 11 12 13 14 15 16 17 18 19 20 238s -0.3997 -2.1865 -1.2675 -0.2978 1.5508 -3.6150 -1.2820 -1.9260 1.8848 0.0305 238s > 238s > 238s > ## *************** coefficients ********************* 238s > print( round( coef( fitwls1e ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income supply_(Intercept) 238s 99.895 -0.316 0.335 58.275 238s supply_price supply_farmPrice supply_trend 238s 0.160 0.248 0.248 238s > print( round( coef( fitwls1e$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s 99.895 -0.316 0.335 238s > 238s > print( round( coef( fitwlsi2 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income supply_(Intercept) 238s 99.661 -0.299 0.320 56.183 238s supply_price supply_farmPrice supply_trend 238s 0.164 0.258 0.320 238s > print( round( coef( fitwlsi2$eq[[ 2 ]] ), digits = 6 ) ) 238s (Intercept) price farmPrice trend 238s 56.183 0.164 0.258 0.320 238s > 238s > print( round( coef( fitwls3e ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income supply_(Intercept) 238s 99.646 -0.298 0.319 56.210 238s supply_price supply_farmPrice supply_trend 238s 0.164 0.258 0.319 238s > print( round( coef( fitwls3e, modified.regMat = TRUE ), digits = 6 ) ) 238s C1 C2 C3 C4 C5 C6 238s 99.646 -0.298 0.319 56.210 0.164 0.258 238s > print( round( coef( fitwls3e$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s 99.646 -0.298 0.319 238s > 238s > print( round( coef( fitwls4 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income supply_(Intercept) 238s 100.914 -0.316 0.324 53.942 238s supply_price supply_farmPrice supply_trend 238s 0.184 0.260 0.324 238s > print( round( coef( fitwls4$eq[[ 2 ]] ), digits = 6 ) ) 238s (Intercept) price farmPrice trend 238s 53.942 0.184 0.260 0.324 238s > 238s > print( round( coef( fitwlsi5 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income supply_(Intercept) 238s 100.903 -0.316 0.324 53.938 238s supply_price supply_farmPrice supply_trend 238s 0.184 0.260 0.324 238s > print( round( coef( fitwlsi5, modified.regMat = TRUE ), digits = 6 ) ) 238s C1 C2 C3 C4 C5 C6 238s 100.903 -0.316 0.324 53.938 0.184 0.260 238s > print( round( coef( fitwlsi5$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s 100.903 -0.316 0.324 238s > 238s > 238s > ## *************** coefficients with stats ********************* 238s > print( round( coef( summary( fitwls1e ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.895 6.9325 14.41 0.000000 238s demand_price -0.316 0.0836 -3.78 0.001483 238s demand_income 0.335 0.0419 7.99 0.000000 238s supply_(Intercept) 58.275 10.2527 5.68 0.000034 238s supply_price 0.160 0.0849 1.89 0.077067 238s supply_farmPrice 0.248 0.0413 6.01 0.000018 238s supply_trend 0.248 0.0872 2.85 0.011659 238s > print( round( coef( summary( fitwls1e$eq[[ 1 ]] ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.895 6.9325 14.41 0.00000 238s price -0.316 0.0836 -3.78 0.00148 238s income 0.335 0.0419 7.99 0.00000 238s > 238s > print( round( coef( summary( fitwlsi2 ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.661 7.5378 13.22 0.000000 238s demand_price -0.299 0.0884 -3.39 0.001805 238s demand_income 0.320 0.0414 7.72 0.000000 238s supply_(Intercept) 56.183 11.3487 4.95 0.000020 238s supply_price 0.164 0.0963 1.71 0.097239 238s supply_farmPrice 0.258 0.0453 5.70 0.000002 238s supply_trend 0.320 0.0414 7.72 0.000000 238s > print( round( coef( summary( fitwlsi2$eq[[ 2 ]] ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 56.183 11.3487 4.95 0.000020 238s price 0.164 0.0963 1.71 0.097239 238s farmPrice 0.258 0.0453 5.70 0.000002 238s trend 0.320 0.0414 7.72 0.000000 238s > 238s > print( round( coef( summary( fitwls3e ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 99.646 6.9734 14.29 0.000000 238s demand_price -0.298 0.0816 -3.65 0.000863 238s demand_income 0.319 0.0381 8.37 0.000000 238s supply_(Intercept) 56.210 10.1248 5.55 0.000003 238s supply_price 0.164 0.0859 1.91 0.064384 238s supply_farmPrice 0.258 0.0404 6.38 0.000000 238s supply_trend 0.319 0.0381 8.37 0.000000 238s > print( round( coef( summary( fitwls3e ), modified.regMat = TRUE ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s C1 99.646 6.9734 14.29 0.000000 238s C2 -0.298 0.0816 -3.65 0.000863 238s C3 0.319 0.0381 8.37 0.000000 238s C4 56.210 10.1248 5.55 0.000003 238s C5 0.164 0.0859 1.91 0.064384 238s C6 0.258 0.0404 6.38 0.000000 238s > print( round( coef( summary( fitwls3e$eq[[ 1 ]] ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 99.646 6.9734 14.29 0.000000 238s price -0.298 0.0816 -3.65 0.000863 238s income 0.319 0.0381 8.37 0.000000 238s > 238s > print( round( coef( summary( fitwls4, useDfSys = FALSE ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 100.914 6.0474 16.69 0.000000 238s demand_price -0.316 0.0648 -4.87 0.000143 238s demand_income 0.324 0.0385 8.42 0.000000 238s supply_(Intercept) 53.942 7.9687 6.77 0.000005 238s supply_price 0.184 0.0648 2.84 0.011833 238s supply_farmPrice 0.260 0.0446 5.84 0.000025 238s supply_trend 0.324 0.0385 8.42 0.000000 238s > print( round( coef( summary( fitwls4$eq[[ 2 ]], useDfSys = FALSE ) ), 238s + digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 53.942 7.9687 6.77 0.000005 238s price 0.184 0.0648 2.84 0.011833 238s farmPrice 0.260 0.0446 5.84 0.000025 238s trend 0.324 0.0385 8.42 0.000000 238s > 238s > print( round( coef( summary( fitwlsi5, useDfSys = FALSE ) ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s demand_(Intercept) 100.903 6.0396 16.71 0.000000 238s demand_price -0.316 0.0648 -4.88 0.000142 238s demand_income 0.324 0.0384 8.43 0.000000 238s supply_(Intercept) 53.938 7.9718 6.77 0.000005 238s supply_price 0.184 0.0648 2.84 0.011806 238s supply_farmPrice 0.260 0.0447 5.83 0.000026 238s supply_trend 0.324 0.0384 8.43 0.000000 238s > print( round( coef( summary( fitwlsi5, useDfSys = FALSE ), 238s + modified.regMat = TRUE ), digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s C1 100.903 6.0396 16.71 NA 238s C2 -0.316 0.0648 -4.88 NA 238s C3 0.324 0.0384 8.43 NA 238s C4 53.938 7.9718 6.77 NA 238s C5 0.184 0.0648 2.84 NA 238s C6 0.260 0.0447 5.83 NA 238s > print( round( coef( summary( fitwlsi5$eq[[ 1 ]], useDfSys = FALSE ) ), 238s + digits = 6 ) ) 238s Estimate Std. Error t value Pr(>|t|) 238s (Intercept) 100.903 6.0396 16.71 0.000000 238s price -0.316 0.0648 -4.88 0.000142 238s income 0.324 0.0384 8.43 0.000000 238s > 238s > 238s > ## *********** variance covariance matrix of the coefficients ******* 238s > print( round( vcov( fitwls1e ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 48.0597 -0.50558 0.02734 238s demand_price -0.5056 0.00699 -0.00198 238s demand_income 0.0273 -0.00198 0.00175 238s supply_(Intercept) 0.0000 0.00000 0.00000 238s supply_price 0.0000 0.00000 0.00000 238s supply_farmPrice 0.0000 0.00000 0.00000 238s supply_trend 0.0000 0.00000 0.00000 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) 0.000 0.000000 0.000000 238s demand_price 0.000 0.000000 0.000000 238s demand_income 0.000 0.000000 0.000000 238s supply_(Intercept) 105.119 -0.790000 -0.243489 238s supply_price -0.790 0.007202 0.000675 238s supply_farmPrice -0.243 0.000675 0.001707 238s supply_trend -0.223 0.000418 0.001052 238s supply_trend 238s demand_(Intercept) 0.000000 238s demand_price 0.000000 238s demand_income 0.000000 238s supply_(Intercept) -0.223347 238s supply_price 0.000418 238s supply_farmPrice 0.001052 238s supply_trend 0.007608 238s > print( round( vcov( fitwls1e$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s (Intercept) 48.0597 -0.50558 0.02734 238s price -0.5056 0.00699 -0.00198 238s income 0.0273 -0.00198 0.00175 238s > 238s > print( round( vcov( fitwls2 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 57.21413 -0.596328 0.026850 238s demand_price -0.59633 0.007862 -0.001948 238s demand_income 0.02685 -0.001948 0.001722 238s supply_(Intercept) -0.78825 0.057190 -0.050565 238s supply_price 0.00147 -0.000107 0.000095 238s supply_farmPrice 0.00371 -0.000269 0.000238 238s supply_trend 0.02685 -0.001948 0.001722 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) -0.7883 0.001474 0.003714 238s demand_price 0.0572 -0.000107 -0.000269 238s demand_income -0.0506 0.000095 0.000238 238s supply_(Intercept) 128.0635 -1.001596 -0.280017 238s supply_price -1.0016 0.009225 0.000806 238s supply_farmPrice -0.2800 0.000806 0.002038 238s supply_trend -0.0506 0.000095 0.000238 238s supply_trend 238s demand_(Intercept) 0.026850 238s demand_price -0.001948 238s demand_income 0.001722 238s supply_(Intercept) -0.050565 238s supply_price 0.000095 238s supply_farmPrice 0.000238 238s supply_trend 0.001722 238s > print( round( vcov( fitwls2$eq[[ 2 ]] ), digits = 6 ) ) 238s (Intercept) price farmPrice trend 238s (Intercept) 128.0635 -1.001596 -0.280017 -0.050565 238s price -1.0016 0.009225 0.000806 0.000095 238s farmPrice -0.2800 0.000806 0.002038 0.000238 238s trend -0.0506 0.000095 0.000238 0.001722 238s > 238s > print( round( vcov( fitwls3e ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 48.62814 -0.506597 0.022574 238s demand_price -0.50660 0.006662 -0.001638 238s demand_income 0.02257 -0.001638 0.001448 238s supply_(Intercept) -0.66271 0.048082 -0.042512 238s supply_price 0.00124 -0.000090 0.000079 238s supply_farmPrice 0.00312 -0.000227 0.000200 238s supply_trend 0.02257 -0.001638 0.001448 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) -0.6627 0.001239 0.003123 238s demand_price 0.0481 -0.000090 -0.000227 238s demand_income -0.0425 0.000079 0.000200 238s supply_(Intercept) 102.5112 -0.801390 -0.224299 238s supply_price -0.8014 0.007381 0.000645 238s supply_farmPrice -0.2243 0.000645 0.001632 238s supply_trend -0.0425 0.000079 0.000200 238s supply_trend 238s demand_(Intercept) 0.022574 238s demand_price -0.001638 238s demand_income 0.001448 238s supply_(Intercept) -0.042512 238s supply_price 0.000079 238s supply_farmPrice 0.000200 238s supply_trend 0.001448 238s > print( round( vcov( fitwls3e, modified.regMat = TRUE ), digits = 6 ) ) 238s C1 C2 C3 C4 C5 C6 238s C1 48.62814 -0.506597 0.022574 -0.6627 0.001239 0.003123 238s C2 -0.50660 0.006662 -0.001638 0.0481 -0.000090 -0.000227 238s C3 0.02257 -0.001638 0.001448 -0.0425 0.000079 0.000200 238s C4 -0.66271 0.048082 -0.042512 102.5112 -0.801390 -0.224299 238s C5 0.00124 -0.000090 0.000079 -0.8014 0.007381 0.000645 238s C6 0.00312 -0.000227 0.000200 -0.2243 0.000645 0.001632 238s > print( round( vcov( fitwls3e$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s (Intercept) 48.6281 -0.50660 0.02257 238s price -0.5066 0.00666 -0.00164 238s income 0.0226 -0.00164 0.00145 238s > 238s > print( round( vcov( fitwls4 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 36.5710 -0.321554 -0.043279 238s demand_price -0.3216 0.004201 -0.001011 238s demand_income -0.0433 -0.001011 0.001481 238s supply_(Intercept) 35.8467 -0.431417 0.074877 238s supply_price -0.3216 0.004201 -0.001011 238s supply_farmPrice -0.0334 0.000226 0.000111 238s supply_trend -0.0433 -0.001011 0.001481 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) 35.8467 -0.321554 -0.033436 238s demand_price -0.4314 0.004201 0.000226 238s demand_income 0.0749 -0.001011 0.000111 238s supply_(Intercept) 63.5001 -0.431417 -0.215648 238s supply_price -0.4314 0.004201 0.000226 238s supply_farmPrice -0.2156 0.000226 0.001986 238s supply_trend 0.0749 -0.001011 0.000111 238s supply_trend 238s demand_(Intercept) -0.043279 238s demand_price -0.001011 238s demand_income 0.001481 238s supply_(Intercept) 0.074877 238s supply_price -0.001011 238s supply_farmPrice 0.000111 238s supply_trend 0.001481 238s > print( round( vcov( fitwls4$eq[[ 2 ]] ), digits = 6 ) ) 238s (Intercept) price farmPrice trend 238s (Intercept) 63.5001 -0.431417 -0.215648 0.074877 238s price -0.4314 0.004201 0.000226 -0.001011 238s farmPrice -0.2156 0.000226 0.001986 0.000111 238s trend 0.0749 -0.001011 0.000111 0.001481 238s > 238s > print( round( vcov( fitwls5 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 36.5710 -0.321554 -0.043279 238s demand_price -0.3216 0.004201 -0.001011 238s demand_income -0.0433 -0.001011 0.001481 238s supply_(Intercept) 35.8467 -0.431417 0.074877 238s supply_price -0.3216 0.004201 -0.001011 238s supply_farmPrice -0.0334 0.000226 0.000111 238s supply_trend -0.0433 -0.001011 0.001481 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) 35.8467 -0.321554 -0.033436 238s demand_price -0.4314 0.004201 0.000226 238s demand_income 0.0749 -0.001011 0.000111 238s supply_(Intercept) 63.5001 -0.431417 -0.215648 238s supply_price -0.4314 0.004201 0.000226 238s supply_farmPrice -0.2156 0.000226 0.001986 238s supply_trend 0.0749 -0.001011 0.000111 238s supply_trend 238s demand_(Intercept) -0.043279 238s demand_price -0.001011 238s demand_income 0.001481 238s supply_(Intercept) 0.074877 238s supply_price -0.001011 238s supply_farmPrice 0.000111 238s supply_trend 0.001481 238s > print( round( vcov( fitwls5, modified.regMat = TRUE ), digits = 6 ) ) 238s C1 C2 C3 C4 C5 C6 238s C1 36.5710 -0.321554 -0.043279 35.8467 -0.321554 -0.033436 238s C2 -0.3216 0.004201 -0.001011 -0.4314 0.004201 0.000226 238s C3 -0.0433 -0.001011 0.001481 0.0749 -0.001011 0.000111 238s C4 35.8467 -0.431417 0.074877 63.5001 -0.431417 -0.215648 238s C5 -0.3216 0.004201 -0.001011 -0.4314 0.004201 0.000226 238s C6 -0.0334 0.000226 0.000111 -0.2156 0.000226 0.001986 238s > print( round( vcov( fitwls5$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s (Intercept) 36.5710 -0.32155 -0.04328 238s price -0.3216 0.00420 -0.00101 238s income -0.0433 -0.00101 0.00148 238s > 238s > print( round( vcov( fitwlsi1 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 56.5408 -0.59480 0.03216 238s demand_price -0.5948 0.00822 -0.00233 238s demand_income 0.0322 -0.00233 0.00206 238s supply_(Intercept) 0.0000 0.00000 0.00000 238s supply_price 0.0000 0.00000 0.00000 238s supply_farmPrice 0.0000 0.00000 0.00000 238s supply_trend 0.0000 0.00000 0.00000 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) 0.000 0.000000 0.000000 238s demand_price 0.000 0.000000 0.000000 238s demand_income 0.000 0.000000 0.000000 238s supply_(Intercept) 131.398 -0.987500 -0.304361 238s supply_price -0.988 0.009003 0.000844 238s supply_farmPrice -0.304 0.000844 0.002133 238s supply_trend -0.279 0.000522 0.001316 238s supply_trend 238s demand_(Intercept) 0.000000 238s demand_price 0.000000 238s demand_income 0.000000 238s supply_(Intercept) -0.279183 238s supply_price 0.000522 238s supply_farmPrice 0.001316 238s supply_trend 0.009510 238s > print( round( vcov( fitwlsi1$eq[[ 2 ]] ), digits = 6 ) ) 238s (Intercept) price farmPrice trend 238s (Intercept) 131.398 -0.987500 -0.304361 -0.279183 238s price -0.988 0.009003 0.000844 0.000522 238s farmPrice -0.304 0.000844 0.002133 0.001316 238s trend -0.279 0.000522 0.001316 0.009510 238s > 238s > print( round( vcov( fitwlsi2e ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 48.32515 -0.503487 0.022480 238s demand_price -0.50349 0.006624 -0.001631 238s demand_income 0.02248 -0.001631 0.001442 238s supply_(Intercept) -0.65995 0.047882 -0.042335 238s supply_price 0.00123 -0.000090 0.000079 238s supply_farmPrice 0.00311 -0.000226 0.000199 238s supply_trend 0.02248 -0.001631 0.001442 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) -0.6600 0.001234 0.003110 238s demand_price 0.0479 -0.000090 -0.000226 238s demand_income -0.0423 0.000079 0.000199 238s supply_(Intercept) 103.0226 -0.805456 -0.225388 238s supply_price -0.8055 0.007418 0.000649 238s supply_farmPrice -0.2254 0.000649 0.001640 238s supply_trend -0.0423 0.000079 0.000199 238s supply_trend 238s demand_(Intercept) 0.022480 238s demand_price -0.001631 238s demand_income 0.001442 238s supply_(Intercept) -0.042335 238s supply_price 0.000079 238s supply_farmPrice 0.000199 238s supply_trend 0.001442 238s > print( round( vcov( fitwlsi2e$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s (Intercept) 48.3251 -0.50349 0.02248 238s price -0.5035 0.00662 -0.00163 238s income 0.0225 -0.00163 0.00144 238s > 238s > print( round( vcov( fitwlsi3 ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 56.81857 -0.592263 0.026724 238s demand_price -0.59226 0.007812 -0.001939 238s demand_income 0.02672 -0.001939 0.001714 238s supply_(Intercept) -0.78454 0.056921 -0.050327 238s supply_price 0.00147 -0.000106 0.000094 238s supply_farmPrice 0.00370 -0.000268 0.000237 238s supply_trend 0.02672 -0.001939 0.001714 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) -0.7845 0.001467 0.003697 238s demand_price 0.0569 -0.000106 -0.000268 238s demand_income -0.0503 0.000094 0.000237 238s supply_(Intercept) 128.7924 -1.007391 -0.281572 238s supply_price -1.0074 0.009279 0.000811 238s supply_farmPrice -0.2816 0.000811 0.002049 238s supply_trend -0.0503 0.000094 0.000237 238s supply_trend 238s demand_(Intercept) 0.026724 238s demand_price -0.001939 238s demand_income 0.001714 238s supply_(Intercept) -0.050327 238s supply_price 0.000094 238s supply_farmPrice 0.000237 238s supply_trend 0.001714 238s > print( round( vcov( fitwlsi3, modified.regMat = TRUE ), digits = 6 ) ) 238s C1 C2 C3 C4 C5 C6 238s C1 56.81857 -0.592263 0.026724 -0.7845 0.001467 0.003697 238s C2 -0.59226 0.007812 -0.001939 0.0569 -0.000106 -0.000268 238s C3 0.02672 -0.001939 0.001714 -0.0503 0.000094 0.000237 238s C4 -0.78454 0.056921 -0.050327 128.7924 -1.007391 -0.281572 238s C5 0.00147 -0.000106 0.000094 -1.0074 0.009279 0.000811 238s C6 0.00370 -0.000268 0.000237 -0.2816 0.000811 0.002049 238s > print( round( vcov( fitwlsi3$eq[[ 2 ]] ), digits = 6 ) ) 238s (Intercept) price farmPrice trend 238s (Intercept) 128.7924 -1.007391 -0.281572 -0.050327 238s price -1.0074 0.009279 0.000811 0.000094 238s farmPrice -0.2816 0.000811 0.002049 0.000237 238s trend -0.0503 0.000094 0.000237 0.001714 238s > 238s > print( round( vcov( fitwlsi4e ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 30.4377 -0.265752 -0.037918 238s demand_price -0.2658 0.003463 -0.000827 238s demand_income -0.0379 -0.000827 0.001237 238s supply_(Intercept) 29.6762 -0.355820 0.060620 238s supply_price -0.2658 0.003463 -0.000827 238s supply_farmPrice -0.0279 0.000187 0.000094 238s supply_trend -0.0379 -0.000827 0.001237 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) 29.6762 -0.265752 -0.027921 238s demand_price -0.3558 0.003463 0.000187 238s demand_income 0.0606 -0.000827 0.000094 238s supply_(Intercept) 52.0044 -0.355820 -0.173988 238s supply_price -0.3558 0.003463 0.000187 238s supply_farmPrice -0.1740 0.000187 0.001596 238s supply_trend 0.0606 -0.000827 0.000094 238s supply_trend 238s demand_(Intercept) -0.037918 238s demand_price -0.000827 238s demand_income 0.001237 238s supply_(Intercept) 0.060620 238s supply_price -0.000827 238s supply_farmPrice 0.000094 238s supply_trend 0.001237 238s > print( round( vcov( fitwlsi4e$eq[[ 1 ]] ), digits = 6 ) ) 238s (Intercept) price income 238s (Intercept) 30.4377 -0.265752 -0.037918 238s price -0.2658 0.003463 -0.000827 238s income -0.0379 -0.000827 0.001237 238s > 238s > print( round( vcov( fitwlsi5e ), digits = 6 ) ) 238s demand_(Intercept) demand_price demand_income 238s demand_(Intercept) 30.4377 -0.265752 -0.037918 238s demand_price -0.2658 0.003463 -0.000827 238s demand_income -0.0379 -0.000827 0.001237 238s supply_(Intercept) 29.6762 -0.355820 0.060620 238s supply_price -0.2658 0.003463 -0.000827 238s supply_farmPrice -0.0279 0.000187 0.000094 238s supply_trend -0.0379 -0.000827 0.001237 238s supply_(Intercept) supply_price supply_farmPrice 238s demand_(Intercept) 29.6762 -0.265752 -0.027921 238s demand_price -0.3558 0.003463 0.000187 238s demand_income 0.0606 -0.000827 0.000094 238s supply_(Intercept) 52.0044 -0.355820 -0.173988 238s supply_price -0.3558 0.003463 0.000187 238s supply_farmPrice -0.1740 0.000187 0.001596 238s supply_trend 0.0606 -0.000827 0.000094 238s supply_trend 238s demand_(Intercept) -0.037918 238s demand_price -0.000827 238s demand_income 0.001237 238s supply_(Intercept) 0.060620 238s supply_price -0.000827 238s supply_farmPrice 0.000094 238s supply_trend 0.001237 238s > print( round( vcov( fitwlsi5e, modified.regMat = TRUE ), digits = 6 ) ) 238s C1 C2 C3 C4 C5 C6 238s C1 30.4377 -0.265752 -0.037918 29.6762 -0.265752 -0.027921 238s C2 -0.2658 0.003463 -0.000827 -0.3558 0.003463 0.000187 238s C3 -0.0379 -0.000827 0.001237 0.0606 -0.000827 0.000094 238s C4 29.6762 -0.355820 0.060620 52.0044 -0.355820 -0.173988 238s C5 -0.2658 0.003463 -0.000827 -0.3558 0.003463 0.000187 238s C6 -0.0279 0.000187 0.000094 -0.1740 0.000187 0.001596 238s > print( round( vcov( fitwlsi5e$eq[[ 2 ]] ), digits = 6 ) ) 238s (Intercept) price farmPrice trend 238s (Intercept) 52.0044 -0.355820 -0.173988 0.060620 238s price -0.3558 0.003463 0.000187 -0.000827 238s farmPrice -0.1740 0.000187 0.001596 0.000094 238s trend 0.0606 -0.000827 0.000094 0.001237 238s > 238s > 238s > ## *********** confidence intervals of coefficients ************* 238s > print( confint( fitwls1 ) ) 238s 2.5 % 97.5 % 238s demand_(Intercept) 84.031 115.760 238s demand_price -0.508 -0.125 238s demand_income 0.239 0.430 238s supply_(Intercept) 33.975 82.576 238s supply_price -0.041 0.362 238s supply_farmPrice 0.150 0.346 238s supply_trend 0.042 0.455 238s > print( confint( fitwls1$eq[[ 2 ]], level = 0.9 ) ) 238s 5 % 95 % 238s (Intercept) 38.263 78.288 238s price -0.005 0.326 238s farmPrice 0.167 0.329 238s trend 0.078 0.419 238s > 238s > print( confint( fitwls2e, level = 0.9 ) ) 238s 5 % 95 % 238s demand_(Intercept) 85.474 113.818 238s demand_price -0.464 -0.132 238s demand_income 0.241 0.396 238s supply_(Intercept) 35.634 76.786 238s supply_price -0.010 0.339 238s supply_farmPrice 0.176 0.340 238s supply_trend 0.241 0.396 238s > print( confint( fitwls2e$eq[[ 1 ]], level = 0.99 ) ) 238s 0.5 % 99.5 % 238s (Intercept) 80.620 118.672 238s price -0.521 -0.076 238s income 0.215 0.422 238s > 238s > print( confint( fitwls3, level = 0.99 ) ) 238s 0.5 % 99.5 % 238s demand_(Intercept) 84.286 115.030 238s demand_price -0.479 -0.119 238s demand_income 0.235 0.404 238s supply_(Intercept) 33.190 79.186 238s supply_price -0.031 0.359 238s supply_farmPrice 0.166 0.350 238s supply_trend 0.235 0.404 238s > print( confint( fitwls3$eq[[ 2 ]], level = 0.5 ) ) 238s 25 % 75 % 238s (Intercept) 48.472 63.903 238s price 0.099 0.230 238s farmPrice 0.227 0.289 238s trend 0.291 0.348 238s > 238s > print( confint( fitwls4e, level = 0.5 ) ) 238s 25 % 75 % 238s demand_(Intercept) 89.763 112.189 238s demand_price -0.436 -0.197 238s demand_income 0.252 0.395 238s supply_(Intercept) 39.328 68.598 238s supply_price 0.064 0.303 238s supply_farmPrice 0.179 0.341 238s supply_trend 0.252 0.395 238s > print( confint( fitwls4e$eq[[ 1 ]], level = 0.25 ) ) 238s 37.5 % 62.5 % 238s (Intercept) 99.202 102.750 238s price -0.335 -0.297 238s income 0.312 0.335 238s > 238s > print( confint( fitwls5, level = 0.25 ) ) 238s 37.5 % 62.5 % 238s demand_(Intercept) 88.637 113.191 238s demand_price -0.448 -0.184 238s demand_income 0.246 0.402 238s supply_(Intercept) 37.764 70.119 238s supply_price 0.052 0.316 238s supply_farmPrice 0.170 0.351 238s supply_trend 0.246 0.402 238s > print( confint( fitwls5$eq[[ 2 ]], level = 0.975 ) ) 238s 1.3 % 98.8 % 238s (Intercept) 35.279 72.604 238s price 0.032 0.336 238s farmPrice 0.156 0.365 238s trend 0.234 0.414 238s > 238s > print( confint( fitwlsi1e, level = 0.975, useDfSys = TRUE ) ) 238s 1.3 % 98.8 % 238s demand_(Intercept) 85.791 114.000 238s demand_price -0.486 -0.146 238s demand_income 0.249 0.420 238s supply_(Intercept) 37.416 79.135 238s supply_price -0.012 0.333 238s supply_farmPrice 0.164 0.332 238s supply_trend 0.071 0.426 238s > print( confint( fitwlsi1e$eq[[ 1 ]], level = 0.999, useDfSys = TRUE ) ) 238s 0.1 % 100 % 238s (Intercept) 74.863 124.928 238s price -0.618 -0.014 238s income 0.183 0.486 238s > 238s > print( confint( fitwlsi2, level = 0.999 ) ) 238s 0.1 % 100 % 238s demand_(Intercept) 84.342 114.979 238s demand_price -0.479 -0.120 238s demand_income 0.235 0.404 238s supply_(Intercept) 33.120 79.246 238s supply_price -0.031 0.360 238s supply_farmPrice 0.166 0.350 238s supply_trend 0.235 0.404 238s > print( confint( fitwlsi2$eq[[ 2 ]], level = 0.1 ) ) 238s 45 % 55 % 238s (Intercept) 54.746 57.620 238s price 0.152 0.176 238s farmPrice 0.252 0.264 238s trend 0.314 0.325 238s > 238s > print( confint( fitwlsi3e, level = 0.1 ) ) 238s 45 % 55 % 238s demand_(Intercept) 85.521 113.776 238s demand_price -0.464 -0.133 238s demand_income 0.242 0.396 238s supply_(Intercept) 35.579 76.833 238s supply_price -0.011 0.339 238s supply_farmPrice 0.176 0.340 238s supply_trend 0.242 0.396 238s > print( confint( fitwlsi3e$eq[[ 1 ]], level = 0.01 ) ) 238s 49.5 % 50.5 % 238s (Intercept) 99.561 99.736 238s price -0.299 -0.297 238s income 0.318 0.319 238s > 238s > print( confint( fitwlsi4, level = 0.01 ) ) 238s 49.5 % 50.5 % 238s demand_(Intercept) 88.642 113.164 238s demand_price -0.447 -0.184 238s demand_income 0.246 0.402 238s supply_(Intercept) 37.754 70.122 238s supply_price 0.053 0.316 238s supply_farmPrice 0.170 0.351 238s supply_trend 0.246 0.402 238s > print( confint( fitwlsi4$eq[[ 2 ]], level = 0.33 ) ) 238s 33.5 % 66.5 % 238s (Intercept) 50.512 57.364 238s price 0.156 0.212 238s farmPrice 0.241 0.279 238s trend 0.307 0.340 238s > 238s > print( confint( fitwlsi5e, level = 0.33 ) ) 238s 33.5 % 66.5 % 238s demand_(Intercept) 89.766 112.166 238s demand_price -0.435 -0.197 238s demand_income 0.252 0.395 238s supply_(Intercept) 39.320 68.599 238s supply_price 0.065 0.303 238s supply_farmPrice 0.179 0.341 238s supply_trend 0.252 0.395 238s > print( confint( fitwlsi5e$eq[[ 1 ]] ) ) 238s 2.5 % 97.5 % 238s (Intercept) 89.766 112.166 238s price -0.435 -0.197 238s income 0.252 0.395 238s > 238s > 238s > ## *********** fitted values ************* 238s > print( fitted( fitwls1 ) ) 238s demand supply 238s 1 97.4 98.9 238s 2 99.6 100.1 238s 3 99.5 100.2 238s 4 99.7 100.4 238s 5 102.3 102.7 238s 6 102.1 102.6 238s 7 102.5 102.4 238s 8 102.8 104.3 238s 9 101.7 102.9 238s 10 100.8 100.4 238s 11 95.6 96.0 238s 12 94.4 94.1 238s 13 95.7 95.6 238s 14 99.0 97.8 238s 15 104.3 102.6 238s 16 103.9 104.1 238s 17 104.8 103.8 238s 18 101.9 102.4 238s 19 103.5 102.1 238s 20 106.5 104.5 238s > print( fitted( fitwls1$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 98.9 100.1 100.2 100.4 102.7 102.6 102.4 104.3 102.9 100.4 96.0 94.1 95.6 238s 14 15 16 17 18 19 20 238s 97.8 102.6 104.1 103.8 102.4 102.1 104.5 238s > 238s > print( fitted( fitwls2e ) ) 238s demand supply 238s 1 97.6 98.3 238s 2 99.7 99.5 238s 3 99.6 99.7 238s 4 99.8 99.9 238s 5 102.2 102.5 238s 6 102.0 102.4 238s 7 102.4 102.3 238s 8 102.8 104.3 238s 9 101.7 102.9 238s 10 100.8 100.3 238s 11 95.8 95.9 238s 12 94.7 93.9 238s 13 95.9 95.5 238s 14 99.1 97.9 238s 15 104.1 103.0 238s 16 103.8 104.6 238s 17 104.6 104.3 238s 18 101.9 102.9 238s 19 103.4 102.7 238s 20 106.3 105.2 238s > print( fitted( fitwls2e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 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 238s 14 15 16 17 18 19 20 238s 99.1 104.1 103.8 104.6 101.9 103.4 106.3 238s > 238s > print( fitted( fitwls3 ) ) 238s demand supply 238s 1 97.6 98.3 238s 2 99.6 99.5 238s 3 99.6 99.7 238s 4 99.8 99.9 238s 5 102.2 102.5 238s 6 102.0 102.4 238s 7 102.4 102.3 238s 8 102.8 104.3 238s 9 101.7 102.9 238s 10 100.8 100.3 238s 11 95.8 95.9 238s 12 94.7 93.9 238s 13 95.9 95.5 238s 14 99.1 97.9 238s 15 104.1 103.0 238s 16 103.8 104.6 238s 17 104.6 104.3 238s 18 101.9 102.9 238s 19 103.4 102.7 238s 20 106.3 105.2 238s > print( fitted( fitwls3$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 98.3 99.5 99.7 99.9 102.5 102.4 102.3 104.3 102.9 100.3 95.9 93.9 95.5 238s 14 15 16 17 18 19 20 238s 97.9 103.0 104.6 104.3 102.9 102.7 105.2 238s > 238s > print( fitted( fitwls4e ) ) 238s demand supply 238s 1 97.5 98.2 238s 2 99.6 99.6 238s 3 99.5 99.7 238s 4 99.7 100.0 238s 5 102.3 102.4 238s 6 102.0 102.4 238s 7 102.4 102.3 238s 8 102.7 104.4 238s 9 101.7 102.9 238s 10 100.9 100.2 238s 11 95.8 95.7 238s 12 94.6 93.9 238s 13 95.8 95.5 238s 14 99.1 97.8 238s 15 104.2 102.9 238s 16 103.8 104.6 238s 17 104.8 104.1 238s 18 101.9 103.0 238s 19 103.3 102.8 238s 20 106.2 105.5 238s > print( fitted( fitwls4e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 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 238s 14 15 16 17 18 19 20 238s 99.1 104.2 103.8 104.8 101.9 103.3 106.2 238s > 238s > print( fitted( fitwls5 ) ) 238s demand supply 238s 1 97.5 98.2 238s 2 99.6 99.6 238s 3 99.5 99.7 238s 4 99.7 100.0 238s 5 102.3 102.4 238s 6 102.0 102.3 238s 7 102.4 102.3 238s 8 102.7 104.4 238s 9 101.7 102.9 238s 10 100.9 100.2 238s 11 95.8 95.7 238s 12 94.6 93.9 238s 13 95.8 95.5 238s 14 99.1 97.8 238s 15 104.2 102.9 238s 16 103.8 104.6 238s 17 104.8 104.1 238s 18 101.9 103.0 238s 19 103.3 102.8 238s 20 106.2 105.5 238s > print( fitted( fitwls5$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 98.2 99.6 99.7 100.0 102.4 102.3 102.3 104.4 102.9 100.2 95.7 93.9 95.5 238s 14 15 16 17 18 19 20 238s 97.8 102.9 104.6 104.1 103.0 102.8 105.5 238s > 238s > print( fitted( fitwlsi1e ) ) 238s demand supply 238s 1 97.4 98.9 238s 2 99.6 100.1 238s 3 99.5 100.2 238s 4 99.7 100.4 238s 5 102.3 102.7 238s 6 102.1 102.6 238s 7 102.5 102.4 238s 8 102.8 104.3 238s 9 101.7 102.9 238s 10 100.8 100.4 238s 11 95.6 96.0 238s 12 94.4 94.1 238s 13 95.7 95.6 238s 14 99.0 97.8 238s 15 104.3 102.6 238s 16 103.9 104.1 238s 17 104.8 103.8 238s 18 101.9 102.4 238s 19 103.5 102.1 238s 20 106.5 104.5 238s > print( fitted( fitwlsi1e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 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 238s 14 15 16 17 18 19 20 238s 99.0 104.3 103.9 104.8 101.9 103.5 106.5 238s > 238s > print( fitted( fitwlsi2 ) ) 238s demand supply 238s 1 97.6 98.3 238s 2 99.6 99.5 238s 3 99.6 99.7 238s 4 99.8 99.9 238s 5 102.2 102.5 238s 6 102.0 102.4 238s 7 102.4 102.3 238s 8 102.8 104.3 238s 9 101.7 102.9 238s 10 100.8 100.3 238s 11 95.8 95.9 238s 12 94.7 93.9 238s 13 95.9 95.5 238s 14 99.1 97.9 238s 15 104.1 103.0 238s 16 103.8 104.6 238s 17 104.6 104.3 238s 18 101.9 102.9 238s 19 103.4 102.7 238s 20 106.3 105.2 238s > print( fitted( fitwlsi2$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 98.3 99.5 99.7 99.9 102.5 102.4 102.3 104.3 102.9 100.3 95.9 93.9 95.5 238s 14 15 16 17 18 19 20 238s 97.9 103.0 104.6 104.3 102.9 102.7 105.2 238s > 238s > print( fitted( fitwlsi3e ) ) 238s demand supply 238s 1 97.6 98.3 238s 2 99.7 99.5 238s 3 99.6 99.7 238s 4 99.8 99.9 238s 5 102.2 102.5 238s 6 102.0 102.4 238s 7 102.4 102.3 238s 8 102.8 104.3 238s 9 101.7 102.9 238s 10 100.8 100.3 238s 11 95.8 95.9 238s 12 94.7 93.9 238s 13 95.9 95.5 238s 14 99.1 97.9 238s 15 104.1 103.0 238s 16 103.8 104.6 238s 17 104.6 104.3 238s 18 101.9 102.9 238s 19 103.4 102.7 238s 20 106.3 105.2 238s > print( fitted( fitwlsi3e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 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 238s 14 15 16 17 18 19 20 238s 99.1 104.1 103.8 104.6 101.9 103.4 106.3 238s > 238s > print( fitted( fitwlsi4 ) ) 238s demand supply 238s 1 97.5 98.2 238s 2 99.6 99.6 238s 3 99.5 99.7 238s 4 99.7 100.0 238s 5 102.3 102.4 238s 6 102.0 102.3 238s 7 102.4 102.3 238s 8 102.7 104.4 238s 9 101.7 102.9 238s 10 100.9 100.2 238s 11 95.8 95.7 238s 12 94.6 93.9 238s 13 95.8 95.5 238s 14 99.1 97.8 238s 15 104.2 102.9 238s 16 103.8 104.6 238s 17 104.8 104.1 238s 18 101.9 103.0 238s 19 103.3 102.8 238s 20 106.2 105.5 238s > print( fitted( fitwlsi4$eq[[ 2 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 98.2 99.6 99.7 100.0 102.4 102.3 102.3 104.4 102.9 100.2 95.7 93.9 95.5 238s 14 15 16 17 18 19 20 238s 97.8 102.9 104.6 104.1 103.0 102.8 105.5 238s > 238s > print( fitted( fitwlsi5e ) ) 238s demand supply 238s 1 97.5 98.2 238s 2 99.6 99.6 238s 3 99.5 99.7 238s 4 99.7 100.0 238s 5 102.3 102.4 238s 6 102.0 102.4 238s 7 102.4 102.3 238s 8 102.7 104.4 238s 9 101.7 102.9 238s 10 100.9 100.2 238s 11 95.8 95.7 238s 12 94.6 93.9 238s 13 95.8 95.5 238s 14 99.1 97.8 238s 15 104.2 102.9 238s 16 103.8 104.6 238s 17 104.8 104.1 238s 18 101.9 103.0 238s 19 103.3 102.8 238s 20 106.2 105.5 238s > print( fitted( fitwlsi5e$eq[[ 1 ]] ) ) 238s 1 2 3 4 5 6 7 8 9 10 11 12 13 238s 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 238s 14 15 16 17 18 19 20 238s 99.1 104.2 103.8 104.8 101.9 103.3 106.2 238s > 238s > 238s > ## *********** predicted values ************* 238s > predictData <- Kmenta 238s > predictData$consump <- NULL 238s > predictData$price <- Kmenta$price * 0.9 238s > predictData$income <- Kmenta$income * 1.1 238s > 238s > print( predict( fitwls1, se.fit = TRUE, interval = "prediction" ) ) 238s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 238s 1 97.4 0.643 93.1 101.7 98.9 1.056 238s 2 99.6 0.577 95.3 103.8 100.1 1.037 238s 3 99.5 0.545 95.3 103.8 100.2 0.939 238s 4 99.7 0.582 95.4 104.0 100.4 0.912 238s 5 102.3 0.502 98.1 106.5 102.7 0.895 238s 6 102.1 0.463 97.9 106.3 102.6 0.791 238s 7 102.5 0.484 98.3 106.7 102.4 0.719 238s 8 102.8 0.601 98.6 107.1 104.3 0.963 238s 9 101.7 0.527 97.5 105.9 102.9 0.788 238s 10 100.8 0.788 96.4 105.2 100.4 0.981 238s 11 95.6 0.946 91.0 100.1 96.0 1.185 238s 12 94.4 0.980 89.8 98.9 94.1 1.394 238s 13 95.7 0.880 91.2 100.1 95.6 1.244 238s 14 99.0 0.508 94.8 103.2 97.8 0.896 238s 15 104.3 0.758 99.9 108.7 102.6 0.874 238s 16 103.9 0.616 99.7 108.2 104.1 0.916 238s 17 104.8 1.273 99.9 109.7 103.8 1.605 238s 18 101.9 0.536 97.7 106.2 102.4 0.962 238s 19 103.5 0.680 99.2 107.8 102.1 1.098 238s 20 106.5 1.274 101.7 111.4 104.5 1.664 238s supply.lwr supply.upr 238s 1 93.4 104 238s 2 94.5 106 238s 3 94.7 106 238s 4 94.9 106 238s 5 97.3 108 238s 6 97.2 108 238s 7 97.1 108 238s 8 98.8 110 238s 9 97.6 108 238s 10 94.8 106 238s 11 90.3 102 238s 12 88.2 100 238s 13 89.9 101 238s 14 92.3 103 238s 15 97.2 108 238s 16 98.6 110 238s 17 97.7 110 238s 18 96.9 108 238s 19 96.5 108 238s 20 98.3 111 238s > print( predict( fitwls1$eq[[ 2 ]], se.fit = TRUE, interval = "prediction" ) ) 238s fit se.fit lwr upr 238s 1 98.9 1.056 93.4 104 238s 2 100.1 1.037 94.5 106 238s 3 100.2 0.939 94.7 106 238s 4 100.4 0.912 94.9 106 238s 5 102.7 0.895 97.3 108 238s 6 102.6 0.791 97.2 108 238s 7 102.4 0.719 97.1 108 238s 8 104.3 0.963 98.8 110 238s 9 102.9 0.788 97.6 108 238s 10 100.4 0.981 94.8 106 238s 11 96.0 1.185 90.3 102 238s 12 94.1 1.394 88.2 100 238s 13 95.6 1.244 89.9 101 238s 14 97.8 0.896 92.3 103 238s 15 102.6 0.874 97.2 108 238s 16 104.1 0.916 98.6 110 238s 17 103.8 1.605 97.7 110 238s 18 102.4 0.962 96.9 108 238s 19 102.1 1.098 96.5 108 238s 20 104.5 1.664 98.3 111 238s > 238s > print( predict( fitwls2e, se.pred = TRUE, interval = "confidence", 238s + level = 0.999, newdata = predictData ) ) 238s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 238s 1 103 2.12 100.2 106 96.6 2.65 238s 2 106 2.12 102.7 109 97.8 2.57 238s 3 106 2.13 102.6 109 98.0 2.58 238s 4 106 2.12 102.9 109 98.2 2.56 238s 5 108 2.35 103.5 113 100.9 2.72 238s 6 108 2.31 103.6 113 100.7 2.67 238s 7 109 2.30 104.2 113 100.6 2.62 238s 8 109 2.27 105.0 114 102.6 2.58 238s 9 108 2.36 102.8 112 101.4 2.74 238s 10 106 2.46 100.8 112 98.8 2.92 238s 11 101 2.28 96.7 105 94.4 2.98 238s 12 100 2.12 97.0 103 92.3 2.96 238s 13 102 2.05 99.3 104 93.8 2.81 238s 14 105 2.20 101.2 109 96.3 2.78 238s 15 110 2.53 104.4 116 101.4 2.78 238s 16 110 2.44 104.7 115 102.9 2.69 238s 17 110 2.81 102.9 118 102.9 3.14 238s 18 108 2.23 104.3 112 101.2 2.58 238s 19 110 2.30 105.6 115 100.9 2.57 238s 20 114 2.50 108.1 119 103.3 2.52 238s supply.lwr supply.upr 238s 1 92.9 100.3 238s 2 95.0 100.6 238s 3 95.1 100.9 238s 4 95.5 100.9 238s 5 96.6 105.1 238s 6 96.9 104.6 238s 7 97.2 104.0 238s 8 99.6 105.5 238s 9 96.9 105.9 238s 10 93.1 104.6 238s 11 88.2 100.5 238s 12 86.3 98.4 238s 13 88.8 98.9 238s 14 91.5 101.0 238s 15 96.7 106.2 238s 16 98.9 106.9 238s 17 95.8 110.0 238s 18 98.2 104.1 238s 19 98.1 103.8 238s 20 101.1 105.6 238s > print( predict( fitwls2e$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 238s + level = 0.999, newdata = predictData ) ) 238s fit se.pred lwr upr 238s 1 103 2.12 100.2 106 238s 2 106 2.12 102.7 109 238s 3 106 2.13 102.6 109 238s 4 106 2.12 102.9 109 238s 5 108 2.35 103.5 113 238s 6 108 2.31 103.6 113 238s 7 109 2.30 104.2 113 238s 8 109 2.27 105.0 114 238s 9 108 2.36 102.8 112 238s 10 106 2.46 100.8 112 238s 11 101 2.28 96.7 105 238s 12 100 2.12 97.0 103 238s 13 102 2.05 99.3 104 238s 14 105 2.20 101.2 109 238s 15 110 2.53 104.4 116 238s 16 110 2.44 104.7 115 238s 17 110 2.81 102.9 118 238s 18 108 2.23 104.3 112 238s 19 110 2.30 105.6 115 238s 20 114 2.50 108.1 119 238s > 238s > print( predict( fitwls3, se.pred = TRUE, interval = "prediction", 238s + level = 0.975 ) ) 238s demand.pred demand.se.pred demand.lwr demand.upr supply.pred supply.se.pred 238s 1 97.6 2.03 92.8 102.3 98.3 2.54 238s 2 99.6 2.02 94.9 104.4 99.5 2.56 238s 3 99.6 2.01 94.9 104.3 99.7 2.55 238s 4 99.8 2.02 95.0 104.5 99.9 2.56 238s 5 102.2 2.00 97.5 106.9 102.5 2.59 238s 6 102.0 1.99 97.3 106.7 102.4 2.56 238s 7 102.4 1.99 97.7 107.1 102.3 2.54 238s 8 102.8 2.03 98.0 107.5 104.3 2.63 238s 9 101.7 2.01 97.0 106.4 102.9 2.57 238s 10 100.8 2.09 95.9 105.7 100.3 2.64 238s 11 95.8 2.14 90.8 100.8 95.9 2.72 238s 12 94.7 2.14 89.6 99.7 93.9 2.82 238s 13 95.9 2.11 91.0 100.8 95.5 2.75 238s 14 99.1 2.00 94.4 103.8 97.9 2.61 238s 15 104.1 2.07 99.3 109.0 103.0 2.56 238s 16 103.8 2.03 99.0 108.5 104.6 2.55 238s 17 104.6 2.31 99.2 110.0 104.3 2.85 238s 18 101.9 2.01 97.2 106.6 102.9 2.55 238s 19 103.4 2.05 98.6 108.2 102.7 2.59 238s 20 106.3 2.31 100.9 111.7 105.2 2.84 238s supply.lwr supply.upr 238s 1 92.3 104 238s 2 93.5 106 238s 3 93.7 106 238s 4 93.9 106 238s 5 96.4 109 238s 6 96.4 108 238s 7 96.3 108 238s 8 98.1 110 238s 9 96.9 109 238s 10 94.1 107 238s 11 89.5 102 238s 12 87.3 101 238s 13 89.1 102 238s 14 91.8 104 238s 15 97.0 109 238s 16 98.6 111 238s 17 97.6 111 238s 18 96.9 109 238s 19 96.6 109 238s 20 98.6 112 238s > print( predict( fitwls3$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 238s + level = 0.975 ) ) 238s fit se.pred lwr upr 238s 1 98.3 2.54 92.3 104 238s 2 99.5 2.56 93.5 106 238s 3 99.7 2.55 93.7 106 238s 4 99.9 2.56 93.9 106 238s 5 102.5 2.59 96.4 109 238s 6 102.4 2.56 96.4 108 238s 7 102.3 2.54 96.3 108 238s 8 104.3 2.63 98.1 110 238s 9 102.9 2.57 96.9 109 238s 10 100.3 2.64 94.1 107 238s 11 95.9 2.72 89.5 102 238s 12 93.9 2.82 87.3 101 238s 13 95.5 2.75 89.1 102 238s 14 97.9 2.61 91.8 104 238s 15 103.0 2.56 97.0 109 238s 16 104.6 2.55 98.6 111 238s 17 104.3 2.85 97.6 111 238s 18 102.9 2.55 96.9 109 238s 19 102.7 2.59 96.6 109 238s 20 105.2 2.84 98.6 112 238s > 238s > print( predict( fitwls4e, se.fit = TRUE, interval = "confidence", 238s + level = 0.25 ) ) 238s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 238s 1 97.5 0.541 97.4 97.7 98.2 0.598 238s 2 99.6 0.471 99.4 99.7 99.6 0.679 238s 3 99.5 0.454 99.4 99.7 99.7 0.634 238s 4 99.7 0.475 99.5 99.8 100.0 0.643 238s 5 102.3 0.434 102.1 102.4 102.4 0.753 238s 6 102.0 0.418 101.9 102.2 102.4 0.680 238s 7 102.4 0.440 102.3 102.5 102.3 0.625 238s 8 102.7 0.537 102.5 102.9 104.4 0.799 238s 9 101.7 0.447 101.6 101.9 102.9 0.700 238s 10 100.9 0.628 100.7 101.1 100.2 0.716 238s 11 95.8 0.833 95.6 96.1 95.7 0.916 238s 12 94.6 0.807 94.4 94.9 93.9 1.226 238s 13 95.8 0.677 95.6 96.0 95.5 1.130 238s 14 99.1 0.459 98.9 99.2 97.8 0.796 238s 15 104.2 0.572 104.1 104.4 102.9 0.656 238s 16 103.8 0.509 103.7 104.0 104.6 0.644 238s 17 104.8 0.877 104.5 105.1 104.1 1.150 238s 18 101.9 0.478 101.7 102.0 103.0 0.575 238s 19 103.3 0.604 103.1 103.5 102.8 0.649 238s 20 106.2 1.102 105.8 106.6 105.5 0.875 238s supply.lwr supply.upr 238s 1 98.0 98.4 238s 2 99.4 99.8 238s 3 99.5 99.9 238s 4 99.8 100.2 238s 5 102.2 102.7 238s 6 102.1 102.6 238s 7 102.1 102.5 238s 8 104.1 104.6 238s 9 102.7 103.1 238s 10 99.9 100.4 238s 11 95.4 96.0 238s 12 93.5 94.3 238s 13 95.2 95.9 238s 14 97.6 98.1 238s 15 102.7 103.1 238s 16 104.4 104.8 238s 17 103.8 104.5 238s 18 102.8 103.2 238s 19 102.6 103.0 238s 20 105.2 105.8 238s > print( predict( fitwls4e$eq[[ 1 ]], se.fit = TRUE, interval = "confidence", 238s + level = 0.25 ) ) 238s fit se.fit lwr upr 238s 1 97.5 0.541 97.4 97.7 238s 2 99.6 0.471 99.4 99.7 238s 3 99.5 0.454 99.4 99.7 238s 4 99.7 0.475 99.5 99.8 238s 5 102.3 0.434 102.1 102.4 238s 6 102.0 0.418 101.9 102.2 238s 7 102.4 0.440 102.3 102.5 238s 8 102.7 0.537 102.5 102.9 238s 9 101.7 0.447 101.6 101.9 238s 10 100.9 0.628 100.7 101.1 238s 11 95.8 0.833 95.6 96.1 238s 12 94.6 0.807 94.4 94.9 238s 13 95.8 0.677 95.6 96.0 238s 14 99.1 0.459 98.9 99.2 238s 15 104.2 0.572 104.1 104.4 238s 16 103.8 0.509 103.7 104.0 238s 17 104.8 0.877 104.5 105.1 238s 18 101.9 0.478 101.7 102.0 238s 19 103.3 0.604 103.1 103.5 238s 20 106.2 1.102 105.8 106.6 238s > 238s > print( predict( fitwls5, se.fit = TRUE, se.pred = TRUE, 238s + interval = "prediction", level = 0.5, newdata = predictData ) ) 238s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 238s 1 104 0.749 2.07 102.1 105 96.4 238s 2 106 0.784 2.09 104.6 107 97.7 238s 3 106 0.793 2.09 104.5 107 97.8 238s 4 106 0.792 2.09 104.8 108 98.1 238s 5 109 1.136 2.24 107.1 110 100.6 238s 6 108 1.086 2.22 106.9 110 100.5 238s 7 109 1.097 2.22 107.4 110 100.4 238s 8 110 1.107 2.23 108.0 111 102.5 238s 9 108 1.126 2.24 106.4 109 101.1 238s 10 107 1.243 2.30 105.1 108 98.5 238s 11 101 1.066 2.21 99.7 103 94.0 238s 12 100 0.814 2.10 98.8 102 92.0 238s 13 102 0.617 2.03 100.4 103 93.7 238s 14 105 0.874 2.12 103.7 107 96.0 238s 15 111 1.377 2.37 109.0 112 101.2 238s 16 110 1.279 2.32 108.8 112 102.8 238s 17 111 1.656 2.55 108.9 112 102.5 238s 18 109 1.014 2.18 107.0 110 101.1 238s 19 110 1.180 2.27 108.7 112 100.9 238s 20 114 1.635 2.53 112.2 116 103.4 238s supply.se.fit supply.se.pred supply.lwr supply.upr 238s 1 0.799 2.58 94.6 98.1 238s 2 0.679 2.55 95.9 99.4 238s 3 0.692 2.55 96.1 99.6 238s 4 0.657 2.54 96.3 99.8 238s 5 1.051 2.67 98.8 102.5 238s 6 0.947 2.63 98.7 102.3 238s 7 0.845 2.59 98.7 102.2 238s 8 0.849 2.60 100.7 104.2 238s 9 1.100 2.69 99.3 103.0 238s 10 1.276 2.77 96.6 100.4 238s 11 1.422 2.84 92.1 95.9 238s 12 1.595 2.93 90.1 94.0 238s 13 1.401 2.82 91.7 95.6 238s 14 1.201 2.73 94.2 97.9 238s 15 1.169 2.72 99.3 103.0 238s 16 1.060 2.67 100.9 104.6 238s 17 1.727 3.00 100.5 104.6 238s 18 0.831 2.59 99.3 102.8 238s 19 0.834 2.59 99.1 102.6 238s 20 0.653 2.54 101.7 105.2 238s > print( predict( fitwls5$eq[[ 2 ]], se.fit = TRUE, se.pred = TRUE, 238s + interval = "prediction", level = 0.5, newdata = predictData ) ) 238s fit se.fit se.pred lwr upr 238s 1 96.4 0.799 2.58 94.6 98.1 238s 2 97.7 0.679 2.55 95.9 99.4 238s 3 97.8 0.692 2.55 96.1 99.6 238s 4 98.1 0.657 2.54 96.3 99.8 238s 5 100.6 1.051 2.67 98.8 102.5 238s 6 100.5 0.947 2.63 98.7 102.3 238s 7 100.4 0.845 2.59 98.7 102.2 238s 8 102.5 0.849 2.60 100.7 104.2 238s 9 101.1 1.100 2.69 99.3 103.0 238s 10 98.5 1.276 2.77 96.6 100.4 238s 11 94.0 1.422 2.84 92.1 95.9 238s 12 92.0 1.595 2.93 90.1 94.0 238s 13 93.7 1.401 2.82 91.7 95.6 238s 14 96.0 1.201 2.73 94.2 97.9 238s 15 101.2 1.169 2.72 99.3 103.0 238s 16 102.8 1.060 2.67 100.9 104.6 238s 17 102.5 1.727 3.00 100.5 104.6 238s 18 101.1 0.831 2.59 99.3 102.8 238s 19 100.9 0.834 2.59 99.1 102.6 238s 20 103.4 0.653 2.54 101.7 105.2 238s > 238s > print( predict( fitwlsi1e, se.fit = TRUE, se.pred = TRUE, 238s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 238s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 238s 1 97.4 0.593 2.02 95.8 99.0 98.9 238s 2 99.6 0.532 2.00 98.1 101.0 100.1 238s 3 99.5 0.502 1.99 98.2 100.9 100.2 238s 4 99.7 0.537 2.00 98.2 101.2 100.4 238s 5 102.3 0.463 1.98 101.0 103.6 102.7 238s 6 102.1 0.427 1.98 100.9 103.2 102.6 238s 7 102.5 0.446 1.98 101.2 103.7 102.4 238s 8 102.8 0.554 2.01 101.3 104.3 104.3 238s 9 101.7 0.486 1.99 100.4 103.0 102.9 238s 10 100.8 0.727 2.06 98.8 102.8 100.4 238s 11 95.6 0.872 2.12 93.2 98.0 96.0 238s 12 94.4 0.903 2.13 91.9 96.8 94.1 238s 13 95.7 0.811 2.09 93.4 97.9 95.6 238s 14 99.0 0.468 1.99 97.7 100.3 97.8 238s 15 104.3 0.699 2.05 102.4 106.2 102.6 238s 16 103.9 0.568 2.01 102.4 105.5 104.1 238s 17 104.8 1.174 2.26 101.6 108.0 103.8 238s 18 101.9 0.494 1.99 100.6 103.3 102.4 238s 19 103.5 0.627 2.03 101.8 105.2 102.1 238s 20 106.5 1.175 2.26 103.3 109.7 104.5 238s supply.se.fit supply.se.pred supply.lwr supply.upr 238s 1 0.945 2.58 96.3 101.5 238s 2 0.928 2.58 97.5 102.6 238s 3 0.839 2.55 97.9 102.5 238s 4 0.816 2.54 98.1 102.6 238s 5 0.800 2.53 100.5 104.9 238s 6 0.707 2.51 100.6 104.5 238s 7 0.643 2.49 100.7 104.2 238s 8 0.862 2.55 102.0 106.7 238s 9 0.705 2.51 101.0 104.9 238s 10 0.877 2.56 98.0 102.7 238s 11 1.060 2.63 93.1 98.9 238s 12 1.247 2.71 90.7 97.5 238s 13 1.113 2.65 92.6 98.6 238s 14 0.801 2.53 95.6 100.0 238s 15 0.782 2.53 100.5 104.8 238s 16 0.819 2.54 101.9 106.3 238s 17 1.436 2.80 99.9 107.7 238s 18 0.861 2.55 100.0 104.7 238s 19 0.982 2.60 99.4 104.8 238s 20 1.489 2.83 100.4 108.6 238s > print( predict( fitwlsi1e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 238s + interval = "confidence", level = 0.99, useDfSys = TRUE ) ) 238s fit se.fit se.pred lwr upr 238s 1 97.4 0.593 2.02 95.8 99.0 238s 2 99.6 0.532 2.00 98.1 101.0 238s 3 99.5 0.502 1.99 98.2 100.9 238s 4 99.7 0.537 2.00 98.2 101.2 238s 5 102.3 0.463 1.98 101.0 103.6 238s 6 102.1 0.427 1.98 100.9 103.2 238s 7 102.5 0.446 1.98 101.2 103.7 238s 8 102.8 0.554 2.01 101.3 104.3 238s 9 101.7 0.486 1.99 100.4 103.0 238s 10 100.8 0.727 2.06 98.8 102.8 238s 11 95.6 0.872 2.12 93.2 98.0 238s 12 94.4 0.903 2.13 91.9 96.8 238s 13 95.7 0.811 2.09 93.4 97.9 238s 14 99.0 0.468 1.99 97.7 100.3 238s 15 104.3 0.699 2.05 102.4 106.2 238s 16 103.9 0.568 2.01 102.4 105.5 238s 17 104.8 1.174 2.26 101.6 108.0 238s 18 101.9 0.494 1.99 100.6 103.3 238s 19 103.5 0.627 2.03 101.8 105.2 238s 20 106.5 1.175 2.26 103.3 109.7 238s > 238s > print( predict( fitwlsi2, se.fit = TRUE, interval = "prediction", 238s + level = 0.9, newdata = predictData ) ) 239s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 239s 1 103 0.937 99.7 107 96.6 1.151 239s 2 106 0.942 102.2 110 97.8 0.875 239s 3 106 0.966 102.1 109 98.0 0.909 239s 4 106 0.947 102.4 110 98.2 0.833 239s 5 108 1.448 104.3 112 100.9 1.327 239s 6 108 1.368 104.2 112 100.7 1.192 239s 7 109 1.352 104.7 113 100.6 1.052 239s 8 109 1.293 105.4 113 102.6 0.914 239s 9 108 1.459 103.5 112 101.4 1.400 239s 10 106 1.647 102.0 111 98.8 1.787 239s 11 101 1.300 97.0 105 94.4 1.911 239s 12 100 0.938 96.4 104 92.3 1.880 239s 13 102 0.722 98.2 105 93.8 1.565 239s 14 105 1.121 101.1 109 96.3 1.479 239s 15 110 1.769 105.8 115 101.4 1.481 239s 16 110 1.602 105.8 114 102.9 1.248 239s 17 110 2.210 105.3 115 102.9 2.201 239s 18 108 1.205 104.5 112 101.2 0.911 239s 19 110 1.353 106.1 114 100.9 0.877 239s 20 114 1.714 109.4 118 103.3 0.705 239s supply.lwr supply.upr 239s 1 92.0 101.2 239s 2 93.4 102.2 239s 3 93.6 102.4 239s 4 93.9 102.6 239s 5 96.2 105.6 239s 6 96.1 105.3 239s 7 96.1 105.1 239s 8 98.1 107.0 239s 9 96.6 106.1 239s 10 93.7 103.9 239s 11 89.1 99.6 239s 12 87.1 97.5 239s 13 88.9 98.8 239s 14 91.4 101.1 239s 15 96.6 106.3 239s 16 98.3 107.6 239s 17 97.4 108.5 239s 18 96.8 105.6 239s 19 96.5 105.3 239s 20 99.0 107.7 239s > print( predict( fitwlsi2$eq[[ 2 ]], se.fit = TRUE, interval = "prediction", 239s + level = 0.9, newdata = predictData ) ) 239s fit se.fit lwr upr 239s 1 96.6 1.151 92.0 101.2 239s 2 97.8 0.875 93.4 102.2 239s 3 98.0 0.909 93.6 102.4 239s 4 98.2 0.833 93.9 102.6 239s 5 100.9 1.327 96.2 105.6 239s 6 100.7 1.192 96.1 105.3 239s 7 100.6 1.052 96.1 105.1 239s 8 102.6 0.914 98.1 107.0 239s 9 101.4 1.400 96.6 106.1 239s 10 98.8 1.787 93.7 103.9 239s 11 94.4 1.911 89.1 99.6 239s 12 92.3 1.880 87.1 97.5 239s 13 93.8 1.565 88.9 98.8 239s 14 96.3 1.479 91.4 101.1 239s 15 101.4 1.481 96.6 106.3 239s 16 102.9 1.248 98.3 107.6 239s 17 102.9 2.201 97.4 108.5 239s 18 101.2 0.911 96.8 105.6 239s 19 100.9 0.877 96.5 105.3 239s 20 103.3 0.705 99.0 107.7 239s > 239s > print( predict( fitwlsi3e, interval = "prediction", level = 0.925 ) ) 239s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 239s 1 97.6 93.9 101.3 98.3 93.6 103 239s 2 99.7 96.0 103.3 99.5 94.9 104 239s 3 99.6 95.9 103.3 99.7 95.1 104 239s 4 99.8 96.1 103.5 99.9 95.3 105 239s 5 102.2 98.6 105.9 102.5 97.8 107 239s 6 102.0 98.4 105.7 102.4 97.7 107 239s 7 102.4 98.7 106.0 102.3 97.6 107 239s 8 102.8 99.1 106.5 104.3 99.5 109 239s 9 101.7 98.0 105.3 102.9 98.3 108 239s 10 100.8 97.0 104.6 100.3 95.5 105 239s 11 95.8 91.9 99.7 95.9 91.0 101 239s 12 94.7 90.8 98.6 93.9 88.9 99 239s 13 95.9 92.1 99.7 95.5 90.6 100 239s 14 99.1 95.4 102.7 97.9 93.2 103 239s 15 104.1 100.4 107.9 103.0 98.3 108 239s 16 103.8 100.1 107.5 104.6 99.9 109 239s 17 104.6 100.4 108.7 104.3 99.2 109 239s 18 101.9 98.2 105.6 102.9 98.2 108 239s 19 103.4 99.6 107.1 102.7 98.0 107 239s 20 106.3 102.2 110.4 105.2 100.1 110 239s > print( predict( fitwlsi3e$eq[[ 1 ]], interval = "prediction", level = 0.925 ) ) 239s fit lwr upr 239s 1 97.6 93.9 101.3 239s 2 99.7 96.0 103.3 239s 3 99.6 95.9 103.3 239s 4 99.8 96.1 103.5 239s 5 102.2 98.6 105.9 239s 6 102.0 98.4 105.7 239s 7 102.4 98.7 106.0 239s 8 102.8 99.1 106.5 239s 9 101.7 98.0 105.3 239s 10 100.8 97.0 104.6 239s 11 95.8 91.9 99.7 239s 12 94.7 90.8 98.6 239s 13 95.9 92.1 99.7 239s 14 99.1 95.4 102.7 239s 15 104.1 100.4 107.9 239s 16 103.8 100.1 107.5 239s 17 104.6 100.4 108.7 239s 18 101.9 98.2 105.6 239s 19 103.4 99.6 107.1 239s 20 106.3 102.2 110.4 239s > 239s > print( predict( fitwlsi4, interval = "confidence", newdata = predictData ) ) 239s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 239s 1 104 102.0 105 96.4 94.8 98.0 239s 2 106 104.4 108 97.7 96.3 99.0 239s 3 106 104.3 108 97.8 96.4 99.2 239s 4 106 104.6 108 98.1 96.7 99.4 239s 5 109 106.3 111 100.6 98.5 102.8 239s 6 108 106.2 111 100.5 98.6 102.4 239s 7 109 106.7 111 100.4 98.7 102.2 239s 8 110 107.3 112 102.5 100.7 104.2 239s 9 108 105.6 110 101.1 98.9 103.4 239s 10 107 104.1 109 98.5 95.9 101.1 239s 11 101 99.0 103 94.0 91.1 96.9 239s 12 100 98.6 102 92.0 88.8 95.3 239s 13 102 100.5 103 93.7 90.8 96.5 239s 14 105 103.3 107 96.0 93.6 98.5 239s 15 111 107.8 113 101.2 98.8 103.6 239s 16 110 107.8 113 102.8 100.6 104.9 239s 17 111 107.3 114 102.5 99.0 106.0 239s 18 109 106.5 111 101.1 99.4 102.8 239s 19 110 107.9 113 100.9 99.2 102.6 239s 20 114 110.6 117 103.4 102.1 104.7 239s > print( predict( fitwlsi4$eq[[ 2 ]], interval = "confidence", 239s + newdata = predictData ) ) 239s fit lwr upr 239s 1 96.4 94.8 98.0 239s 2 97.7 96.3 99.0 239s 3 97.8 96.4 99.2 239s 4 98.1 96.7 99.4 239s 5 100.6 98.5 102.8 239s 6 100.5 98.6 102.4 239s 7 100.4 98.7 102.2 239s 8 102.5 100.7 104.2 239s 9 101.1 98.9 103.4 239s 10 98.5 95.9 101.1 239s 11 94.0 91.1 96.9 239s 12 92.0 88.8 95.3 239s 13 93.7 90.8 96.5 239s 14 96.0 93.6 98.5 239s 15 101.2 98.8 103.6 239s 16 102.8 100.6 104.9 239s 17 102.5 99.0 106.0 239s 18 101.1 99.4 102.8 239s 19 100.9 99.2 102.6 239s 20 103.4 102.1 104.7 239s > 239s > print( predict( fitwlsi5e, se.fit = TRUE, se.pred = TRUE, 239s + interval = "prediction", level = 0.01 ) ) 239s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 239s 1 97.5 0.540 2.01 97.5 97.6 98.2 239s 2 99.6 0.470 1.99 99.6 99.6 99.6 239s 3 99.5 0.453 1.99 99.5 99.6 99.7 239s 4 99.7 0.474 1.99 99.7 99.7 100.0 239s 5 102.3 0.433 1.98 102.2 102.3 102.4 239s 6 102.0 0.417 1.98 102.0 102.1 102.4 239s 7 102.4 0.439 1.98 102.4 102.4 102.3 239s 8 102.7 0.536 2.01 102.7 102.7 104.4 239s 9 101.7 0.446 1.99 101.7 101.8 102.9 239s 10 100.9 0.627 2.03 100.9 100.9 100.2 239s 11 95.8 0.831 2.11 95.8 95.9 95.7 239s 12 94.6 0.806 2.10 94.6 94.6 93.9 239s 13 95.8 0.676 2.05 95.8 95.8 95.5 239s 14 99.1 0.458 1.99 99.0 99.1 97.8 239s 15 104.2 0.571 2.02 104.2 104.3 102.9 239s 16 103.8 0.508 2.00 103.8 103.9 104.6 239s 17 104.8 0.877 2.12 104.8 104.8 104.1 239s 18 101.9 0.477 1.99 101.8 101.9 103.0 239s 19 103.3 0.602 2.03 103.3 103.4 102.8 239s 20 106.2 1.100 2.23 106.2 106.2 105.5 239s supply.se.fit supply.se.pred supply.lwr supply.upr 239s 1 0.598 2.52 98.2 98.3 239s 2 0.680 2.54 99.5 99.6 239s 3 0.634 2.53 99.7 99.8 239s 4 0.644 2.54 100.0 100.0 239s 5 0.754 2.57 102.4 102.5 239s 6 0.681 2.55 102.3 102.4 239s 7 0.626 2.53 102.3 102.3 239s 8 0.800 2.58 104.4 104.4 239s 9 0.701 2.55 102.9 102.9 239s 10 0.716 2.55 100.1 100.2 239s 11 0.918 2.62 95.7 95.8 239s 12 1.229 2.74 93.8 93.9 239s 13 1.132 2.70 95.5 95.6 239s 14 0.797 2.58 97.8 97.9 239s 15 0.657 2.54 102.9 103.0 239s 16 0.645 2.54 104.5 104.6 239s 17 1.151 2.71 104.1 104.2 239s 18 0.575 2.52 103.0 103.0 239s 19 0.649 2.54 102.8 102.8 239s 20 0.875 2.60 105.5 105.5 239s > print( predict( fitwlsi5e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 239s + interval = "prediction", level = 0.01 ) ) 239s fit se.fit se.pred lwr upr 239s 1 97.5 0.540 2.01 97.5 97.6 239s 2 99.6 0.470 1.99 99.6 99.6 239s 3 99.5 0.453 1.99 99.5 99.6 239s 4 99.7 0.474 1.99 99.7 99.7 239s 5 102.3 0.433 1.98 102.2 102.3 239s 6 102.0 0.417 1.98 102.0 102.1 239s 7 102.4 0.439 1.98 102.4 102.4 239s 8 102.7 0.536 2.01 102.7 102.7 239s 9 101.7 0.446 1.99 101.7 101.8 239s 10 100.9 0.627 2.03 100.9 100.9 239s 11 95.8 0.831 2.11 95.8 95.9 239s 12 94.6 0.806 2.10 94.6 94.6 239s 13 95.8 0.676 2.05 95.8 95.8 239s 14 99.1 0.458 1.99 99.0 99.1 239s 15 104.2 0.571 2.02 104.2 104.3 239s 16 103.8 0.508 2.00 103.8 103.9 239s 17 104.8 0.877 2.12 104.8 104.8 239s 18 101.9 0.477 1.99 101.8 101.9 239s 19 103.3 0.602 2.03 103.3 103.4 239s 20 106.2 1.100 2.23 106.2 106.2 239s > 239s > # predict just one observation 239s > smallData <- data.frame( price = 130, income = 150, farmPrice = 120, 239s + trend = 25 ) 239s > 239s > print( predict( fitwls1, newdata = smallData ) ) 239s demand.pred supply.pred 239s 1 109 115 239s > print( predict( fitwls1$eq[[ 1 ]], newdata = smallData ) ) 239s fit 239s 1 109 239s > 239s > print( predict( fitwls2e, se.fit = TRUE, level = 0.9, 239s + newdata = smallData ) ) 239s demand.pred demand.se.fit supply.pred supply.se.fit 239s 1 109 2.23 116 3.03 239s > print( predict( fitwls2e$eq[[ 1 ]], se.pred = TRUE, level = 0.99, 239s + newdata = smallData ) ) 239s fit se.pred 239s 1 109 2.96 239s > 239s > print( predict( fitwls3, interval = "prediction", level = 0.975, 239s + newdata = smallData ) ) 239s demand.pred demand.lwr demand.upr supply.pred supply.lwr supply.upr 239s 1 109 101 116 116 107 126 239s > print( predict( fitwls3$eq[[ 1 ]], interval = "confidence", level = 0.8, 239s + newdata = smallData ) ) 239s fit lwr upr 239s 1 109 106 112 239s > 239s > print( predict( fitwls4e, se.fit = TRUE, interval = "confidence", 239s + level = 0.999, newdata = smallData ) ) 239s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 239s 1 108 2.02 101 116 117 2.02 239s supply.lwr supply.upr 239s 1 110 124 239s > print( predict( fitwls4e$eq[[ 2 ]], se.pred = TRUE, interval = "prediction", 239s + level = 0.75, newdata = smallData ) ) 239s fit se.pred lwr upr 239s 1 117 3.18 113 121 239s > 239s > print( predict( fitwls5, se.fit = TRUE, interval = "prediction", 239s + newdata = smallData ) ) 239s demand.pred demand.se.fit demand.lwr demand.upr supply.pred supply.se.fit 239s 1 108 2.2 102 114 117 2.23 239s supply.lwr supply.upr 239s 1 110 124 239s > print( predict( fitwls5$eq[[ 1 ]], se.pred = TRUE, interval = "confidence", 239s + newdata = smallData ) ) 239s fit se.pred lwr upr 239s 1 108 2.93 104 113 239s > 239s > print( predict( fitwlsi3e, se.fit = TRUE, se.pred = TRUE, 239s + interval = "prediction", level = 0.5, newdata = smallData ) ) 239s demand.pred demand.se.fit demand.se.pred demand.lwr demand.upr supply.pred 239s 1 109 2.23 2.95 107 111 116 239s supply.se.fit supply.se.pred supply.lwr supply.upr 239s 1 3.04 3.9 114 119 239s > print( predict( fitwlsi3e$eq[[ 1 ]], se.fit = TRUE, se.pred = TRUE, 239s + interval = "confidence", level = 0.25, newdata = smallData ) ) 239s fit se.fit se.pred lwr upr 239s 1 109 2.23 2.95 108 109 239s > 239s > 239s > ## ************ correlation of predicted values *************** 239s > print( correlation.systemfit( fitwls1, 2, 1 ) ) 239s [,1] 239s [1,] 0 239s [2,] 0 239s [3,] 0 239s [4,] 0 239s [5,] 0 239s [6,] 0 239s [7,] 0 239s [8,] 0 239s [9,] 0 239s [10,] 0 239s [11,] 0 239s [12,] 0 239s [13,] 0 239s [14,] 0 239s [15,] 0 239s [16,] 0 239s [17,] 0 239s [18,] 0 239s [19,] 0 239s [20,] 0 239s > 239s > print( correlation.systemfit( fitwls2e, 1, 2 ) ) 239s [,1] 239s [1,] 0.411525 239s [2,] 0.147624 239s [3,] 0.147711 239s [4,] 0.107654 239s [5,] -0.069284 239s [6,] -0.053039 239s [7,] -0.051551 239s [8,] -0.006153 239s [9,] -0.000333 239s [10,] -0.001262 239s [11,] 0.048574 239s [12,] 0.064996 239s [13,] 0.024618 239s [14,] -0.028485 239s [15,] 0.174980 239s [16,] 0.252722 239s [17,] 0.103392 239s [18,] 0.074219 239s [19,] 0.156545 239s [20,] 0.135438 239s > 239s > print( correlation.systemfit( fitwls3, 2, 1 ) ) 239s [,1] 239s [1,] 0.405901 239s [2,] 0.145364 239s [3,] 0.145375 239s [4,] 0.105835 239s [5,] -0.067958 239s [6,] -0.052026 239s [7,] -0.050543 239s [8,] -0.006031 239s [9,] -0.000326 239s [10,] -0.001237 239s [11,] 0.047534 239s [12,] 0.063493 239s [13,] 0.024060 239s [14,] -0.027910 239s [15,] 0.171580 239s [16,] 0.248212 239s [17,] 0.101409 239s [18,] 0.073084 239s [19,] 0.153950 239s [20,] 0.132944 239s > 239s > print( correlation.systemfit( fitwls4e, 1, 2 ) ) 239s [,1] 239s [1,] 0.38162 239s [2,] 0.29173 239s [3,] 0.25421 239s [4,] 0.28598 239s [5,] -0.02775 239s [6,] -0.04974 239s [7,] -0.05850 239s [8,] 0.09388 239s [9,] 0.09469 239s [10,] 0.43814 239s [11,] 0.10559 239s [12,] 0.00876 239s [13,] 0.04090 239s [14,] -0.03984 239s [15,] 0.40767 239s [16,] 0.24571 239s [17,] 0.64160 239s [18,] 0.24037 239s [19,] 0.34075 239s [20,] 0.54270 239s > 239s > print( correlation.systemfit( fitwls5, 2, 1 ) ) 239s [,1] 239s [1,] 0.3775 239s [2,] 0.2936 239s [3,] 0.2553 239s [4,] 0.2875 239s [5,] -0.0274 239s [6,] -0.0492 239s [7,] -0.0578 239s [8,] 0.0932 239s [9,] 0.0944 239s [10,] 0.4375 239s [11,] 0.1027 239s [12,] 0.0072 239s [13,] 0.0404 239s [14,] -0.0396 239s [15,] 0.4062 239s [16,] 0.2430 239s [17,] 0.6406 239s [18,] 0.2362 239s [19,] 0.3347 239s [20,] 0.5378 239s > 239s > print( correlation.systemfit( fitwlsi1e, 1, 2 ) ) 239s [,1] 239s [1,] 0 239s [2,] 0 239s [3,] 0 239s [4,] 0 239s [5,] 0 239s [6,] 0 239s [7,] 0 239s [8,] 0 239s [9,] 0 239s [10,] 0 239s [11,] 0 239s [12,] 0 239s [13,] 0 239s [14,] 0 239s [15,] 0 239s [16,] 0 239s [17,] 0 239s [18,] 0 239s [19,] 0 239s [20,] 0 239s > 239s > print( correlation.systemfit( fitwlsi2, 2, 1 ) ) 239s [,1] 239s [1,] 0.404696 239s [2,] 0.144881 239s [3,] 0.144877 239s [4,] 0.105448 239s [5,] -0.067678 239s [6,] -0.051812 239s [7,] -0.050330 239s [8,] -0.006005 239s [9,] -0.000325 239s [10,] -0.001232 239s [11,] 0.047315 239s [12,] 0.063179 239s [13,] 0.023943 239s [14,] -0.027789 239s [15,] 0.170862 239s [16,] 0.247256 239s [17,] 0.100990 239s [18,] 0.072842 239s [19,] 0.153398 239s [20,] 0.132415 239s > 239s > print( correlation.systemfit( fitwlsi3e, 1, 2 ) ) 239s [,1] 239s [1,] 0.410485 239s [2,] 0.147206 239s [3,] 0.147278 239s [4,] 0.107316 239s [5,] -0.069036 239s [6,] -0.052850 239s [7,] -0.051363 239s [8,] -0.006130 239s [9,] -0.000331 239s [10,] -0.001257 239s [11,] 0.048379 239s [12,] 0.064714 239s [13,] 0.024513 239s [14,] -0.028377 239s [15,] 0.174345 239s [16,] 0.251882 239s [17,] 0.103022 239s [18,] 0.074009 239s [19,] 0.156063 239s [20,] 0.134974 239s > 239s > print( correlation.systemfit( fitwlsi4, 2, 1 ) ) 239s [,1] 239s [1,] 0.37672 239s [2,] 0.29387 239s [3,] 0.25544 239s [4,] 0.28775 239s [5,] -0.02729 239s [6,] -0.04911 239s [7,] -0.05771 239s [8,] 0.09311 239s [9,] 0.09437 239s [10,] 0.43736 239s [11,] 0.10223 239s [12,] 0.00693 239s [13,] 0.04035 239s [14,] -0.03961 239s [15,] 0.40591 239s [16,] 0.24248 239s [17,] 0.64034 239s [18,] 0.23551 239s [19,] 0.33360 239s [20,] 0.53687 239s > 239s > print( correlation.systemfit( fitwlsi5e, 1, 2 ) ) 239s [,1] 239s [1,] 0.38098 239s [2,] 0.29204 239s [3,] 0.25439 239s [4,] 0.28624 239s [5,] -0.02769 239s [6,] -0.04966 239s [7,] -0.05840 239s [8,] 0.09378 239s [9,] 0.09465 239s [10,] 0.43805 239s [11,] 0.10513 239s [12,] 0.00851 239s [13,] 0.04083 239s [14,] -0.03981 239s [15,] 0.40746 239s [16,] 0.24528 239s [17,] 0.64146 239s [18,] 0.23972 239s [19,] 0.33979 239s [20,] 0.54192 239s > 239s > 239s > ## ************ Log-Likelihood values *************** 239s > print( logLik( fitwls1 ) ) 239s 'log Lik.' -67.8 (df=9) 239s > print( logLik( fitwls1, residCovDiag = TRUE ) ) 239s 'log Lik.' -83.6 (df=9) 239s > all.equal( logLik( fitwls1, residCovDiag = TRUE ), 239s + logLik( lmDemand ) + logLik( lmSupply ), 239s + check.attributes = FALSE ) 239s [1] TRUE 239s > 239s > print( logLik( fitwls2e ) ) 239s 'log Lik.' -61.5 (df=8) 239s > print( logLik( fitwls2e, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=8) 239s > 239s > print( logLik( fitwls3 ) ) 239s 'log Lik.' -61.4 (df=8) 239s > print( logLik( fitwls3, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=8) 239s > 239s > print( logLik( fitwls4e ) ) 239s 'log Lik.' -62.2 (df=7) 239s > print( logLik( fitwls4e, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=7) 239s > 239s > print( logLik( fitwls5 ) ) 239s 'log Lik.' -62.1 (df=7) 239s > print( logLik( fitwls5, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=7) 239s > 239s > print( logLik( fitwlsi1e ) ) 239s 'log Lik.' -67.8 (df=9) 239s > print( logLik( fitwlsi1e, residCovDiag = TRUE ) ) 239s 'log Lik.' -83.6 (df=9) 239s > 239s > print( logLik( fitwlsi2 ) ) 239s 'log Lik.' -61.4 (df=8) 239s > print( logLik( fitwlsi2, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=8) 239s > 239s > print( logLik( fitwlsi3e ) ) 239s 'log Lik.' -61.5 (df=8) 239s > print( logLik( fitwlsi3e, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=8) 239s > 239s > print( logLik( fitwlsi4 ) ) 239s 'log Lik.' -62.1 (df=7) 239s > print( logLik( fitwlsi4, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=7) 239s > 239s > print( logLik( fitwlsi5e ) ) 239s 'log Lik.' -62.2 (df=7) 239s > print( logLik( fitwlsi5e, residCovDiag = TRUE ) ) 239s 'log Lik.' -84 (df=7) 239s > 239s > 239s > ## ************** F tests **************** 239s > # testing first restriction 239s > print( linearHypothesis( fitwls1, restrm ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwls1 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.64 0.43 239s > linearHypothesis( fitwls1, restrict ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwls1 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.64 0.43 239s > 239s > print( linearHypothesis( fitwlsi1e, restrm ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1e 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.66 0.42 239s > linearHypothesis( fitwlsi1e, restrict ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1e 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.66 0.42 239s > 239s > # testing second restriction 239s > restrOnly2m <- matrix(0,1,7) 239s > restrOnly2q <- 0.5 239s > restrOnly2m[1,2] <- -1 239s > restrOnly2m[1,5] <- 1 239s > restrictOnly2 <- "- demand_price + supply_price = 0.5" 239s > # first restriction not imposed 239s > print( linearHypothesis( fitwls1e, restrOnly2m, restrOnly2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.03 0.86 239s > linearHypothesis( fitwls1e, restrictOnly2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.03 0.86 239s > 239s > print( linearHypothesis( fitwlsi1, restrOnly2m, restrOnly2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.03 0.86 239s > linearHypothesis( fitwlsi1, restrictOnly2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df F Pr(>F) 239s 1 34 239s 2 33 1 0.03 0.86 239s > 239s > # first restriction imposed 239s > print( linearHypothesis( fitwls2, restrOnly2m, restrOnly2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls2 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.78 239s > linearHypothesis( fitwls2, restrictOnly2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls2 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.78 239s > 239s > print( linearHypothesis( fitwls3, restrOnly2m, restrOnly2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls3 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.78 239s > linearHypothesis( fitwls3, restrictOnly2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls3 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.78 239s > 239s > print( linearHypothesis( fitwlsi2e, restrOnly2m, restrOnly2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi2e 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.77 239s > linearHypothesis( fitwlsi2e, restrictOnly2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi2e 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.77 239s > 239s > print( linearHypothesis( fitwlsi3e, restrOnly2m, restrOnly2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi3e 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.77 239s > linearHypothesis( fitwlsi3e, restrictOnly2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi3e 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 34 1 0.08 0.77 239s > 239s > # testing both of the restrictions 239s > print( linearHypothesis( fitwls1e, restr2m, restr2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 33 2 0.37 0.69 239s > linearHypothesis( fitwls1e, restrict2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 33 2 0.37 0.69 239s > 239s > print( linearHypothesis( fitwlsi1, restr2m, restr2q ) ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 33 2 0.36 0.7 239s > linearHypothesis( fitwlsi1, restrict2 ) 239s Linear hypothesis test (Theil's F test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df F Pr(>F) 239s 1 35 239s 2 33 2 0.36 0.7 239s > 239s > 239s > ## ************** Wald tests **************** 239s > # testing first restriction 239s > print( linearHypothesis( fitwls1, restrm, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwls1 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.64 0.42 239s > linearHypothesis( fitwls1, restrict, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwls1 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.64 0.42 239s > 239s > print( linearHypothesis( fitwlsi1e, restrm, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.8 0.37 239s > linearHypothesis( fitwlsi1e, restrict, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.8 0.37 239s > 239s > # testing second restriction 239s > # first restriction not imposed 239s > print( linearHypothesis( fitwls1e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.04 0.84 239s > linearHypothesis( fitwls1e, restrictOnly2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.04 0.84 239s > 239s > print( linearHypothesis( fitwlsi1, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.03 0.86 239s > linearHypothesis( fitwlsi1, restrictOnly2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 34 239s 2 33 1 0.03 0.86 239s > 239s > # first restriction imposed 239s > print( linearHypothesis( fitwls2, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls2 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.08 0.78 239s > linearHypothesis( fitwls2, restrictOnly2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls2 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.08 0.78 239s > 239s > print( linearHypothesis( fitwls3, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls3 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.08 0.78 239s > linearHypothesis( fitwls3, restrictOnly2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls3 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.08 0.78 239s > 239s > print( linearHypothesis( fitwlsi2e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi2e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.1 0.75 239s > linearHypothesis( fitwlsi2e, restrictOnly2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi2e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.1 0.75 239s > 239s > print( linearHypothesis( fitwlsi3e, restrOnly2m, restrOnly2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi3e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.1 0.75 239s > linearHypothesis( fitwlsi3e, restrictOnly2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi3e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 34 1 0.1 0.75 239s > 239s > # testing both of the restrictions 239s > print( linearHypothesis( fitwls1e, restr2m, restr2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 33 2 0.9 0.64 239s > linearHypothesis( fitwls1e, restrict2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwls1e 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 33 2 0.9 0.64 239s > 239s > print( linearHypothesis( fitwlsi1, restr2m, restr2q, test = "Chisq" ) ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 33 2 0.72 0.7 239s > linearHypothesis( fitwlsi1, restrict2, test = "Chisq" ) 239s Linear hypothesis test (Chi^2 statistic of a Wald test) 239s 239s Hypothesis: 239s demand_income - supply_trend = 0 239s - demand_price + supply_price = 0.5 239s 239s Model 1: restricted model 239s Model 2: fitwlsi1 239s 239s Res.Df Df Chisq Pr(>Chisq) 239s 1 35 239s 2 33 2 0.72 0.7 239s > 239s > 239s > ## ****************** model frame ************************** 239s > print( mf <- model.frame( fitwls1 ) ) 239s consump price income farmPrice trend 239s 1 98.5 100.3 87.4 98.0 1 239s 2 99.2 104.3 97.6 99.1 2 239s 3 102.2 103.4 96.7 99.1 3 239s 4 101.5 104.5 98.2 98.1 4 239s 5 104.2 98.0 99.8 110.8 5 239s 6 103.2 99.5 100.5 108.2 6 239s 7 104.0 101.1 103.2 105.6 7 239s 8 99.9 104.8 107.8 109.8 8 239s 9 100.3 96.4 96.6 108.7 9 239s 10 102.8 91.2 88.9 100.6 10 239s 11 95.4 93.1 75.1 81.0 11 239s 12 92.4 98.8 76.9 68.6 12 239s 13 94.5 102.9 84.6 70.9 13 239s 14 98.8 98.8 90.6 81.4 14 239s 15 105.8 95.1 103.1 102.3 15 239s 16 100.2 98.5 105.1 105.0 16 239s 17 103.5 86.5 96.4 110.5 17 239s 18 99.9 104.0 104.4 92.5 18 239s 19 105.2 105.8 110.7 89.3 19 239s 20 106.2 113.5 127.1 93.0 20 239s > print( mf1 <- model.frame( fitwls1$eq[[ 1 ]] ) ) 239s consump price income 239s 1 98.5 100.3 87.4 239s 2 99.2 104.3 97.6 239s 3 102.2 103.4 96.7 239s 4 101.5 104.5 98.2 239s 5 104.2 98.0 99.8 239s 6 103.2 99.5 100.5 239s 7 104.0 101.1 103.2 239s 8 99.9 104.8 107.8 239s 9 100.3 96.4 96.6 239s 10 102.8 91.2 88.9 239s 11 95.4 93.1 75.1 239s 12 92.4 98.8 76.9 239s 13 94.5 102.9 84.6 239s 14 98.8 98.8 90.6 239s 15 105.8 95.1 103.1 239s 16 100.2 98.5 105.1 239s 17 103.5 86.5 96.4 239s 18 99.9 104.0 104.4 239s 19 105.2 105.8 110.7 239s 20 106.2 113.5 127.1 239s > print( attributes( mf1 )$terms ) 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s > print( mf2 <- model.frame( fitwls1$eq[[ 2 ]] ) ) 239s consump price farmPrice trend 239s 1 98.5 100.3 98.0 1 239s 2 99.2 104.3 99.1 2 239s 3 102.2 103.4 99.1 3 239s 4 101.5 104.5 98.1 4 239s 5 104.2 98.0 110.8 5 239s 6 103.2 99.5 108.2 6 239s 7 104.0 101.1 105.6 7 239s 8 99.9 104.8 109.8 8 239s 9 100.3 96.4 108.7 9 239s 10 102.8 91.2 100.6 10 239s 11 95.4 93.1 81.0 11 239s 12 92.4 98.8 68.6 12 239s 13 94.5 102.9 70.9 13 239s 14 98.8 98.8 81.4 14 239s 15 105.8 95.1 102.3 15 239s 16 100.2 98.5 105.0 16 239s 17 103.5 86.5 110.5 17 239s 18 99.9 104.0 92.5 18 239s 19 105.2 105.8 89.3 19 239s 20 106.2 113.5 93.0 20 239s > print( attributes( mf2 )$terms ) 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s > 239s > print( all.equal( mf, model.frame( fitwls2e ) ) ) 239s [1] TRUE 239s > print( all.equal( mf1, model.frame( fitwls2e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwls3 ) ) ) 239s [1] TRUE 239s > print( all.equal( mf2, model.frame( fitwls3$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwls4e ) ) ) 239s [1] TRUE 239s > print( all.equal( mf1, model.frame( fitwls4e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwls5 ) ) ) 239s [1] TRUE 239s > print( all.equal( mf2, model.frame( fitwls5$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwlsi1e ) ) ) 239s [1] TRUE 239s > print( all.equal( mf1, model.frame( fitwlsi1e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwlsi2 ) ) ) 239s [1] TRUE 239s > print( all.equal( mf2, model.frame( fitwlsi2$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwlsi3e ) ) ) 239s [1] TRUE 239s > print( all.equal( mf1, model.frame( fitwlsi3e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwlsi4 ) ) ) 239s [1] TRUE 239s > print( all.equal( mf2, model.frame( fitwlsi4$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > print( all.equal( mf, model.frame( fitwlsi5e ) ) ) 239s [1] TRUE 239s > print( all.equal( mf1, model.frame( fitwlsi5e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > 239s > 239s > ## **************** model matrix ************************ 239s > # with x (returnModelMatrix) = TRUE 239s > print( !is.null( fitwls1e$eq[[ 1 ]]$x ) ) 239s [1] TRUE 239s > print( mm <- model.matrix( fitwlsi1e ) ) 239s demand_(Intercept) demand_price demand_income supply_(Intercept) 239s demand_1 1 100.3 87.4 0 239s demand_2 1 104.3 97.6 0 239s demand_3 1 103.4 96.7 0 239s demand_4 1 104.5 98.2 0 239s demand_5 1 98.0 99.8 0 239s demand_6 1 99.5 100.5 0 239s demand_7 1 101.1 103.2 0 239s demand_8 1 104.8 107.8 0 239s demand_9 1 96.4 96.6 0 239s demand_10 1 91.2 88.9 0 239s demand_11 1 93.1 75.1 0 239s demand_12 1 98.8 76.9 0 239s demand_13 1 102.9 84.6 0 239s demand_14 1 98.8 90.6 0 239s demand_15 1 95.1 103.1 0 239s demand_16 1 98.5 105.1 0 239s demand_17 1 86.5 96.4 0 239s demand_18 1 104.0 104.4 0 239s demand_19 1 105.8 110.7 0 239s demand_20 1 113.5 127.1 0 239s supply_1 0 0.0 0.0 1 239s supply_2 0 0.0 0.0 1 239s supply_3 0 0.0 0.0 1 239s supply_4 0 0.0 0.0 1 239s supply_5 0 0.0 0.0 1 239s supply_6 0 0.0 0.0 1 239s supply_7 0 0.0 0.0 1 239s supply_8 0 0.0 0.0 1 239s supply_9 0 0.0 0.0 1 239s supply_10 0 0.0 0.0 1 239s supply_11 0 0.0 0.0 1 239s supply_12 0 0.0 0.0 1 239s supply_13 0 0.0 0.0 1 239s supply_14 0 0.0 0.0 1 239s supply_15 0 0.0 0.0 1 239s supply_16 0 0.0 0.0 1 239s supply_17 0 0.0 0.0 1 239s supply_18 0 0.0 0.0 1 239s supply_19 0 0.0 0.0 1 239s supply_20 0 0.0 0.0 1 239s supply_price supply_farmPrice supply_trend 239s demand_1 0.0 0.0 0 239s demand_2 0.0 0.0 0 239s demand_3 0.0 0.0 0 239s demand_4 0.0 0.0 0 239s demand_5 0.0 0.0 0 239s demand_6 0.0 0.0 0 239s demand_7 0.0 0.0 0 239s demand_8 0.0 0.0 0 239s demand_9 0.0 0.0 0 239s demand_10 0.0 0.0 0 239s demand_11 0.0 0.0 0 239s demand_12 0.0 0.0 0 239s demand_13 0.0 0.0 0 239s demand_14 0.0 0.0 0 239s demand_15 0.0 0.0 0 239s demand_16 0.0 0.0 0 239s demand_17 0.0 0.0 0 239s demand_18 0.0 0.0 0 239s demand_19 0.0 0.0 0 239s demand_20 0.0 0.0 0 239s supply_1 100.3 98.0 1 239s supply_2 104.3 99.1 2 239s supply_3 103.4 99.1 3 239s supply_4 104.5 98.1 4 239s supply_5 98.0 110.8 5 239s supply_6 99.5 108.2 6 239s supply_7 101.1 105.6 7 239s supply_8 104.8 109.8 8 239s supply_9 96.4 108.7 9 239s supply_10 91.2 100.6 10 239s supply_11 93.1 81.0 11 239s supply_12 98.8 68.6 12 239s supply_13 102.9 70.9 13 239s supply_14 98.8 81.4 14 239s supply_15 95.1 102.3 15 239s supply_16 98.5 105.0 16 239s supply_17 86.5 110.5 17 239s supply_18 104.0 92.5 18 239s supply_19 105.8 89.3 19 239s supply_20 113.5 93.0 20 239s > print( mm1 <- model.matrix( fitwlsi1e$eq[[ 1 ]] ) ) 239s (Intercept) price income 239s 1 1 100.3 87.4 239s 2 1 104.3 97.6 239s 3 1 103.4 96.7 239s 4 1 104.5 98.2 239s 5 1 98.0 99.8 239s 6 1 99.5 100.5 239s 7 1 101.1 103.2 239s 8 1 104.8 107.8 239s 9 1 96.4 96.6 239s 10 1 91.2 88.9 239s 11 1 93.1 75.1 239s 12 1 98.8 76.9 239s 13 1 102.9 84.6 239s 14 1 98.8 90.6 239s 15 1 95.1 103.1 239s 16 1 98.5 105.1 239s 17 1 86.5 96.4 239s 18 1 104.0 104.4 239s 19 1 105.8 110.7 239s 20 1 113.5 127.1 239s attr(,"assign") 239s [1] 0 1 2 239s > print( mm2 <- model.matrix( fitwlsi1e$eq[[ 2 ]] ) ) 239s (Intercept) price farmPrice trend 239s 1 1 100.3 98.0 1 239s 2 1 104.3 99.1 2 239s 3 1 103.4 99.1 3 239s 4 1 104.5 98.1 4 239s 5 1 98.0 110.8 5 239s 6 1 99.5 108.2 6 239s 7 1 101.1 105.6 7 239s 8 1 104.8 109.8 8 239s 9 1 96.4 108.7 9 239s 10 1 91.2 100.6 10 239s 11 1 93.1 81.0 11 239s 12 1 98.8 68.6 12 239s 13 1 102.9 70.9 13 239s 14 1 98.8 81.4 14 239s 15 1 95.1 102.3 15 239s 16 1 98.5 105.0 16 239s 17 1 86.5 110.5 17 239s 18 1 104.0 92.5 18 239s 19 1 105.8 89.3 19 239s 20 1 113.5 93.0 20 239s attr(,"assign") 239s [1] 0 1 2 3 239s > 239s > # with x (returnModelMatrix) = FALSE 239s > print( all.equal( mm, model.matrix( fitwlsi1 ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwlsi1$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwlsi1$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > print( !is.null( fitwls1$eq[[ 1 ]]$x ) ) 239s [1] FALSE 239s > 239s > # with x (returnModelMatrix) = TRUE 239s > print( !is.null( fitwls2$eq[[ 1 ]]$x ) ) 239s [1] TRUE 239s > print( all.equal( mm, model.matrix( fitwls2 ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwls2$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwls2$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > # with x (returnModelMatrix) = FALSE 239s > print( all.equal( mm, model.matrix( fitwls2e ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwls2e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwls2e$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > print( !is.null( fitwls2e$eq[[ 1 ]]$x ) ) 239s [1] FALSE 239s > 239s > # with x (returnModelMatrix) = TRUE 239s > print( !is.null( fitwlsi3$eq[[ 1 ]]$x ) ) 239s [1] TRUE 239s > print( all.equal( mm, model.matrix( fitwlsi3 ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwlsi3$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwlsi3$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > # with x (returnModelMatrix) = FALSE 239s > print( all.equal( mm, model.matrix( fitwlsi3e ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwlsi3e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwlsi3e$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > print( !is.null( fitwlsi3e$eq[[ 1 ]]$x ) ) 239s [1] FALSE 239s > 239s > # with x (returnModelMatrix) = TRUE 239s > print( !is.null( fitwls4e$eq[[ 1 ]]$x ) ) 239s [1] TRUE 239s > print( all.equal( mm, model.matrix( fitwls4e ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwls4e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwls4e$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > # with x (returnModelMatrix) = FALSE 239s > print( all.equal( mm, model.matrix( fitwls4Sym ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwls4Sym$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwls4Sym$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > print( !is.null( fitwls4Sym$eq[[ 1 ]]$x ) ) 239s [1] FALSE 239s > 239s > # with x (returnModelMatrix) = TRUE 239s > print( !is.null( fitwls5$eq[[ 1 ]]$x ) ) 239s [1] TRUE 239s > print( all.equal( mm, model.matrix( fitwls5 ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwls5$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwls5$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > 239s > # with x (returnModelMatrix) = FALSE 239s > print( all.equal( mm, model.matrix( fitwls5e ) ) ) 239s [1] TRUE 239s > print( all.equal( mm1, model.matrix( fitwls5e$eq[[ 1 ]] ) ) ) 239s [1] TRUE 239s > print( all.equal( mm2, model.matrix( fitwls5e$eq[[ 2 ]] ) ) ) 239s [1] TRUE 239s > print( !is.null( fitwls5e$eq[[ 1 ]]$x ) ) 239s [1] FALSE 239s > 239s > 239s > ## **************** formulas ************************ 239s > formula( fitwls1 ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwls1$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s > 239s > formula( fitwls2e ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwls2e$eq[[ 1 ]] ) 239s consump ~ price + income 239s > 239s > formula( fitwls3 ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwls3$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s > 239s > formula( fitwls4e ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwls4e$eq[[ 1 ]] ) 239s consump ~ price + income 239s > 239s > formula( fitwls5 ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwls5$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s > 239s > formula( fitwlsi1e ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwlsi1e$eq[[ 1 ]] ) 239s consump ~ price + income 239s > 239s > formula( fitwlsi2 ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwlsi2$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s > 239s > formula( fitwlsi3e ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwlsi3e$eq[[ 1 ]] ) 239s consump ~ price + income 239s > 239s > formula( fitwlsi4 ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwlsi4$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s > 239s > formula( fitwlsi5e ) 239s $demand 239s consump ~ price + income 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s 239s > formula( fitwlsi5e$eq[[ 1 ]] ) 239s consump ~ price + income 239s > 239s > 239s > ## **************** model terms ******************* 239s > terms( fitwls1 ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwls1$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s > 239s > terms( fitwls2e ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwls2e$eq[[ 1 ]] ) 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s > 239s > terms( fitwls3 ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwls3$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s > 239s > terms( fitwls4e ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwls4e$eq[[ 1 ]] ) 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s > 239s > terms( fitwls5 ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwls5$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s > 239s > terms( fitwlsi1e ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwlsi1e$eq[[ 1 ]] ) 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s > 239s > terms( fitwlsi2 ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwlsi2$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s > 239s > terms( fitwlsi3e ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwlsi3e$eq[[ 1 ]] ) 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s > 239s > terms( fitwlsi4 ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwlsi4$eq[[ 2 ]] ) 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s > 239s > terms( fitwlsi5e ) 239s $demand 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s 239s $supply 239s consump ~ price + farmPrice + trend 239s attr(,"variables") 239s list(consump, price, farmPrice, trend) 239s attr(,"factors") 239s price farmPrice trend 239s consump 0 0 0 239s price 1 0 0 239s farmPrice 0 1 0 239s trend 0 0 1 239s attr(,"term.labels") 239s [1] "price" "farmPrice" "trend" 239s attr(,"order") 239s [1] 1 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, farmPrice, trend) 239s attr(,"dataClasses") 239s consump price farmPrice trend 239s "numeric" "numeric" "numeric" "numeric" 239s 239s > terms( fitwlsi5e$eq[[ 1 ]] ) 239s consump ~ price + income 239s attr(,"variables") 239s list(consump, price, income) 239s attr(,"factors") 239s price income 239s consump 0 0 239s price 1 0 239s income 0 1 239s attr(,"term.labels") 239s [1] "price" "income" 239s attr(,"order") 239s [1] 1 1 239s attr(,"intercept") 239s [1] 1 239s attr(,"response") 239s [1] 1 239s attr(,".Environment") 239s 239s attr(,"predvars") 239s list(consump, price, income) 239s attr(,"dataClasses") 239s consump price income 239s "numeric" "numeric" "numeric" 239s > 239s > 239s > ## **************** estfun ************************ 239s > library( "sandwich" ) 239s > 239s > estfun( fitwls1 ) 239s demand_(Intercept) demand_price demand_income supply_(Intercept) 239s demand_1 0.2884 28.93 25.21 0.0000 239s demand_2 -0.1048 -10.92 -10.22 0.0000 239s demand_3 0.7045 72.87 68.13 0.0000 239s demand_4 0.4838 50.56 47.51 0.0000 239s demand_5 0.5222 51.18 52.12 0.0000 239s demand_6 0.3153 31.36 31.68 0.0000 239s demand_7 0.4108 41.51 42.39 0.0000 239s demand_8 -0.7872 -82.47 -84.86 0.0000 239s demand_9 -0.3665 -35.35 -35.41 0.0000 239s demand_10 0.5451 49.73 48.46 0.0000 239s demand_11 -0.0400 -3.72 -3.00 0.0000 239s demand_12 -0.5246 -51.83 -40.34 0.0000 239s demand_13 -0.3009 -30.96 -25.45 0.0000 239s demand_14 -0.0591 -5.83 -5.35 0.0000 239s demand_15 0.3991 37.96 41.14 0.0000 239s demand_16 -0.9934 -97.80 -104.40 0.0000 239s demand_17 -0.3417 -29.56 -32.94 0.0000 239s demand_18 -0.5375 -55.90 -56.11 0.0000 239s demand_19 0.4665 49.34 51.65 0.0000 239s demand_20 -0.0802 -9.10 -10.20 0.0000 239s supply_1 0.0000 0.00 0.00 -0.0768 239s supply_2 0.0000 0.00 0.00 -0.1548 239s supply_3 0.0000 0.00 0.00 0.3397 239s supply_4 0.0000 0.00 0.00 0.1961 239s supply_5 0.0000 0.00 0.00 0.2617 239s supply_6 0.0000 0.00 0.00 0.1176 239s supply_7 0.0000 0.00 0.00 0.2712 239s supply_8 0.0000 0.00 0.00 -0.7619 239s supply_9 0.0000 0.00 0.00 -0.4493 239s supply_10 0.0000 0.00 0.00 0.4269 239s supply_11 0.0000 0.00 0.00 -0.1034 239s supply_12 0.0000 0.00 0.00 -0.2934 239s supply_13 0.0000 0.00 0.00 -0.1839 239s supply_14 0.0000 0.00 0.00 0.1677 239s supply_15 0.0000 0.00 0.00 0.5461 239s supply_16 0.0000 0.00 0.00 -0.6683 239s supply_17 0.0000 0.00 0.00 -0.0458 239s supply_18 0.0000 0.00 0.00 -0.4234 239s supply_19 0.0000 0.00 0.00 0.5376 239s supply_20 0.0000 0.00 0.00 0.2963 239s supply_price supply_farmPrice supply_trend 239s demand_1 0.00 0.00 0.0000 239s demand_2 0.00 0.00 0.0000 239s demand_3 0.00 0.00 0.0000 239s demand_4 0.00 0.00 0.0000 239s demand_5 0.00 0.00 0.0000 239s demand_6 0.00 0.00 0.0000 239s demand_7 0.00 0.00 0.0000 239s demand_8 0.00 0.00 0.0000 239s demand_9 0.00 0.00 0.0000 239s demand_10 0.00 0.00 0.0000 239s demand_11 0.00 0.00 0.0000 239s demand_12 0.00 0.00 0.0000 239s demand_13 0.00 0.00 0.0000 239s demand_14 0.00 0.00 0.0000 239s demand_15 0.00 0.00 0.0000 239s demand_16 0.00 0.00 0.0000 239s demand_17 0.00 0.00 0.0000 239s demand_18 0.00 0.00 0.0000 239s demand_19 0.00 0.00 0.0000 239s demand_20 0.00 0.00 0.0000 239s supply_1 -7.70 -7.53 -0.0768 239s supply_2 -16.14 -15.34 -0.3096 239s supply_3 35.14 33.67 1.0192 239s supply_4 20.49 19.24 0.7843 239s supply_5 25.65 29.00 1.3085 239s supply_6 11.70 12.73 0.7057 239s supply_7 27.41 28.64 1.8987 239s supply_8 -79.82 -83.66 -6.0955 239s supply_9 -43.33 -48.84 -4.0437 239s supply_10 38.95 42.95 4.2691 239s supply_11 -9.63 -8.38 -1.1377 239s supply_12 -28.99 -20.13 -3.5213 239s supply_13 -18.93 -13.04 -2.3913 239s supply_14 16.56 13.65 2.3480 239s supply_15 51.95 55.87 8.1920 239s supply_16 -65.79 -70.17 -10.6922 239s supply_17 -3.96 -5.06 -0.7779 239s supply_18 -44.04 -39.16 -7.6205 239s supply_19 56.86 48.01 10.2144 239s supply_20 33.63 27.56 5.9267 239s > round( colSums( estfun( fitwls1 ) ), digits = 7 ) 239s demand_(Intercept) demand_price demand_income supply_(Intercept) 239s 0 0 0 0 239s supply_price supply_farmPrice supply_trend 239s 0 0 0 239s > 239s > estfun( fitwlsi1e ) 239s demand_(Intercept) demand_price demand_income supply_(Intercept) 239s demand_1 0.3393 34.04 29.66 0.0000 239s demand_2 -0.1232 -12.85 -12.03 0.0000 239s demand_3 0.8289 85.73 80.15 0.0000 239s demand_4 0.5692 59.49 55.90 0.0000 239s demand_5 0.6144 60.21 61.32 0.0000 239s demand_6 0.3709 36.89 37.28 0.0000 239s demand_7 0.4832 48.84 49.87 0.0000 239s demand_8 -0.9261 -97.03 -99.84 0.0000 239s demand_9 -0.4312 -41.59 -41.66 0.0000 239s demand_10 0.6413 58.51 57.01 0.0000 239s demand_11 -0.0470 -4.38 -3.53 0.0000 239s demand_12 -0.6172 -60.98 -47.46 0.0000 239s demand_13 -0.3540 -36.43 -29.95 0.0000 239s demand_14 -0.0695 -6.86 -6.29 0.0000 239s demand_15 0.4695 44.66 48.40 0.0000 239s demand_16 -1.1687 -115.06 -122.83 0.0000 239s demand_17 -0.4020 -34.78 -38.76 0.0000 239s demand_18 -0.6323 -65.77 -66.01 0.0000 239s demand_19 0.5489 58.05 60.76 0.0000 239s demand_20 -0.0944 -10.71 -12.00 0.0000 239s supply_1 0.0000 0.00 0.00 -0.0960 239s supply_2 0.0000 0.00 0.00 -0.1935 239s supply_3 0.0000 0.00 0.00 0.4247 239s supply_4 0.0000 0.00 0.00 0.2451 239s supply_5 0.0000 0.00 0.00 0.3271 239s supply_6 0.0000 0.00 0.00 0.1470 239s supply_7 0.0000 0.00 0.00 0.3390 239s supply_8 0.0000 0.00 0.00 -0.9524 239s supply_9 0.0000 0.00 0.00 -0.5616 239s supply_10 0.0000 0.00 0.00 0.5336 239s supply_11 0.0000 0.00 0.00 -0.1293 239s supply_12 0.0000 0.00 0.00 -0.3668 239s supply_13 0.0000 0.00 0.00 -0.2299 239s supply_14 0.0000 0.00 0.00 0.2096 239s supply_15 0.0000 0.00 0.00 0.6827 239s supply_16 0.0000 0.00 0.00 -0.8353 239s supply_17 0.0000 0.00 0.00 -0.0572 239s supply_18 0.0000 0.00 0.00 -0.5292 239s supply_19 0.0000 0.00 0.00 0.6720 239s supply_20 0.0000 0.00 0.00 0.3704 239s supply_price supply_farmPrice supply_trend 239s demand_1 0.00 0.00 0.000 239s demand_2 0.00 0.00 0.000 239s demand_3 0.00 0.00 0.000 239s demand_4 0.00 0.00 0.000 239s demand_5 0.00 0.00 0.000 239s demand_6 0.00 0.00 0.000 239s demand_7 0.00 0.00 0.000 239s demand_8 0.00 0.00 0.000 239s demand_9 0.00 0.00 0.000 239s demand_10 0.00 0.00 0.000 239s demand_11 0.00 0.00 0.000 239s demand_12 0.00 0.00 0.000 239s demand_13 0.00 0.00 0.000 239s demand_14 0.00 0.00 0.000 239s demand_15 0.00 0.00 0.000 239s demand_16 0.00 0.00 0.000 239s demand_17 0.00 0.00 0.000 239s demand_18 0.00 0.00 0.000 239s demand_19 0.00 0.00 0.000 239s demand_20 0.00 0.00 0.000 239s supply_1 -9.63 -9.41 -0.096 239s supply_2 -20.18 -19.18 -0.387 239s supply_3 43.92 42.08 1.274 239s supply_4 25.61 24.04 0.980 239s supply_5 32.06 36.25 1.636 239s supply_6 14.62 15.91 0.882 239s supply_7 34.27 35.80 2.373 239s supply_8 -99.78 -104.58 -7.619 239s supply_9 -54.17 -61.05 -5.055 239s supply_10 48.68 53.68 5.336 239s supply_11 -12.03 -10.47 -1.422 239s supply_12 -36.24 -25.16 -4.402 239s supply_13 -23.66 -16.30 -2.989 239s supply_14 20.70 17.06 2.935 239s supply_15 64.93 69.84 10.240 239s supply_16 -82.24 -87.71 -13.365 239s supply_17 -4.95 -6.32 -0.972 239s supply_18 -55.05 -48.95 -9.526 239s supply_19 71.08 60.01 12.768 239s supply_20 42.04 34.45 7.408 239s > round( colSums( estfun( fitwlsi1e ) ), digits = 7 ) 239s demand_(Intercept) demand_price demand_income supply_(Intercept) 239s 0 0 0 0 239s supply_price supply_farmPrice supply_trend 239s 0 0 0 239s > 239s > 239s > ## **************** bread ************************ 239s > bread( fitwls1 ) 239s demand_(Intercept) demand_price demand_income supply_(Intercept) 239s [1,] 2261.63 -23.7921 1.2865 0.0 239s [2,] -23.79 0.3289 -0.0933 0.0 239s [3,] 1.29 -0.0933 0.0825 0.0 239s [4,] 0.00 0.0000 0.0000 5255.9 239s [5,] 0.00 0.0000 0.0000 -39.5 239s [6,] 0.00 0.0000 0.0000 -12.2 239s [7,] 0.00 0.0000 0.0000 -11.2 239s supply_price supply_farmPrice supply_trend 239s [1,] 0.0000 0.0000 0.0000 239s [2,] 0.0000 0.0000 0.0000 239s [3,] 0.0000 0.0000 0.0000 239s [4,] -39.5000 -12.1744 -11.1673 239s [5,] 0.3601 0.0338 0.0209 239s [6,] 0.0338 0.0853 0.0526 239s [7,] 0.0209 0.0526 0.3804 239s > 239s > bread( fitwlsi1e ) 239s demand_(Intercept) demand_price demand_income supply_(Intercept) 239s [1,] 1922.39 -20.2232 1.0935 0.00 239s [2,] -20.22 0.2796 -0.0793 0.00 239s [3,] 1.09 -0.0793 0.0701 0.00 239s [4,] 0.00 0.0000 0.0000 4204.75 239s [5,] 0.00 0.0000 0.0000 -31.60 239s [6,] 0.00 0.0000 0.0000 -9.74 239s [7,] 0.00 0.0000 0.0000 -8.93 239s supply_price supply_farmPrice supply_trend 239s [1,] 0.0000 0.0000 0.0000 239s [2,] 0.0000 0.0000 0.0000 239s [3,] 0.0000 0.0000 0.0000 239s [4,] -31.6000 -9.7395 -8.9339 239s [5,] 0.2881 0.0270 0.0167 239s [6,] 0.0270 0.0683 0.0421 239s [7,] 0.0167 0.0421 0.3043 239s > 239s autopkgtest [20:26:20]: test run-unit-test: -----------------------] 240s run-unit-test PASS 240s autopkgtest [20:26:21]: test run-unit-test: - - - - - - - - - - results - - - - - - - - - - 241s autopkgtest [20:26:22]: test pkg-r-autopkgtest: preparing testbed 242s Reading package lists... 242s Building dependency tree... 242s Reading state information... 243s Starting pkgProblemResolver with broken count: 0 243s Starting 2 pkgProblemResolver with broken count: 0 243s Done 243s The following additional packages will be installed: 243s build-essential cpp cpp-13 cpp-13-aarch64-linux-gnu cpp-aarch64-linux-gnu 243s dctrl-tools g++ g++-13 g++-13-aarch64-linux-gnu g++-aarch64-linux-gnu gcc 243s gcc-13 gcc-13-aarch64-linux-gnu gcc-aarch64-linux-gnu gfortran gfortran-13 243s gfortran-13-aarch64-linux-gnu gfortran-aarch64-linux-gnu icu-devtools 243s libasan8 libatomic1 libblas-dev libbz2-dev libc-dev-bin libc6-dev libcc1-0 243s libcrypt-dev libgcc-13-dev libgfortran-13-dev libhwasan0 libicu-dev libisl23 243s libitm1 libjpeg-dev libjpeg-turbo8-dev libjpeg8-dev liblapack-dev liblsan0 243s liblzma-dev libmpc3 libncurses-dev libnsl-dev libpcre2-16-0 libpcre2-32-0 243s libpcre2-dev libpcre2-posix3 libpkgconf3 libpng-dev libreadline-dev 243s libstdc++-13-dev libtirpc-dev libtsan2 libubsan1 linux-libc-dev pkg-config 243s pkg-r-autopkgtest pkgconf pkgconf-bin r-base-dev r-cran-arm r-cran-coda 243s r-cran-mi r-cran-sem rpcsvc-proto zlib1g-dev 243s Suggested packages: 243s cpp-doc gcc-13-locales cpp-13-doc debtags gcc-13-doc gcc-multilib 243s manpages-dev autoconf automake libtool flex bison gdb gcc-doc 243s gdb-aarch64-linux-gnu gfortran-doc gfortran-13-doc libcoarrays-dev 243s liblapack-doc glibc-doc icu-doc liblzma-doc ncurses-doc readline-doc 243s libstdc++-13-doc texlive-base texlive-latex-base texlive-plain-generic 243s texlive-fonts-recommended texlive-fonts-extra texlive-extra-utils 243s texlive-latex-recommended texlive-latex-extra texinfo r-cran-sn 243s r-cran-polycor 243s Recommended packages: 243s bzip2-doc manpages manpages-dev libc-devtools libpng-tools r-cran-truncnorm 244s The following NEW packages will be installed: 244s autopkgtest-satdep build-essential cpp cpp-13 cpp-13-aarch64-linux-gnu 244s cpp-aarch64-linux-gnu dctrl-tools g++ g++-13 g++-13-aarch64-linux-gnu 244s g++-aarch64-linux-gnu gcc gcc-13 gcc-13-aarch64-linux-gnu 244s gcc-aarch64-linux-gnu gfortran gfortran-13 gfortran-13-aarch64-linux-gnu 244s gfortran-aarch64-linux-gnu icu-devtools libasan8 libatomic1 libblas-dev 244s libbz2-dev libc-dev-bin libc6-dev libcc1-0 libcrypt-dev libgcc-13-dev 244s libgfortran-13-dev libhwasan0 libicu-dev libisl23 libitm1 libjpeg-dev 244s libjpeg-turbo8-dev libjpeg8-dev liblapack-dev liblsan0 liblzma-dev libmpc3 244s libncurses-dev libnsl-dev libpcre2-16-0 libpcre2-32-0 libpcre2-dev 244s libpcre2-posix3 libpkgconf3 libpng-dev libreadline-dev libstdc++-13-dev 244s libtirpc-dev libtsan2 libubsan1 linux-libc-dev pkg-config pkg-r-autopkgtest 244s pkgconf pkgconf-bin r-base-dev r-cran-arm r-cran-coda r-cran-mi r-cran-sem 244s rpcsvc-proto zlib1g-dev 244s 0 upgraded, 66 newly installed, 0 to remove and 0 not upgraded. 244s Need to get 96.0 MB/96.0 MB of archives. 244s After this operation, 347 MB of additional disk space will be used. 244s Get:1 /tmp/autopkgtest.34lrrc/2-autopkgtest-satdep.deb autopkgtest-satdep arm64 0 [732 B] 244s Get:2 http://ftpmaster.internal/ubuntu noble/main arm64 libc-dev-bin arm64 2.39-0ubuntu2 [19.7 kB] 244s Get:3 http://ftpmaster.internal/ubuntu noble/main arm64 linux-libc-dev arm64 6.8.0-11.11 [1569 kB] 244s Get:4 http://ftpmaster.internal/ubuntu noble/main arm64 libcrypt-dev arm64 1:4.4.36-4 [136 kB] 244s Get:5 http://ftpmaster.internal/ubuntu noble/main arm64 libtirpc-dev arm64 1.3.4+ds-1build1 [232 kB] 244s Get:6 http://ftpmaster.internal/ubuntu noble/main arm64 libnsl-dev arm64 1.3.0-3 [71.9 kB] 244s Get:7 http://ftpmaster.internal/ubuntu noble/main arm64 rpcsvc-proto arm64 1.4.2-0ubuntu6 [65.4 kB] 244s Get:8 http://ftpmaster.internal/ubuntu noble/main arm64 libc6-dev arm64 2.39-0ubuntu2 [1596 kB] 244s Get:9 http://ftpmaster.internal/ubuntu noble/main arm64 libisl23 arm64 0.26-3 [713 kB] 244s Get:10 http://ftpmaster.internal/ubuntu noble/main arm64 libmpc3 arm64 1.3.1-1 [55.3 kB] 244s Get:11 http://ftpmaster.internal/ubuntu noble/main arm64 cpp-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [10.3 MB] 245s Get:12 http://ftpmaster.internal/ubuntu noble/main arm64 cpp-13 arm64 13.2.0-17ubuntu2 [1028 B] 245s Get:13 http://ftpmaster.internal/ubuntu noble/main arm64 cpp-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [5316 B] 245s Get:14 http://ftpmaster.internal/ubuntu noble/main arm64 cpp arm64 4:13.2.0-7ubuntu1 [22.4 kB] 245s Get:15 http://ftpmaster.internal/ubuntu noble/main arm64 libcc1-0 arm64 14-20240303-1ubuntu1 [44.7 kB] 245s Get:16 http://ftpmaster.internal/ubuntu noble/main arm64 libitm1 arm64 14-20240303-1ubuntu1 [27.7 kB] 245s Get:17 http://ftpmaster.internal/ubuntu noble/main arm64 libatomic1 arm64 14-20240303-1ubuntu1 [11.4 kB] 245s Get:18 http://ftpmaster.internal/ubuntu noble/main arm64 libasan8 arm64 14-20240303-1ubuntu1 [2919 kB] 245s Get:19 http://ftpmaster.internal/ubuntu noble/main arm64 liblsan0 arm64 14-20240303-1ubuntu1 [1282 kB] 245s Get:20 http://ftpmaster.internal/ubuntu noble/main arm64 libtsan2 arm64 14-20240303-1ubuntu1 [2687 kB] 245s Get:21 http://ftpmaster.internal/ubuntu noble/main arm64 libubsan1 arm64 14-20240303-1ubuntu1 [1151 kB] 245s Get:22 http://ftpmaster.internal/ubuntu noble/main arm64 libhwasan0 arm64 14-20240303-1ubuntu1 [1597 kB] 245s Get:23 http://ftpmaster.internal/ubuntu noble/main arm64 libgcc-13-dev arm64 13.2.0-17ubuntu2 [2464 kB] 245s Get:24 http://ftpmaster.internal/ubuntu noble/main arm64 gcc-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [20.1 MB] 245s Get:25 http://ftpmaster.internal/ubuntu noble/main arm64 gcc-13 arm64 13.2.0-17ubuntu2 [467 kB] 245s Get:26 http://ftpmaster.internal/ubuntu noble/main arm64 gcc-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [1198 B] 245s Get:27 http://ftpmaster.internal/ubuntu noble/main arm64 gcc arm64 4:13.2.0-7ubuntu1 [5018 B] 245s Get:28 http://ftpmaster.internal/ubuntu noble/main arm64 libstdc++-13-dev arm64 13.2.0-17ubuntu2 [2322 kB] 245s Get:29 http://ftpmaster.internal/ubuntu noble/main arm64 g++-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [11.7 MB] 246s Get:30 http://ftpmaster.internal/ubuntu noble/main arm64 g++-13 arm64 13.2.0-17ubuntu2 [14.4 kB] 246s Get:31 http://ftpmaster.internal/ubuntu noble/main arm64 g++-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [962 B] 246s Get:32 http://ftpmaster.internal/ubuntu noble/main arm64 g++ arm64 4:13.2.0-7ubuntu1 [1082 B] 246s Get:33 http://ftpmaster.internal/ubuntu noble/main arm64 build-essential arm64 12.10ubuntu1 [4932 B] 246s Get:34 http://ftpmaster.internal/ubuntu noble/main arm64 dctrl-tools arm64 2.24-3build2 [65.2 kB] 246s Get:35 http://ftpmaster.internal/ubuntu noble/main arm64 libgfortran-13-dev arm64 13.2.0-17ubuntu2 [478 kB] 246s Get:36 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran-13-aarch64-linux-gnu arm64 13.2.0-17ubuntu2 [10.8 MB] 246s Get:37 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran-13 arm64 13.2.0-17ubuntu2 [10.3 kB] 246s Get:38 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran-aarch64-linux-gnu arm64 4:13.2.0-7ubuntu1 [1022 B] 246s Get:39 http://ftpmaster.internal/ubuntu noble/main arm64 gfortran arm64 4:13.2.0-7ubuntu1 [1164 B] 246s Get:40 http://ftpmaster.internal/ubuntu noble/main arm64 icu-devtools arm64 74.2-1ubuntu1 [209 kB] 246s Get:41 http://ftpmaster.internal/ubuntu noble/main arm64 libblas-dev arm64 3.12.0-3 [111 kB] 246s Get:42 http://ftpmaster.internal/ubuntu noble/main arm64 libbz2-dev arm64 1.0.8-5ubuntu1 [35.8 kB] 246s Get:43 http://ftpmaster.internal/ubuntu noble/main arm64 libicu-dev arm64 74.2-1ubuntu1 [11.9 MB] 246s Get:44 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg-turbo8-dev arm64 2.1.5-2ubuntu1 [304 kB] 246s Get:45 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg8-dev arm64 8c-2ubuntu11 [1484 B] 246s Get:46 http://ftpmaster.internal/ubuntu noble/main arm64 libjpeg-dev arm64 8c-2ubuntu11 [1482 B] 246s Get:47 http://ftpmaster.internal/ubuntu noble/main arm64 liblapack-dev arm64 3.12.0-3 [4293 kB] 246s Get:48 http://ftpmaster.internal/ubuntu noble/main arm64 libncurses-dev arm64 6.4+20240113-1ubuntu1 [385 kB] 246s Get:49 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-16-0 arm64 10.42-4ubuntu1 [195 kB] 246s Get:50 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-32-0 arm64 10.42-4ubuntu1 [183 kB] 246s Get:51 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-posix3 arm64 10.42-4ubuntu1 [6654 B] 246s Get:52 http://ftpmaster.internal/ubuntu noble/main arm64 libpcre2-dev arm64 10.42-4ubuntu1 [679 kB] 246s Get:53 http://ftpmaster.internal/ubuntu noble/main arm64 libpkgconf3 arm64 1.8.1-2 [31.2 kB] 246s Get:54 http://ftpmaster.internal/ubuntu noble/main arm64 zlib1g-dev arm64 1:1.3.dfsg-3ubuntu1 [895 kB] 246s Get:55 http://ftpmaster.internal/ubuntu noble/main arm64 libpng-dev arm64 1.6.43-1 [266 kB] 246s Get:56 http://ftpmaster.internal/ubuntu noble/main arm64 libreadline-dev arm64 8.2-3 [177 kB] 246s Get:57 http://ftpmaster.internal/ubuntu noble/main arm64 pkgconf-bin arm64 1.8.1-2 [20.4 kB] 246s Get:58 http://ftpmaster.internal/ubuntu noble/main arm64 pkgconf arm64 1.8.1-2 [16.7 kB] 246s Get:59 http://ftpmaster.internal/ubuntu noble/main arm64 pkg-config arm64 1.8.1-2 [7170 B] 246s Get:60 http://ftpmaster.internal/ubuntu noble/main arm64 liblzma-dev arm64 5.4.5-0.3 [209 kB] 246s Get:61 http://ftpmaster.internal/ubuntu noble/universe arm64 r-base-dev all 4.3.2-1build1 [4336 B] 246s Get:62 http://ftpmaster.internal/ubuntu noble/universe arm64 pkg-r-autopkgtest all 20231212ubuntu1 [6448 B] 246s Get:63 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-coda all 0.19-4.1-1 [321 kB] 246s Get:64 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-arm all 1.13-1-1 [407 kB] 246s Get:65 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-mi all 1.1-1 [1840 kB] 247s Get:66 http://ftpmaster.internal/ubuntu noble/universe arm64 r-cran-sem arm64 3.1.15-1 [627 kB] 247s Fetched 96.0 MB in 3s (33.0 MB/s) 247s Selecting previously unselected package libc-dev-bin. 247s (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 ... 95539 files and directories currently installed.) 247s Preparing to unpack .../00-libc-dev-bin_2.39-0ubuntu2_arm64.deb ... 247s Unpacking libc-dev-bin (2.39-0ubuntu2) ... 247s Selecting previously unselected package linux-libc-dev:arm64. 247s Preparing to unpack .../01-linux-libc-dev_6.8.0-11.11_arm64.deb ... 247s Unpacking linux-libc-dev:arm64 (6.8.0-11.11) ... 247s Selecting previously unselected package libcrypt-dev:arm64. 247s Preparing to unpack .../02-libcrypt-dev_1%3a4.4.36-4_arm64.deb ... 247s Unpacking libcrypt-dev:arm64 (1:4.4.36-4) ... 248s Selecting previously unselected package libtirpc-dev:arm64. 248s Preparing to unpack .../03-libtirpc-dev_1.3.4+ds-1build1_arm64.deb ... 248s Unpacking libtirpc-dev:arm64 (1.3.4+ds-1build1) ... 248s Selecting previously unselected package libnsl-dev:arm64. 248s Preparing to unpack .../04-libnsl-dev_1.3.0-3_arm64.deb ... 248s Unpacking libnsl-dev:arm64 (1.3.0-3) ... 248s Selecting previously unselected package rpcsvc-proto. 248s Preparing to unpack .../05-rpcsvc-proto_1.4.2-0ubuntu6_arm64.deb ... 248s Unpacking rpcsvc-proto (1.4.2-0ubuntu6) ... 248s Selecting previously unselected package libc6-dev:arm64. 248s Preparing to unpack .../06-libc6-dev_2.39-0ubuntu2_arm64.deb ... 248s Unpacking libc6-dev:arm64 (2.39-0ubuntu2) ... 248s Selecting previously unselected package libisl23:arm64. 248s Preparing to unpack .../07-libisl23_0.26-3_arm64.deb ... 248s Unpacking libisl23:arm64 (0.26-3) ... 248s Selecting previously unselected package libmpc3:arm64. 248s Preparing to unpack .../08-libmpc3_1.3.1-1_arm64.deb ... 248s Unpacking libmpc3:arm64 (1.3.1-1) ... 248s Selecting previously unselected package cpp-13-aarch64-linux-gnu. 248s Preparing to unpack .../09-cpp-13-aarch64-linux-gnu_13.2.0-17ubuntu2_arm64.deb ... 248s Unpacking cpp-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 248s Selecting previously unselected package cpp-13. 248s Preparing to unpack .../10-cpp-13_13.2.0-17ubuntu2_arm64.deb ... 248s Unpacking cpp-13 (13.2.0-17ubuntu2) ... 248s Selecting previously unselected package cpp-aarch64-linux-gnu. 248s Preparing to unpack .../11-cpp-aarch64-linux-gnu_4%3a13.2.0-7ubuntu1_arm64.deb ... 248s Unpacking cpp-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 248s Selecting previously unselected package cpp. 248s Preparing to unpack .../12-cpp_4%3a13.2.0-7ubuntu1_arm64.deb ... 248s Unpacking cpp (4:13.2.0-7ubuntu1) ... 248s Selecting previously unselected package libcc1-0:arm64. 248s Preparing to unpack .../13-libcc1-0_14-20240303-1ubuntu1_arm64.deb ... 248s Unpacking libcc1-0:arm64 (14-20240303-1ubuntu1) ... 248s Selecting previously unselected package libitm1:arm64. 248s Preparing to unpack .../14-libitm1_14-20240303-1ubuntu1_arm64.deb ... 248s Unpacking libitm1:arm64 (14-20240303-1ubuntu1) ... 248s Selecting previously unselected package libatomic1:arm64. 248s Preparing to unpack .../15-libatomic1_14-20240303-1ubuntu1_arm64.deb ... 248s Unpacking libatomic1:arm64 (14-20240303-1ubuntu1) ... 248s Selecting previously unselected package libasan8:arm64. 248s Preparing to unpack .../16-libasan8_14-20240303-1ubuntu1_arm64.deb ... 248s Unpacking libasan8:arm64 (14-20240303-1ubuntu1) ... 249s Selecting previously unselected package liblsan0:arm64. 249s Preparing to unpack .../17-liblsan0_14-20240303-1ubuntu1_arm64.deb ... 249s Unpacking liblsan0:arm64 (14-20240303-1ubuntu1) ... 249s Selecting previously unselected package libtsan2:arm64. 249s Preparing to unpack .../18-libtsan2_14-20240303-1ubuntu1_arm64.deb ... 249s Unpacking libtsan2:arm64 (14-20240303-1ubuntu1) ... 249s Selecting previously unselected package libubsan1:arm64. 249s Preparing to unpack .../19-libubsan1_14-20240303-1ubuntu1_arm64.deb ... 249s Unpacking libubsan1:arm64 (14-20240303-1ubuntu1) ... 249s Selecting previously unselected package libhwasan0:arm64. 249s Preparing to unpack .../20-libhwasan0_14-20240303-1ubuntu1_arm64.deb ... 249s Unpacking libhwasan0:arm64 (14-20240303-1ubuntu1) ... 249s Selecting previously unselected package libgcc-13-dev:arm64. 249s Preparing to unpack .../21-libgcc-13-dev_13.2.0-17ubuntu2_arm64.deb ... 249s Unpacking libgcc-13-dev:arm64 (13.2.0-17ubuntu2) ... 249s Selecting previously unselected package gcc-13-aarch64-linux-gnu. 249s Preparing to unpack .../22-gcc-13-aarch64-linux-gnu_13.2.0-17ubuntu2_arm64.deb ... 249s Unpacking gcc-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 249s Selecting previously unselected package gcc-13. 250s Preparing to unpack .../23-gcc-13_13.2.0-17ubuntu2_arm64.deb ... 250s Unpacking gcc-13 (13.2.0-17ubuntu2) ... 250s Selecting previously unselected package gcc-aarch64-linux-gnu. 250s Preparing to unpack .../24-gcc-aarch64-linux-gnu_4%3a13.2.0-7ubuntu1_arm64.deb ... 250s Unpacking gcc-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 250s Selecting previously unselected package gcc. 250s Preparing to unpack .../25-gcc_4%3a13.2.0-7ubuntu1_arm64.deb ... 250s Unpacking gcc (4:13.2.0-7ubuntu1) ... 250s Selecting previously unselected package libstdc++-13-dev:arm64. 250s Preparing to unpack .../26-libstdc++-13-dev_13.2.0-17ubuntu2_arm64.deb ... 250s Unpacking libstdc++-13-dev:arm64 (13.2.0-17ubuntu2) ... 250s Selecting previously unselected package g++-13-aarch64-linux-gnu. 250s Preparing to unpack .../27-g++-13-aarch64-linux-gnu_13.2.0-17ubuntu2_arm64.deb ... 250s Unpacking g++-13-aarch64-linux-gnu (13.2.0-17ubuntu2) ... 250s Selecting previously unselected package g++-13. 250s Preparing to unpack .../28-g++-13_13.2.0-17ubuntu2_arm64.deb ... 250s Unpacking g++-13 (13.2.0-17ubuntu2) ... 250s Selecting previously unselected package g++-aarch64-linux-gnu. 250s Preparing to unpack .../29-g++-aarch64-linux-gnu_4%3a13.2.0-7ubuntu1_arm64.deb ... 250s Unpacking g++-aarch64-linux-gnu (4:13.2.0-7ubuntu1) ... 250s Selecting previously unselected package g++. 250s Preparing to unpack .../30-g++_4%3a13.2.0-7ubuntu1_arm64.deb ... 250s Unpacking g++ (4:13.2.0-7ubuntu1) ... 251s Selecting previously unselected package build-essential. 251s Preparing to unpack .../31-build-essential_12.10ubuntu1_arm64.deb ... 251s Unpacking build-essential (12.10ubuntu1) ... 251s Selecting previously unselected package dctrl-tools. 251s Preparing to unpack .../32-dctrl-tools_2.24-3build2_arm64.deb ... 251s Unpacking dctrl-tools (2.24-3build2) ... 251s Selecting previously unselected package libgfortran-13-dev:arm64. 251s Preparing to unpack .../33-libgfortran-13-dev_13.2.0-17ubuntu2_arm64.deb ... 251s Unpacking 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/usr/bin/gfortran to provide /usr/bin/f77 (f77) in auto mode 255s 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 255s Setting up g++ (4:13.2.0-7ubuntu1) ... 255s update-alternatives: using /usr/bin/g++ to provide /usr/bin/c++ (c++) in auto mode 255s Setting up build-essential (12.10ubuntu1) ... 255s Setting up r-base-dev (4.3.2-1build1) ... 255s Setting up pkg-r-autopkgtest (20231212ubuntu1) ... 255s Setting up autopkgtest-satdep (0) ... 255s Processing triggers for man-db (2.12.0-3) ... 256s Processing triggers for install-info (7.1-3) ... 256s Processing triggers for libc-bin (2.39-0ubuntu2) ... 260s (Reading database ... 99258 files and directories currently installed.) 260s Removing autopkgtest-satdep (0) ... 261s autopkgtest [20:26:42]: test pkg-r-autopkgtest: /usr/share/dh-r/pkg-r-autopkgtest 261s autopkgtest [20:26:42]: test pkg-r-autopkgtest: [----------------------- 261s Test: Try to load the R library systemfit 261s 261s R version 4.3.2 (2023-10-31) -- "Eye Holes" 261s Copyright (C) 2023 The R Foundation for Statistical Computing 261s Platform: aarch64-unknown-linux-gnu (64-bit) 261s 261s R is free software and comes with ABSOLUTELY NO WARRANTY. 261s You are welcome to redistribute it under certain conditions. 261s Type 'license()' or 'licence()' for distribution details. 261s 261s R is a collaborative project with many contributors. 261s Type 'contributors()' for more information and 261s 'citation()' on how to cite R or R packages in publications. 261s 261s Type 'demo()' for some demos, 'help()' for on-line help, or 261s 'help.start()' for an HTML browser interface to help. 261s Type 'q()' to quit R. 261s 261s > library('systemfit') 261s Loading required package: Matrix 262s Loading required package: car 262s Loading required package: carData 262s Loading required package: lmtest 262s Loading required package: zoo 262s 262s Attaching package: ‘zoo’ 262s 262s The following objects are masked from ‘package:base’: 262s 262s as.Date, as.Date.numeric 262s 262s 262s Please cite the 'systemfit' package as: 262s 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/. 262s 262s If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site: 262s https://r-forge.r-project.org/projects/systemfit/ 262s > 262s > 262s Other tests are currently unsupported! 262s They will be progressively added. 263s autopkgtest [20:26:44]: test pkg-r-autopkgtest: -----------------------] 263s autopkgtest [20:26:44]: test pkg-r-autopkgtest: - - - - - - - - - - results - - - - - - - - - - 263s pkg-r-autopkgtest PASS 264s autopkgtest [20:26:45]: @@@@@@@@@@@@@@@@@@@@ summary 264s run-unit-test PASS 264s pkg-r-autopkgtest PASS 274s Creating nova instance adt-noble-arm64-r-cran-systemfit-20240316-202221-juju-7f2275-prod-proposed-migration-environment-3 from image adt/ubuntu-noble-arm64-server-20240314.img (UUID 7faf5f09-d335-4346-a441-4eab2f9c04fe)...