This worked example introduces estimation in panel data in R using example on partisan governments and economics measures for a panel of OECD states.
This tutor
library("lmtest")
library("car")
library("dplyr")
library("ggplot2")The panel data specific packages used are plm and pcse:
library("plm")
library("pcse")This example data was the data from Garrett (1989) Partisan Politics in the Global Economy. The analyses are similar (but not the same) as those run in King, Wittenberg and Tomz (2000), Bailey and Katz, and Beck and Katz (2011). The replication data is from Beck and Katz (2011).
data_path <- "http://pols503.github.io/pols_503_sp15/data/garrett1998.csv"
garrett1998 <- read.csv(data_path, stringsAsFactors = FALSE)The data consist of 350 observations for 0 countries for 25 years (1966 – 1990 with the following variables
A country identifier (number)
Year
unemployment
inflation
Growth in GDP
Political power of left parties in the government. Index from 0–5.
A measure of corporatism or how encompassing the labor movement, e.g. encompassing unions. Index from 0–4.
Capital mobility. Index from 0–4.
Oil dependency
OECD demand (growth rate in all OECD countries)
The country name
Effect of the left parties, corporatism and the interaction of the two.
Garret’s theories involve the combination of left-leaning parties in government and encompassing trade unions.
Pooled time-series, cross-section
mod1 <- lm(gdp ~ corp * leftlab + demand + oild + trade, data = garrett1998)Controlling for country
mod2 <- lm(gdp ~ corp * leftlab + demand + oild + trade + countryname,
data = garrett1998)Controlling for country and year
mod3 <- lm(gdp ~ corp * leftlab + demand + oild + trade + countryname + factor(year),
data = garrett1998)Lagged dependent variable
mod_ldv <- lm(gdp ~ gdpl + corp * leftlab + demand + oild + trade + year,
data = garrett1998)
mod_ldv##
## Call:
## lm(formula = gdp ~ gdpl + corp * leftlab + demand + oild + trade +
## year, data = garrett1998)
##
## Coefficients:
## (Intercept) gdpl corp leftlab demand
## 80.061094 0.293309 -0.403889 -0.617747 0.008225
## oild trade year corp:leftlab
## -4.890031 -0.029882 -0.038558 0.176266Estimating panel-corrected standard errors after a lagged dependent variable model.
pcse(mod_ldv, groupN = garrett1998$country, groupT = garrett1998$year)## $vcov
## X.Intercept. gdpl corp leftlab
## X.Intercept. 1836.07724475 -8.924833e-01 -8.923448e-01 -1.273943e+00
## gdpl -0.89248334 4.478574e-03 1.994741e-03 3.057399e-03
## corp -0.89234485 1.994741e-03 4.242712e-02 3.088963e-02
## leftlab -1.27394332 3.057399e-03 3.088963e-02 5.725434e-02
## demand -0.01518286 -6.371204e-06 -1.063662e-06 2.820008e-06
## oild -29.92733871 4.525943e-02 1.336451e-01 2.754657e-02
## trade 0.08391008 4.116534e-05 -3.151312e-04 -7.239340e-05
## year -0.92611645 4.391191e-04 4.148240e-04 5.941080e-04
## corp.leftlab 0.37348774 -6.823238e-04 -1.435762e-02 -1.581397e-02
## demand oild trade year
## X.Intercept. -1.518286e-02 -2.992734e+01 8.391008e-02 -9.261165e-01
## gdpl -6.371204e-06 4.525943e-02 4.116534e-05 4.391191e-04
## corp -1.063662e-06 1.336451e-01 -3.151312e-04 4.148240e-04
## leftlab 2.820008e-06 2.754657e-02 -7.239340e-05 5.941080e-04
## demand 2.179216e-06 6.272688e-04 -6.702467e-06 7.665887e-06
## oild 6.272688e-04 1.878762e+01 -5.358596e-03 1.493209e-02
## trade -6.702467e-06 -5.358596e-03 5.530314e-05 -4.329927e-05
## year 7.665887e-06 1.493209e-02 -4.329927e-05 4.672369e-04
## corp.leftlab 1.644199e-06 -2.245614e-02 1.168068e-04 -1.758201e-04
## corp.leftlab
## X.Intercept. 3.734877e-01
## gdpl -6.823238e-04
## corp -1.435762e-02
## leftlab -1.581397e-02
## demand 1.644199e-06
## oild -2.245614e-02
## trade 1.168068e-04
## year -1.758201e-04
## corp.leftlab 6.166286e-03
##
## $pcse
## X.Intercept. gdpl corp leftlab demand
## 42.849471931 0.066922150 0.205978457 0.239278794 0.001476217
## oild trade year corp.leftlab
## 4.334469083 0.007436608 0.021615663 0.078525705
##
## $b
## (Intercept) gdpl corp leftlab demand
## 80.061094407 0.293309090 -0.403889158 -0.617746797 0.008224868
## oild trade year corp:leftlab
## -4.890031278 -0.029882287 -0.038558261 0.176266133
##
## $tstats
## (Intercept) gdpl corp leftlab demand
## 1.868427 4.382840 -1.960832 -2.581703 5.571586
## oild trade year corp:leftlab
## -1.128173 -4.018268 -1.783811 2.244693
##
## $df
## [1] 341
##
## $pval
## (Intercept) gdpl corp leftlab demand
## 6.255993e-02 1.561865e-05 5.071226e-02 1.024822e-02 5.130916e-08
## oild trade year corp:leftlab
## 2.600400e-01 7.217957e-05 7.534352e-02 2.542850e-02
##
## $pairwise
## [1] FALSE
##
## $nobs
## [1] 350
##
## $nmiss
## [1] 0
##
## $call
## pcse(object = mod_ldv, groupN = garrett1998$country, groupT = garrett1998$year)
##
## attr(,"class")
## [1] "pcse"The functions in plm need to know which variables correspond to id and time in the data frame. So use the function pdata.frame to create a data frame friendly with the plm functions.
pgarrett <- pdata.frame(garrett1998, index = c("countryname", "year"))Within (fixed-effects) model
mod_within <- plm(gdp ~ corp * leftlab + demand + oild + trade + year,
data = pgarrett, model = "within")
summary(mod_within)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = gdp ~ corp * leftlab + demand + oild + trade +
## year, data = pgarrett, model = "within")
##
## Balanced Panel: n=14, T=25, N=350
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -5.2100 -1.0200 0.0369 1.0000 4.6900
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## corp 0.5669585 0.5685383 0.9972 0.3194451
## leftlab -0.6490591 0.3874089 -1.6754 0.0948802 .
## demand -0.0080754 0.0021784 -3.7070 0.0002489 ***
## oild -8.4801198 6.2795243 -1.3504 0.1778728
## trade 0.0374468 0.0167635 2.2338 0.0262167 *
## year1967 -1.0224698 0.6636366 -1.5407 0.1244215
## year1968 0.6208874 0.6420478 0.9670 0.3342866
## year1969 2.0101661 0.6418841 3.1317 0.0019062 **
## year1970 0.1680420 0.6725343 0.2499 0.8028603
## year1971 -1.5533423 0.6667365 -2.3298 0.0204686 *
## year1972 0.4941926 0.6511567 0.7589 0.4484692
## year1973 1.5523570 0.6517948 2.3817 0.0178457 *
## year1974 -4.1051472 0.8180272 -5.0184 8.857e-07 ***
## year1975 -6.9624994 0.9505922 -7.3244 2.141e-12 ***
## year1976 0.2075046 0.6640872 0.3125 0.7548993
## year1977 -2.8350941 0.6890417 -4.1145 4.992e-05 ***
## year1978 -1.8088430 0.6766242 -2.6733 0.0079131 **
## year1979 -1.3251267 0.6991356 -1.8954 0.0589845 .
## year1980 -4.1802011 0.8343638 -5.0100 9.218e-07 ***
## year1981 -5.2619782 0.8083506 -6.5095 3.083e-10 ***
## year1982 -6.6518768 0.9856099 -6.7490 7.465e-11 ***
## year1983 -3.3253888 0.7473295 -4.4497 1.206e-05 ***
## year1984 -1.1318565 0.7041248 -1.6075 0.1089835
## year1985 -1.8905450 0.7322675 -2.5818 0.0102944 *
## year1986 -2.9050938 0.7536212 -3.8548 0.0001412 ***
## year1987 -2.4052672 0.6997451 -3.4373 0.0006688 ***
## year1988 -0.9238201 0.6783068 -1.3620 0.1742153
## year1989 -2.0653889 0.7054172 -2.9279 0.0036687 **
## year1990 -3.1559856 0.7564154 -4.1723 3.933e-05 ***
## corp:leftlab 0.2758505 0.1437601 1.9188 0.0559365 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1793.5
## Residual Sum of Squares: 881.08
## R-Squared : 0.50873
## Adj. R-Squared : 0.44477
## F-statistic: 10.5625 on 30 and 306 DF, p-value: < 2.22e-16Recover the fixed effects
fixef(mod_within)## Austria Belgium Canada Denmark Finland France
## 0.1183194 1.6125709 4.0759096 0.4528291 2.1303994 4.9929682
## Germany Italy Japan Netherlands Norway Sweden
## 1.5925973 2.5675705 6.4440796 2.5177996 1.9605038 -0.1088838
## UK US
## 2.0211691 3.7676501Random effects model
mod_re <- plm(gdp ~ corp * leftlab + demand + oild + trade,
data = pgarrett, model = "random")
summary(mod_re)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = gdp ~ corp * leftlab + demand + oild + trade, data = pgarrett,
## model = "random")
##
## Balanced Panel: n=14, T=25, N=350
##
## Effects:
## var std.dev share
## idiosyncratic 3.909 1.977 0.773
## individual 1.145 1.070 0.227
## theta: 0.6533
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -5.9900 -1.2400 -0.0819 1.0800 6.9700
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 5.9879526 1.1294870 5.3015 2.062e-07 ***
## corp -0.5845495 0.4308488 -1.3567 0.17576
## leftlab -0.9230097 0.4168615 -2.2142 0.02747 *
## demand 0.0086524 0.0010632 8.1383 7.468e-15 ***
## oild -10.8127060 5.5343674 -1.9537 0.05154 .
## trade -0.0500292 0.0091757 -5.4524 9.523e-08 ***
## corp:leftlab 0.3400063 0.1454336 2.3379 0.01997 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1826.1
## Residual Sum of Squares: 1334.9
## R-Squared : 0.26899
## Adj. R-Squared : 0.26361
## F-statistic: 21.0351 on 6 and 343 DF, p-value: < 2.22e-16Compare the random effects model with the fixed effects model using a Hausman test
phtest(mod_within, mod_re)##
## Hausman Test
##
## data: gdp ~ corp * leftlab + demand + oild + trade + year
## chisq = 97.216, df = 6, p-value < 2.2e-16
## alternative hypothesis: one model is inconsistentIf we can reject the null, then we should use the fixed effects estimator.