Chapter 14: Advanced Panel Data Methods
library(wooldridge)In order to estimate panel data models, I use the plm function from the plm package. The intuition behind its structure is similar to the ordinary linear model, except that it allows you to specify the panel’s group and time variables and the effects model.
Example 14.1
Similar to the lm function, you can specify your model’s equation and the sample. Since you want to use panel data methods for you estimation, you also have to specify which variables in your sample contain the information used to distinguish different groups and which variable contains the time measurement. In our example this is done with index = c("fcode", "year"). Note, that the order of the variables is important. The group variable always has to be at the first and the time variable at the second position.
The specification model = "within" indicates that the effects occur within a group. This is the fixed effects estimator. And the effect = "individual" specifies that we are only interested in effects of the group variable and that there are no time specific effects. (See ?plm for further information on this.)
data("jtrain")
# install.packages("plm")
library(plm)
summary(plm(lscrap ~ d88 + d89 + grant + grant_1,
data = jtrain,
index= c("fcode", "year"),
model = "within",
effect = "individual"
))## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = lscrap ~ d88 + d89 + grant + grant_1, data = jtrain,
## effect = "individual", model = "within", index = c("fcode",
## "year"))
##
## Balanced Panel: n = 54, T = 3, N = 162
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -2.286936 -0.112387 -0.017841 0.144272 1.426674
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## d88 -0.080216 0.109475 -0.7327 0.46537
## d89 -0.247203 0.133218 -1.8556 0.06634 .
## grant -0.252315 0.150629 -1.6751 0.09692 .
## grant_1 -0.421590 0.210200 -2.0057 0.04749 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 32.25
## Residual Sum of Squares: 25.766
## R-Squared: 0.20105
## Adj. R-Squared: -0.23684
## F-statistic: 6.54259 on 4 and 104 DF, p-value: 9.7741e-05Example 14.2
The basic structure of plm remains the same in this example, except that interaction terms are added. Additionally, a specific F-test pFtest(estimatedmodel1, estimatedmodel2) is available to test for joint significance of those terms.
data("wagepan")
plm.1 <- plm(lwage ~ married + union +
d81 + d82 + d83 +d84 + d85 + d86 + d87 +
I(d81*educ) + I(d82*educ) + I(d83*educ) + I(d84*educ) + I(d85*educ) +
I(d86*educ) + I(d87*educ),
data=wagepan,
model="within",
effect="individual",
index=c("nr", "year"))
summary(plm.1)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = lwage ~ married + union + d81 + d82 + d83 + d84 +
## d85 + d86 + d87 + I(d81 * educ) + I(d82 * educ) + I(d83 *
## educ) + I(d84 * educ) + I(d85 * educ) + I(d86 * educ) + I(d87 *
## educ), data = wagepan, effect = "individual", model = "within",
## index = c("nr", "year"))
##
## Balanced Panel: n = 545, T = 8, N = 4360
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -4.152111 -0.125630 0.010897 0.160800 1.483401
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## married 0.0548205 0.0184126 2.9773 0.002926 **
## union 0.0829785 0.0194461 4.2671 2.029e-05 ***
## d81 -0.0224158 0.1458885 -0.1537 0.877893
## d82 -0.0057611 0.1458558 -0.0395 0.968495
## d83 0.0104297 0.1458579 0.0715 0.942999
## d84 0.0843743 0.1458518 0.5785 0.562965
## d85 0.0497253 0.1458602 0.3409 0.733190
## d86 0.0656064 0.1458917 0.4497 0.652958
## d87 0.0904448 0.1458505 0.6201 0.535216
## I(d81 * educ) 0.0115854 0.0122625 0.9448 0.344827
## I(d82 * educ) 0.0147905 0.0122635 1.2061 0.227872
## I(d83 * educ) 0.0171182 0.0122633 1.3959 0.162830
## I(d84 * educ) 0.0165839 0.0122657 1.3521 0.176437
## I(d85 * educ) 0.0237085 0.0122738 1.9316 0.053479 .
## I(d86 * educ) 0.0274123 0.0122740 2.2334 0.025583 *
## I(d87 * educ) 0.0304332 0.0122723 2.4798 0.013188 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 572.05
## Residual Sum of Squares: 474.35
## R-Squared: 0.1708
## Adj. R-Squared: 0.048567
## F-statistic: 48.9069 on 16 and 3799 DF, p-value: < 2.22e-16plm.2 <- plm(lwage ~ married + union +
d81 + d82 + d83 +d84 + d85 + d86 + d87,
data = wagepan,
model = "within",
effect = "individual",
index = c("nr", "year"))
pFtest(plm.1,plm.2)##
## F test for individual effects
##
## data: lwage ~ married + union + d81 + d82 + d83 + d84 + d85 + d86 + ...
## F = 1.2365, df1 = 7, df2 = 3799, p-value = 0.2787
## alternative hypothesis: significant effectsExample 14.3
See example 14.1.
summary(plm(lscrap ~ d88 + d89 + grant + grant_1 + lsales + lemploy,
data = jtrain,
model = "within",
effect = "individual",
index = c("fcode", "year")))## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = lscrap ~ d88 + d89 + grant + grant_1 + lsales +
## lemploy, data = jtrain, effect = "individual", model = "within",
## index = c("fcode", "year"))
##
## Unbalanced Panel: n = 51, T = 1-3, N = 148
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -1.858663 -0.133752 -0.021483 0.148632 1.580473
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## d88 -0.0039609 0.1195487 -0.0331 0.97364
## d89 -0.1321930 0.1536863 -0.8601 0.39197
## grant -0.2967542 0.1570861 -1.8891 0.06206 .
## grant_1 -0.5355783 0.2242060 -2.3888 0.01897 *
## lsales -0.0868577 0.2596985 -0.3345 0.73881
## lemploy -0.0763679 0.3502902 -0.2180 0.82791
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 27.934
## Residual Sum of Squares: 21.982
## R-Squared: 0.21306
## Adj. R-Squared: -0.27121
## F-statistic: 4.10625 on 6 and 91 DF, p-value: 0.0010818Example 14.4
This example compares the estimated coefficients of an OLS, random effects and fixed effects model with each other. The random effects model is estimated by setting model= “random”`. Note that you do not need to specify the effect option.
OLS
# OLS
lm.1 <- lm(lwage ~ educ + black + hisp + exper + expersq + married + union +
d81 + d82 + d83 + d84 + d85 + d86 + d87,
data = wagepan)Random effects
plm.re <- plm(lwage ~ educ + black + hisp + exper + expersq + married + union +
d81 + d82 + d83 + d84 + d85 + d86 + d87,
data = wagepan,
model = "random",
index = c("nr", "year"))Fixed effects
plm.fe <- plm(lwage ~ expersq + married + union +
d81 + d82 + d83 + d84 + d85 + d86 + d87,
data = wagepan,
effect = "individual",
model = "within",
index = c("nr", "year"))Table of results (rounded to 3 digits)
results <- round(
data.frame("Pooled OLS" = lm.1$coefficients[2:8],
"Random Effects" = plm.re$coeff[2:8],
"Fixed Effects" = c(NA, NA, NA, NA, plm.re$coeff[2:4])
),3)
results## Pooled.OLS Random.Effects Fixed.Effects
## educ 0.091 0.092 NA
## black -0.139 -0.139 NA
## hisp 0.016 0.022 NA
## exper 0.067 0.106 NA
## expersq -0.002 -0.005 0.092
## married 0.108 0.064 -0.139
## union 0.182 0.106 0.022