The purpose of this in-class lab is to use R to practice with panel data estimation methods. To get credit, upload your .R script to the appropriate place on Canvas.

## For starters

Open up a new R script (named ICL15_XYZ.R, where XYZ are your initials) and add the usual “preamble” to the top:

library(tidyverse)
library(wooldridge)
library(broom)
library(magrittr)
library(clubSandwich)
library(modelsummary)
library(estimatr)
library(plm)   # You may need to install this package

Our data set will be a panel of wages for 545 men. Load the data from the wooldridge package, format year to be a factor, and rename the variable nr to something more descriptive (id):

df <- as_tibble(wagepan)
df %<>% mutate(year=as.factor(year))
df %<>% rename(id = nr)

### Summary statistics for panel data

It is important to know what your panel looks like. How many units? How many time periods? The easiest way to do this is the pdim() function in the plm package.

pdim(df)

It is also helpful to “convert” the data to a cross-section of within-unit averages. Let’s do this for some of the key variables of our analysis.

df.within <- df %>% select(id,year,educ,married,union,rur) %>%
group_by(id) %>%
summarize(
mean.edu = mean(educ),
var.edu  = var(educ),
mean.marr = mean(married),
var.marr = var(married),
mean.union = mean(union),
var.union = var(union),
mean.rural = mean(rur),
var.rural = var(rur)
)
df.within %>% datasummary_skim()
1. Is there any within-person variance in the educ variable? What about married, union, and rural?

2. What does it mean for the married, union, or rural variables to have a positive within-person variance?

3. Why is it important to know if a variable has positive within-person variance?

## Pooled OLS, Random Effects, and Fixed Effects Models

Now estimate the following model using various options of the plm() function:

\begin{align*} \log(wage_{it}) & = \beta_0 + \beta_1 educ_{i} + \beta_2 black_{i} + \beta_3 hisp_{i} + \beta_4 exper_{it} + \beta_5 exper_{it}^2 + \beta_6 married_{it} + \\ &\phantom{=\,\,}\beta_7 union_{it} + \beta_8 rur_{it} + \sum_t \beta_{9,t}year_{it} + a_i + u_{it} \end{align*}

### Pooled OLS

The pooled OLS model can be run from the lm_robust() function as follows.

est.pols <- lm_robust(lwage ~ educ + black + hisp + exper + I(exper^2) + married + union + rur + year,
data = df, clusters=id)
1. Interpret the coefficient on $$\beta_7$$ in the pooled OLS model

### Random effects

RE uses the plm() function as follows.

est.re <- plm(lwage ~ educ + black + hisp + exper + I(exper^2) + married + union + rur + year,
data = df, index = c("id","year"), model = "random")
1. What is the estimate of $$\theta$$ in the RE model? (Hint: check est.re$ercomp$theta) What does this tell you about what you expect the random effects estimates to be relative to the fixed effects estimates?

### Fixed effects

FE also come from the lm_robust() function:

est.fe <- lm_robust(lwage ~ I(exper^2) + married + union + rur + year,
data = df, fixed_effects = ~id)
1. Explain why we cannot estimate coefficients on educ, black, hisp, or exper in the fixed effects model. (Note: the reason for not being able to estimate exper is more nuanced)

## Clustered standard errors

As discussed in class, the most appropriate standard errors account for within-person serial correlation and are robust to heteroskedasticity. We already used these for pooled OLS and fixed effects, but not for random effects.

clust.re <- coef_test(est.re, vcov = "CR1", cluster = "individual")
clust.re.SE <- clust.re$SE names(clust.re.SE) <- names(est.re$coefficients)

We can put these all in one modelsummary table:

modelsummary(list("POLS"=est.pols,"RE"=est.re,"FE"=est.fe),
statistic_override=list(sqrt(diag(est.pols$vcov)),clust.re.SE,sqrt(diag(est.fe$vcov))),
output="markdown")
POLS RE FE
(Intercept) 0.165 0.036
(0.163) (0.161)
educ 0.087 0.091
(0.011) (0.011)
black -0.149 -0.141
(0.051) (0.051)
hisp -0.016 0.016
(0.040) (0.040)
exper 0.069 0.106
(0.019) (0.016)
I(exper^2) -0.002 -0.005 -0.005
(0.001) (0.001) (0.001)
married 0.126 0.065 0.047
(0.026) (0.019) (0.018)
union 0.182 0.107 0.079
(0.028) (0.021) (0.019)
rur -0.138 -0.023 0.049
(0.035) (0.031) (0.031)
year1981 0.053 0.040 0.152
(0.028) (0.028) (0.027)
year1982 0.055 0.030 0.254
(0.037) (0.035) (0.028)
year1983 0.049 0.019 0.357
(0.046) (0.044) (0.032)
year1984 0.074 0.041 0.494
(0.057) (0.055) (0.040)
year1985 0.090 0.056 0.622
(0.066) (0.064) (0.048)
year1986 0.120 0.089 0.771
(0.076) (0.075) (0.059)
year1987 0.151 0.132 0.931
(0.085) (0.085) (0.070)
Num.Obs. 4360 4360 4360
R2 0.199 0.181 0.621
1. Interpret the coefficient on union across the three models.