3. Difference-In-Differences

# Original post: https://towardsdatascience.com/does-minimum-wage-decrease-employment-a-difference-in-differences-approach-cb208ed07327
# by carefully selecting cases in the experimental groups, it is possible to detect the treatment effect even handling with obervational data. 
# Difference-in-Differences, DID, is one of the most established methods of causal inference.

d <- read.csv(“wage_data.csv”,convert.factors = FALSE)
head(d[, c(“ID”, “nj”, “postperiod”, “emptot”)])
with(d, 
 (
 mean(emptot[nj == 1 & postperiod == 1], na.rm = TRUE) — mean(emptot[nj == 1 & postperiod == 0], na.rm = TRUE) 
 )-
 (mean(emptot[nj == 0 & postperiod == 1], na.rm = TRUE) — mean(emptot[nj == 0 & postperiod == 0], na.rm = TRUE)
 )
)
ols <- lm(emptot ~ postperiod * nj, data = d)
coeftest(ols)

#A set of estimators and tests for panel data 
library(plm)
library(lmtest)
d$Dit <- d$nj * d$postperiod
d <- plm.data(d, indexes = c("ID", "postperiod"))
did.reg <- plm(emptot ~ postperiod + Dit, data = d,model = "within")
coeftest(did.reg, vcov=function(x)

#Heteroskedasticity-Consistent Covariance Matrix Estimation
vcovHC(x, cluster="group", type="HC1"))