In the context of panel data analysis my key independent variable wage affects the response not immediately but rather over time. Therefore I would like to use some lagged values of wage $X_{it-1}$, $X_{it-2}$, $X_{it-3}$ ... I read that in order to avoid multicollinearity by using some Finite Distributed Lags one can try to use the Infinite Distributed Lag model.
I would like to estimate the infinite
distributed lag model with a GMM and the time fixed effects R library plm:
$$Y_{t} =\alpha+\sum_{s=0}^{\infty} \beta X_{t-s}+e_t$$
I read that this equation can be transformed for the panel data context as follows: $$Y_{it} =\lambda+Y_{it-1}+\beta X_{it}+ \gamma Z_{t} + e_{it}$$
Im trying to implement that model with some covariates using plm.
Question: Is that model correct? Is the following implementation of that model correct?
\ Some R code
data("EmplUK", package = "plm")
library(plm)
pdata <- pdata.frame(EmplUK, index=c("year", "firm"))
# Here I lag the key independent variable as well:
plm.gmm<- pgmm(log(emp) ~ lag(log(emp),1)+lag(log(wage),2)+output+factor(year)| lag(log(emp), 2:99),
data = pdata,
transformation = "ld",
effect = "individual")
# Here I lag only the dependent variable(which seems to correspond to the transformed equation above:
plm.gmm<- pgmm(log(emp) ~ lag(log(emp),1)+wage+output+factor(year)| lag(log(emp), 2:99),
data = pdata,
transformation = "ld",
effect = "individual")
