Clustered standard errors using pgmm()

Question

I am estimating a system-GMM model using the pgmm function from the plm package in R:

pgmm(Y ~ lag(Y, 1) + X1 + X2 + X3 + x4 |
       lag(Y, 2:99) + factor(Industry),
     data = df.dat, 
     index = c("Firm", "Year"),
     effect = "individual", model = "twosteps",
     collapse = TRUE, transformation = "ld", robust = TRUE)

The package documentation says "The robust argument of the summary method enables to use the robust covariance matrix proposed by Windmeijer (2005)" but I don't understand exactly what corrections are made. Specifically, I would like to know if I am estimating firm-clustered standard errors or not.

And, if not, how could I do that?

Thank you!

Answer 1

Yes, the standard errors are clustered on firm. That's the general approach to robust variance estimation in this package, as in the subsection Inference in the panel model in the documentation you linked.

The cited reference, Windmeijer (2005), is about something a bit different; it's a small-sample improvement to the clustered variance estimator

The weight matrix used in the calculation of the efficient two-step GMM estimator is based on initial consistent parameter estimates. In this paper it is shown that the extra variation due to the presence of these estimated parameters in the weight matrix accounts for much of the difference between the finite sample and the usual asymptotic variance of the two-step GMM estimator, when the moment conditions used are linear in the parameters. This difference can be estimated, resulting in a finite sample corrected estimate of the variance.