Asymptotic properties of a robust variance matrix estimator for panel data when is large

I consider the asymptotic properties of a commonly advocated covariance matrix estimator for panel data. Under asymptotics where the cross-section dimension, n, grows large with the time dimension, T, fixed, the estimator is consistent while allowing essentially arbitrary correlation within each individual. However, many panel data sets have a non-negligible time dimension. I extend the usual analysis to cases where n and T go to infinity jointly and where T → ∞ with n fixed. I provide conditions under which t and F statistics based on the covariance matrix estimator provide valid inference and illustrate the properties of the estimator in a simulation study.