Estimation of panel model with heteroskedasticity in both idiosyncratic and individual specific errors

In this paper we consider adaptive estimation of a panel data model with unknown heteroskedasticity in both the idiosyncratic and the individual specific random components. We use the kernel estimator for the unknown variances first and then implement the GLS estimator. We also examine the finite sample performance of the adaptive estimators and compare them with several widely used estimators via Monte Carlo experiments. We find that with a proper bandwidth, our adaptive estimator performs much better than other estimators in terms of both estimation efficiency and test size. Besides, a larger bandwidth yields better estimation efficiency and lower test size.