Heteroskedasticity and Spatiotemporal Dependence Robust Inference for Linear Panel Models with Fixed Effects

This paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms. We propose a bivariate kernel covariance estimator that is flexible to nest existing estimators as special cases with certain choices of bandwidths. For distributional approximations, we embed the level of smoothing and the sample size in two different limiting sequences. In the first case where the level of smoothing increases with the sample size, the proposed covariance estimator is consistent and the associated Wald statistic converges to a chi square distribution. We show that our covariance estimator improves upon existing estimators in terms of robustness and efficiency. In the second case where the level of smoothing is fixed, the covariance estimator has a random limit and we show by asymptotic expansion that the limiting distribution of the Wald statistic depends on the bandwidth parameters, the kernel function, and the number of restrictions being tested. As this distribution is nonstandard, we establish the validity of a convenient F-approximation to this distribution. For bandwidth selection, we employ and optimize a modified asymptotic mean square error criterion. The fl exibility of our estimator and the proposed bandwidth selection procedure make our estimator adaptive to the dependence structure. This adaptiveness effectively automates the selection of covariance estimators. Simulation results show that our proposed testing procedure works reasonably well in finite samples.