Asymptotic F Test in a GMM Framework with Cross Sectional Dependence

Abstract

The paper develops an asymptotically valid F test that is robust to spatial autocorrelation in a GMM framework. The test is based on the class of series covariance matrix estimators and fixed-smoothing asymptotics. The fixed-smoothing asymptotics and F approximation are established under mild sufficient conditions for a central limit theorem. These conditions can accommodate a wide range of spatial processes. This is in contrast with the standard arguments, which often impose very restrictive assumptions so that a functional central limit theorem holds. The proposed F test is very easy to implement, as critical values are from a standard F distribution. To a great extent, the asymptotic F test achieves triple robustness: it is asymptotically valid regardless of the spatial autocorrelation, the sampling region, and the limiting behavior of the smoothing parameter. Simulation shows that the F test is more accurate in size than the conventional chi-square tests, and it has the same size accuracy and power property as nonstandard tests that require computationally intensive simulation or bootstrap.