Simple and powerful GMM over-identification tests with accurate size

Based on the series long run variance estimator, we propose a new class of over-identification tests that are robust to heteroscedasticity and autocorrelation of unknown forms. We show that when the number of terms used in the series long run variance estimator is fixed, the conventional J statistic, after a simple correction, is asymptotically F -distributed. We apply the idea of the F -approximation to the conventional kernel-based J tests. Simulations show that the J ∗ tests based on the finite sample corrected J statistic and the F -approximation have virtually no size distortion, and yet are as powerful as the standard J tests.