Simple and Powerful GMM Over-identication Tests with Accurate Size

The paper provides a new class of over-identi…cation tests that are robust to heteroscedasticity and autocorrelation of unknown forms. The tests are based on the series long run variance estimator that is designed to pivotalize the moment restrictions. We show that when the number of terms used in the series long run variance estimator is …xed, 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 …nite sample corrected J statistic and the F approximation have virtually no size distortion, and yet are as powerful as the standard J tests. JEL Classi…cation: C12, C32 Keywords: F-distribution, Heteroscedasticity and Autocorrelation Robust, Long-run variance, Over-identi…cation test, Robust standard error, Series Estimator