Asymptotic F and t tests in an efficient GMM setting

Abstract

This paper considers two-step efficient GMM estimation and inference where the weighting matrix and asymptotic variance matrix are based on the series long run variance estimator. We propose a simple and easy-to-implement modification to the trinity of test statistics in the two-step efficient GMM setting and show that the modified test statistics are all asymptotically F distributed under the so-called fixed-smoothing asymptotics. The modification is multiplicative and involves the J statistic for testing over-identifying restrictions. This leads to convenient asymptotic F tests whose critical values, i.e., the standard F critical values, are readily available from standard statistical tables and programming environments. For testing a single restriction with a one-sided alternative, an asymptotic t test theory using the standard t distribution as the reference distribution is also developed.