Asymptotic F and T Tests in an Efficient GMM Setting

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 that use standard F critical values. Simulation shows that, in terms of both size and power, the asymptotic F tests perform as well as the nonstandard tests proposed recently by Sun (2014b) in finite samples. But the F tests are more appealing as the critical values are readily available from standard statistical tables. Compared to the conventional chi-square tests, the F tests are as powerful, but are much more accurate in size