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Asymptotic F and t tests in an efficient GMM setting
- Hwang, Jungbin, Sun, Yixiao
- Journal of econometrics 2017 v.198 no.2 pp. 277-295
- econometric models, economic analysis, economic theory, t-test, variance
- 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.