Simple and Trustworthy Cluster-Robust GMM Inference

This paper develops a new asymptotic theory for two-step GMM estimation and inference in the presence of clustered dependence. The key feature of alternative asymptotics is the number of clusters G is regarded as small or fixed when the sample size increases. Under the small-G asymptotics, this paper shows the centered two-step GMM estimator and the two continuously-updating GMM estimators we consider have the same asymptotic mixed normal distribution. In addition, the J statistic, the trinity of two-step GMM statistics (QLR, LM and Wald), and the t statistic are all asymptotically pivotal, and each can be modified to have an asymptotic standard F distribution or t distribution. We suggest a finite sample variance correction to further improve the accuracy of the F and t approximations. Our proposed asymptotic F and t tests are very appealing to practitioners because our test statistics are simple modifications of the usual test statistics, and critical values are readily available from standard statistical tables. A Monte Carlo study shows that our proposed tests are more accurate than the conventional inferences under the large-G asymptotics. JEL Classification: C12, C21, C23, C31