Simple and trustworthy cluster-robust GMM inference

This paper develops a new asymptotic theory for GMM estimation and inference in the presence of clustered dependence. The key feature of our alternative asymptotics is that the number of clusters G is regarded as fixed as the sample size increases. Under the fixed-G asymptotics, we show that the Wald and t tests in two-step GMM are asymptotically pivotal only if we recenter the estimated moment process in the clustered covariance estimator (CCE). Also, the J statistic, the trinity of two-step GMM statistics (QLR, LM, and Wald), and the t statistic 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. The proposed tests are very appealing to practitioners because the test statistics are simple modifications of conventional GMM test statistics, and critical values are readily available from F and t tables. No further simulations or resampling methods are needed. A Monte Carlo study shows that our proposed tests are more accurate than the conventional large-G asymptotic inferences.