Asymptotic Behavior of a t-Test Robust to Cluster Heterogeneity
研究了在集群异质性下，集群稳健t统计量的渐近分布为正态分布，并提出了有效集群数的概念，指导实际应用中应报告集群数而非观测数作为样本量。
For a cluster-robust t -statistic under cluster heterogeneity we establish that the cluster-robust t -statistic has a gaussian asymptotic null distribution and develop the effective number of clusters, which scales down the actual number of clusters, as a guide to the behavior of the test statistic. The implications for hypothesis testing in applied work are that the number of clusters, rather than the number of observations, should be reported as the sample size, and the effective number of clusters should be reported to guide inference. If the effective number of clusters is large, testing based on critical values from a normal distribution is appropriate.