Inference with few heterogeneous clusters

Suppose estimating a model on each of a small number of potentially heterogeneous clusters yields approximately independent, unbiased, and Gaussian parameter estimators. We make two contributions in this setup. First, we showhowto compare a scalar parameter of interest between treatment and control units using a Two-Sample T-Statistic, extending previous results for the One-Sample T-Statistic. Second, we develop a test for the appropriate level of clustering, it tests the null hypothesis that clustered standard errors from a much finer partition are correct. We illustrate the approach by revisiting empirical studies involving clustered, time series, and spatially correlated data.