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 set-up. First, we show how to 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, which 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