Permutation Inference with a Finite Number of Heterogeneous Clusters

I introduce a simple permutation procedure to test conventional (non-sharp) hypotheses about the effect of a binary treatment in the presence of a finite number of large, heterogeneous clusters when the treatment effect is identified by comparisons across clusters. The procedure asymptotically controls size by applying a level-adjusted permutation test to a suitable statistic. The adjusted permutation test is easy to implement in practice and performs well at conventional levels of significance with at least four treated clusters and a similar number of control clusters. It is particularly robust to situations where some clusters are much more variable than others.