Randomization inference for difference-in-differences with few treated clusters

Abstract

Inference using difference-in-differences with clustered data requires care. Previous research has shown that, when there are few treated clusters, t-tests based on cluster-robust variance estimators (CRVEs) severely overreject, and different variants of the wild cluster bootstrap can either overreject or underreject dramatically. We study two randomization inference (RI) procedures. A procedure based on estimated coefficients may be unreliable when clusters are heterogeneous. A procedure based on t-statistics typically performs better (although by no means perfectly) under the null, but at the cost of some power loss. An empirical example demonstrates that RI procedures can yield inferences that differ dramatically from those of other methods.