Randomization Inference for Difference-in-Differences with Few Treated Clusters

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 over-reject, different variants of the wild cluster bootstrap can either over-reject or under-reject dramatically, and procedures based on randomization inference show promise. We study two randomization inference (RI) procedures. A procedure based on estimated coeffcients, which is essentially the one proposed by Conley and Taber (2011), has excellent power but may not perform well when the treated clusters are atypical. We therefore propose a new RI procedure based on t statistics. It typically performs better under the null, except when there is just one treated cluster, but at the cost of some power loss. Two empirical examples demonstrate that alternative procedures can yield dramatically different inferences