Inference with “Difference in Differences” with a Small Number of Policy Changes

Abstract

In difference-in-differences applications, identification of the key parameter often arises from changes in policy by a small number of groups. In contrast, typical inference assumes that the number of groups changing policy is large. We present an alternative inference approach for a small (finite) number of policy changers, using information from a large sample of nonchanging groups. Treatment effect point estimators are not consistent, but we can consistently estimate their asymptotic distribution under any point null hypothesis about the treatment. Thus, treatment point estimators can be used as test statistics, and confidence intervals can be constructed using test statistic inversion.