Finitely Heterogeneous Treatment Effect in Event-study

Abstract: A key assumption of the differences-in-differences designs is that the average evolution of untreated potential outcomes is the same across different treatment cohorts: a parallel trends assumption. In this paper, we relax the parallel trend assumption by assuming a latent type variable and developing a type-specific parallel trend assumption. With a finite support assumption on the latent type variable and long pretreatment time periods, we show that an extremum classifier consistently estimates the type assignment. Based on the classification result, we propose a type-specific diff-in-diff estimator for type-specific ATT. By estimating the type-specific ATT, we study heterogeneity in treatment effect, in addition to heterogeneity in baseline outcomes.