Finitely Heterogeneous Treatment Effect in Event-study

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: parallel trend assumption. In this paper, we relax the parallel trend assumption by assuming a latent type variable and developing a type-specific parallel trend. With a finite support assumption on the latent type and long pretreatment time periods, an extremum classifier consistently estimates the type assignment. Based on the classification, we propose a type-specific DiD estimator for type-specific ATT. By estimating the type-specific ATT, we study heterogeneity in treatment effect, in addition to heterogeneity in baseline outcomes.