Finitely Heterogeneous Treatment Effect in Event-study

Treatment effect estimation strategies in the event-study setup, namely panel data with variation in treatment timing, often use the parallel trend assumption that assumes mean independence across different treatment timings. In this paper, I relax the parallel trend assumption by including a latent type variable and develop a conditional two-way fixed-effects model. With a finite support assumption on the latent type variable, I show that an extremum classifier consistently estimates the type assignment. Then I solve the endogeneity problem of the selection into treatment by conditioning on the latent type, through which the treatment timing is correlated with the outcome. I also allow treatment to affect units of different types differently and thus directly model and estimate type-level heterogeneity in treatment effect.