Finitely Heterogeneous Treatment Effect in Event-study
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Treatment effect estimation strategies in the event-study setup, namely a 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 finite support assumption on the latent type variable, I show that an extremum classifier consistently estimates the type assignment. Firstly, 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. Secondly, as the type assignment is explicitly estimated, further heterogeneity than the usual unit fixed-effects across units can be documented; treatment is allowed to affect units of different types differently and the variation in treatment effect is documented jointly with the variation in untreated outcome.
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