Event-Study Designs for Discrete Outcomes with Latent Transition Heterogeneity

Abstract

We develop an identification strategy for average treatment effects on the treated (ATT) in panel data with discrete outcomes. For such outcomes, the parallel trends assumption underlying difference-in-differences (DiD) fails in three distinct ways: mean reversion generates divergent trends when groups differ at baseline, counterfactual probabilities can leave the unit interval, and no single trend is well defined for multi-category outcomes. We replace parallel trends with \textit{transition independence}: absent treatment, transition dynamics conditional on pre-treatment outcomes would be identical between treated and control groups. To accommodate selection on persistent unobserved heterogeneity in transition dynamics, we require transition independence to hold only within latent types. Modeling outcomes as a finite mixture of Markov chains, we identify latent-type and aggregate ATTs from short panels. The framework also yields a flow decomposition of the ATT into inflow and outflow channels. In three empirical applications, our ATT estimates differ substantially from conventional DiD.