Finitely Heterogeneous Treatment Effect in Event-study

TL;DR

This paper relaxes the parallel trends assumption in difference-in-differences designs by introducing a finite heterogeneity model with latent types, enabling consistent estimation of type-specific treatment effects using long pretreatment periods.

Contribution

It develops a novel framework for identifying and estimating heterogeneity in treatment effects through latent types and a type-specific diff-in-diff estimator.

Findings

Consistent classification of latent types using extremum classifiers.

Estimation of type-specific average treatment effects.

Enhanced understanding of heterogeneity beyond baseline outcomes.

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.