Bayesian Estimation of Cohort-Time-Stratum Specific Effects in Staggered Difference-in-Differences

TL;DR

This paper introduces a Bayesian framework for estimating detailed treatment effects in staggered difference-in-differences studies, accounting for heterogeneity across cohorts, time, and subgroups.

Contribution

It develops a unified probabilistic model that stabilizes inference for high-dimensional effect arrays and proves asymptotic validity of credible intervals.

Findings

Finite-sample improvements demonstrated in simulations.

Application reveals significant subgroup heterogeneity.

Framework stabilizes inference in sparse settings.

Abstract

Difference-in-Differences designs with staggered treatment adoption are widely used to study heterogeneous treatment effects across cohorts and time periods. We develop a probabilistic framework for estimating potentially high-dimensional ATT arrays that vary across cohorts, periods, and strata defined by baseline covariates. The framework jointly estimates subgroup-specific treatment effects through a unified likelihood-based model, stabilizing inference in sparse cohort-by-time-by-stratum settings. We establish a Bernstein-von Mises theorem for the ATT array, implying asymptotically valid frequentist coverage of posterior credible intervals. Simulations and an application to minimum wage increases and teen employment demonstrate meaningful finite-sample improvements and important subgroup heterogeneity.