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

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  • Siddhartha Chib
  • Kenichi Shimizu

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.

Suggested Citation

  • Siddhartha Chib & Kenichi Shimizu, 2025. "Bayesian Estimation of Cohort-Time-Stratum Specific Effects in Staggered Difference-in-Differences," Papers 2505.18391, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2505.18391
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    References listed on IDEAS

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