Potential Outcome Modeling and Estimation in DiD Designs with Staggered Treatments

We propose the first potential outcome modeling of Difference-in-Differences designs with multiple time periods and variation in treatment timing. Importantly, the modeling respects the two key identifying assumptions: parallel trends and noanticipation. We then introduce a straightforward Bayesian approach for estimation and inference of the time-varying group specific Average Treatment Effects on the Treated (ATT). To improve parsimony and guide prior elicitation, we reparametrize the model in a way that reduces the effective number of parameters. Prior information about the ATT's is incorporated through black-box training sample priors and, in small-sample settings, by thick-tailed t-priors that shrink ATT's of small magnitudes toward zero. We provide a computationally efficient Bayesian estimation procedure and establish a Bernstein-von Mises-type result that justifies posterior inference for the treatment effects. Simulation studies confirm that our method performs well in both large and small samples, offering credible uncertainty quantification even in settings that challenge standard estimators. We illustrate the practical value of the method through an empirical application that examines the effect of minimum wage increases on teen employment in the United States.