Model-based Estimation of Difference-in-Differences with Staggered Treatments
🤖 AI Summary
In staggered-treatment difference-in-differences (DiD) designs with small samples, conventional asymptotic inference fails and average treatment effect on the treated (ATT) estimation is unreliable. To address this, we propose a Bayesian framework based on reparameterization of potential outcomes. Our method employs heavy-tailed t-priors to shrink small effects toward zero, thereby avoiding reliance on asymptotic approximations. We establish a Bernstein–von Mises-type theorem, ensuring valid posterior inference even in finite samples. Simulation studies demonstrate substantial improvements in ATT estimation accuracy and nominal coverage of credible intervals relative to existing approaches. Applied to evaluating the impact of U.S. minimum wage policies on teen employment, our method yields more robust causal estimates. The core contribution lies in the first systematic integration of interpretable potential-outcome modeling, heavy-tailed shrinkage priors, and finite-sample theoretical guarantees—providing a principled Bayesian solution for small-sample staggered DiD analysis.
Application Category
📝 Abstract
We propose a model-based framework for estimating treatment effects in Difference-in-Differences (DiD) designs with multiple time-periods and variation in treatment timing. We first present a simple model for potential outcomes that respects the identifying conditions for the average treatment effects on the treated (ATT's). The model-based perspective is particularly valuable in applications with small sample sizes, where existing estimators that rely on asymptotic arguments may yield poor approximations to the sampling distribution of group-time ATT's. To improve parsimony and guide prior elicitation, we reparametrize the model in a way that reduces the effective number of parameters. Prior information about treatment effects 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 straightforward and 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.
Problem
Research questions and friction points this paper is trying to address.
Estimating treatment effects in staggered DiD designs
Improving small-sample accuracy for ATT estimation
Incorporating prior information via Bayesian methods
Innovation
Methods, ideas, or system contributions that make the work stand out.
Model-based framework for staggered DiD designs
Reparametrization reduces effective parameters
Bayesian estimation with robust uncertainty quantification
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