Semiparametric Bayesian Difference-in-Differences
- URL: http://arxiv.org/abs/2412.04605v3
- Date: Sun, 15 Jun 2025 20:34:25 GMT
- Title: Semiparametric Bayesian Difference-in-Differences
- Authors: Christoph Breunig, Ruixuan Liu, Zhengfei Yu,
- Abstract summary: We study semiparametric Bayesian inference for the average treatment effect on the treated (ATT) within the difference-in-differences (DiD) research design.<n>We propose two new Bayesian methods with frequentist validity.
- Score: 2.458652618559425
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper studies semiparametric Bayesian inference for the average treatment effect on the treated (ATT) within the difference-in-differences (DiD) research design. We propose two new Bayesian methods with frequentist validity. The first one places a standard Gaussian process prior on the conditional mean function of the control group. The second method is a double robust Bayesian procedure that adjusts the prior distribution of the conditional mean function and subsequently corrects the posterior distribution of the resulting ATT. We prove new semiparametric Bernstein-von Mises (BvM) theorems for both proposals. Monte Carlo simulations and an empirical application demonstrate that the proposed Bayesian DiD methods exhibit strong finite-sample performance compared to existing frequentist methods. We also present extensions of the canonical DiD approach, incorporating both the staggered design and the repeated cross-sectional design.
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