# Semiparametric Bayesian Difference-in-Differences

arXiv: https://arxiv.org/abs/2412.04605 · HTML: https://mlsanity.com/paper/2412.04605/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2024.

## Abstract (arXiv)

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 is the semiparametric Bayesian outcome regression, where we place a Gaussian process prior on the conditional mean function of the control group. The second method is a doubly 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. We also present extensions of the canonical DiD approach, incorporating clustered data and staggered entry with multiple periods.