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.

翻译：本文研究了双重差分（DiD）研究设计中处理组平均处理效应（ATT）的半参数贝叶斯推断。我们提出了两种具有频率学派有效性的新贝叶斯方法。第一种是半参数贝叶斯结果回归，其中我们对对照组的条件均值函数采用高斯过程先验。第二种方法是双重稳健贝叶斯程序，它调整条件均值函数的先验分布，进而修正所得ATT的后验分布。我们为这两种方案证明了新的半参数贝叶斯-冯·米塞斯定理（BvM）。蒙特卡洛模拟和实证应用表明，所提出的贝叶斯DiD方法表现出良好的有限样本性能。我们还介绍了规范DiD方法的扩展，包括聚类数据和交错进入和多时期设置。