We develop a unified model for both treated and untreated potential outcomes for Difference-in-Differences designs with multiple time periods and staggered treatment adoption that respects parallel trends and no anticipation. The model incorporates unobserved heterogeneity through sequence-specific random effects and covariate-dependent random intercepts, allowing for flexible baseline dynamics while preserving causal identification. The model lends itself to straightforward inference about group-specific, time-varying Average Treatment Effects on the Treated (ATTs). In contrast to existing methods, it is easy to regularize the ATT parameters in our framework. For Bayesian inference, prior information on the ATTs is incorporated through black-box training sample priors and, in small-sample settings, through thick-tailed t-priors that shrink ATTs of small magnitude toward zero. A hierarchical prior can be employed when ATTs are defined at sub-categories. A Bernstein-von Mises result justifies posterior inference for the treatment effects. To show that the model provides a common foundation for Bayesian and frequentist inference, we develop an iterated feasible GLS based estimation of the ATTs that is based on the updates in the Bayesian posterior sampling. The model and methodology are illustrated in an empirical study of the effects of minimum wage increases on teen employment in the U.S.

翻译：本文针对具有多时期和交错处理采纳的双重差分设计，构建了一个统一模型，该模型同时涵盖处理组与对照组的潜在结果，并满足平行趋势假设和无预期假设。该模型通过序列特异性随机效应和协变量依赖型随机截距项纳入未观测异质性，在保持因果识别的同时允许灵活的基线动态变化。该模型便于对组别特异性、时变的处理组平均处理效应进行直接推断。与现有方法相比，本框架中的ATT参数易于正则化处理。在贝叶斯推断中，ATT的先验信息可通过黑箱训练样本先验进行整合；在小样本场景下，则通过厚尾t先验将幅度较小的ATT收缩至零。当ATT在子类别层面定义时，可采用分层先验。伯恩斯坦-冯·米塞斯定理为处理效应的后验推断提供了理论依据。为证明该模型为贝叶斯与频率学派推断提供了共同基础，我们基于贝叶斯后验采样中的更新步骤，开发了一种基于迭代可行广义最小二乘法的ATT估计方法。通过美国最低工资上涨对青少年就业影响的实证研究，展示了该模型与方法论的实际应用。