Difference-in-Differences designs with staggered treatment adoption are widely used to study heterogeneous treatment effects across cohorts and time periods. We develop a probabilistic framework for estimating potentially high-dimensional ATT arrays that vary across cohorts, periods, and strata defined by baseline covariates. The framework jointly estimates subgroup-specific treatment effects through a unified likelihood-based model, stabilizing inference in sparse cohort-by-time-by-stratum settings. We establish a Bernstein-von Mises theorem for the ATT array, implying asymptotically valid frequentist coverage of posterior credible intervals. Simulations and an application to minimum wage increases and teen employment demonstrate meaningful finite-sample improvements and important subgroup heterogeneity.

翻译：交错采用双重差分设计被广泛用于研究不同队列和时间段内的异质性处理效应。我们开发了一个概率框架，用于估计跨队列、时间段及由基线协变量定义的分层变化的高维ATT数组。该框架通过统一的基于似然的模型联合估计子组特定处理效应，在稀疏的队列-时间-分层设定下稳定推断。我们为ATT数组建立了Bernstein-von Mises定理，这意味着后验可信区间的渐近有效频率推断。模拟实验及一项关于最低工资增长与青少年就业的应用研究展示了有意义的有限样本改进及重要的子组异质性。