This paper studies efficient estimation of causal effects when treatment is (quasi-) randomly rolled out to units at different points in time. We solve for the most efficient estimator in a class of estimators that nests two-way fixed effects models and other popular generalized difference-in-differences methods. A feasible plug-in version of the efficient estimator is asymptotically unbiased with efficiency (weakly) dominating that of existing approaches. We provide both $t$-based and permutation-test based methods for inference. We illustrate the performance of the plug-in efficient estimator in simulations and in an application to Wood et al. (2020a)'s study of the staggered rollout of a procedural justice training program for police officers. We find that confidence intervals based on the plug-in efficient estimator have good coverage and can be as much as five times shorter than confidence intervals based on existing state-of-the-art methods. As an empirical contribution of independent interest, our application provides the most precise estimates to date on the effectiveness of procedural justice training programs for police officers.

翻译：本文研究在治疗(quasi-)随机向不同时间点的单位推广时,对因果关系的有效估计。我们解决了搭建双向固定效应模型和其他普遍普遍差异方法的一类估测器中最高效的估测员的问题。一个可行的高效估测器插座版本是零星的,效率(微弱)高于现有方法。我们提供了基于美元和基于调整测试的推断方法。我们在模拟和对Wood等人的应用(2020年a)中演示了高效估测器的性能。我们发现,基于插座高效估测器的信任期覆盖面良好,比基于现有最新方法的信任期短五倍。作为独立利益的经验贡献,我们的应用为警官程序司法培训方案的实效提供了最准确的估计。