This paper studies efficient estimation of causal effects in settings where there is staggered treatment adoption and the timing of treatment is as good as randomly assigned. We derive the most efficient estimator in a class of estimators that nests several 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. In an application to a training program for police officers, confidence intervals for the proposed estimator are as much as 8 times shorter than for existing approaches.

翻译：本文研究了在治疗交错采用且治疗时机近似随机分配的设定中，因果效应的高效估计问题。我们在一个涵盖多种广义双重差分方法的估计量类别中推导出最有效的估计量。该高效估计量的可行插件版本具有渐进无偏性，且其效率（弱）优于现有方法。我们提供了基于t检验和置换检验的推断方法。在一项针对警官培训项目的应用中，所提估计量的置信区间比现有方法缩短多达8倍。