We study estimation of causal effects in staggered rollout designs, i.e. 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 eight times shorter than for existing approaches.

翻译：我们研究交错推广设计中因果效应的估计问题，即治疗采用时间交错且治疗时机近似随机分配的场景。我们在嵌套多种主流广义双重差分法的估计器类别中推导出最有效估计量。该有效估计量的可行插件版本具有渐近无偏性，其效率（弱）优于现有方法。我们提供基于t检验和置换检验的推断方法。在针对警察培训项目的应用中，所提估计量的置信区间比现有方法短八倍。