Efficient Estimation for Staggered Rollout Designs

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.