  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.
