Efficient Estimation for Staggered Rollout Designs

TL;DR

This paper develops a highly efficient estimator for causal effects in staggered rollout designs, improving inference accuracy and providing shorter confidence intervals compared to existing methods.

Contribution

It introduces the most efficient estimator within a class of generalized difference-in-differences methods, with a feasible plug-in version that outperforms current approaches.

Findings

Feasible estimator is asymptotically unbiased and more efficient.

Confidence intervals are up to eight times shorter in real data application.

Provides both t-based and permutation-test inference methods.

Abstract

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.