810 research outputs found
Efficient Estimation for Staggered Rollout Designs
Researchers are frequently interested in the causal effect of a treatment
that is (quasi-)randomly rolled out to different units at different points in
time. This paper studies how to efficiently estimate a variety of causal
parameters in a Neymanian-randomization based framework of random treatment
timing. We solve for the most efficient estimator in a class of estimators that
nests two-way fixed effects models as well as several popular generalized
difference-in-differences methods. The efficient estimator is not feasible in
practice because it requires knowledge of the optimal weights to be placed on
pre-treatment outcomes. However, the optimal weights can be estimated from the
data, and in large datasets the plug-in estimator that uses the estimated
weights has similar properties to the "oracle" efficient estimator. We
illustrate the performance of the plug-in efficient estimator in simulations
and in an application to Wood et al. (2020a,b)'s study of the staggered rollout
of a procedural justice training program for police officers. We find that
confidence intervals based on the plug-in efficient estimator have good
coverage and can be as much as five times shorter than confidence intervals
based on existing methods. As an empirical contribution of independent
interest, our application provides the most precise estimates to date on the
effectiveness of procedural justice training programs for police officers
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