Targeted Difference-in-Differences Estimation with Staggered Treatment Designs
Date:
The difference-in-differences (DiD) is a fundamental econometric technique for estimating causal effects by comparing changes in outcomes over time between the treated and control groups. In the context of staggered DiD with multiple treatment groups and periods, conventional estimation based on the two-way fixed effects model yields negative weights when averaging heterogeneous group-period treatment effects. Although extensive efforts have been devoted to empirically diagnosing negative weights, they rarely focus on improving estimation efficiency. In this work, we define the overall average treatment effect on the treated (ATT) nonparametrically as a weighted average of heterogeneous group-period treatment effects, allowing time-varying covariates to adjust for parallel trends. We propose semiparametric estimators for the group-period, groupwise, periodwise, and dynamic ATTs, as well as the overall ATT. They are doubly robust and locally efficient under some data-generating mechanisms. We show that the overall ATT can be estimated as an equivalent weighted average of the residuals from an outcome regression. The proposed method is applied to examine the effect of parallel admission on justified envy relative to immediate admission in the national college admission examination in China.