The difference-in-differences (DiD) design is a quasi-experimental method for estimating treatment effects from panel data. With staggered adoption, the average treatment effect on the treated (ATT) is defined at the group-period level and aggregated into groupwise, periodwise, dynamic, and overall estimands. Existing doubly robust estimators typically compare treated groups to a single reference group and do not account for differing variability across multiple not-yet-treated cohorts. We propose an augmented inverse variance weighting (AIVW) estimator that pools information across all available not-yet-treated groups using conditional-variance weights, extending this approach to settings with time-varying covariates under an explicit covariate-exogeneity condition. Under a homoskedastic working model, AIVW reduces to an augmented inverse probability weighting (AIPW) estimator that is simpler to compute and more robust in finite samples. Both estimators are doubly robust, and we characterize the specific conditions under which they attain the semiparametric efficiency bound. In simulation studies, AIVW and AIPW achieve lower bias and variance than existing doubly robust estimators when not-yet-treated groups differ in conditional variability. As an illustration, we study the effect of a parallel college admission mechanism, relative to immediate admission, on justified envy using staggered provincial reform data from the China National College Entrance Examination.

翻译：暂无翻译