Efficient Difference-in-Differences and Event-Study Estimators

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Joint with Pedro Sant'Anna (Emory), and Haitian Xie (Peking University)

Abstract: This paper provides guidelines for optimal Difference-in-Differences (DiD) and Event Study (ES) estimators based on semiparametric efficient variance, both with and without variation in treatment timing. We characterize the semiparametric efficiency bounds for estimating average treatment effect for the treated (ATT) parameters under different parallel trends assumptions with short panel data, which provides a benchmark for evaluating existing and new DiD estimators. Our results show that efficient DiD and ES estimators should generally assign non-uniform weights to pre-treatment periods and untreated comparison cohorts, with weighting also influenced by covariate values and the temporal correlation of outcome changes. Building on these insights, we propose data-driven, easy-to-implement estimators that achieve the semiparametric efficiency bound. We also discuss testing procedures for assessing the validity of key identification assumptions, offering practical tools for improving inference in DiD and ES applications.