Semiparametric Triple Difference Estimators

Abstract: The triple difference causal inference framework is an extension of the well-known difference-in-differences framework. It relaxes the parallel trends assumption of the difference-in-differences framework through leveraging data from an auxiliary domain. Despite being commonly applied in empirical research, the triple difference framework has received relatively limited attention in the statistics literature. Specifically, investigating the intricacies of identification and the design of robust and efficient estimators for this framework has remained largely unexplored. This work aims to address these gaps in the literature. From the identification standpoint, we present outcome regression and weighting methods to identify the average treatment effect on the treated in both panel data and repeated cross-section settings. For the latter, we relax the commonly made assumption of time-invariant covariates. From the estimation perspective, we consider semiparametric estimators for the triple difference framework in both panel data and repeated cross-sections settings. These estimators are based upon the cross-fitting technique, and flexible machine learning tools can be used to estimate the nuisance components. We demonstrate that our proposed estimators are doubly robust, and we characterize the conditions under which they are consistent and asymptotically normal.