We contribute to the theoretical literature on difference-in-differences estimation for policy evaluation by allowing the common trend assumption to hold conditional on a high-dimensional covariate set. In particular, the covariates can enter the difference-in-differences model in a very flexible form leading to estimation procedures that involve supervised machine learning methods. We derive asymptotic results for semiparametric and parametric estimators for repeated cross-sections and panel data and show  desirable statistical properties . Notably, a non-standard semiparametric efficiency bound for  difference-in-differences estimation that incorporates the repeated cross-section case is established. Our proposed semiparametric estimator is shown to attain this bound. The usability of the methods is assessed by replicating a study on an employment protection reform. We demonstrate that the notion of high-dimensional common trend confounding has implications for the economic interpretation of  policy evaluation results via difference-in-differences .
In this study, we consider difference-in-differences models with a common trend assumption that is only valid after conditioning on covariates. We suggest estimators that allow the covariates to enter the model in a very flexible form . In particular, we propose estimation procedures that involve supervised machine learning methods. We derive asymptotic results for new semiparametric and linear model based estimators for repeated cross-sections and panel data and show that they have desirable statistical properties like asymptotic normality and double robustness. Further, we establish a semiparametric efficiency bound for panel difference-in-differences estimation . The proposed semiparametric estimator attains this bound. The usability of the methods is assessed by replicating a study on an employment protection reform. We demonstrate that the notion of high-dimensional common trend confounding has implications for the economic interpretation of the policy evaluation results . Notably, measured reform effects are substantially decreased or even reversed when covariates are included in a data-driven manner .
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