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.
In this study, we consider difference-in-differences models with a common trend assumption that is only valid after conditioning on covariates. We suggest novel two-step estimators that allow the covariates to enter the model in a very flexible form. In particular, the first stages can be estimated using 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 semiparametric efficiency bounds for difference-in-differences estimation with cross-sectional and panel data . The proposed semiparametric estimators attain the bounds . 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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novel two-step
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we propose estimation procedures that involve
the first stages can be estimated using
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a semiparametric efficiency bound for panel
semiparametric efficiency bounds for
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with cross-sectional and panel data
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estimator attains this bound
estimators attain the bounds