Before revision: 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.
After revision: In this study , we consider difference-in-differences models under different assumptions on the relation between the treatment group identifier, time and covariates for cross-sectional and panel data and show that they have desirable statistical properties like asymptotic normality and double robustness.