Before revision:  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 .
After revision:  We derive asymptotic results for new semiparametric and linear model based estimators for repeated cross-sections and panel data . The variance lower bound is shown to be sensitive to the model assumptions imposed implying a robustness-efficiency trade-off. The obtained efficient influence functions lead to estimators that are rate double robust and have desirable asymptotic properties under weak first stage convergence conditions. This enables to use sophisticated machine-learning algorithms that can cope with settings where common trend confounding is high-dimensional. The usefulness of the proposed estimators is assessed in an empirical example. It is shown that the efficiency-robustness trade-offs and the choice of first stage predictors can lead to divergent empirical results in practice .