Efficient Difference-in-Differences Estimation with High-Dimensional\n Common Trend Confounding

This study considers various semiparametric difference-in-differences models\nunder different assumptions on the relation between the treatment group\nidentifier, time and covariates for cross-sectional and panel data. The\nvariance lower bound is shown to be sensitive to the model assumptions imposed\nimplying a robustness-efficiency trade-off. The obtained efficient influence\nfunctions lead to estimators that are rate double robust and have desirable\nasymptotic properties under weak first stage convergence conditions. This\nenables to use sophisticated machine-learning algorithms that can cope with\nsettings where common trend confounding is high-dimensional. The usefulness of\nthe proposed estimators is assessed in an empirical example. It is shown that\nthe efficiency-robustness trade-offs and the choice of first stage predictors\ncan lead to divergent empirical results in practice.\n