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 .
This study considers various semiparametric difference-in-differences models under different assumptions on the relation between the treatment group identifier, time and covariates for cross-sectional 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 .
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In this study , we consider
This study considers various semiparametric
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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
under different assumptions on the relation between the treatment group identifier, time and covariates for cross-sectional
R
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
. 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