Nonparametric estimation of Conditional Average Treatment Effects under high-dimensional confounding

Abstract This study considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where the number of possible confounders is very large. We propose a two-step estimator for which the first step is estimated by machine learning. We show that this estimator has desirable statistical properties like consistency, asymptotic normality and rate double robustness. In particular, we derive the coupled convergence conditions between the nonparametric and the machine learning steps. We also show that estimating population average treatment effects by averaging the estimated heterogeneous effects is semiparametrically efficient. The resulting estimators are compared to other suggestions in the literature in Monte Carlo experiments that are inspired by real data. They are found to perform relatively better in most settings. The new estimators are applied to the empirical example of the effects of mothers’ smoking during pregnancy on the resulting birth weight.