  This paper 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
semi-parametrically efficient. The new estimator is an empirical example of the
effects of mothers' smoking during pregnancy on the resulting birth weight.
