  Given the unconfoundedness assumption, we propose new nonparametric
estimators for the reduced dimensional conditional average treatment effect
(CATE) function. In the first stage, the nuisance functions necessary for
identifying CATE are estimated by machine learning methods, allowing the number
of covariates to be comparable to or larger than the sample size. The second
stage consists of a low-dimensional local linear regression, reducing CATE to a
function of the covariate(s) of interest. We consider two variants of the
estimator depending on whether the nuisance functions are estimated over the
full sample or over a hold-out sample. Building on Belloni at al. (2017) and
Chernozhukov et al. (2018), we derive functional limit theory for the
estimators and provide an easy-to-implement procedure for uniform inference
based on the multiplier bootstrap. The empirical application revisits the
effect of maternal smoking on a baby's birth weight as a function of the
mother's age.
