Estimation of Conditional Average Treatment Effects With High-Dimensional Data

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. and Chernozhukov et al., 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.

Automated summary

This study proposes new nonparametric estimators for the reduced dimensional conditional average treatment effect function, with the nuisiance functions estimated by machine learning in the first stage and local linear regression in the second stage. The functional limit theory is derived and a uniform inference procedure based on multiplier bootstrap is provided. The empirical application examines the effect of maternal smoking on a baby's birth weight as a function of the mother's age.