Estimation of conditional average treatment effects with high-dimensional data

• Main Authors: FAN, Qingliang, HSU, Yu-Chin, LIELI, Robert P., ZHANG, Yichong
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2020
• Subjects: Heterogenous treatment effects; high-dimensional data; uniform confidence band; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2455; https://ink.library.smu.edu.sg/context/soe_research/article/3454/viewcontent/Unconditional_Quantile_Regression_High_D_sv.pdf
• Institution: Singapore Management University

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. This is a key feature since identification is generally more credible if the full vector of conditioning variables, including possible transformations, is high-dimensional. The second stage consists of a low-dimensional kernel 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.