Nonparametric estimation of causal heterogeneity under high-dimensional confounding

TL;DR

This paper develops a two-step nonparametric estimator for heterogeneous treatment effects in high-dimensional settings, combining machine learning with theoretical guarantees for consistency and efficiency.

Contribution

It introduces a novel two-step estimator that handles high-dimensional confounders and provides theoretical properties like consistency, asymptotic normality, and efficiency.

Findings

Estimator achieves consistency and asymptotic normality.

Estimates are semi-parametrically efficient.

Application to maternal smoking and birth weight.

Abstract

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.