Doubly-Robust Inference for Conditional Average Treatment Effects with High-Dimensional Controls

TL;DR

This paper introduces a doubly-robust estimator for conditional average treatment effects (CATEs) in high-dimensional settings, providing valid inference even when one of the models is misspecified, using Lasso for estimation.

Contribution

It proposes a new CATE estimator with Wald-type confidence intervals that are doubly-robust and valid under model misspecification, addressing high-dimensional confounders.

Findings

Estimator remains consistent at the nonparametric rate.

Confidence intervals are asymptotically valid under misspecification.

Uses Lasso for high-dimensional model estimation.

Abstract

Plausible identification of conditional average treatment effects (CATEs) may rely on controlling for a large number of variables to account for confounding factors. In these high-dimensional settings, estimation of the CATE requires estimating first-stage models whose consistency relies on correctly specifying their parametric forms. While doubly-robust estimators of the CATE exist, inference procedures based on the second stage CATE estimator are not doubly-robust. Using the popular augmented inverse propensity weighting signal, we propose an estimator for the CATE whose resulting Wald-type confidence intervals are doubly-robust. We assume a logistic model for the propensity score and a linear model for the outcome regression, and estimate the parameters of these models using an $\ell_1$ (Lasso) penalty to address the high dimensional covariates. Our proposed estimator remains consistent at the nonparametric rate and our proposed pointwise and uniform confidence intervals remain asymptotically valid even if one of the logistic propensity score or linear outcome regression models are misspecified. These results are obtained under similar conditions to existing analyses in the high-dimensional and nonparametric literatures.