Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions

TL;DR

This paper introduces a method called Approximate Residual Balancing that enables accurate inference of average treatment effects in high-dimensional settings by de-biasing penalized regression adjustments, requiring only overlap assumptions.

Contribution

It develops a novel de-biasing technique combining balancing weights with regularized regression, allowing sqrt{n}-consistent inference without sparsity assumptions on treatment effects.

Findings

Method achieves consistent ATE estimation in high dimensions.

Requires only overlap, not sparsity of treatment effects.

Enables use of lasso for treatment effect inference.

Abstract

There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on pre-treatment variables. The unconfoundedness assumption is often more plausible if a large number of pre-treatment variables are included in the analysis, but this can worsen the performance of standard approaches to treatment effect estimation. In this paper, we develop a method for de-biasing penalized regression adjustments to allow sparse regression methods like the lasso to be used for sqrt{n}-consistent inference of average treatment effects in high-dimensional linear models. Given linearity, we do not need to assume that the treatment propensities are estimable, or that the average treatment effect is a sparse contrast of the outcome model parameters. Rather, in addition standard assumptions used to make lasso regression on the outcome model consistent under 1-norm error, we only require overlap, i.e., that the propensity score be uniformly bounded away from 0 and 1. Procedurally, our method combines balancing weights with a regularized regression adjustment.