High-dimensional regression adjustments in randomized experiments

TL;DR

This paper explores how high-dimensional regression adjustments, including machine learning methods, can be used to efficiently estimate treatment effects in randomized experiments, extending their valid application.

Contribution

It introduces a broad theoretical framework for using various regression adjustments, including non-parametric methods, to improve treatment effect estimation in high-dimensional settings.

Findings

Any risk-consistent regression adjustment yields efficient estimates.

Proposes cross-estimation for unbiased treatment effect estimates.

Extends analysis to machine learning methods like random forests and neural networks.

Abstract

We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information, and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the average treatment effect. Our results considerably extend the range of settings where high-dimensional regression adjustments are guaranteed to provide valid inference about the population average treatment effect. We then propose cross-estimation, a simple method for obtaining finite-sample-unbiased treatment effect estimates that leverages high-dimensional regression adjustments. Our method can be used when the regression model is estimated using the lasso, the elastic net, subset selection, etc. Finally, we extend our analysis to allow for adaptive specification search via cross-validation, and flexible non-parametric regression adjustments with machine learning methods such as random forests or neural networks.