On regression-adjusted imputation estimators of the average treatment effect

TL;DR

This paper proves that a broad class of regression-adjusted imputation estimators are doubly robust and semiparametrically efficient for estimating average treatment effects, covering methods like matching and random forests.

Contribution

It formalizes the doubly robust property of regression-adjusted imputation estimators and establishes their efficiency under correct model specification.

Findings

Many regression-adjusted imputation methods are doubly robust.

These estimators are semiparametrically efficient with correct models.

Examples include kernel matching, nearest neighbor, local linear, and random forests.

Abstract

Imputing missing potential outcomes using an estimated regression function is a natural idea for estimating causal effects. In the literature, estimators that combine imputation and regression adjustments are believed to be comparable to augmented inverse probability weighting. Accordingly, people for a long time conjectured that such estimators, while avoiding directly constructing the weights, are also doubly robust (Imbens, 2004; Stuart, 2010). Generalizing an earlier result of the authors (Lin et al., 2021), this paper formalizes this conjecture, showing that a large class of regression-adjusted imputation methods are indeed doubly robust for estimating the average treatment effect. In addition, they are provably semiparametrically efficient as long as both the density and regression models are correctly specified. Notable examples of imputation methods covered by our theory include kernel matching, (weighted) nearest neighbor matching, local linear matching, and (honest) random forests.