Efficient Inference of Average Treatment Effects in High Dimensions via Approximate Residual Balancing

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 finite sample properties of standard approaches to treatment effect estimation. There are some recent proposals on how to extend classical methods to the high dimensional setting; however, to our knowledge, all existing method rely on consistent estimability of the propensity score, i.e., the probability of receiving treatment given pre-treatment variables. In this paper, we propose a new method for estimating average treatment effects in high dimensional linear settings that attains dimension-free rates of convergence for estimating average treatment effects under substantially weaker assumptions than existing methods: Instead of requiring the propensity score to be estimable, we only require overlap, i.e., that the propensity score be uniformly bounded away from 0 and 1. Procedurally, out method combines balancing weights with a regularized regression adjustment.