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

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