Title: Confidence Intervals for Causal Effects with Propensity Score and Outcome Regression Estimated with Machine Learning: When are They Valid?

Abstract: In estimation of causal effects (such as the average causal effect or the variance weighted average causal effect) in the presence of high dimensional covariates sufficient to control confounding, an increasingly popular procedure is to estimate the causal effect using doubly robust estimators with the propensity score and outcome regression estimated by machine learning and then to construct Wald confidence intervals based on a estimator of the standard error. The validity of these intervals depends critically on the assumption that the bias is less than the standard error.  If the latter assumption is wrong, the intervals will undercover, perhaps dramatically. Can anything be done about this problem since the bias of the estimator is unknown. Recently a number of approaches to this problem have been offered. I will discuss these and then offer my own approach which generally greatly improves upon alternatives..