The LOOP Estimator: Adjusting for Covariates in Randomized Experiments

When conducting a randomized controlled trial, it is common to specify in advance the statistical analyses that will be used to analyze the data. Typically, these analyses will involve adjusting for small imbalances in baseline covariates. However, this poses a dilemma, as adjusting for too many covariates can hurt precision more than it helps, and it is often unclear which covariates are predictive of outcome prior to conducting the experiment.

This article aims to produce a covariate adjustment method that allows for automatic variable selection, so that practitioners need not commit to any specific set of covariates prior to seeing the data.

In this article, we propose the "leave-one-out potential outcomes" estimator. We leave out each observation and then impute that observation's treatment and control potential outcomes using a prediction algorithm such as a random forest. In addition to allowing for automatic variable selection, this estimator is unbiased under the Neyman-Rubin model, generally performs at least as well as the unadjusted estimator, and the experimental randomization largely justifies the statistical assumptions made.