Debiased Machine Learning of Aggregated Intersection Bounds and Other Causal Parameters

This paper proposes a novel framework of aggregated intersection of regression functions, where the target parameter is obtained by averaging the minimum (or maximum) of a collection of regression functions over the covariate space. Such quantities include the lower and upper bounds on distributional effects (Frechet-Hoeffding, Makarov) and the optimal welfare in the statistical treatment choice problem. The proposed estimator -- the envelope score estimator -- is shown to have an oracle property, where the oracle knows the identity of the minimizer for each covariate value. I apply this result to the bounds in the Roy model and the Horowitz-Manski-Lee bounds with a discrete outcome. The proposed approach performs well empirically on the data from the Oregon Health Insurance Experiment.