Debiased Machine Learning of Aggregated Intersection Bounds and Other Causal Parameters

2023/03/02 by В. М. Семенова, Semenova, Vira
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Econometrics (econ.EM) #FOS: Economics and business #Machine Learning and Algorithms #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2303.00982

openalex publication_date 2023/03/02 · openalex created_date 2023/03/05 · openalex updated_date 2026/07/28

Abstract

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.

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