Debiased Machine Learning of Set-Identified Linear Models

TL;DR

This paper develops estimation and inference methods for the boundary of set-identified linear models using modern regularization, semiparametric moment equations, and Neyman-orthogonality, enabling robust inference in high-dimensional settings.

Contribution

It introduces a novel estimator for the boundary of set-identified models that is root-N consistent and asymptotically Gaussian, utilizing sample splitting and bootstrap inference.

Findings

Estimator achieves root-N consistency and asymptotic normality.

Applicable to partially linear and IV models with interval outcomes.

Provides a bootstrap procedure for valid inference.

Abstract

This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the boundary and propose a multiplier bootstrap procedure to conduct inference. I apply this result to the partially linear model, the partially linear IV model and the average partial derivative with an interval-valued outcome.