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Machine Learning for Set-Identified Linear Models

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Document pages: 82 pages

Abstract: This paper provides estimation and inference methods for an identified setwhere the selection among a very large number of covariates is based on modernmachine learning tools. I characterize the boundary of the identified set(i.e., support function) using a semiparametric moment condition. CombiningNeyman-orthogonality and sample splitting ideas, I construct a root-Nconsistent, uniformly asymptotically Gaussian estimator of the support functionand propose a weighted bootstrap procedure to conduct inference about theidentified set. I provide a general method to construct a Neyman-orthogonalmoment condition for the support function. Applying my method to Lee (2008) sendogenous selection model, I provide the asymptotic theory for the sharp(i.e., the tightest possible) bounds on the Average Treatment Effect in thepresence of high-dimensional covariates. Furthermore, I relax the conventionalmonotonicity assumption and allow the sign of the treatment effect on theselection (e.g., employment) to be determined by covariates. Using JobCorpsdata set with very rich baseline characteristics, I substantially tighten thebounds on the JobCorps effect on wages under weakened monotonicity assumption.

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