Debiased Machine Learning of Set-Identified Linear Models
This work addresses statistical inference challenges in econometrics and causal inference when dealing with high-dimensional data and set-identified models.
The paper tackles the problem of estimating and conducting inference on the boundary of identified sets in linear models with high-dimensional covariates, achieving root-N consistent, uniformly asymptotically Gaussian estimators. It applies the methods to partially linear models, partially linear IV models, and average partial derivatives with interval-valued outcomes.
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.