Machine Learning for Partial Identification: Example of Bracketed Data

Partially identified models occur commonly in economic applications. A common problem in this literature is a regression problem with bracketed (interval-censored) outcome variable Y, which creates a set-identified parameter of interest. The recent studies have only considered finite-dimensional linear regression in such context. To incorporate more complex controls into the problem, we consider a partially linear projection of Y on the set functions that are linear in treatment/policy variables and nonlinear in the controls. We characterize the identified set for the linear component of this projection and propose an estimator of its support function. Our estimator converges at parametric rate and has asymptotic normality properties. It may be useful for labor economics applications that involve bracketed salaries and rich, high-dimensional demographic data about the subjects of the study.

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