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Tuesday, February 5, 2019 at 11:40am to 1:10pm
Sage Hall, 141
Johnson Graduate School-Management, 106 Sage Hall, Ithaca, NY 14853-6201, USA
Vira Semenova, MIT
Machine Learning for Set-Identified Linear Models
Abstract: Set-identified models often restrict the number of covariates leading to wide identified sets in practice. This paper provides estimation and inference methods for set-identified linear models with high-dimensional covariates where the model selection is based on modern machine learning tools. I characterize the support function of the identified set using a semiparametric moment condition. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the support function. I also prove the validity of the Bayesian bootstrap procedure to conduct inference about the identified set. I provide a general method to construct a Neyman-orthogonal moment condition for the support function. I apply this result to estimate sharp non-parametric bounds on the average treatment effect in Lee (2008)’s model of endogenous selection and substantially tighten the bounds on this parameter in Angrist et al. (2006)’s empirical setting. I also apply this result to estimate sharp identified sets for two other parameters - a new parameter, called a partially linear predictor, and the average partial derivative when the outcome variable is interval-censored.