Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators for Binary Response Models

Econometrics Journal 18 (2015), 172–199.

33 Pages Posted: 24 Feb 2014 Last revised: 15 Aug 2015

Jason R. Blevins

Ohio State University (OSU) - Economics

Date Written: February 18, 2015

Abstract

This paper establishes consistency and non-standard rates of convergence for set estimators based on contour sets of criterion functions for a semiparametric binary response model under a conditional median restriction. The model may be partially identified due to potentially limited-support regressors. A set estimator analogous to the maximum score estimator is essentially cube-root consistent for the identified set when a continuous but possibly bounded regressor is present. Arbitrarily fast convergence occurs when all regressors are discrete. We also establish the validity of a subsampling procedure for constructing confidence sets for the identified set. As a technical contribution, we provide more convenient sufficient conditions on the underlying empirical processes for cube root convergence and a sufficient condition for arbitrarily fast convergence, both of which can be applied to other models. Finally, we carry out a series of Monte Carlo experiments which verify our theoretical findings and shed light on the finite sample performance of the proposed procedures.

Keywords: partial identification, cube-root asymptotics, semiparametric models, limited support regressors, transformation model, binary response model, maximum score estimator

JEL Classification: C13, C14, C25

Suggested Citation

Blevins, Jason R., Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators for Binary Response Models (February 18, 2015). Econometrics Journal 18 (2015), 172–199.. Available at SSRN: https://ssrn.com/abstract=2370487 or http://dx.doi.org/10.2139/ssrn.2370487

Jason R. Blevins (Contact Author)

Ohio State University (OSU) - Economics ( email )

Columbus, OH 43210-1172
United States

HOME PAGE: http://jblevins.org/

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