Non‐standard rates of convergence of criterion‐function‐based set estimators for binary response models. Issue 2 (24th June 2015)

• Record Type: Journal Article
• Authors: Blevins, Jason R.
• Is Part Of: Econometrics journal. Volume 18:Issue 2(2015)
• Page Start: 172
• Page End: 199
• Publication Date: 2015-06-24
• Subjects: Econometrics -- Periodicals; 330.015195
• DOI: 10.1111/ectj.12048
• Languages: English
• ISSNs: 1368-4221

Abstract

<abstract abstract-type="main"> <title>Summary</title> <p>This paper establishes consistency and non‐standard rates of convergence for set estimators based on contour sets of criterion functions for a semi‐parametric binary response model under a conditional median restriction. The model can be partially identified due to potentially limited‐support regressors and an unknown distribution of errors. 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.</p> </abstract>