Slope Consistency of Quasi-Maximum Likelihood Estimator for Binary Choice Models

Yoosoon Chang, Joon Y. Park and Guo Yan

Papers from arXiv.org

Abstract: Although QMLE is generally inconsistent, logistic regression relying on the binary choice model (BCM) with logistic errors is widely used, especially in machine learning contexts with many covariates and high-dimensional slope coefficients. This paper revisits the slope consistency of QMLE for BCMs. Ruud (1983) introduced a set of conditions under which QMLE may yield a constant multiple of the slope coefficient of BCMs asymptotically. However, he did not fully establish slope consistency of QMLE, which requires the existence of a positive multiple of slope coefficient identified as an interior maximizer of the population QMLE likelihood function over an appropriately restricted parameter space. We fill this gap by providing a formal proof of slope consistency under the same set of conditions for any binary choice model identified as in Manski (1975, 1985). Our result implies that logistic regression yields a consistent estimate for the slope coefficient of BCMs under suitable conditions.

Date: 2025-05, Revised 2025-09
New Economics Papers: this item is included in nep-dcm and nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2505.02327 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2505.02327

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().