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

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Hauptverfasser: Chang, Yoosoon, Park, Joon Y., Yan, Guo
Format: Preprint
Veröffentlicht: 2025
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author Chang, Yoosoon
Park, Joon Y.
Yan, Guo
author_facet Chang, Yoosoon
Park, Joon Y.
Yan, Guo
contents 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. 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 the slope consistency of QMLE, which requires the existence of a positive multiple of the true slope that maximizes the population QMLE likelihood over an appropriately restricted parameter space. We close this gap by providing a formal proof of slope consistency under the same set of conditions for BCMs identified as in Manski (1975, 1985). Our result implies that, under suitable conditions, logistic regression yields a consistent estimate of the slope coefficient for BCMs.
format Preprint
id arxiv_https___arxiv_org_abs_2505_02327
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Slope Consistency of Quasi-Maximum Likelihood Estimator for Binary Choice Models
Chang, Yoosoon
Park, Joon Y.
Yan, Guo
Econometrics
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. 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 the slope consistency of QMLE, which requires the existence of a positive multiple of the true slope that maximizes the population QMLE likelihood over an appropriately restricted parameter space. We close this gap by providing a formal proof of slope consistency under the same set of conditions for BCMs identified as in Manski (1975, 1985). Our result implies that, under suitable conditions, logistic regression yields a consistent estimate of the slope coefficient for BCMs.
title Slope Consistency of Quasi-Maximum Likelihood Estimator for Binary Choice Models
topic Econometrics
url https://arxiv.org/abs/2505.02327