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

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  • Yoosoon Chang
  • Joon Y. Park
  • Guo Yan

Abstract

This paper revisits the slope consistency of QMLE for binary choice models. Ruud (1983, \emph{Econometrica}) introduced a set of conditions under which QMLE may yield a constant multiple of the slope coefficient of binary choice models 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 for slope consistency under the same set of conditions for any binary choice model identified as in Horowitz (1992, \emph{Econometrica}). Our result implies that the logistic regression, which is used extensively in machine learning to analyze binary outcomes associated with a large number of covariates, yields a consistent estimate for the slope coefficient of binary choice models under suitable conditions.

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  • Yoosoon Chang & Joon Y. Park & Guo Yan, 2025. "Slope Consistency of Quasi-Maximum Likelihood Estimator for Binary Choice Models," Papers 2505.02327, arXiv.org.
    • Handle: RePEc:arx:papers:2505.02327
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    References listed on IDEAS

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    1. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    2. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
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