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

Yoosoon Chang, Joon Y. Park, Guo Yan

arXiv 5 May 2025 · Econometrics

arXiv:2505.02327 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Paul A Ruud (1983) Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecification of Distribution in Multinomi…1.00053100%
2Charles F. Manski (1975) Maximum Score Estimation of the Stochastic Utility Model of Choice0.84333100%
3Charles F. Manski (1985) Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator0.84333100%
4Newey, Whitney K and Ruud, Paul A (1994) Density weighted linear least squares0.84333100%
5Paul A Ruud (1986) Consistent Estimation of Limited Dependent Variable Models Despite Misspecification of Distribution0.84333100%
6Ichimura, Hidehiko (1993) Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models0.64422100%
7Roger W. Klein and Richard H. Spady (1993) An Efficient Semiparametric Estimator for Binary Response Models0.64422100%
8White, Halbert (1982) Maximum Likelihood Estimation of Misspecified Models0.64422100%
9Ahn, Hyungtaik and Ichimura, Hidehiko and Powell, James L and Ruud,… (2018) Simple estimators for invertible index models0.40511100%
10Gourieroux, Christian and Monfort, Alain and Trognon, Alain (1984) Pseudo Maximum Likelihood Methods: Theory0.40511100%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Using SVM to Estimate and Predict Binary Choice Models1.00063