Yoosoon Chang, Joon Y. Park, Guo Yan
arXiv 5 May 2025 · Econometrics
arXiv:2505.02327 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Paul A Ruud (1983) Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecification of Distribution in Multinomi… | 1.000 | 5 | 3 | 100% |
| 2 | Charles F. Manski (1975) Maximum Score Estimation of the Stochastic Utility Model of Choice | 0.843 | 3 | 3 | 100% |
| 3 | Charles F. Manski (1985) Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator | 0.843 | 3 | 3 | 100% |
| 4 | Newey, Whitney K and Ruud, Paul A (1994) Density weighted linear least squares | 0.843 | 3 | 3 | 100% |
| 5 | Paul A Ruud (1986) Consistent Estimation of Limited Dependent Variable Models Despite Misspecification of Distribution | 0.843 | 3 | 3 | 100% |
| 6 | Ichimura, Hidehiko (1993) Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models | 0.644 | 2 | 2 | 100% |
| 7 | Roger W. Klein and Richard H. Spady (1993) An Efficient Semiparametric Estimator for Binary Response Models | 0.644 | 2 | 2 | 100% |
| 8 | White, Halbert (1982) Maximum Likelihood Estimation of Misspecified Models | 0.644 | 2 | 2 | 100% |
| 9 | Ahn, Hyungtaik and Ichimura, Hidehiko and Powell, James L and Ruud,… (2018) Simple estimators for invertible index models | 0.405 | 1 | 1 | 100% |
| 10 | Gourieroux, Christian and Monfort, Alain and Trognon, Alain (1984) Pseudo Maximum Likelihood Methods: Theory | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 15 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Using SVM to Estimate and Predict Binary Choice Models | 1.000 | 6 | 3 |