Shakeeb Khan, Tatiana Komarova, Denis Nekipelov
arXiv 3 Oct 2023 · Econometrics
arXiv:2310.02414 · PDF · DOI · OpenAlex · Extracted main text
Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are discrete. In this paper we find that classical estimators, including the maximum score estimator, (Manski (1975)), loose their attractive statistical properties without point identification. First of all, they are not sharp with the estimator converging to an outer region of the identified set, (Komarova (2013)), and in many discrete designs it weakly converges to a random set. Second, they are not robust, with their distribution limit discontinuously changing with respect to the parameters of the model. We propose a novel class of estimators based on the concept of a quantile of a random set, which we show to be both sharp and robust. We demonstrate that our approach extends from cross-sectional settings to classical static and dynamic discrete panel data models.
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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 | Komarova (2013) Binary choice models with discrete regressors: Identification and misspecification self | 1.000 | 6 | 3 | 100% |
| 2 | Manski (1975) Maximum Score Estimation of the Stochastic Utility Model of Choice | 0.956 | 8 | 5 | 88% |
| 3 | Ichimura (1994) Local Quantile Regression Estimation of Binary Response Models with Conditional Heteroskedasticity | 0.909 | 8 | 4 | 75% |
| 4 | Molchanov (2006) Theory of Random Sets | 0.874 | 12 | 7 | 67% |
| 5 | Ahn, Ichimura, Powell, and Ruud (2018) Simple Estimators for Invertible Index Models | 0.843 | 5 | 4 | 60% |
| 6 | Ibragimov and Has' Minskii (1981) Statistical estimation: asymptotic theory | 0.737 | 3 | 3 | 67% |
| 7 | Manski (1987) Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data | 0.693 | 8 | 1 | 100% |
| 8 | Han (1987) The Maximum Rank Correlation Estimator | 0.644 | 4 | 2 | 50% |
| 9 | Horowitz (1992) A Smoothed Maximum Score Estimator for the Binary Response Model | 0.644 | 2 | 2 | 100% |
| 10 | Manski (1985) Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 39 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Privacy-aware identification | 0.405 | 1 | 1 |
| 2 | Binary Classification with the Maximum Score Model and Linear Programming | 0.405 | 1 | 1 |