Shakeeb Khan, Tatiana Komarova, Denis Nekipelov
arXiv 1 Jun 2026 · Econometrics
arXiv:2606.02200 · PDF · DOI · OpenAlex · Extracted main text
Semiparametric discrete choice models are widely applied in economics, yet a fundamental tension arises when covariates are discrete as regression coefficients that are point identified under continuous regressors may become only partially identified. We show that this is not merely an identification problem but creates serious estimation pathologies. Classical estimators, including the maximum score estimator of Manski (1975), not only have population maximizers that are outer regions of the identified set (Komarova (2013)) but also converge to a random set drawn from a finite collection of deterministic regions that partition that outer region. To resolve this failure, we introduce the Random Set Quantile (RSQ) estimator which extracts the $τ$-quantile of the classical estimator for $τ\in (1/2,1)$. We prove this result for a class of widely used models, which includes binary/multinomial choice and discrete outcome panel data models. This construction is consistent and locally robust across the full parameter space, including precisely those configurations where classical estimators break down. A feasible implementation based on the $m$-out-of-$n$ bootstrap inherits both properties. We apply the methodology to the 2019 UK General Election, where the discrete support of Brexit-related covariates generates the partial identification our theory analyzes.
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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 | Charles F Manski (1975) Maximum Score Estimation of the Stochastic Utility Model of Choice | 1.000 | 14 | 3 | 100% |
| 2 | Molchanov, Ilya (2006) Theory of Random Sets | 1.000 | 8 | 4 | 100% |
| 3 | Tatiana Komarova (2013) Binary choice models with discrete regressors: Identification and misspecification self | 1.000 | 6 | 3 | 100% |
| 4 | Arie Beresteanu and Francesca Molinari (2008) Asymptotic Properties for a Class of Partially Identified Models | 1.000 | 5 | 3 | 100% |
| 5 | D. W. K. Andrews and P. Guggenberger (2009) Hybrid and size-corrected subsampling methods | 0.928 | 4 | 3 | 100% |
| 6 | Charles F Manski (1985) Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator | 0.874 | 10 | 2 | 100% |
| 7 | Charles F. Manski (1987) Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data | 0.874 | 8 | 2 | 100% |
| 8 | Donald Andrews (1999) Estimation When a Parameter Is on the Boundary | 0.737 | 3 | 2 | 100% |
| 9 | H. Kaido and F. Molinari and J. Stoye (2019) Confidence Intervals for Projections of Partially Identified Parameters | 0.737 | 3 | 2 | 100% |
| 10 | F. Bugni and I. Canay and X. Shi (2017) Inference for subvectors and other functions of partially identified parameters in moment inequality models | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 32 scored citations.