Random Set Quantile Estimation of Partially Identified Discrete Response Models

Shakeeb Khan (), Tatiana Komarova () and Denis Nekipelov
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Shakeeb Khan: Boston College, Postal: Dept. of Economics, Boston College, Chestnut Hill, MA 02467 USA
Tatiana Komarova: Faculty of Economics, University of Cambridge

No 1117, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: Semiparametric discrete choice models are widely used in economics, yet discrete covariates create a fundamental tension as coefficients point identified under continuous regressors may become only partially identified. We show this generates serious estimation pathologies. Classical estimators, including the maximum score estimators of Manski (1975, 1985, 1987), may have population maximizers that are outer regions of the identified set (Komarova (2013)) and converge to a random set over deterministic regions partitioning that outer region. We introduce the Random Set Quantile (RSQ) estimator, establish consistency and local robustness, and apply it to the 2019 UK General Election.

Keywords: Maximum score estimation; Partial identification; Identified set; Robustness; Random Set Quantile; Panel data discrete choice; Multinomial choice (search for similar items in EconPapers)
JEL-codes: C14 C25 C31 (search for similar items in EconPapers)
Date: 2026-09-20
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