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Random Set Quantile Estimation of Partially Identified Discrete Response Models

Author

Listed:
  • Shakeeb Khan

    (Boston College)

  • Tatiana Komarova

    (Faculty of Economics, University of Cambridge)

  • Denis Nekipelov

    (Amazon)

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.

Suggested Citation

  • Shakeeb Khan & Tatiana Komarova & Denis Nekipelov, 2026. "Random Set Quantile Estimation of Partially Identified Discrete Response Models," Boston College Working Papers in Economics 1117, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:1117
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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