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Moment inequalities for multinomial choice with fixed effects

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  • Ariel Pakes
  • Jack Porter

Abstract

This paper proposes a new approach to identification of the semiparametric multinomial choice model with fixed effects. The framework employed is the semiparametric version of the traditional multinomial logit with the fixed‐effects model (Chamberlain (1980)). This semiparametric multinomial choice model places no restrictions on either the joint distribution of the random utility disturbances across choices or their within group (or across time) correlations. We show that a novel within‐group comparison leads to a set of conditional moment inequalities. Our main finding shows that the derived conditional moment inequalities yield the sharp identified set for the random utility covariate index, while avoiding the incidental parameter problem. Specializing this result to the binary choice case shows that Manski (1987)'s conditional moment inequalities still lead to sharp bounds without restrictions on covariates.

Suggested Citation

  • Ariel Pakes & Jack Porter, 2024. "Moment inequalities for multinomial choice with fixed effects," Quantitative Economics, Econometric Society, vol. 15(1), pages 1-25, January.
    • Handle: RePEc:wly:quante:v:15:y:2024:i:1:p:1-25
    DOI: 10.3982/QE1776
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    Cited by:

    1. Chen, Le-Yu & Lee, Sokbae, 2019. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," Journal of Econometrics, Elsevier, vol. 210(2), pages 482-497.
    2. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2023. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," Econometrica, Econometric Society, vol. 91(1), pages 107-146, January.
    3. Williams, Benjamin, 2020. "Nonparametric identification of discrete choice models with lagged dependent variables," Journal of Econometrics, Elsevier, vol. 215(1), pages 286-304.
    4. Bo E Honoré & Áureo de Paula, 2021. "Identification in simple binary outcome panel data models," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 78-93.
    5. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Discrete Choice Models for Bundles," Discussion Papers Series 625, School of Economics, University of Queensland, Australia.
    6. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    7. Wayne Yuan Gao & Ming Li, 2020. "Identification of Semiparametric Panel Multinomial Choice Models with Infinite-Dimensional Fixed Effects," Papers 2009.00085, arXiv.org, revised Nov 2024.
    8. Irene Botosaru & Chris Muris, 2017. "Binarization for panel models with fixed effects," CeMMAP working papers 31/17, Institute for Fiscal Studies.
    9. Fu Ouyang & Thomas Tao Yang, 2022. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Papers 2202.12062, arXiv.org, revised Feb 2024.
    10. Fu Ouyang & Thomas T. Yang, 2023. "Semiparametric Discrete Choice Models for Bundles," Papers 2306.04135, arXiv.org, revised Nov 2023.
    11. Jiarui Liu, 2021. "Sequential Search Models: A Pairwise Maximum Rank Approach," Papers 2104.13865, arXiv.org, revised Nov 2021.
    12. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," ANU Working Papers in Economics and Econometrics 2020-671, Australian National University, College of Business and Economics, School of Economics.
    13. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Discussion Papers Series 626, School of Economics, University of Queensland, Australia.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal 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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