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Duality in dynamic discrete‐choice models

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  • Khai Xiang Chiong
  • Alfred Galichon
  • Matt Shum

Abstract

Using results from Convex Analysis, we investigate a novel approach to identification and estimation of discrete‐choice models that we call the mass transport approach. We show that the conditional choice probabilities and the choice‐specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem. Based on this, we propose a new two‐step estimator for these models; interestingly, the first step of our estimator involves solving a linear program that is identical to the classic assignment (two‐sided matching) game of Shapley and Shubik (1971). The application of convex‐analytic tools to dynamic discrete‐choice models and the connection with two‐sided matching models is new in the literature. Monte Carlo results demonstrate the good performance of this estimator, and we provide an empirical application based on Rust's (1987) bus engine replacement model.

Suggested Citation

  • Khai Xiang Chiong & Alfred Galichon & Matt Shum, 2016. "Duality in dynamic discrete‐choice models," Quantitative Economics, Econometric Society, vol. 7(1), pages 83-115, March.
    • Handle: RePEc:wly:quante:v:7:y:2016:i:1:p:83-115
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    Cited by:

    1. Fosgerau, Mogens & Melo, Emerson & Shum, Matthew & Sørensen, Jesper R.-V., 2021. "Some remarks on CCP-based estimators of dynamic models," Economics Letters, Elsevier, vol. 204(C).
    2. Mogens Fosgerau & Julien Monardo & André de Palma, 2024. "The Inverse Product Differentiation Logit Model," American Economic Journal: Microeconomics, American Economic Association, vol. 16(4), pages 329-370, November.
    3. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    4. Fosgerau, Mogens & Melo, Emerson & Shum, Matt, 2017. "Discrete Choice and Rational Inattention: a General Equivalence Result�," MPRA Paper 76605, University Library of Munich, Germany.
    5. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
    6. Kalouptsidi, Myrto & Scott, Paul T. & Souza-Rodrigues, Eduardo, 2021. "Linear IV regression estimators for structural dynamic discrete choice models," Journal of Econometrics, Elsevier, vol. 222(1), pages 778-804.
    7. Sørensen, Jesper R.-V. & Fosgerau, Mogens, 2022. "How McFadden met Rockafellar and learned to do more with less," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    8. David Muller & Emerson Melo & Ruben Schlotter, 2023. "A Distributionally Robust Random Utility Model," Papers 2303.05888, arXiv.org.
    9. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    10. Kalouptsidi, Myrto & Scott, Paul T. & Souza-Rodrigues, Eduardo, 2018. "Linear IV Regression Estimators for Structural Dynamic Discrete Choice Models," CEPR Discussion Papers 13240, C.E.P.R. Discussion Papers.
    11. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    12. Myrto Kalouptsidi & Paul T. Scott & Eduardo Souza-Rodrigues, 2018. "Linear IV Regression Estimators for Structural Dynamic Discrete Choice Models," NBER Working Papers 25134, National Bureau of Economic Research, Inc.
    13. Hsieh, Yu-Wei & Shi, Xiaoxia & Shum, Matthew, 2022. "Inference on estimators defined by mathematical programming," Journal of Econometrics, Elsevier, vol. 226(2), pages 248-268.
    14. Myrto Kalouptsidi & Paul T. Scott & Eduardo Souza‐Rodrigues, 2021. "Identification of counterfactuals in dynamic discrete choice models," Quantitative Economics, Econometric Society, vol. 12(2), pages 351-403, May.
    15. Emerson Melo, 2022. "On the uniqueness of quantal response equilibria and its application to network games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 681-725, October.
    16. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    17. Paul S. Koh, 2024. "Merger Analysis with Latent Price," Papers 2404.07684, arXiv.org, revised Jul 2024.
    18. Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2023. "Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models," Papers 2309.11416, arXiv.org.
    19. Khai Xiang Chiong & Matthew Shum, 2019. "Random Projection Estimation of Discrete-Choice Models with Large Choice Sets," Management Science, INFORMS, vol. 65(1), pages 256-271, January.
    20. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.
    21. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    22. Grey Gordon, 2019. "Efficient Computation with Taste Shocks," Working Paper 19-15, Federal Reserve Bank of Richmond.
    23. Arcidiacono, Peter & Miller, Robert A., 2020. "Identifying dynamic discrete choice models off short panels," Journal of Econometrics, Elsevier, vol. 215(2), pages 473-485.

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