IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v7y2016i1p83-115.html
   My bibliography  Save this article

Duality in dynamic discrete‐choice models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    9. 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.
    10. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    11. Mike G. Tsionas & Dionisis Philippas, 2023. "Measures of global sensitivity in linear programming: applications in banking sector," Annals of Operations Research, Springer, vol. 330(1), pages 585-607, November.
    12. Fosgerau, Mogens & Melo, Emerson & Shum, Matt, 2017. "Discrete Choice and Rational Inattention: a General Equivalence Result�," MPRA Paper 76605, University Library of Munich, Germany.
    13. 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).
    14. David Muller & Emerson Melo & Ruben Schlotter, 2023. "A Distributionally Robust Random Utility Model," Papers 2303.05888, arXiv.org.
    15. 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.
    16. 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.
    17. Paul S. Koh, 2024. "Merger Analysis with Latent Price," Papers 2404.07684, arXiv.org, revised Feb 2025.
    18. Arcidiacono, Peter & Miller, Robert A., 2020. "Identifying dynamic discrete choice models off short panels," Journal of Econometrics, Elsevier, vol. 215(2), pages 473-485.
    19. Enoch H. Kang & Hema Yoganarasimhan & Lalit Jain, 2025. "An Empirical Risk Minimization Approach for Offline Inverse RL and Dynamic Discrete Choice Model," Papers 2502.14131, arXiv.org, revised May 2025.
    20. 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.
    21. 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.
    22. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.
    23. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    24. Grey Gordon, 2019. "Efficient Computation with Taste Shocks," Working Paper 19-15, Federal Reserve Bank of Richmond.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:quante:v:7:y:2016:i:1:p:83-115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.