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Some Remarks on CCP-based Estimators of Dynamic Models

Author

Listed:
  • Mogens Fosgerau

    (University of Copenhagen)

  • Emerson Melo

    (Indiana University)

  • Matthew Shum

    (California Institute of Technology)

  • Jesper R.-V. Sørensen

    (University of Copenhagen)

Abstract

This note provides several remarks relating to the conditional-choice probability (CCP) based estimation approaches for dynamic discrete-choice models. Specifically, the Arcidiacono and Miller [2011] estimation procedure relies on the “inverse-CCP” mapping (p) from CCP’s to choice-specific value functions. Exploiting the convex-analytic structure of discrete choice models, we discuss two approaches for computing this, using either linear or convex programming, for models where the utility shocks can follow arbitrary parametric distributions. Furthermore, the function is generally distinct from the “selection adjustment” term (i.e. the expectation of the utility shock for the chosen alternative), so that computational approaches for computing the latter may not be appropriate for computing .

Suggested Citation

  • Mogens Fosgerau & Emerson Melo & Matthew Shum & Jesper R.-V. Sørensen, 2021. "Some Remarks on CCP-based Estimators of Dynamic Models," Discussion Papers 21-03, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:2103
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    References listed on IDEAS

    as
    1. Emerson Melo & Kirill Pogorelskiy & Matthew Shum, 2019. "Testing The Quantal Response Hypothesis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(1), pages 53-74, February.
    2. Lixiong Li, 2018. "A General Method for Demand Inversion," Papers 1802.04444, arXiv.org, revised Feb 2018.
    3. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 497-529.
    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. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    6. 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).
    7. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
    8. 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.
    9. 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.
    10. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    11. Xiaoxia Shi & Matthew Shum & Wei Song, 2018. "Estimating Semi‐Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity," Econometrica, Econometric Society, vol. 86(2), pages 737-761, March.
    12. Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, June.
    13. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    14. Fosgerau, Mogens & Lindberg, Per Olov & Mattsson, Lars-Göran & Weibull, Jörgen, 2018. "A note on the invariance of the distribution of the maximum," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 56-61.
    15. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    16. Steven Berry & Ariel Pakes, 2007. "The Pure Characteristics Demand Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1193-1225, November.
    17. Andriy Norets & Satoru Takahashi, 2013. "On the surjectivity of the mapping between utilities and choice probabilities," Quantitative Economics, Econometric Society, vol. 4(1), pages 149-155, March.
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    Citations

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    Cited by:

    1. Mogens Fosgerau & Nikolaj Nielsen & Mads Paulsen & Thomas Kj{ae}r Rasmussen & Rui Yao, 2024. "Substitution in the perturbed utility route choice model," Papers 2409.08347, arXiv.org.
    2. 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).
    3. David Muller & Emerson Melo & Ruben Schlotter, 2023. "A Distributionally Robust Random Utility Model," Papers 2303.05888, arXiv.org.

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    More about this item

    Keywords

    dynamic discrete choice; random utility; linear programming; convex analysis; convex optimization;
    All these keywords.

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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