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Semiparametric estimation of Markov decision processes with continuous state space

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  • Srisuma, Sorawoot
  • Linton, Oliver

Abstract

We propose a general two-step estimator for a popular Markov discrete choice model that includes a class of Markovian games with continuous observable state space. Our estimation procedure generalizes the computationally attractive methodology of Pesendorfer and Schmidt-Dengler (2008) that assumed finite observable states. This extension is non-trivial as the policy value functions are solutions to some type II integral equations. We show that the inverse problem is well-posed. We provide a set of primitive conditions to ensure root-T consistent estimation for the finite dimensional structural parameters and the distribution theory for the value functions in a time series framework.

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  • Srisuma, Sorawoot & Linton, Oliver, 2012. "Semiparametric estimation of Markov decision processes with continuous state space," Journal of Econometrics, Elsevier, vol. 166(2), pages 320-341.
    • Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:320-341
    DOI: 10.1016/j.jeconom.2011.10.003
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    Cited by:

    1. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2013. "Testing for Equilibrium Multiplicity in Dynamic Markov Games," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 423, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    2. Truquet, Lionel, 2023. "Strong mixing properties of discrete-valued time series with exogenous covariates," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 294-317.
    3. Jason R. Blevins & Wei Shi & Donald R. Haurin & Stephanie Moulton, 2020. "A Dynamic Discrete Choice Model Of Reverse Mortgage Borrower Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1437-1477, November.
    4. Komarova, Tatiana & Sanches, Fábio Adriano & Silva Junior, Daniel & Srisuma, Sorawoot, 2018. "Joint analysis of the discount factor and payoff parameters in dynamic discrete choice games," LSE Research Online Documents on Economics 86858, London School of Economics and Political Science, LSE Library.
    5. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," NBER Working Papers 29291, National Bureau of Economic Research, Inc.
    6. Taisuke Otsu & Martin Pesendorfer, 2021. "Equilibrium multiplicity in dynamic games: testing and estimation," STICERD - Econometrics Paper Series 618, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Pesendorfer, Martin & Takahashi, Yuya & Otsu, Taisuke, 2014. "Testing Equilibrium Multiplicity in Dynamic Games," CEPR Discussion Papers 10111, C.E.P.R. Discussion Papers.
    8. Taisuke Otsu & Martin Pesendorfer & Yuya Takahashi, 2016. "Pooling data across markets in dynamic Markov games," Quantitative Economics, Econometric Society, vol. 7(2), pages 523-559, July.
    9. Taisuke Otsu & Martin Pesendorfer, 2023. "Equilibrium multiplicity in dynamic games: Testing and estimation," The Econometrics Journal, Royal Economic Society, vol. 26(1), pages 26-42.
    10. Fabio A. Miessi Sanches & Daniel Silva Junior, Sorawoot Srisuma, 2014. "Ordinary Least Squares Estimation for a Dynamic Game," Working Papers, Department of Economics 2014_19, University of São Paulo (FEA-USP), revised 23 Feb 2015.
    11. Ariel Neufeld & Julian Sester & Mario v{S}iki'c, 2022. "Markov Decision Processes under Model Uncertainty," Papers 2206.06109, arXiv.org, revised Jan 2023.
    12. Ariel Neufeld & Julian Sester & Mario Šikić, 2023. "Markov decision processes under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 618-665, July.
    13. Hiroyuki Kasahara & Katsumi Shimotsu, 2018. "Estimation of Discrete Choice Dynamic Programming Models," The Japanese Economic Review, Springer, vol. 69(1), pages 28-58, March.
    14. Buchholz, Nicholas & Shum, Matthew & Xu, Haiqing, 2021. "Semiparametric estimation of dynamic discrete choice models," Journal of Econometrics, Elsevier, vol. 223(2), pages 312-327.
    15. Armstrong, Timothy B. & Bertanha, Marinho & Hong, Han, 2014. "A fast resample method for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 179(2), pages 128-133.
    16. Otero, Karina V., 2016. "Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability," MPRA Paper 86784, University Library of Munich, Germany.
    17. Sears, Louis S. & Lin Lawell, C.-Y. Cynthia & Walter, M. Todd, 2020. "Groundwater Under Open Access: A Structural Model of the Dynamic Common Pool Extraction Game," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304276, Agricultural and Applied Economics Association.

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    More about this item

    Keywords

    Discrete Markov decision models; Kernel smoothing semiparametric estimation; Well-posed inverse problem;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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