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Semiparametric Estimation of Markov Decision Processeswith Continuous State Space

Author

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  • Oliver Linton
  • Sorawoot Srisuma
Abstract
We propose a general two-step estimation method for the structural parameters ofpopular semiparametric Markovian discrete choice models that include a class ofMarkovian Games andallow for continuous observable state space. The estimation procedure is simpleas it directly generalizes the computationally attractive methodology of Pesendorferand Schmidt-Dengler (2008) that assumed finite observable states. This extensionis non-trivial as the value functions, to be estimated nonparametrically in the firststage, are defined recursively in a non-linear functional equation. Utilizingstructural assumptions, we show how to consistently estimate the infinitedimensional parameters as the solution to some type II integral equations, thesolving of which is a well-posed problem. We provide sufficient set of primitives toobtain root-T consistent estimators for the finite dimensional structural parametersand the distribution theory for the value functions in a time series framework.

Suggested Citation

  • Oliver Linton & Sorawoot Srisuma, 2010. "Semiparametric Estimation of Markov Decision Processeswith Continuous State Space," STICERD - Econometrics Paper Series 550, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:550
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    Citations

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    Cited by:

    1. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," Papers 2109.01725, arXiv.org, revised Sep 2021.
    2. Ariel Neufeld & Julian Sester & Mario v{S}iki'c, 2022. "Markov Decision Processes under Model Uncertainty," Papers 2206.06109, arXiv.org, revised Jan 2023.
    3. Ariel Neufeld & Julian Sester & Mario Šikić, 2023. "Markov decision processes under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 618-665, July.
    4. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2013. "Testing for equilibrium multiplicity in dynamic Markov games," LSE Research Online Documents on Economics 101968, London School of Economics and Political Science, LSE Library.
    5. 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.
    6. Hiroyuki Kasahara & Katsumi Shimotsu, 2018. "Estimation of Discrete Choice Dynamic Programming Models," The Japanese Economic Review, Springer, vol. 69(1), pages 28-58, March.
    7. 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.
    8. 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.
    9. Pesendorfer, Martin & Takahashi, Yuya & Otsu, Taisuke, 2014. "Testing Equilibrium Multiplicity in Dynamic Games," CEPR Discussion Papers 10111, C.E.P.R. Discussion Papers.
    10. 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.
    11. Buchholz, Nicholas & Shum, Matthew & Xu, Haiqing, 2021. "Semiparametric estimation of dynamic discrete choice models," Journal of Econometrics, Elsevier, vol. 223(2), pages 312-327.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.

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    More about this item

    Keywords

    Discrete Markov Decision Models; Kernel Smoothing; Markovian Games; Semi-parametric Estimation; Well-Posed Inverse Problem.D;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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