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Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models

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  • Kasahara, Hiroyuki
  • Shimotsu, Katsumi

Abstract

This paper analyzes the higher-order properties of the estimators based on the nested pseudo-likelihood (NPL) algorithm and the practical implementation of such estimators for parametric discrete Markov decision models. We derive the rate at which the NPL algorithm converges to the MLE and provide a theoretical explanation for the simulation results in Aguirregabiria and Mira [Aguirregabiria, V., Mira, P., 2002. Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models. Econometrica 70, 1519-1543], in which iterating the NPL algorithm improves the accuracy of the estimator. We then propose a new NPL algorithm that can achieve quadratic convergence without fully solving the fixed point problem in every iteration and apply our estimation procedure to a finite mixture model. We also develop one-step NPL bootstrap procedures for discrete Markov decision models. The Monte Carlo simulation evidence based on a machine replacement model of Rust [Rust, J., 1987. Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica 55, 999-1033] shows that the proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations.

Suggested Citation

  • Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.
  • Handle: RePEc:eee:econom:v:146:y:2008:i:1:p:92-106
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    Cited by:

    1. 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.
    2. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    3. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, September.
    4. Victor Aguirregabiria & Arvind Magesan, 2013. "Euler Equations for the Estimation of Dynamic Discrete Choice Structural Models," Working Papers tecipa-489, University of Toronto, Department of Economics.
    5. Marmer, Vadim & Otsu, Taisuke, 2012. "Optimal comparison of misspecified moment restriction models under a chosen measure of fit," Journal of Econometrics, Elsevier, vol. 170(2), pages 538-550.
    6. Aguirregabiria, Victor & Magesan, Arvind, 2013. "Euler Equations for the Estimation of Dynamic Discrete Choice Structural," MPRA Paper 46056, University Library of Munich, Germany.
    7. Aguirregabiria, Victor & Ho, Chun-Yu, 2012. "A dynamic oligopoly game of the US airline industry: Estimation and policy experiments," Journal of Econometrics, Elsevier, vol. 168(1), pages 156-173.
    8. Federico Bugni & Jackson Bunting, 2018. "On the iterated estimation of dynamic discrete choice games," Papers 1802.06665, arXiv.org, revised Mar 2018.
    9. Yu Zheng & Juan Pantano, 2012. "Using Subjective Expectations Data to Allow for Unobserved Heterogeneity in Hotz-Miller Estimation Strategies," 2012 Meeting Papers 940, Society for Economic Dynamics.
    10. Aguirregabiria, Victor, 2009. "Estimation of Dynamic Discrete Games Using the Nested Pseudo Likelihood Algorithm: Code and Application," MPRA Paper 17329, University Library of Munich, Germany.
    11. 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.
    12. 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.

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