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

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Author Info

  • 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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 146 (2008)
Issue (Month): 1 (September)
Pages: 92-106

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Handle: RePEc:eee:econom:v:146:y:2008:i:1:p:92-106

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Edgeworth expansion Finite mixture k-step bootstrap Maximum pseudo-likelihood estimators Nested fixed point algorithm Newton-Raphson method Policy iteration;

References

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Citations

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Cited by:
  1. Victor Aguirregabiria & Chun-Yu Ho, 2008. "A Dynamic Oligopoly Game of the US Airline Industry: Estimation and Policy Experiments," Working Papers tecipa-337, University of Toronto, Department of Economics.
  2. 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.
  3. Hiroyuki Kasahara & Katsumi Shimotsu, 2008. "Sequential Estimation of Structural Models with a Fixed Point Constraint," CESifo Working Paper Series 2507, CESifo Group Munich.
  4. Aguirregabiria, Victor & Magesan, Arvind, 2013. "Euler Equations for the Estimation of Dynamic Discrete Choice Structural," MPRA Paper 46056, University Library of Munich, Germany.
  5. 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.
  6. Aguirregabiria, Victor & Nevo, Aviv, 2010. "Recent developments in empirical IO: dynamic demand and dynamic games," MPRA Paper 27814, University Library of Munich, Germany.
  7. 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.
  8. 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.
  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.

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