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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

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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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Publisher 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

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

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  1. Vadim Marmer & Taisuke Otsu, 2009. "Optimal Comparison of Misspecified Moment Restriction Models," Cowles Foundation Discussion Papers 1724, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Aguirregabiria, Victor & Ho, Chun-Yu, 2009. "A Dynamic Oligopoly Game of the US Airline Industry: Estimation and Policy Experiments," MPRA Paper 16739, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  3. Hiroyuki Kasahara & Katsumi Shimotsu, 2008. "Sequential Estimation of Structural Models with a Fixed Point Constraint," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!]
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