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Nested Pseudo-likelihood Estimation and Bootstrap-based Inference for Structural Discrete Markov Decision Models

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  • Hiroyuki Kasahara

    () (University of Western Ontario)

  • Katsumi Shimotsu

    () (Queen's University)

Abstract

This paper analyzes the higher-order properties of nested pseudo-likelihood (NPL) estimators and their practical implementation for parametric discrete Markov decision models in which the probability distribution is defined as a fixed point. We propose a new NPL estimator that can achieve quadratic convergence without fully solving the fixed point problem in every iteration. We then extend the NPL estimators to develop one-step NPL bootstrap procedures for discrete Markov decision models and provide some Monte Carlo evidence based on a machine replacement model of Rust (1987). The proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations. Improvements are particularly noticeable when analyzing the dynamic impacts of counterfactual policies.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1063.pdf
File Function: First version 2006
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1063.

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Length: 56 pages
Date of creation: Feb 2006
Date of revision:
Handle: RePEc:qed:wpaper:1063

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Related research

Keywords: Edgeworth expansion; k-step bootstrap; maximum pseudo-likelihood estimators; nested fixed point algorithm; Newton-Raphson method; policy iteration;

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References

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  4. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230, Cowles Foundation for Research in Economics, Yale University.
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  18. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
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  20. Donald W.K. Andrews, 2001. "Higher-order Improvements of the Parametric Bootstrap for Markov Processes," Cowles Foundation Discussion Papers 1334, Cowles Foundation for Research in Economics, Yale University.
  21. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
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Citations

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Cited by:
  1. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
  2. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, 09.
  3. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices," UWO Department of Economics Working Papers 20065, University of Western Ontario, Department of Economics.

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