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Nested Pseudo-likelihood Estimation And Bootstrap-based Inference For Structural Discrete Markov Decision Models

Author

Listed:
  • Hiroyuki Kasahara

    (Department of Economics, University of Western Ontario)

  • Katsumi Shimotsu

    (Department of Economics, 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.

Suggested Citation

  • Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nested Pseudo-likelihood Estimation And Bootstrap-based Inference For Structural Discrete Markov Decision Models," Working Paper 1063, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1063
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    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Berkovec, James & Stern, Steven, 1991. "Job Exit Behavior of Older Men," Econometrica, Econometric Society, vol. 59(1), pages 189-210, January.
    3. Andrews, Donald W.K., 2002. "EQUIVALENCE OF THE HIGHER ORDER ASYMPTOTIC EFFICIENCY OF k-STEP AND EXTREMUM STATISTICS," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1040-1085, October.
    4. Donald W. K. Andrews, 2002. "Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators," Econometrica, Econometric Society, vol. 70(1), pages 119-162, January.
    5. Donna B. Gilleskie, 1998. "A Dynamic Stochastic Model of Medical Care Use and Work Absence," Econometrica, Econometric Society, vol. 66(1), pages 1-46, January.
    6. 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.
    7. John Rust & Christopher Phelan, 1997. "How Social Security and Medicare Affect Retirement Behavior in a World of Incomplete Markets," Econometrica, Econometric Society, vol. 65(4), pages 781-832, July.
    8. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 497-529.
    9. Ichimura, Hidehiko & Lee, Sokbae, 2010. "Characterization of the asymptotic distribution of semiparametric M-estimators," Journal of Econometrics, Elsevier, vol. 159(2), pages 252-266, December.
    10. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    11. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    12. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, September.
    13. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
    14. Susumu Imai & Michael P. Keane, 2004. "Intertemporal Labor Supply and Human Capital Accumulation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 601-641, May.
    15. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
    16. John Haltiwanger & Russell Cooper & Laura Power, 1999. "Machine Replacement and the Business Cycle: Lumps and Bumps," American Economic Review, American Economic Association, vol. 89(4), pages 921-946, September.
    17. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    18. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-1120, December.
    19. Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
    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. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    22. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    23. Zvi Eckstein & Kenneth I. Wolpin, 1999. "Why Youths Drop Out of High School: The Impact of Preferences, Opportunities, and Abilities," Econometrica, Econometric Society, vol. 67(6), pages 1295-1340, November.
    24. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729, Elsevier.
    25. H. M. Amman & D. A. Kendrick & J. Rust (ed.), 1996. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 1, number 1.
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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, September.
    3. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nonparametric Identification And Estimation Of Finite Mixture Models Of Dynamic Discrete Choices," Working Paper 1092, Economics Department, Queen's University.

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    More about this item

    Keywords

    Edgeworth expansion; k-step bootstrap; maximum pseudo-likelihood estimators; nested fixed point algorithm; Newton-Raphson method; policy iteration;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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