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Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood

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  • Dennis Kristensen
  • Yongseok Shin

    () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We propose a simulated maximum likelihood estimator for dynamic models based on non-parametric kernel methods. Our method is designed for models without latent dynamics from which one can simulate observations but cannot obtain a closed-form representation of the likelihood function. Using the simulated observations, we nonparametrically estimate the density - which is unknown in closed form - by kernel methods, and then construct a likelihood function that can be maximized. We prove for dynamic models that this nonparametric simulated maximum likelihood (NPSML) estimator is consistent and asymptotically efficient. NPSML is applicable to general classes of models and is easy to implement in practice.

Suggested Citation

  • Dennis Kristensen & Yongseok Shin, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-58, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2008-58
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    Cited by:

    1. Jakob Grazzini & Matteo G. Richiardi, 2013. "Consistent Estimation of Agent-Based Models by Simulated Minimum Distance," LABORatorio R. Revelli Working Papers Series 130, LABORatorio R. Revelli, Centre for Employment Studies.
    2. repec:eee:econom:v:198:y:2017:i:2:p:189-208 is not listed on IDEAS
    3. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1433-1445, October.
    4. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    5. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    6. Judge, George, 2012. "The Information Theoretic Foundations of a Probabilistic and Predictive Micro and Macro Economics," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt5d98g7wg, Department of Agricultural & Resource Economics, UC Berkeley.
    7. Michael Creel & Dennis Kristensen, 2013. "Indirect Likelihood Inference (revised)," UFAE and IAE Working Papers 931.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    8. Bruins, Marianne & Duffy, James A. & Keane, Michael P. & Smith, Anthony A., 2018. "Generalized indirect inference for discrete choice models," Journal of Econometrics, Elsevier, vol. 205(1), pages 177-203.
    9. Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    10. repec:eee:dyncon:v:85:y:2017:i:c:p:21-45 is not listed on IDEAS
    11. Corradi, Valentina & Swanson, Norman R., 2011. "Predictive density construction and accuracy testing with multiple possibly misspecified diffusion models," Journal of Econometrics, Elsevier, vol. 161(2), pages 304-324, April.
    12. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    13. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    14. repec:hal:journl:peer-00796745 is not listed on IDEAS
    15. Michael Creel & Dennis Kristensen, "undated". "Indirect Likelihood Inference," Working Papers 558, Barcelona Graduate School of Economics.
    16. Dennis Kristensen & Bernard Salanié, 2010. "Higher Order Improvements for Approximate Estimators," CAM Working Papers 2010-04, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    17. Mathias Barkhagen & Jörgen Blomvall & Eckhard Platen, 2016. "Recovering the real-world density and liquidity premia from option data," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1147-1164, July.
    18. Lee, Donghoon & Song, Kyungchul, 2015. "Simulated maximum likelihood estimation for discrete choices using transformed simulated frequencies," Journal of Econometrics, Elsevier, vol. 187(1), pages 131-153.
    19. Grazzini, Jakob & Richiardi, Matteo, 2015. "Estimation of ergodic agent-based models by simulated minimum distance," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 148-165.
    20. Diep Duong & Norman Swanson, 2013. "Density and Conditional Distribution Based Specification Analysis," Departmental Working Papers 201312, Rutgers University, Department of Economics.
    21. Dennis Kristensen, 2007. "Nonparametric Estimation and Misspecification Testing of Diffusion Models," CREATES Research Papers 2007-01, Department of Economics and Business Economics, Aarhus University.
    22. Jiti Gao & Han Hong, 2014. "A Computational Implementation of GMM," Monash Econometrics and Business Statistics Working Papers 24/14, Monash University, Department of Econometrics and Business Statistics.
    23. Judge, George G., 2012. "The information theoretic foundations of a probabilistic and predictive micro and macro economics," CUDARE Working Papers 122890, University of California, Berkeley, Department of Agricultural and Resource Economics.
    24. Kukacka, Jiri & Barunik, Jozef, 2017. "Estimation of financial agent-based models with simulated maximum likelihood," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 21-45.

    More about this item

    Keywords

    dynamic models; estimation; kernel density estimation; maximum-likelihood; simulation;

    JEL classification:

    • 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
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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