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Efficient likelihood evaluation of state-space representations

Author

Listed:
  • DeJong, David Neil
  • Dharmarajan, Hariharan
  • Liesenfeld, Roman
  • Moura, Guilherme V.
  • Richard, Jean-François

Abstract

We develop a numerical procedure that facilitates efficient likelihood evaluation in applications involving non-linear and non-Gaussian state-space models. The procedure approximates necessary integrals using continuous approximations of target densities. Construction is achieved via efficient importance sampling, and approximating densities are adapted to fully incorporate current information. We illustrate our procedure in applications to dynamic stochastic general equilibrium models.

Suggested Citation

  • DeJong, David Neil & Dharmarajan, Hariharan & Liesenfeld, Roman & Moura, Guilherme V. & Richard, Jean-François, 2009. "Efficient likelihood evaluation of state-space representations," Economics Working Papers 2009-02, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:200902
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Schmitt-Grohe, Stephanie & Uribe, Martin, 2003. "Closing small open economy models," Journal of International Economics, Elsevier, vol. 61(1), pages 163-185, October.
    3. Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 891-910.
    4. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    5. Smith, J.Q. & Santos, Antonio A.F., 2006. "Second-Order Filter Distribution Approximations for Financial Time Series With Extreme Outliers," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 329-337, July.
    6. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    7. repec:pit:wpaper:317 is not listed on IDEAS
    8. Pitt, Michael K, 2002. "Smooth Particle Filters for Likelihood Evaluation and Maximisation," The Warwick Economics Research Paper Series (TWERPS) 651, University of Warwick, Department of Economics.
    9. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    10. Mendoza, Enrique G, 1991. "Real Business Cycles in a Small Open Economy," American Economic Review, American Economic Association, vol. 81(4), pages 797-818, September.
    11. DeJong, David N. & Ingram, Beth F. & Whiteman, Charles H., 2000. "A Bayesian approach to dynamic macroeconomics," Journal of Econometrics, Elsevier, vol. 98(2), pages 203-223, October.
    12. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
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    Citations

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    Cited by:

    1. Jean-François Richard, 2015. "Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables," Working Paper 5778, Department of Economics, University of Pittsburgh.
    2. Steffen Henzel & Malte Rengel, 2013. "Dimensions of macroeconomic uncertainty: A common factor analysis," ifo Working Paper Series 167, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    3. Hall, Jamie & Pitt, Michael K. & Kohn, Robert, 2014. "Bayesian inference for nonlinear structural time series models," Journal of Econometrics, Elsevier, vol. 179(2), pages 99-111.
    4. repec:eee:ecosta:v:4:y:2017:i:c:p:39-56 is not listed on IDEAS
    5. Moura, Guilherme V. & Turatti, Douglas Eduardo, 2014. "Efficient estimation of conditionally linear and Gaussian state space models," Economics Letters, Elsevier, vol. 124(3), pages 494-499.
    6. Ozturk, Serda Selin & Richard, Jean-Francois, 2015. "Stochastic volatility and leverage: Application to a panel of S&P500 stocks," Finance Research Letters, Elsevier, vol. 12(C), pages 67-76.
    7. Andreasen, Martin M., 2011. "Non-linear DSGE models and the optimized central difference particle filter," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1671-1695, October.

    More about this item

    Keywords

    particle filter; adaption; efficient importance sampling; kernel density approximation; dynamic stochastic general equilibrium model;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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