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Efficient Likelihood Evaluation of State-Space Representations

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  • David N. DeJong
  • Hariharan Dharmarajan
  • Roman Liesenfeld
  • Guilherme Moura
  • Jean-Francois Richard

Abstract

We develop a numerical procedure that facilitates efficient likelihood evaluation in applications involving non-linear and non-Gaussian state-space models. The procedure employs continuous approximations of filtering densities, and delivers unconditionally optimal global approximations of targeted integrands to achieve likelihood approximation. Optimized approximations of targeted integrands are constructed via efficient importance sampling. Resulting likelihood approximations are continuous functions of model parameters, greatly enhancing parameter estimation. We illustrate our procedure in applications to dynamic stochastic general equilibrium models.

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Bibliographic Info

Paper provided by Czech National Bank, Research Department in its series Working Papers with number 2009/15.

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Date of creation: Dec 2009
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Handle: RePEc:cnb:wpaper:2009/15

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Keywords: Adaption; dynamic stochastic general equilibrium model; efficient importance sampling; kernel density approximation; particle filter.;

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References

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  1. Frank Smets & Raf Wouters, 2002. "An estimated dynamic stochastic general equilibrium model of the euro area," Working Paper Research 35, National Bank of Belgium.
  2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  3. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Closing Small Open Economy Models," Departmental Working Papers 200115, Rutgers University, Department of Economics.
  4. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  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. 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.
  7. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  8. 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.
  9. 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.
  10. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Papers 321, University of Pittsburgh, Department of Economics, revised Jan 2007.
  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. David N. DeJong & Hariharan Dharmarajan & Liesenfeld Roman & Richard Jean-Francois, 2007. "Efficient Filtering in State-Space Representations," Working Papers 317, University of Pittsburgh, Department of Economics, revised Nov 2008.
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Cited by:
  1. 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.
  2. Steffen Henzel & Malte Rengel, 2013. "Dimensions of macroeconomic uncertainty: A common factor analysis," Ifo Working Paper Series Ifo Working Paper No. 167, Ifo Institute for Economic Research at the University of Munich.
  3. 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.

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