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Solving, Estimating and Selecting Nonlinear Dynamic Models without the Curse of Dimensionality

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  • Viktor Winschel
  • Markus Krätzig

Abstract

We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids. TheSmolyak operator underlying the sparse grids approach frees global approximation from the curse of dimensionality and we apply it to a Chebyshev approximation of the model solution. The operator also eliminates the curse from Gaussian quadrature and we use it for the integrals arising from rational expectations and in three new nonlinear state space filters. The filters substantially decrease the computational burden compared to the sequential importance resampling particle filter. The posterior of the structural parameters is estimated by a new Metropolis-Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifies the choice of the innovation variances, allows for unbiased convergence diagnostics and for a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge4 for the solution and estimation of a general class of models.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2008-018.

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Length: 59 pages
Date of creation: Feb 2008
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2008-018

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Keywords: Dynamic Stochastic General Equilibrium (DSGE) Models; Bayesian Time Series Econometrics; Curse of Dimensionality;

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  1. Gianni Amisano & Oreste Tristani, 2007. "Euro area inflation persistence in an estimated nonlinear DSGE model," Working Papers 0704, University of Brescia, Department of Economics.
  2. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January.
  3. Fernandez-Villaverde, Jesus & Francisco Rubio-Ramirez, Juan, 2004. "Comparing dynamic equilibrium models to data: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 123(1), pages 153-187, November.
  4. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  5. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
  6. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper 2003-27, Federal Reserve Bank of Atlanta.
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