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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.

Suggested Citation

  • Viktor Winschel & Markus Krätzig, 2008. "Solving, Estimating and Selecting Nonlinear Dynamic Models without the Curse of Dimensionality," SFB 649 Discussion Papers SFB649DP2008-018, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2008-018
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2008-018.pdf
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    References listed on IDEAS

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    1. Amisano, Gianni & Tristani, Oreste, 2010. "Euro area inflation persistence in an estimated nonlinear DSGE model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 1837-1858, October.
    2. 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.
    3. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January.
    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. Alessandro Cigno & Annalisa Luporini, 2018. "On the evolution of individual preferences and family rules," Working Paper series 18-07, Rimini Centre for Economic Analysis.
    6. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    7. 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.
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    Cited by:

    1. Daniel Harenberg & Stefano Marelli & Bruno Sudret & Viktor Winschel, 2017. "Uncertainty Quantification and Global Sensitivity Analysis for Economic Models," CER-ETH Economics working paper series 17/265, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    2. Dan S. Rickman, 2010. "Modern Macroeconomics And Regional Economic Modeling," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 23-41.
    3. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2016. "Dynamic Portfolio Optimization with Liquidity Cost and Market Impact: A Simulation-and-Regression Approach," Papers 1610.07694, arXiv.org, revised Oct 2017.

    More about this item

    Keywords

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

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • 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
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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