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

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  • Viktor Winschel
  • Markus Kr‰tzig

Abstract

We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids to overcome the curse of dimensionality for approximations. We apply sparse grids to a global polynomial approximation of the model solution, to the quadrature of integrals arising as rational expectations, and to three new nonlinear state space filters which speed up 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 parameterization for an appropriate acceptance ratio, and allows a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge for the solution and estimation of a general class of models. Copyright 2010 The Econometric Society.

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  • Viktor Winschel & Markus Kr‰tzig, 2010. "Solving, Estimating, and Selecting Nonlinear Dynamic Models Without the Curse of Dimensionality," Econometrica, Econometric Society, vol. 78(2), pages 803-821, March.
  • Handle: RePEc:ecm:emetrp:v:78:y:2010:i:2:p:803-821
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    References listed on IDEAS

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    Cited by:

    1. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, pages 92-123.
    2. Fernández-Villaverde, Jesús & Gordon, Grey & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Nonlinear adventures at the zero lower bound," Journal of Economic Dynamics and Control, Elsevier, pages 182-204.
    3. repec:bla:jorssc:v:66:y:2017:i:5:p:997-1013 is not listed on IDEAS
    4. Christophe Gouel, 2013. "Comparing Numerical Methods for Solving the Competitive Storage Model," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 267-295, February.
    5. Tommaso Proietti & Alessandra Luati, 2013. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 15, pages 334-362 Edward Elgar Publishing.
    6. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
    7. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, pages 240-251.
    8. Tommaso Proietti & Alessandra Luati, 2013. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 15, pages 334-362 Edward Elgar Publishing.
    9. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, pages 240-251.
    10. 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.
    11. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    12. Arne Risa Hole & Hong Il Yoo, 2017. "The use of heuristic optimization algorithms to facilitate maximum simulated likelihood estimation of random parameter logit models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, pages 997-1013.
    13. 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.

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