Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality
AbstractA welfare analysis of a risky policy is impossible within a linear or linearized model and its certainty equivalence property. The presented algorithms are designed as a toolbox for a general model class. The computational challenges are considerable and I concentrate on the numerics and statistics for a simple model of dynamic consumption and labor choice. I calculate the optimal policy and estimate the posterior density of structural parameters and the marginal likelihood within a nonlinear state space model. My approach is even in an interpreted language twenty time faster than the only alternative compiled approach. The model is estimated on simulated data in order to test the routines against known true parameters. The policy function is approximated by Smolyak Chebyshev polynomials and the rational expectation integral by Smolyak Gaussian quadrature. The Smolyak operator is used to extend univariate approximation and integration operators to many dimensions. It reduces the curse of dimensionality from exponential to polynomial growth. The likelihood integrals are evaluated by a Gaussian quadrature and Gaussian quadrature particle filter. The bootstrap or sequential importance resampling particle filter is used as an accuracy benchmark. The posterior is estimated by the Gaussian filter and a Metropolis- Hastings algorithm. I propose a genetic extension of the standard Metropolis-Hastings algorithm by parallel random walk sequences. This improves the robustness of start values and the global maximization properties. Moreover it simplifies a cluster implementation and the random walk variances decision is reduced to only two parameters so that almost no trial sequences are needed. Finally the marginal likelihood is calculated as a criterion for nonnested and quasi-true models in order to select between the nonlinear estimates and a first order perturbation solution combined with the Kalman filter.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by EconWPA in its series GE, Growth, Math methods with number 0507014.
Length: 100 pages
Date of creation: 29 Jul 2005
Date of revision:
Note: Type of Document - pdf; pages: 100
Contact details of provider:
Web page: http://18.104.22.168
stochastic dynamic general equilibrium model; Chebyshev polynomials; Smolyak operator; nonlinear state space filter; Curse of Dimensionality; posterior of structural parameters; marginal likelihood;
Find related papers by JEL classification:
- E0 - Macroeconomics and Monetary Economics - - General
- F0 - International Economics - - General
- 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
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
- 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
- C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-08-13 (All new papers)
- NEP-DGE-2005-08-13 (Dynamic General Equilibrium)
- NEP-ECM-2005-08-13 (Econometrics)
- NEP-MAC-2005-08-13 (Macroeconomics)
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Kenneth L. Judd & Lilia Maliar & Serguei Maliar & Rafael Valero, 2013.
"Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain,"
NBER Working Papers
19326, National Bureau of Economic Research, Inc.
- Kenneth Judd & Lilia Maliar & Rafael Valero & Serguei Maliar, 2013. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Working Papers. Serie AD 2013-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Kenneth L. Judd & Lilia Maliar & Serguei Maliar & Rafael Valero, 2013. "Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain," BYU Macroeconomics and Computational Laboratory Working Paper Series 2013-02, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
- Viktor Winschel & Markus Krätzig, 2008. "JBendge: An Object-Oriented System for Solving, Estimating and Selecting Nonlinear Dynamic Models," SFB 649 Discussion Papers SFB649DP2008-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Fernández-Villaverde, Jesús & Rubio-Ramirez, Juan Francisco, 2006.
"Estimating Macroeconomic Models: A Likelihood Approach,"
CEPR Discussion Papers
5513, C.E.P.R. Discussion Papers.
- Jes�s Fern�ndez-Villaverde & Juan F. Rubio-Ram�rez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
- Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," Levine's Bibliography 122247000000000849, UCLA Department of Economics.
- Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," NBER Technical Working Papers 0321, National Bureau of Economic Research, Inc.
- Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
- Michael Creel & Dennis Kristensen, 2011.
"Indirect likelihood inference,"
UFAE and IAE Working Papers
874.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Christophe Gouel, 2013. "Comparing Numerical Methods for Solving the Competitive Storage Model," Computational Economics, Society for Computational Economics, vol. 41(2), pages 267-295, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.