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

  • Viktor Winschel

    (University of Mannheim)

A 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.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 0507014.

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Length: 100 pages
Date of creation: 29 Jul 2005
Date of revision:
Handle: RePEc:wpa:wuwpge:0507014
Note: Type of Document - pdf; pages: 100
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
  2. Obstfeld, Maurice & Rogoff, Kenneth, 1995. "Exchange Rate Dynamics Redux," Center for International and Development Economics Research (CIDER) Working Papers 233403, University of California-Berkeley, Department of Economics.
  3. Lars Peter Hansen & James J. Heckman, 1996. "The Empirical Foundations of Calibration," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 87-104, Winter.
  4. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
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  6. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
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  8. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
  9. 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.
  10. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
  11. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, December.
  12. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  13. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, March.
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