Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Obstfeld, Maurice & Rogoff, Kenneth S., 1995. "Exchange Rate Dynamics Redux," Scholarly Articles 12491026, Harvard University Department of Economics.
- Obstfeld, Maurice & Rogoff, Kenneth, 1995. "Exchange Rate Dynamics Redux," CEPR Discussion Papers 1131, C.E.P.R. Discussion Papers.
- Maurice Obstfeld & Kenneth Rogoff, 1994. "Exchange Rate Dynamics Redux," NBER Working Papers 4693, National Bureau of Economic Research, Inc.
- Maurice Obstfeld and Kenneth Rogoff., 1995. "Exchange Rate Dynamics Redux," Center for International and Development Economics Research (CIDER) Working Papers C95-048, University of California at Berkeley.
- 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.
- 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.
- John Geweke, 1999.
"Using simulation methods for bayesian econometric models: inference, development,and communication,"
Taylor & Francis Journals, vol. 18(1), pages 1-73.
- John F. Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
- Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
- Ruge-Murcia, Francisco J., 2007.
"Methods to estimate dynamic stochastic general equilibrium models,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 31(8), pages 2599-2636, August.
- Francisco J. Ruge-Murcia, 2004. "Methods to Estimate Dynamic Stochastic General Equilibrium Models," 2004 Meeting Papers 83, Society for Economic Dynamics.
- RUGE-MURCIA, Francisco J., 2003. "Methods to Estimate Dynamic Stochastic General Equilibrium Models," Cahiers de recherche 17-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Ruge-Murcia, Francisco J., 2002. "Methods to Estimate Dynamic Stochastic General Equilibrium Models," University of California at San Diego, Economics Working Paper Series qt4fc8x822, Department of Economics, UC San Diego.
- RUGE-MURCIA, Francisco J., 2003. "Methods to Estimate Dynamic Stochastic General Equilibrium Models," Cahiers de recherche 2003-23, Universite de Montreal, Departement de sciences economiques.
- 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.
- 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.
- 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.
- Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Departmental Working Papers 200106, Rutgers University, Department of Economics.
- 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.
- John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
- Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, December.
- 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.
- Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, March.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpge:0507014. See general information about how to correct material in RePEc.
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.