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

Viktor Winschel

GE, Growth, Math methods from EconWPA

Abstract: 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.

Keywords: stochastic dynamic general equilibrium model; Chebyshev polynomials; Smolyak operator; nonlinear state space filter; Curse of Dimensionality; posterior of structural parameters; marginal likelihood (search for similar items in EconPapers)
JEL-codes: E0 F0 C11 C13 C15 C32 C44 C52 C63 C68 C88 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-dge, nep-ecm and nep-mac
Date: 2005-07-29
Note: Type of Document - pdf; pages: 100
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpge:0507014

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