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.
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Bibliographic InfoPaper provided by EconWPA in its series GE, Growth, Math methods with number 0507014.
Length: 100 pages
Date of creation: 29 Jul 2005
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stochastic dynamic general equilibrium model; Chebyshev polynomials; Smolyak operator; nonlinear state space filter; Curse of Dimensionality; posterior of structural parameters; marginal likelihood;
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- 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
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- C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
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- NEP-DGE-2005-08-13 (Dynamic General Equilibrium)
- NEP-ECM-2005-08-13 (Econometrics)
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