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

Viktor Winschel and Markus Krätzig

SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649

Abstract: We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids. TheSmolyak operator underlying the sparse grids approach frees global approximation from the curse of dimensionality and we apply it to a Chebyshev approximation of the model solution. The operator also eliminates the curse from Gaussian quadrature and we use it for the integrals arising from rational expectations and in three new nonlinear state space filters. The filters substantially decrease the computational burden compared to the sequential importance resampling particle filter. The posterior of the structural parameters is estimated by a new Metropolis-Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifies the choice of the innovation variances, allows for unbiased convergence diagnostics and for a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge4 for the solution and estimation of a general class of models.

Keywords: Dynamic Stochastic General Equilibrium (DSGE) Models; Bayesian Time Series Econometrics; Curse of Dimensionality (search for similar items in EconPapers)
JEL-codes: C11 C13 C15 C32 C52 C63 C68 C87 (search for similar items in EconPapers)
Pages: 59 pages
Date: 2008-02
New Economics Papers: this item is included in nep-cba, nep-cmp, nep-dge, nep-ecm, nep-ets and nep-ict
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