Econometrica: Mar 2010, Volume 78, Issue 2

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

https://doi.org/10.3982/ECTA6297
p. 803-821

Viktor Winschel, Markus Krätzig

We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids to overcome the curse of dimensionality for approximations. We apply sparse grids to a global polynomial approximation of the model solution, to the quadrature of integrals arising as rational expectations, and to three new nonlinear state space filters which speed up 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 parameterization for an appropriate acceptance ratio, and allows a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge for the solution and estimation of a general class of models.

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Supplemental Material

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

This file contains the details on the derivation of the dynamic first-order optimality conditions, the linearization of the general model, the new filters, the parallelized Metropolis-Hastings algorithm, an example of a two-dimensional Smolyak poly-nomial approximation and detailed simulation results.

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

A link to the authors' website where replication files may be found (using their software).

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