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

Abstract

We present a comprehensive framework for Bayesian estima- tion of structural nonlinear dynamic economic models on sparse grids. The Smolyak operator underlying the sparse grids approach frees global approx- imation 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 ratio- nal expectations and in three new nonlinear state space fllters. The fllters substantially decrease the computational burden compared to the sequential importance resampling particle fllter. The posterior of the structural pa- rameters is estimated by a new Metropolis-Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifles 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 JBendge 4 for the solution and estimation of a