Solving, estimating and selecting nonlinear dynamic models without the curse of dimensionality

Arbeitspapier

We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids. The Smolyak 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 JBendge for the solution and estimation of a general class of models.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2008,018

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Estimation: General ; Statistical Simulation Methods: General ; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models ; Model Evaluation, Validation, and Selection ; Computational Techniques; Simulation Modeling ; Computable General Equilibrium Models ; Econometric Software
• Subject: Dynamic Stochastic General Equilibrium (DSGE) Models ; Baye- sian Time Series Econometrics ; Curse of Dimensionality ; Allgemeines Gleichgewicht ; Stochastischer Prozess ; Nichtlineare dynamische Systeme ; Zeitreihenanalyse ; Bayes-Statistik ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Winschel, Viktor ; Krätzig, Markus
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2008

Further information

• Handle: http://hdl.handle.net/10419/25260
• Last update: 10.03.2025, 11:43 AM CET