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Title:

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

Description:

A 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 l...

A 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. ; stochastic dynamic general equilibrium model, Chebyshev polynomials, Smolyak operator, nonlinear state space filter, Curse of Dimensionality, posterior of structural parameters, marginal likelihood Minimize

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Title:

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

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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 cur...

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. ; Dynamic Stochastic General Equilibrium (DSGE) Models, Bayesian Time Series Econometrics, Curse of Dimensionality Minimize

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Title:

JBendge: An Object-Oriented System for Solving, Estimating and Selecting Nonlinear Dynamic Models

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We present an object-oriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The imple- mented solution methods for nding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebyshev...

We present an object-oriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The imple- mented solution methods for nding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebyshev polynomial approximation with the Smolyak op- erator to overcome the course of dimensionality. The operator is also useful for numerical integration and we use it for the integrals arising in rational expecta- tions and in nonlinear state space lters. The estimation step is done by a parallel Metropolis-Hastings (MH) algorithm, using a linear or nonlinear lter. Implemented are the Kalman, Extended Kalman, Particle, Smolyak Kalman, Smolyak Sum, and Smolyak Kalman Particle lters. The MH sampling step can be interactively moni- tored and controlled by sequence and statistics plots. The number of parallel threads can be adjusted to benet from multiprocessor environments. JBendge is based on the framework JStatCom, which provides a standardized ap- plication interface. All tasks are supported by an elaborate multi-threaded graphical user interface (GUI) with project management and data handling facilities. ; Dynamic Stochastic General Equilibrium (DSGE) Models, Bayesian Time Series Econometrics, Java, Software Development Minimize

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Title:

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

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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 ne...

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. Copyright 2010 The Econometric Society. Minimize

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Title:

Solving, Estimating and Selecting Nonlinear Dynamic Models 1

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Description:

We present an object-oriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The implemented solution methods for finding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebyshev...

We present an object-oriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The implemented solution methods for finding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebyshev polynomial approximation with the Smolyak operator to overcome the course of dimensionality. The operator is also useful for numerical integration and we use it for the integrals arising in rational expectations and in nonlinear state space filters. The estimation step is done by a parallel Metropolis-Hastings (MH) algorithm using a linear or nonlinear filter. Implemented are the Kalman, Extended Kalman, Particle, Smolyak Kalman, Smolyak Sum, and Smolyak Kalman Particle filters. The MH sampling step can be monitored and controlled interactively by sequence and statistics plots. The number of parallel threads can be adjusted to benefit from multiprocessor environments. JBendge is based on the framework JStatCom, which provides a standardized application interface. All tasks are supported by an elaborate multi-threaded graphical user interface (GUI) with project management and data handling facilities. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-03-06

Source:

http://edoc.hu-berlin.de/series/sfb-649-papers/2008-34/PDF/34.pdf

http://edoc.hu-berlin.de/series/sfb-649-papers/2008-34/PDF/34.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Java ; Software Development

Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Java ; Software Development Minimize

DDC:

518 Numerical analysis *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

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

Description:

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 cu...

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 JBendge4 for the solution and estimation of a general class of models. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-04-08

Source:

http://edoc.hu-berlin.de/series/sfb-649-papers/2008-18/PDF/18.pdf

http://edoc.hu-berlin.de/series/sfb-649-papers/2008-18/PDF/18.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Curse of Dimensionality

Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Curse of Dimensionality Minimize

DDC:

518 Numerical analysis *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Bayes Network Analysis of Trade Effects of Currency Unions and Free Trade Agreements

Description:

We investigate the effects of trade and currency unions on trade within the reduced form gravity model. The database is a standard database in this field for around 200 countries over the last fifty years. The statistical model we use is a Bayes network from the machine learning and the artificial intelligence research which generalizes many sta...

We investigate the effects of trade and currency unions on trade within the reduced form gravity model. The database is a standard database in this field for around 200 countries over the last fifty years. The statistical model we use is a Bayes network from the machine learning and the artificial intelligence research which generalizes many standard econometric models. The emphasis in this paper is on a simplified specification of models with discrete and continuous variables and on simultaneous equations time series models. The results indicate that trade and currency unions have substantially lower effects on trade than derived in previous empirical work which we reproduce as special cases of our statistical framework. 1 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-24

Source:

http://www.vwl.uni-mannheim.de/winschel/docs/TradeBayesNetworks.pdf

http://www.vwl.uni-mannheim.de/winschel/docs/TradeBayesNetworks.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

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

Description:

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 cur...

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. Minimize

Publisher:

Humboldt University Berlin, Germany

Year of Publication:

2008-02-07

Document Type:

Text ; doc-type:PeriodicalPart ; doc-type:Reports

Language:

eng

Subjects:

Wirtschaft ; Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Curse of Dimensionality ; ddc:330

Wirtschaft ; Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Curse of Dimensionality ; ddc:330 Minimize

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Title:

JBendge ; An Object-Oriented System for Solving, Estimating and Selecting Nonlinear Dynamic Models

Description:

We present an object-oriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The imple- mented solution methods for finding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebysh...

We present an object-oriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The imple- mented solution methods for finding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebyshev polynomial approximation with the Smolyak op- erator to overcome the course of dimensionality. The operator is also useful for numerical integration and we use it for the integrals arising in rational expecta- tions and in nonlinear state space filters. The estimation step is done by a parallel Metropolis-Hastings (MH) algorithm, using a linear or nonlinear filter. Implemented are the Kalman, Extended Kalman, Particle, Smolyak Kalman, Smolyak Sum, and Smolyak Kalman Particle filters. The MH sampling step can be interactively moni- tored and controlled by sequence and statistics plots. The number of parallel threads can be adjusted to benefit from multiprocessor environments. JBendge is based on the framework JStatCom, which provides a standardized ap- plication interface. All tasks are supported by an elaborate multi-threaded graphical user interface (GUI) with project management and data handling facilities. Minimize

Publisher:

Humboldt University Berlin, Germany

Year of Publication:

2008-04-25

Document Type:

Text ; doc-type:PeriodicalPart ; doc-type:Reports

Language:

eng

Subjects:

Wirtschaft ; Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Java ; Software Development ; ddc:330

Wirtschaft ; Dynamic Stochastic General Equilibrium (DSGE) Models ; Bayesian Time Series Econometrics ; Java ; Software Development ; ddc:330 Minimize

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Title:

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

Description:

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 cu...

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. Minimize

Publisher:

SFB 649, Economic Risk Berlin

Year of Publication:

2008

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

C11 ; C13 ; C15 ; C32 ; C52 ; C63 ; C68 ; C87 ; ddc:330 ; 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

C11 ; C13 ; C15 ; C32 ; C52 ; C63 ; C68 ; C87 ; ddc:330 ; 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 Minimize

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SFB 649 discussion paper 2008,018

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