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Displaying results 1 to 6 of 6.

  1. Numerical stability analysis of linear DSGE models
    backward errors, forward errors and condition numbers
    Author: Meyer-Gohde, Alexander
    Published: [2023]
    Publisher:  Institute for Monetary and Financial Stability, Goethe University Frankfurt, Frankfurt am Main

    This paper develops and implements a backward and forward error analysis of and condition numbers for the numerical stability of the solutions of linear dynamic stochastic general equilibrium (DSGE) models. Comparing seven different solution methods... more

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    DS 464
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    This paper develops and implements a backward and forward error analysis of and condition numbers for the numerical stability of the solutions of linear dynamic stochastic general equilibrium (DSGE) models. Comparing seven different solution methods from the literature, I demonstrate an economically significant loss of accuracy specifically in standard, generalized Schur (or QZ) decomposition based solutions methods resulting from large backward errors in solving the associated matrix quadratic problem. This is illustrated in the monetary macro model of Smets and Wouters (2007) and two productionbased asset pricing models, a simple model of external habits with a readily available symbolic solution and the model of Jermann (1998) that lacks such a symbolic solution - QZ-based numerical solutions miss the equity premium by up to several annualized percentage points for parameterizations that either match the chosen calibration targets or are nearby to the parameterization in the literature. While the numerical solution methods from the literature failed to give any indication of these potential errors, easily implementable backward-error metrics and condition numbers are shown to successfully warn of such potential inaccuracies. The analysis is then performed for a database of roughly 100 DSGE models from the literature and a large set of draws from the model of Smets and Wouters (2007). While economically relevant errors do not appear pervasive from these latter applications, accuracies that differ by several orders of magnitude persist.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/279899
    Series: Working paper series / Institute for Monetary and Financial Stability ; no. 193 (2023)
    Subjects: Numerical accuracy; DSGE; Solution methods; Condition number; Backward error; Forward error
    Scope: 1 Online-Ressource (circa 126 Seiten), Illustrationen
  2. Solving linear DSGE models with structure-preserving doubling methods
    Author: Huber, Johannes; Meyer-Gohde, Alexander; Saecker, Johanna
    Published: [2023]
    Publisher:  Institute for Monetary and Financial Stability, Goethe University Frankfurt, Frankfurt am Main

    This paper applies structure preserving doubling methods to solve the matrix quadratic underlying the recursive solution of linear DSGE models. We present and compare two Structure-Preserving Doubling Algorithms (SDAs) to other competing methods -... more

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
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    DS 464
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    This paper applies structure preserving doubling methods to solve the matrix quadratic underlying the recursive solution of linear DSGE models. We present and compare two Structure-Preserving Doubling Algorithms (SDAs) to other competing methods - the QZ method, a Newton algorithm, and an iterative Bernoulli approach - as well as the related cyclic and logarithmic reduction algorithms. Our comparison is completed using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium scale New Keynesian model of Smets and Wouters (2007) iteratively. We find that both SDAs perform very favorably relative to QZ, with generally more accurate solutions computed in less time. While we collect theoretical convergence results that promise quadratic convergence rates to a unique stable solution, the algorithms may fail to converge when there is a breakdown due to singularity of the coefficient matrices in the recursion. One of the proposed algorithms can overcome this problem by an appropriate (re)initialization. This SDA also performs particular well in refining solutions of different methods or from nearby parameterizations.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/280968
    Series: Working paper series / Institute for Monetary and Financial Stability ; no. 195 (2023)
    Subjects: Numerical accuracy; DSGE; Solution methods
    Scope: 1 Online-Ressource (circa 53 Seiten), Illustrationen
  3. Solving linear DSG models with Newton methods
    Author: Meyer-Gohde, Alexander; Saecker, Johanna
    Published: [2022]
    Publisher:  Institute for Monetary and Financial Stability, Goethe University Frankfurt, Frankfurt am Main

    This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models... more

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    This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian model of Smets and Wouters (2007) iteratively. We find that Newton-based methods compare favorably in solving DSGE models, providing higher accuracy as measured by the forward error of the solution at a comparable computation burden. The methods, however, suffer from their inability to guarantee convergence to a particular, e.g. unique stable, solution, but their iterative procedures lend themselves to refining solutions either from different methods or parameterizations.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/264979
    Series: Working paper series / Institute for Monetary and Financial Stability ; no. 174 (2022)
    Subjects: Numerical accuracy; DSGE; Solution methods
    Scope: 1 Online-Ressource (circa 49 Seiten), Illustrationen
  4. Solving non-linear dynamic models (more) efficiently
    application to a simple monetary policy model
    Author: Mkhatrishvili, Shalva; Laxton, Douglas; Tutberidze, Davit; Sopromadze, Tamta; Metreveli, Saba; Arevadze, Lasha; Mdivnishvili, Tamar; Tsutskiridze, Giorgi
    Published: [2019]
    Publisher:  National Bank of Georgia, Tbilisi, Georgia

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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Series: NBG working papers ; WP 2019, 01
    Subjects: Non-linear dynamic models; Solution methods; Monetary policy
    Scope: 1 Online-Ressource (circa 45 Seiten), Illustrationen
  5. On the accuracy of linear DSGE solution methods and the consequences for log-normal asset pricing
    Author: Meyer-Gohde, Alexander
    Published: [2021]
    Publisher:  Institute for Monetary and Financial Stability, Goethe University Frankfurt, Frankfurt am Main

    This paper demonstrates a failure of standard, generalized Schur (orQZ) decomposition based solutions methods for linear dynamic stochastic general equilibrium (DSGE) models when there is insufficient eigenvalue separation about the unit circle. The... more

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    DS 464
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    This paper demonstrates a failure of standard, generalized Schur (orQZ) decomposition based solutions methods for linear dynamic stochastic general equilibrium (DSGE) models when there is insufficient eigenvalue separation about the unit circle. The significance of this is demonstrated in a simple production-based asset pricing model with external habit formation. While the exact solution afforded by the simplicity of the model matches post-war US consumption growth and the equity premium, QZ-based numerical solutions miss the later by many annualized percentage points.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/231983
    Series: Working paper series / Institute for Monetary and Financial Stability ; no. 154 (2021)
    Subjects: Numerical accuracy; Production-based asset pricing; DSGE; Solution methods
    Scope: 1 Online-Ressource (circa 30 Seiten), Illustrationen
  6. Solving linear DSGE models with Bernoulli iterations
    Author: Meyer-Gohde, Alexander
    Published: [2023]
    Publisher:  Institute for Monetary and Financial Stability, Goethe University Frankfurt, Frankfurt am Main

    This paper presents and compares Bernoulli iterative approaches for solving linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary... more

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    Signature:
    DS 464
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    This paper presents and compares Bernoulli iterative approaches for solving linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian model of Smets and Wouters (2007) iteratively. I find that Bernoulli methods compare favorably in solving DSGE models to the QZ, providing similar accuracy as measured by the forward error of the solution at a comparable computation burden. The method can guarantee convergence to a particular, e.g., unique stable, solution and can be combined with other iterative methods, such as the Newton method, lending themselves especially to refining solutions.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/271088
    Series: Working paper series / Institute for Monetary and Financial Stability ; no. 182 (2023)
    Subjects: Numerical accuracy; DSGE; Solution methods
    Scope: 1 Online-Ressource (circa 50 Seiten), Illustrationen