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Solving linear DSGE models with Newton methods

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  • Meyer-Gohde, Alexander
  • Saecker, Johanna

Abstract

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.

Suggested Citation

  • Meyer-Gohde, Alexander & Saecker, Johanna, 2024. "Solving linear DSGE models with Newton methods," Economic Modelling, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:ecmode:v:133:y:2024:i:c:s0264999324000269
    DOI: 10.1016/j.econmod.2024.106670
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    Cited by:

    1. Alexander Meyer-Gohde, 2025. "Solving Linear DSGE Models with Bernoulli Iterations," Computational Economics, Springer;Society for Computational Economics, vol. 66(1), pages 593-643, July.
    2. Chunbing Cai & Jordan Roulleau-Pasdeloup & Zhongxi Zheng, 2025. "Endogenous Persistence at the Effective Lower Bound," Papers 2501.06473, arXiv.org, revised Sep 2025.
    3. Meyer-Gohde, Alexander, 2023. "Numerical stability analysis of linear DSGE models: Backward errors, forward errors and condition numbers," IMFS Working Paper Series 193, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    4. Huber, Johannes & Meyer-Gohde, Alexander & Saecker, Johanna, 2023. "Solving linear DSGE models with structure-preserving doubling methods," IMFS Working Paper Series 195, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).

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    Keywords

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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