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Iterative refinement of the QZ decomposition for solving linear DSGE models

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  • Huber, Johannes
  • Meyer-Gohde, Alexander

Abstract

The standard approach to solving linear DSGE models is to apply the QZ method. It is a one-shot algorithm that leaves the researcher with little alternative than to seek a different algorithm should the result be numerically unsatisfactory. We develop an iterative implementation of QZ that delivers the standard result as its first iteration and further refinements at each subsequent iteration. We demonstrate that our algorithm successful corrects for accuracy losses identified in particular cases of a macro finance model and does not erroneously attempt to refine sufficiently accurate solutions.

Suggested Citation

  • Huber, Johannes & Meyer-Gohde, Alexander, 2025. "Iterative refinement of the QZ decomposition for solving linear DSGE models," IMFS Working Paper Series 217, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    • Handle: RePEc:zbw:imfswp:311846
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    References listed on IDEAS

    as
    1. Heiberger, Christopher & Klarl, Torben & Maussner, Alfred, 2017. "On The Numerical Accuracy Of First-Order Approximate Solutions To Dsge Models," Macroeconomic Dynamics, Cambridge University Press, vol. 21(7), pages 1811-1826, October.
    2. Meyer-Gohde, Alexander, 2023. "Solving linear DSGE models with Bernoulli iterations," IMFS Working Paper Series 182, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    3. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    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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    More about this item

    Keywords

    Numerical accuracy; DSGE; Solution methods;
    All these keywords.

    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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