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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

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    1. Lan, Hong & Meyer-Gohde, Alexander, 2014. "Solvability of perturbation solutions in DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 366-388.
    2. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    3. Jermann, Urban J., 1998. "Asset pricing in production economies," Journal of Monetary Economics, Elsevier, vol. 41(2), pages 257-275, April.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Villemot, Sébastien, 2011. "Solving rational expectations models at first order: what Dynare does," Dynare Working Papers 2, CEPREMAP, revised Dec 2025.
    9. Huber, Johannes & Meyer-Gohde, Alexander, 2025. "Iterative refinement of the QZ decomposition for solving linear DSGE models," Economics Letters, Elsevier, vol. 253(C).
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    1. Huber, Johannes & Meyer-Gohde, Alexander, 2025. "Iterative refinement of the QZ decomposition for solving linear DSGE models," Economics Letters, Elsevier, vol. 253(C).

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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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