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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

We develop an iterative implementation of the QZ method for solving DSGE models. It refines the standard QZ solution and, as demonstrated in a macro-finance application, improves numerical accuracy without altering already accurate solutions.

Suggested Citation

  • Huber, Johannes & Meyer-Gohde, Alexander, 2025. "Iterative refinement of the QZ decomposition for solving linear DSGE models," Economics Letters, Elsevier, vol. 253(C).
    • Handle: RePEc:eee:ecolet:v:253:y:2025:i:c:s0165176525002484
    DOI: 10.1016/j.econlet.2025.112411
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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. 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.
    4. Jermann, Urban J., 1998. "Asset pricing in production economies," Journal of Monetary Economics, Elsevier, vol. 41(2), pages 257-275, April.
    5. 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.
    6. 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).
    7. Villemot, Sébastien, 2011. "Solving rational expectations models at first order: what Dynare does," Dynare Working Papers 2, CEPREMAP, revised Dec 2025.
    8. Huber, Johannes & Meyer-Gohde, Alexander, 2025. "Iterative refinement of the QZ decomposition for solving linear DSGE models," Economics Letters, Elsevier, vol. 253(C).
    9. 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.
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    2. 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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    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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