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Solving linear DSGE models with Bernoulli iterations

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  • Meyer-Gohde, Alexander

Abstract

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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  • 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).
    • Handle: RePEc:zbw:imfswp:182
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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).
    2. 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.
    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).

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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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