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Using a hyperbolic cross to solve non-linear macroeconomic models

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  • Dennis, Richard

Abstract

The paper presents a sparse grid approximation method based on the hyperbolic cross and applies it to solve non-linear macroeconomic models. We show how the standard hyperbolic cross can be extended to give greater control over the approximating grid and we discuss how to implement an anisotropic hyperbolic cross. Applying the approximation method to four macroeconomic models, we establish that it delivers a level of accuracy on par or better than Smolyak's method and that it can produce accurate approximations using fewer points than Smolyak's method.

Suggested Citation

  • Dennis, Richard, 2024. "Using a hyperbolic cross to solve non-linear macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:dyncon:v:163:y:2024:i:c:s0165188924000526
    DOI: 10.1016/j.jedc.2024.104860
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    Cited by:

    1. Dennis, Richard, 2022. "Computing time-consistent equilibria: A perturbation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).

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    More about this item

    Keywords

    Hyperbolic cross; Smolyak; Non-linear models; Projection methods;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E70 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics - - - General

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