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Existence and uniqueness of perturbation solutions to DSGE models

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  • Lan, Hong
  • Meyer-Gohde, Alexander

Abstract

We prove that standard regularity and saddle stability assumptions for linear approximations are sufficient to guarantee the existence of a unique solution for all undetermined coefficients of nonlinear perturbations of arbitrary order to discrete time DSGE models. We derive the perturbation using a matrix calculus that preserves linear algebraic structures to arbitrary orders of derivatives, enabling the direct application of theorems from matrix analysis to prove our main result. As a consequence, we provide insight into several invertibility assumptions from linear solution methods, prove that the local solution is independent of terms first order in the perturbation parameter, and relax the assumptions needed for the local existence theorem of perturbation solutions.

Suggested Citation

  • Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and uniqueness of perturbation solutions to DSGE models," SFB 649 Discussion Papers 2012-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  • Handle: RePEc:zbw:sfb649:sfb649dp2012-015
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    Cited by:

    1. Meyer-Gohde, Alexander, 2024. "Solving and analyzing DSGE models in the frequency domain," IMFS Working Paper Series 207, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    2. Belongia, Michael T. & Ireland, Peter N., 2022. "A reconsideration of money growth rules," Journal of Economic Dynamics and Control, Elsevier, vol. 135(C).
    3. repec:hum:wpaper:sfb649dp2013-024 is not listed on IDEAS
    4. 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.
    5. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and uniqueness of perturbation solutions to DSGE models," SFB 649 Discussion Papers 2012-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Pruning in perturbation DSGE models: Guidance from nonlinear moving average approximations," SFB 649 Discussion Papers 2013-024, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Frank Hespeler & Marco M. Sorge, 2013. "Does Near-Rationality Matter in First-Order Approximate Solutions? A Perturbation Approach," CSEF Working Papers 339, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    8. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
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    More about this item

    Keywords

    perturbation; matrix calculus; DSGE; solution methods; Bézout theorem; Sylvester equations;
    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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