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Existence and Uniqueness of Perturbation Solutions in DSGE Models

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  • Lan, Hong
  • Meyer-Gohde, Alexander

Abstract

We prove the existence of unique solutions for all undetermined coefficients of nonlinear perturbations of arbitrary order in a wide class of discrete time DSGE models under standard regularity and saddle stability assumptions for linear approximations. Our result follows from the straightforward application of matrix analysis to our perturbation derived with Kronecker tensor calculus. Additionally, we relax the assumptions needed for the local existence theorem of perturbation solutions and prove that the local solution is independent of terms first order in the perturbation parameter.

Suggested Citation

  • Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
    • Handle: RePEc:cpm:dynare:014
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    Cited by:

    1. Belongia, Michael T. & Ireland, Peter N., 2022. "A reconsideration of money growth rules," Journal of Economic Dynamics and Control, Elsevier, vol. 135(C).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    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.
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    9. repec:hum:wpaper:sfb649dp2011-087 is not listed on IDEAS

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    More about this item

    Keywords

    perturbation; DSGE; nonlinear; Sylvester equations; matrix calculus; Bézout theorem;
    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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