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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.

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Bibliographic Info

Paper provided by CEPREMAP in its series Dynare Working Papers with number 14.

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Length: 22 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:cpm:dynare:014

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

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References

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Citations

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Cited by:
  1. Hong Lan & Alexander Meyer-Gohde, 2011. "Solving DSGE Models with a Nonlinear Moving Average," SFB 649 Discussion Papers SFB649DP2011-087, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Hong Lan & Alexander Meyer-Gohde, 2013. "Pruning in Perturbation DSGE Models - Guidance from Nonlinear Moving Average Approximations," SFB 649 Discussion Papers SFB649DP2013-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Lan, Hong & Meyer-Gohde, Alexander, 2012. "Existence and Uniqueness of Perturbation Solutions in DSGE Models," Dynare Working Papers 14, CEPREMAP.
  4. 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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