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Existence and Uniqueness of Perturbation Solutions to DSGE Models

  • Hong Lan
  • Alexander Meyer-Gohde

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.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2012-015.

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Length: 48 pages
Date of creation: Feb 2012
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2012-015
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  16. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
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  18. Binder, Michael & Pesaran, M. Hashem, 1997. "Multivariate Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 13(06), pages 877-888, December.
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  20. Eric Swanson & Gary Anderson & Andrew Levin, 2006. "Higher-order perturbation solutions to dynamic, discrete-time rational expectations models," Working Paper Series 2006-01, Federal Reserve Bank of San Francisco.
  21. 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.
  22. King, Robert G & Watson, Mark W, 2002. "System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 57-86, October.
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