Existence and uniqueness of perturbation solutions to DSGE models

Hong Lan and Alexander Meyer-Gohde

No 2012-015, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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.

Keywords: perturbation; matrix calculus; DSGE; solution methods; Bézout theorem; Sylvester equations (search for similar items in EconPapers)
JEL-codes: C61 C63 E17 (search for similar items in EconPapers)
Date: 2012
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Related works:
Working Paper: Existence and Uniqueness of Perturbation Solutions in DSGE Models (2012)
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