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Title:Existence and uniqueness of perturbation solutions to DSGE models PDF Logo
Authors:Lan, Hong
Meyer-Gohde, Alexander
Issue Date:2012
Series/Report no.:SFB 649 discussion paper 2012-015
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.
Subjects:perturbation
matrix calculus
DSGE
solution methods
Bézout theorem
Sylvester equations
JEL:C61
C63
E17
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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