10.18452/4390
Lan, Hong
Meyer-Gohde, Alexander
Existence and Uniqueness of Perturbation Solutions to DSGE Models
Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
2012
DSGE
solution methods
Perturbation
matrix calculus
Bézout theorem
Sylvester equations
330 Wirtschaft
Humboldt-Universität zu Berlin
Humboldt-Universität zu Berlin
2017-06-16
2017-06-16
2012-02-23
2012-02-15
2012-02-15
http://edoc.hu-berlin.de/series/sfb-649-papers/2012-15/PDF/15.pdf
http://edoc.hu-berlin.de/18452/5042
urn:nbn:de:kobv:11-100199537
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.