Existence and Uniqueness of Perturbation Solutions to DSGE Models
Hong Lan () and
No SFB649DP2012-015, SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649
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, BÃ©zout theorem; Sylvester equations (search for similar items in EconPapers)
JEL-codes: C61 C63 E17 (search for similar items in EconPapers)
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Working Paper: Existence and Uniqueness of Perturbation Solutions in DSGE Models (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:hum:wpaper:sfb649dp2012-015
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