Existence and uniqueness of perturbation solutions to DSGE models

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2012-015

Classification and Topics

• Classification: Wirtschaft ; Optimization Techniques; Programming Models; Dynamic Analysis ; Computational Techniques; Simulation Modeling ; General Aggregative Models: Forecasting and Simulation: Models and Applications
• Subject: perturbation ; matrix calculus ; DSGE ; solution methods ; Bézout theorem ; Sylvester equations ; Dynamisches Gleichgewicht ; Matrizenrechnung ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Lan, Hong ; Meyer-Gohde, Alexander
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/56743
• Last update: 10.03.2025, 11:44 AM CET