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Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty

Olaf Posch () and Timo Trimborn ()

DEGIT Conference Papers from DEGIT, Dynamics, Economic Growth, and International Trade

Abstract: We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.

Keywords: Continuous-time DSGE; Poisson uncertainty; Waveform Relaxation (search for similar items in EconPapers)
JEL-codes: C63 E21 O41 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2011-09
New Economics Papers: this item is included in nep-cmp and nep-dge
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Journal Article: Numerical solution of dynamic equilibrium models under Poisson uncertainty (2013) Downloads
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