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Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty

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  • Olaf Posch
  • Timo Trimborn

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.

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Bibliographic Info

Paper provided by DEGIT, Dynamics, Economic Growth, and International Trade in its series DEGIT Conference Papers with number c016_044.

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Length: 36 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:deg:conpap:c016_044

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Keywords: Continuous-time DSGE; Poisson uncertainty; Waveform Relaxation;

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Cited by:
  1. Posch, Olaf, 2011. "Risk premia in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1557-1576, September.
  2. Juan Carlos Parra-Alvarez, 2013. "A comparison of numerical methods for the solution of continuous-time DSGE models," CREATES Research Papers 2013-39, School of Economics and Management, University of Aarhus.

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