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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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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 3431.

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Date of creation: 2011
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Handle: RePEc:ces:ceswps:_3431

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Keywords: continuous-time DSGE; Poisson uncertainty; waveform relaxation;

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Cited by:
  1. Olaf Posch, 2010. "Risk Premia in General Equilibrium," CESifo Working Paper Series 3131, CESifo Group Munich.
  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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