Numerical Solution of Dynamic Equilibrium Models Under Poisson Uncertainty
Universität Hamburg, Department of Economics; CREATES
University of Hannover
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.
Number of Pages in PDF File: 36
Keywords: Continuous-time DSGE, Optimal stochastic control, Waveform Relaxation
JEL Classification: C63, E21, O41working papers series
Date posted: July 17, 2010 ; Last revised: June 14, 2012
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