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Numerical solution of continuous-time DSGE models under Poisson uncertainty

Olaf Posch () and Timo Trimborn ()
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Olaf Posch: Aarhus University, Denmark

Economics Working Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We then use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary differential equations by standard methods and fix-point iteration. Analytical solutions are provided as a benchmark from which our numerical method can be used to explore broader classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We find that, even for non-linear policy functions, the maximum (absolute) error is very small.

Keywords: Continuous-time DSGE; Optimal stochastic control; Waveform Relaxation (search for similar items in EconPapers)
JEL-codes: E21 G11 O41 (search for similar items in EconPapers)
Pages: 33
Date: 2010-06-10
New Economics Papers: this item is included in nep-cba, nep-cmp, nep-mac and nep-ore
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