Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure

Posted: 10 Aug 2010

See all articles by Karl-Josef Koch

Karl-Josef Koch

University of Siegen - School of Economic Disciplines

Timo Trimborn

Leibniz Universität Hannover

Thomas Michael Steger

University of Leipzig/Institute for Theoretical Economics/Macroeconomics; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: December 1, 2004

Abstract

We propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including multi-dimensional systems with stable eigenvalues that di.er drastically in magnitude. (2) The application of the procedure is fairly user friendly. The only input required consists of the dynamic system. (3) The variant of the relaxation algorithm we propose exploits in a natural manner the in.nite time horizon, which usually underlies optimal control problems in economics. Overall, it seems that the relaxation procedure can easily cope with a large number of problems which arise frequently in the context of macroeconomic dynamic models. As an illustrative application, we simulate the transition process of the well-known Jones (1995) model.

Keywords: Transitional Dynamics, Continuous Time Growth Models, Saddle-point Problems, Multidimensional Stable Manifolds

JEL Classification: C61, C63, O40

Suggested Citation

Koch, Karl-Josef and Trimborn, Timo and Steger, Thomas Michael, Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure (December 1, 2004). Macroeconomic Dynamics, Vol. 12, No. 3, 2008, Available at SSRN: https://ssrn.com/abstract=1655652

Karl-Josef Koch

University of Siegen - School of Economic Disciplines ( email )

Hoelderlinstrasse 3
57068 Siegen
Germany

Timo Trimborn (Contact Author)

Leibniz Universität Hannover ( email )

Welfengarten 1
D-30167 Hannover, 30167
Germany

Thomas Michael Steger

University of Leipzig/Institute for Theoretical Economics/Macroeconomics ( email )

Grimmaische Str. 12
D-04109 Leipzig
Germany

CESifo (Center for Economic Studies and Ifo Institute) ( email )

Poschinger Str. 5
Munich, DE-81679
Germany

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