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MULTIDIMENSIONAL TRANSITIONAL DYNAMICS: A SIMPLE NUMERICAL PROCEDURE

Published online by Cambridge University Press:  01 June 2008

TIMO TRIMBORN ,
KARL-JOSEF KOCH  and
THOMAS M. STEGER
TIMO TRIMBORN*
Affiliation:
University of Hannover
KARL-JOSEF KOCH
Affiliation:
University of Siegen
THOMAS M. STEGER
Affiliation:
University of Leipzig
*
Address correspondence to: Timo Trimborn, Department of Economics, Institute for Macroeconomics, University of Hannover, Koenigsworther Platz 1, 30167 Hannover, Germany; e-mail: trimborn@vwl.uni-hannover.de.
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Abstract

We propose the relaxation algorithm as a simple and powerful method for determining the transition process in growth models numerically. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including stiff differential equations and systems giving rise to a continuum of stationary equilibria. (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 infinite time horizon, which usually underlies optimal control problems in economics. As an illustrative application, we compute the transition process of the models of Jones [Jones, C.I. (1995) R&D-based models of economic growth. Journal of Political Economy 103 (3), 759–784] and Lucas [Lucas, R.E., Jr. (1988) On the mechanics of economic development. Journal of Monetary Economics 22, 3–42].

Keywords

Transitional DynamicsContinuous Time Growth ModelsSaddle-point ProblemsMultidimensional Stable Manifolds
Type
Articles
Information
Macroeconomic Dynamics , Volume 12 , Issue 3 , June 2008 , pp. 301 - 319
Copyright
Copyright © Cambridge University Press 2008

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