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Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure

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Author Info
Karl-Josef Koch ()
Timo Trimborn
Thomas M. Steger

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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 differ 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 infinite 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.

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Publisher Info
Paper provided by Universität Siegen, Fachbereich Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht in its series Volkswirtschaftliche Diskussionsbeitraege with number 121-05.

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Date of creation: 2005
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Handle: RePEc:sie:siegen:121-05

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Web page: http://www.uni-siegen.de/fb5/vwl/research/diskussionsbeitraege/

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Keywords: dynamic programming; relaxation algorithm;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Thomas M. Steger, 2005. "Welfare Implications of Non-scale R&D-based Growth Models," Scandinavian Journal of Economics, Blackwell Publishing, vol. 107(4), pages 737-757, December. [Downloadable!] (restricted)
  2. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December. [Downloadable!] (restricted)
    Other versions:
  3. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-84, August. [Downloadable!] (restricted)
  4. Juillard, Michel & Laxton, Douglas & McAdam, Peter & Pioro, Hope, 1998. "An algorithm competition: First-order iterations versus Newton-based techniques," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1291-1318, August. [Downloadable!] (restricted)
  5. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May. [Downloadable!] (restricted)
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  6. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June. [Downloadable!] (restricted)
  7. Eicher, Theo S & Turnovsky, Stephen J, 1999. " Convergence in a Two-Sector Nonscale Growth Model," Journal of Economic Growth, Springer, vol. 4(4), pages 413-28, December. [Downloadable!] (restricted)
  8. Robert J. Barro & Paul Romer, 1993. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr93-1.
    Other versions:
    • Robert J. Barro & Paul M. Romer, 1991. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr91-1.
  9. Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  10. Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, vol. 62(3), pages 635-56, May. [Downloadable!] (restricted)
  11. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation, Yale University. [Downloadable!]
  12. Jonathan Temple, 2003. "The Long-Run implications of Growth Theories," Journal of Economic Surveys, Blackwell Publishing, vol. 17(3), pages 497-510, 07. [Downloadable!] (restricted)
  13. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages S71-102, October. [Downloadable!] (restricted)
    Other versions:
  14. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July. [Downloadable!] (restricted)
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