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Multi-Dimensional Transitional Dynamics: A Simple Numberical Procedure

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Author Info
Timo Trimborn ()
Karl-Josef Koch ()
Thomas 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 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 simulate the transition process of the Jones (1995) and the Lucas (1988) model.

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Publisher Info
Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number CESifo Working Paper No. 1745.

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Date of creation: 2006
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Handle: RePEc:ces:ceswps:_1745

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Related research
Keywords: transitional dynamics; continuous time growth models; saddle-point problems; multi-dimensional stable manifolds;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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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)
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  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, September.
    Other versions:
    • Robert J. Barro & Paul M. Romer, 1991. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr91-1, September.
  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)
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  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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