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Multidimensional Transitional Dynamics: A Simple Numerical Procedure

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  • TRIMBORN, TIMO
  • KOCH, KARL-JOSEF
  • STEGER, THOMAS M.

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].

Suggested Citation

  • Trimborn, Timo & Koch, Karl-Josef & Steger, Thomas M., 2008. "Multidimensional Transitional Dynamics: A Simple Numerical Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 12(3), pages 301-319, June.
  • Handle: RePEc:cup:macdyn:v:12:y:2008:i:03:p:301-319_07
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    References listed on IDEAS

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    1. Thomas M. Steger, 2005. "Welfare Implications of Non‐scale R&D‐based Growth Models," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(4), pages 737-757, December.
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    8. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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