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The Reduction of Dimension in the Study of Economic Growth Models

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  • J. R. Ruiz-Tamarit
  • M. Ventura-Marco

Abstract

We examine the dimension reduction method and prove that it could be isleading if we try to get some insight tinto the dynamics of the original system from the dynamics of the transformed system alone. The reduced system seemingly may give rise to a continuum multiplicity of steady states when, actually, it does exist a unique and isolated steady state or even it does not exist a steady state at all. We show how the dynamics for the primary variables that is recovered from the solution to the reduced system may be refuted by solving the original one. In our opinion there is no alternative because nothing can be regarded as a close substitute for the study of the original system. Although this method has been extensively used in studying different versions of the Lucas-Uzawa two-sector model, we will focus on one-sector models for checking its validity in the simplest way.

Suggested Citation

  • J. R. Ruiz-Tamarit & M. Ventura-Marco, "undated". "The Reduction of Dimension in the Study of Economic Growth Models," Working Papers 2001-13, FEDEA.
    • Handle: RePEc:fda:fdaddt:2001-13
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    1. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
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    3. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 739-773.
    4. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
    5. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    6. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    Cited by:

    1. José Ramón Ruiz-Tamarit, "undated". "Multiplicity, Overtaking and Convergence in the Lucas Two-Sector Growth Model," Working Papers 2002-17, FEDEA.
    2. Trimborn, Timo, 2018. "On the analysis of endogenous growth models with a balanced growth path," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 40-50.

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