IDEAS home Printed from https://ideas.repec.org/p/fda/fdaddt/2001-13.html
   My bibliography  Save this paper

The Reduction of Dimension in the Study of Economic Growth Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://documentos.fedea.net/pubs/dt/2001/dt-2001-13.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. De, Supriyo, 2014. "Intangible capital and growth in the ‘new economy’: Implications of a multi-sector endogenous growth model," Structural Change and Economic Dynamics, Elsevier, vol. 28(C), pages 25-42.
    2. Benhabib, Jess & Gali, Jordi, 1995. "On growth and indeterminacy: some theory and evidence," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 43(1), pages 163-211, December.
    3. Brito, Paulo & Venditti, Alain, 2010. "Local and global indeterminacy in two-sector models of endogenous growth," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 893-911, September.
    4. Neustroev, Dmitry, 2013. "The Uzawa-Lucas Growth Model with Natural Resources," MPRA Paper 52937, University Library of Munich, Germany.
    5. repec:ebl:ecbull:v:4:y:2007:i:38:p:1-12 is not listed on IDEAS
    6. Reiß, Markus & Bethmann, Dirk, 2003. "Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth," SFB 373 Discussion Papers 2003,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Petr Duczynski, 2007. "A Note on the Imbalance Effect in the Uzawa-Lucas Model," Economics Bulletin, AccessEcon, vol. 4(38), pages 1-12.
    8. Benhabib, Jess & Perli, Roberto & Xie, Danyang, 1994. "Monopolistic competition, indeterminacy and growth," MPRA Paper 37411, University Library of Munich, Germany, revised 1994.
    9. Maria João Ribeiro, 2003. "Endogenous Growth: Analytical Review of its Generating Mechanisms," NIPE Working Papers 4/2003, NIPE - Universidade do Minho.
    10. Danyang Xie, 2000. "Power Risk Aversion Utility Functions," Annals of Economics and Finance, Society for AEF, vol. 1(2), pages 265-282, November.
    11. Arnold, Lutz G., 1998. "Growth, Welfare, and Trade in an Integrated Model of Human-Capital Accumulation and Research," Journal of Macroeconomics, Elsevier, vol. 20(1), pages 81-105, January.
    12. Kejak, Michal, 2003. "Stages of growth in economic development," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 771-800, March.
    13. Paolo Mattana & Kazuo Nishimura & Tadashi Shigoka, 2012. "Homoclinic Bifurcation and Global Indeterminacy of Equilibrium in a Two-Sector Endogenous Growth Model," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 427-451, Springer.
    14. Stephen J. Turnovsky, 2000. "Growth in an open economy: some recent developments," Working Paper Research 05, National Bank of Belgium.
    15. Boucekkine, R. & Martínez, B. & Ruiz-Tamarit, J.R., 2013. "Growth vs. level effect of population change on economic development: An inspection into human-capital-related mechanisms," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 312-334.
    16. Shiro Kuwahara, 2017. "Multiple steady states and indeterminacy in the Uzawa–Lucas model with educational externalities," Journal of Economics, Springer, vol. 122(2), pages 173-190, October.
    17. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    18. Long, N.V. & Wong, K.Y., 1996. "Endogenous Growth and International Trade: A Survey," Working Papers 96-07, University of Washington, Department of Economics.
    19. Chilarescu, Constantin, 2009. "A closed-form solution to the transitional dynamics of the Lucas-Uzawa model," Economic Modelling, Elsevier, vol. 26(1), pages 135-138, January.
    20. Ladron-de-Guevara, Antonio & Ortigueira, Salvador & Santos, Manuel S., 1997. "Equilibrium dynamics in two-sector models of endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 21(1), pages 115-143, January.
    21. Bella, Giovanni & Mattana, Paolo & Venturi, Beatrice, 2017. "Shilnikov chaos in the Lucas model of endogenous growth," Journal of Economic Theory, Elsevier, vol. 172(C), pages 451-477.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fda:fdaddt:2001-13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Carmen Arias (email available below). General contact details of provider: https://www.fedea.net .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.