IDEAS home Printed from https://ideas.repec.org/p/ctl/louvir/2004026.html
   My bibliography  Save this paper

Special functions for the study of economic dynamics : The case of the Lucas-Uzawa model

Author

Listed:
  • Raouf, BOUCEKKINE

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

  • José R. , RUIZ-TAMARIT

    (Universitat de Valencia (Spain))

Abstract

The special functions are intensively used in mathematical physics to solve differential systems. We argue that their use should be most useful in economic dynamics, notably in the assessment of the transtion dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reduction

Suggested Citation

  • Raouf, BOUCEKKINE & José R. , RUIZ-TAMARIT, 2004. "Special functions for the study of economic dynamics : The case of the Lucas-Uzawa model," LIDAM Discussion Papers IRES 2004026, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    • Handle: RePEc:ctl:louvir:2004026
    as

    Download full text from publisher

    File URL: http://sites.uclouvain.be/econ/DP/IRES/2004-26.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
    2. Francisco L. Rivera-Batiz & Luis A. Rivera-Batiz, 2018. "Economic Integration and Endogenous Growth," World Scientific Book Chapters, in: Francisco L Rivera-Batiz & Luis A Rivera-Batiz (ed.), International Trade, Capital Flows and Economic Development, chapter 1, pages 3-32, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
    5. 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.
    6. Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January.
    7. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    8. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-1067, December.
    Full references (including those not matched with items on IDEAS)

    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. Mark Vancauteren & Daniel Weiserbs, 2011. "Intra-European Trade of Manufacturing Goods: An Extension of the Gravity Model," International Econometric Review (IER), Econometric Research Association, vol. 3(1), pages 1-24, April.
    2. Pedro Garcia-Castrillo & Marcos Sanso, 2000. "Human Capital and Optimal Policy in a Lucas-type Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 757-770, October.
    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. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.
    5. 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.
    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. Garcia-Belenguer, Fernando, 2007. "Stability, global dynamics and Markov equilibrium in models of endogenous economic growth," Journal of Economic Theory, Elsevier, vol. 136(1), pages 392-416, September.
    8. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
    9. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas–Uzawa model," Economic Modelling, Elsevier, vol. 28(1), pages 109-117.
    10. Xavier Raurich, 2001. "Indeterminancy and Government Spending in a Two-Sector Model of Endogenous Growth," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(1), pages 210-229, January.
    11. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
    12. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
    13. 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.
    14. Kejak, Michal, 2003. "Stages of growth in economic development," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 771-800, March.
    15. Lutz Arnold, 2007. "A generalized multi-country endogenous growth model," International Economics and Economic Policy, Springer, vol. 4(1), pages 61-100, April.
    16. Klaus Wälde, 1996. "Proof of global stability, transitional dynamics, and international capital flows in a two-country model of innovation and growth," Journal of Economics, Springer, vol. 64(1), pages 53-84, February.
    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. Klaus Waelde, 1994. "Transitional dynamics, convergence and international capital flows in two-country models of innovation and growth," International Trade 9403002, University Library of Munich, Germany, revised 03 Jan 1996.
    20. Christian Ghiglino & Kazuo Nishimura & Alain Venditti, 2018. "Non-Balanced Endogenous Growth and Structural Change: When Romer Meets Kaldor and Kuznets," Working Papers halshs-01934872, HAL.

    More about this item

    Keywords

    Special functions; hypergeometric functions; optimal control; Lucas-Uzawa model; economic dynamics;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    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:ctl:louvir:2004026. 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: Virginie LEBLANC (email available below). General contact details of provider: https://edirc.repec.org/data/iruclbe.html .

    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.