IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/47231.html
   My bibliography  Save this paper

Stability analysis of Uzawa-Lucas endogenous growth model

Author

Listed:
  • Barnett, William A.
  • Ghosh, Taniya

Abstract

This paper analyzes, within its feasible parameter space, the dynamics of the Uzawa-Lucas endogenous growth model. The model is solved from a centralized social planner perspective as well as in the model’s decentralized market economy form. We examine the stability properties of both versions of the model and locate Hopf and transcritical bifurcation boundaries. In an extended analysis, we investigate the existence of Andronov-Hopf bifurcation, branch point bifurcation, limit point cycle bifurcation, and period doubling bifurcations. While these all are local bifurcations, the presence of global bifurcation is confirmed as well. We find evidence that the model could produce chaotic dynamics, but our analysis cannot confirm that conjecture. It is important to recognize that bifurcation boundaries do not necessarily separate stable from unstable solution domains. Bifurcation boundaries can separate one kind of unstable dynamics domain from another kind of unstable dynamics domain, or one kind of stable dynamics domain from another kind (called soft bifurcation), such as bifurcation from monotonic stability to damped periodic stability or from damped periodic to damped multiperiodic stability. There are not only an infinite number of kinds of unstable dynamics, some very close to stability in appearance, but also an infinite number of kinds of stable dynamics. Hence subjective prior views on whether the economy is or is not stable provide little guidance without mathematical analysis of model dynamics. When a bifurcation boundary crosses the parameter estimates’ confidence region, robustness of dynamical inferences from policy simulations are compromised, when conducted, in the usual manner, only at the parameters’ point estimates.

Suggested Citation

  • Barnett, William A. & Ghosh, Taniya, 2013. "Stability analysis of Uzawa-Lucas endogenous growth model," MPRA Paper 47231, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:47231
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/47231/1/MPRA_paper_47231.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. McCleary, Rachel & Barro, Robert, 2003. "Religion and Economic Growth across Countries," Scholarly Articles 3708464, Harvard University Department of Economics.
    2. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    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. Alberto Martin & Jaume Ventura, 2012. "Economic Growth with Bubbles," American Economic Review, American Economic Association, vol. 102(6), pages 3033-3058, October.
    5. Banerjee, Sanjibani & A. Barnett, William & A. Duzhak, Evgeniya & Gopalan, Ramu, 2011. "Bifurcation analysis of Zellner's Marshallian Macroeconomic Model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1577-1585, September.
    6. Arnold, Lutz G., 2000. "Stability of the Market Equilibrium in Romer's Model of Endogenous Technological Change: A Complete Characterization," Journal of Macroeconomics, Elsevier, vol. 22(1), pages 69-84, January.
    7. Barnett William A. & He Yijun, 1999. "Stability Analysis of Continuous-Time Macroeconometric Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-22, January.
    8. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    9. Robert J. Barro & Xavier Sala-i-Martin, 2003. "Economic Growth, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262025531, January.
    10. Mondal, Debasis, 2008. "Stability analysis of the Grossman-Helpman model of endogenous product cycles," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1302-1322, September.
    11. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    12. William Barnett & Taniya Ghosh, 2013. "Bifurcation Analysis of an Endogenous Growth Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201306, University of Kansas, Department of Economics, revised Oct 2013.
    13. Marcus Scheiblecker & et al., 2003. "Austria's Economy in 2002: Another Year of Slow Growth," WIFO Monatsberichte (monthly reports), WIFO, vol. 76(4), pages 257-323, April.
    14. Barnett, William A. & He, Yijun, 2002. "Stabilization Policy As Bifurcation Selection: Would Stabilization Policy Work If The Economy Really Were Unstable?," Macroeconomic Dynamics, Cambridge University Press, vol. 6(05), pages 713-747, November.
    15. Robert J. Barro & Rachel McCleary, 2003. "Religion and Economic Growth," NBER Working Papers 9682, National Bureau of Economic Research, Inc.
    16. Robert J. Barro, 2003. "Determinants of Economic Growth in a Panel of Countries," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 231-274, November.
    17. repec:eee:joecas:v:10:y:2013:i:1:p:53-64 is not listed on IDEAS
    18. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    19. Xavier Sala-i-Martín & Elsa V. Artadi, 2003. "Economic growth and investment in the Arab world," Economics Working Papers 683, Department of Economics and Business, Universitat Pompeu Fabra.
    20. 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. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.

    More about this item

    Keywords

    bifurcation; endogenous growth; Lucas-Uzawa model; Hopf; inference robustness; dynamics; stability.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E0 - Macroeconomics and Monetary Economics - - General
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    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:pra:mprapa:47231. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.