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Stability analysis of Uzawa-Lucas endogenous growth model

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  • 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
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    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. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
    10. Robert J. Barro & Xavier Sala-i-Martin, 2003. "Economic Growth, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262025531, April.
    11. 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.
    12. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    13. Barnett, William A. & Ghosh, Taniya, 2013. "Bifurcation analysis of an endogenous growth model," The Journal of Economic Asymmetries, Elsevier, vol. 10(1), pages 53-64.
    14. Marcus Scheiblecker & et al., 2003. "Österreichs Wirtschaft im Jahr 2002: Neuerlich ungenügendes Wachstum," WIFO Monatsberichte (monthly reports), WIFO, vol. 76(4), pages 257-323, April.
    15. 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(5), pages 713-747, November.
    16. Robert J. Barro & Rachel McCleary, 2003. "Religion and Economic Growth," NBER Working Papers 9682, National Bureau of Economic Research, Inc.
    17. Barnett, William A. & Eryilmaz, Unal, 2016. "An Analytical And Numerical Search For Bifurcations In Open Economy New Keynesian Models," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 482-503, March.
    18. 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.
    19. 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.
    20. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    21. 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.
    22. 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. 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.

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    More about this item

    Keywords

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

    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

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