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Stability analysis of Uzawa–Lucas endogenous growth model

Author

Listed:
  • William A. Barnett

    (University of Kansas
    Center for Financial Stability)

  • Taniya Ghosh

    (Reserve Bank of India)

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 multi-periodic stability. While there are an infinite number of kinds of unstable dynamics, some very close to stability in appearance, there also are 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

  • William A. Barnett & Taniya Ghosh, 2014. "Stability analysis of Uzawa–Lucas endogenous growth model," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 33-44, April.
  • Handle: RePEc:spr:etbull:v:2:y:2014:i:1:d:10.1007_s40505-013-0024-2
    DOI: 10.1007/s40505-013-0024-2
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    1. 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.
    2. Alberto Martin & Jaume Ventura, 2012. "Economic Growth with Bubbles," American Economic Review, American Economic Association, vol. 102(6), pages 3033-3058, October.
    3. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    4. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
    5. Robert J. Barro & Xavier Sala-i-Martin, 2003. "Economic Growth, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262025531, December.
    6. 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.
    7. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    16. McCleary, Rachel & Barro, Robert, 2003. "Religion and Economic Growth across Countries," Scholarly Articles 3708464, Harvard University Department of Economics.
    17. 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.
    18. 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.
    19. Robert J. Barro & Rachel McCleary, 2003. "Religion and Economic Growth," NBER Working Papers 9682, National Bureau of Economic Research, Inc.
    20. 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.
    21. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    22. 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.
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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:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

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