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Stochastic stability of endogenous growth:Theory and applications

Author

Listed:
  • Raouf Boucekkine

    () (GREQAM, Aix Marseille University)

  • Patrick Pintus

    () (GREQAM, Aix Marseille University)

  • Benteng Zou

    () (CREA, Université de Luxembourg)

Abstract

We examine the issue of stability of stochastic endogenous growth. First, stochastic stability concepts are introduced and applied to stochastic linear homogenous differen- tial equations to which several stochastic endogenous growth models reduce. Second, we apply the mathematical theory to two models, starting with the stochastic AK model. It’s shown that in this case exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty: the economy may almost surely collapse at exponential speed even though productivity is initially arbitrarily high. Finally, we revisit the seminal global diversification endogenous growth model (Obstfeld, 1994): taking into account stochastic stability calls for a redefinition of the mean growth concept, which leads to revisit the established wisdom on the growth effect of global diversification.

Suggested Citation

  • Raouf Boucekkine & Patrick Pintus & Benteng Zou, 2015. "Stochastic stability of endogenous growth:Theory and applications," CREA Discussion Paper Series 15-09, Center for Research in Economic Analysis, University of Luxembourg.
  • Handle: RePEc:luc:wpaper:15-09
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    References listed on IDEAS

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    1. anonymous, 1995. "Does the bouncing ball lead to economic growth?," Regional Update, Federal Reserve Bank of Atlanta, issue Jul, pages 1-2,4-6.
    2. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    3. Obstfeld, Maurice, 1994. "Risk-Taking, Global Diversification, and Growth," American Economic Review, American Economic Association, vol. 84(5), pages 1310-1329, December.
    4. Boucekkine, R. & Fabbri, G. & Pintus, P., 2014. "Growth and financial liberalization under capital collateral constraints: The striking case of the stochastic AK model with CARA preferences," Economics Letters, Elsevier, vol. 122(2), pages 303-307.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Takashi Kamihigashi, 2006. "Almost sure convergence to zero in stochastic growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 231-237, September.
    7. Xavier Sala-I-Martin, 1997. "Transfers, Social Safety Nets, and Economic Growth," IMF Staff Papers, Palgrave Macmillan, vol. 44(1), pages 81-102, March.
    8. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 375-393.
    9. Jones, Larry E. & Manuelli, Rodolfo E., 2005. "Neoclassical Models of Endogenous Growth: The Effects of Fiscal Policy, Innovation and Fluctuations," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.),Handbook of Economic Growth, edition 1, volume 1, chapter 1, pages 13-65, Elsevier.
    10. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    11. de Hek, Paul A, 1999. "On Endogenous Growth under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 727-744, August.
    12. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
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    Cited by:

    1. Maxime Menuet, 2019. "Fiscal rule and shock amplification : A stochastic endogenous growth model," Working Papers hal-02153887, HAL.
    2. Raouf Boucekkine & Giorgio Fabbri & Patrick A. Pintus, 2015. "Risk Sharing and Growth in Small-Open Economies," AMSE Working Papers 1537, Aix-Marseille School of Economics, France.
    3. Raouf Boucekkine & Fabien Prieur & Benteng Zou, 2015. "Symmetric vs Asymmetric Equilibria and Stochastic Stability in a Dynamic Game of Legislative Lobbying," AMSE Working Papers 1531, Aix-Marseille School of Economics, France, revised Jan 2018.

    More about this item

    Keywords

    Endogenous growth; stochastic growth; stochastic stability; AK model; Global diversification;

    JEL classification:

    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • 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

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