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Stochastic Stability of Endogenous Growth: Theory and Applications

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  • Raouf Boucekkine

    (IUF - Institut universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche, GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Patrick Pintus

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Benteng Zou

    (CREA - Center for Research in Economic Analysis - uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg)

Abstract

We examine the issue of stability of stochastic endogenous growth. First, stochastic stability concepts are introduced and applied to stochastic linear homogenous differential 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," Working Papers halshs-01181505, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01181505
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01181505v1
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    References listed on IDEAS

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    1. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    2. Obstfeld, Maurice, 1994. "Risk-Taking, Global Diversification, and Growth," American Economic Review, American Economic Association, vol. 84(5), pages 1310-1329, December.
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    5. 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.
    6. Xavier Sala-I-Martin, 1997. "Transfers, Social Safety Nets, and Economic Growth," IMF Staff Papers, Palgrave Macmillan, vol. 44(1), pages 81-102, March.
    7. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 375-393.
    8. 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.
    9. 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.
    10. 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.
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    Cited by:

    1. Raouf Boucekkine & Giorgio Fabbri & Patrick A. Pintus, 2015. "Risk Sharing and Growth in Small-Open Economies," Working Papers halshs-01201872, HAL.
    2. Maxime Menuet, 2019. "Fiscal rule and shock amplification : A stochastic endogenous growth model," Working Papers hal-02153887, HAL.
    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.

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    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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