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Stochastic Stability of Endogenous Growth: The AK Case

Author

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  • Raouf Boucekkine

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

  • Benteng Zou

    (CREA - Center for Research in Economic Analysis - Uni.lu - Université du Luxembourg)

Abstract

This note studies the stochastic stability of the standard AK growth model under uncertain output technology. Capital accumulation follows a stochastic linear homogenous differential equation. It's shown that exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty. Precisely, it's demonstrated that the economy almost surely collapses at exponential speed even though productivity is initially arbitrarily high.

Suggested Citation

  • Raouf Boucekkine & Benteng Zou, 2014. "Stochastic Stability of Endogenous Growth: The AK Case," Working Papers halshs-01090877, HAL.
  • Handle: RePEc:hal:wpaper:halshs-01090877
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01090877
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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. 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.
    4. 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.
    5. Xavier Sala-I-Martin, 1997. "Transfers, Social Safety Nets, and Economic Growth," IMF Staff Papers, Palgrave Macmillan, vol. 44(1), pages 81-102, March.
    6. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 375-393.
    7. 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.
    8. 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.
    9. 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. Patrick A. Pintus, 2015. "Risk-Taking, Global Diversification and Growth: Comment," Working Papers halshs-01113024, HAL.
    2. Raouf Boucekkine & Fabien Prieur & Benteng Zou, 2015. "Institutional dynamics under revenue volatility and revenue-dependent lobbying power: A stochastic differential game approach," DEM Discussion Paper Series 15-08, Department of Economics at the University of Luxembourg.
    3. Anne Epaulard & Aude Pommeret, 2016. "Financial Integration, Growth and Volatility," Pacific Economic Review, Wiley Blackwell, vol. 21(3), pages 330-357, August.
    4. 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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    More about this item

    Keywords

    Ito stochastic differential equation; optimal growth; AK model; balanced growth paths; stochastic stability;
    All these keywords.

    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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