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Mean growth and stochastic stability in endogenous growth models

Author

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  • Raouf Boucekkine

    (AMSE - Aix-Marseille Sciences Economiques - 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

    (AMSE - Aix-Marseille Sciences Economiques - 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

Under uncertainty, mean growth of, say, wealth is often defined as the growth rate of average wealth, but it can alternatively be defined as the average growth rate of wealth. We argue that stochastic stability points to the latter notion of mean growth as the theoretically relevant one. Our discussion is cast within the class of continuous-time AK-type models subject to geometric Brownian motions. First, stability concepts related to stochastic linear homogeneous differential equations are introduced and applied to the canonical AK model. It is readily shown that exponential balanced-growth paths are not robust to uncertainty. In a second application, we evaluate the quantitative implications of adopting the stochastic-stability-related concept of mean growth for the comparative statics of global diversification in the seminal model due to Obstfeld (1994).

Suggested Citation

  • Raouf Boucekkine & Patrick Pintus & Benteng Zou, 2018. "Mean growth and stochastic stability in endogenous growth models," Post-Print hal-01793166, HAL.
    • Handle: RePEc:hal:journl:hal-01793166
    DOI: 10.1016/j.econlet.2018.02.014
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    References listed on IDEAS

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    Cited by:

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    2. Liao, Zhong-Wei & Shao, Jinghai, 2024. "Stability and mean growth rate of stochastic Solow model driven by jump–diffusion process," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    3. Solomon Samanhyia & Danny Cassimon, 2019. "The Effect of Aid on Growth in the Presence of Economic Regime Change," The African Finance Journal, Africagrowth Institute, vol. 21(2), pages 1-23.
    4. Ibrahima Amadou Diallo, 2020. "A Sensitivity Analysis on the Economic Vulnerability-Growth Nexus: Theory and Practice," Working Papers hal-03109383, HAL.
    5. R. Boucekkine & F. Prieur & W. Ruan & B. Zou, 2024. "Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 1127-1171, June.
    6. Diallo, Ibrahima Amadou, 2018. "How Internal Violence Lowers Economic Growth: A Theoretical and Empirical Study," MPRA Paper 88285, University Library of Munich, Germany.
    7. Motoh Tsujimura & Hidekazu Yoshioka, 2023. "A robust consumption model when the intensity of technological progress is ambiguous," Mathematics and Financial Economics, Springer, volume 17, number 2, March.

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    More about this item

    Keywords

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