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Business Cycle Fluctuations and Learning-by-doing Externalities in a One-sector Model

Author

Listed:
  • Hippolyte d'Albis

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Emmanuelle Augeraud-Véron

  • Alain Venditti

    (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, EDHEC Business School - Département Comptabilité, Droit, Finance et Economie)

Abstract

We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow (1962), to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.

Suggested Citation

  • Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2012. "Business Cycle Fluctuations and Learning-by-doing Externalities in a One-sector Model," Post-Print hal-00759198, HAL.
    • Handle: RePEc:hal:journl:hal-00759198
    DOI: 10.1016/j.jmateco.2012.07.002
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    Citations

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    Cited by:

    1. Fabbri Giorgio & Federico Salvatore, 2014. "On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 33-43, November.
    2. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
    3. Manjira Datta & Kevin Reffett & Łukasz Woźny, 2018. "Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 593-626, October.
    4. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
    5. Bambi, Mauro & Gozzi, Fausto & Licandro, Omar, 2014. "Endogenous growth and wave-like business fluctuations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 68-111.
    6. Fabbri, Giorgio, 2017. "International borrowing without commitment and informational lags: Choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 103-114.
    7. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Papers 2102.09851, arXiv.org, revised Feb 2021.
    8. Usman, Umer & Batabyal, Amitrajeet A., 2014. "Goods production, learning by doing, and growth in a region with creative and physical capital," International Review of Economics & Finance, Elsevier, vol. 33(C), pages 92-99.
    9. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Backward- versus Forward-Looking Feedback Interest Rate Rules," Documents de travail du Centre d'Economie de la Sorbonne 12051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    10. Frédéric Zumer & Jacques Le Cacheux & Marc Flandreau, 1998. "Stability without a pact? Lessons from the European Gold Standard, 1880-1913," Sciences Po publications n°98-01, Sciences Po.
    11. Augeraud-Veron, Emmanuelle & Boucekkine, Raouf & Gozzi, Fausto & Venditti, Alain & Zou, Benteng, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    12. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2016. "Sunspot fluctuations in two-sector models: New results with additively separable preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 67-83, March.
    13. William Lefebvre & Enzo Miller, 2021. "Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 134-168, October.
    14. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Post-Print hal-03145949, HAL.

    More about this item

    Keywords

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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