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Beyond the Linearity Critique: The Knife-Edge Assumption of Steady State Growth

Author

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  • Jakub Growiec

    (Warsaw School of Economics)

Abstract

The "linearity critique" of endogenous growth models is presented in a general context of an arbitrary growth model and reassessed. It is argued, that presence of linearities is not a valid criterion for rejecting growth models. Existence of exponential/geometrical steady- state growth (i.e. of a balanced growth path with strictly positive growth rates) necessarily requires some knife-edge condition, which is not satisfied by typical parameter values. Hence, balanced growth paths are fragile and sensitive to smallest disturbances in parameter values. Adding higher order differential/difference equations to a model does not change the knife-edge character of steady-state growth.

Suggested Citation

  • Jakub Growiec, 2005. "Beyond the Linearity Critique: The Knife-Edge Assumption of Steady State Growth," GE, Growth, Math methods 0505003, University Library of Munich, Germany, revised 17 Jan 2006.
    • Handle: RePEc:wpa:wuwpge:0505003
    Note: Type of Document - pdf; pages: 20
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    Cited by:

    1. Zhou, Yuwen & Tian, Lixin & Yang, Xiaoguang & Wan, Bingyue, 2024. "Robust green Schumpeterian endogenous growth model and spatial Kuznets curve," Energy Economics, Elsevier, vol. 133(C).
    2. Growiec, Jakub, 2022. "R&D capital: An engine of growth," Economics Letters, Elsevier, vol. 217(C).
    3. Bugajewski, Dariusz & Maćkowiak, Piotr, 2015. "On knife-edge conditions with unbounded growth," Journal of Macroeconomics, Elsevier, vol. 45(C), pages 274-283.
    4. Jakub Growiec, 2007. "Warunki zrównoważonego wzrostu gospodarczego," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 11-12, pages 1-16.
    5. Ryo Horii, 2023. "Non-Exponential Growth Theory," ISER Discussion Paper 1212rr, Institute of Social and Economic Research, The University of Osaka, revised Sep 2024.
    6. Attar, M. Aykut, 2016. "Economic Growth and Technological Progress in Turkey: An Analysis of Schumpeterian Mechanisms," MPRA Paper 73255, University Library of Munich, Germany.
    7. Peretto, Pietro F., 2018. "Robust endogenous growth," European Economic Review, Elsevier, vol. 108(C), pages 49-77.
    8. Gregory Casey & Ryo Horii, 2019. "A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change," ISER Discussion Paper 1051, Institute of Social and Economic Research, The University of Osaka.
    9. Jakub Growiec, 2018. "The Digital Era, Viewed From a Perspective of Millennia of Economic Growth," KAE Working Papers 2018-034, Warsaw School of Economics, Collegium of Economic Analysis.
    10. Christian Groth & Karl-Josef Koch & Thomas Steger, 2010. "When economic growth is less than exponential," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 213-242, August.
    11. Christiaans, Thomas, 2008. "International trade and industrialization in a non-scale model of economic growth," Structural Change and Economic Dynamics, Elsevier, vol. 19(3), pages 221-236, September.
    12. Tobias Kronenberg, 2010. "Energy conservation, unemployment and the direction of technical change," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 9(1), pages 1-17, April.
    13. Attar, Mustafa A., 2008. "Science in the Third Dimension of R&D," MPRA Paper 9427, University Library of Munich, Germany.
    14. Pengfei Zhang, 2023. "Endogenous capital-augmenting R&D, intersectoral labor reallocation, and the movement of the labor share," Journal of Economics, Springer, vol. 140(1), pages 1-36, September.
    15. Growiec, Jakub, 2013. "A microfoundation for normalized CES production functions with factor-augmenting technical change," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2336-2350.
    16. Growiec, Jakub, 2010. "Knife-edge conditions in the modeling of long-run growth regularities," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1143-1154, December.
    17. Daniel Cardona & Fernando Sanchez Losada, 2007. "Cost-Based Models of Economic Growth," Working Papers in Economics 179, Universitat de Barcelona. Espai de Recerca en Economia.
    18. Sriket, Hongsilp & Suen, Richard M.H., 2022. "Sources of economic growth in models with non-renewable resources," Journal of Macroeconomics, Elsevier, vol. 72(C).

    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
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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