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Beyond the Linearity Critique: The Knife-edge Assumption of Steady-state Growth

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  • Jakub Growiec

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.
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  • Jakub Growiec, 2007. "Beyond the Linearity Critique: The Knife-edge Assumption of Steady-state Growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 489-499, June.
    • Handle: RePEc:spr:joecth:v:31:y:2007:i:3:p:489-499
    DOI: 10.1007/s00199-006-0107-5
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    1. Jones Charles I., 2001. "Was an Industrial Revolution Inevitable? Economic Growth Over the Very Long Run," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(2), pages 1-45, August.
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    Citations

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    Cited by:

    1. Sriket, Hongsilp & Suen, Richard M.H., 2022. "Sources of economic growth in models with non-renewable resources," Journal of Macroeconomics, Elsevier, vol. 72(C).
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. Growiec, Jakub, 2022. "R&D capital: An engine of growth," Economics Letters, Elsevier, vol. 217(C).
    7. Attar, M. Aykut, 2016. "Economic Growth and Technological Progress in Turkey: An Analysis of Schumpeterian Mechanisms," MPRA Paper 73255, University Library of Munich, Germany.
    8. Bugajewski, Dariusz & Maćkowiak, Piotr, 2015. "On knife-edge conditions with unbounded growth," Journal of Macroeconomics, Elsevier, vol. 45(C), pages 274-283.
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    10. 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.
    11. 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.
    12. Attar, Mustafa A., 2008. "Science in the Third Dimension of R&D," MPRA Paper 9427, University Library of Munich, Germany.
    13. Peretto, Pietro F., 2018. "Robust endogenous growth," European Economic Review, Elsevier, vol. 108(C), pages 49-77.
    14. 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.
    15. 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.
    16. Gregory Casey & Ryo Horii, 2019. "A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change," 2019 Meeting Papers 1458, Society for Economic Dynamics.
    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. Jakub Growiec, 2007. "Warunki zrównoważonego wzrostu gospodarczego," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 11-12, pages 1-16.

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    More about this item

    Keywords

    Long-run economic growth; Knife-edge condition; Balanced growth path; Linearity critique; C62; O40; O41;
    All these keywords.

    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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