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

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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, EconWPA, revised 17 Jan 2006.
  • Handle: RePEc:wpa:wuwpge:0505003
    Note: Type of Document - pdf; pages: 20
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    References listed on IDEAS

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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.
    2. Jones, Charles I., 2005. "Growth and Ideas," Handbook of Economic Growth,in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 16, pages 1063-1111 Elsevier.
    3. Connolly, Michelle & Peretto, Pietro F, 2003. "Industry and the Family: Two Engines of Growth," Journal of Economic Growth, Springer, vol. 8(1), pages 115-148, March.
    4. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    5. Jonathan Temple, 2003. "The Long-Run implications of Growth Theories," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 497-510, July.
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    Citations

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    Cited by:

    1. 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.
    2. Attar, M. Aykut, 2016. "Economic Growth and Technological Progress in Turkey: An Analysis of Schumpeterian Mechanisms," MPRA Paper 73255, University Library of Munich, Germany.
    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. 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.
    5. 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.
    6. 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.
    7. Attar, Mustafa A., 2008. "Science in the Third Dimension of R&D," MPRA Paper 9427, 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.
    9. 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.

    More about this item

    Keywords

    long-run economic growth; knife-edge conditions; linearity critique; ordinary differential equations;

    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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