IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpge/0505003.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0505/0505003.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Philippe Aghion & Steven Durlauf (ed.), 2005. "Handbook of Economic Growth," Handbook of Economic Growth, Elsevier, edition 1, volume 1, number 1.
    4. 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.
    5. 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.
    6. Jonathan Temple, 2003. "The Long‐Run implications of Growth Theories," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 497-510, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Growiec, Jakub, 2022. "R&D capital: An engine of growth," Economics Letters, Elsevier, vol. 217(C).
    4. 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.
    5. Attar, Mustafa A., 2008. "Science in the Third Dimension of R&D," MPRA Paper 9427, University Library of Munich, Germany.
    6. Bugajewski, Dariusz & Maćkowiak, Piotr, 2015. "On knife-edge conditions with unbounded growth," Journal of Macroeconomics, Elsevier, vol. 45(C), pages 274-283.
    7. 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.
    8. Jakub Growiec, 2007. "Warunki zrównoważonego wzrostu gospodarczego," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 11-12, pages 1-16.
    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.
    10. Ryo Horii, 2023. "Non-Exponential Growth Theory," ISER Discussion Paper 1212, Institute of Social and Economic Research, Osaka University.
    11. 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.
    12. 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.
    13. Attar, M. Aykut, 2016. "Economic Growth and Technological Progress in Turkey: An Analysis of Schumpeterian Mechanisms," MPRA Paper 73255, University Library of Munich, Germany.
    14. Peretto, Pietro F., 2018. "Robust endogenous growth," European Economic Review, Elsevier, vol. 108(C), pages 49-77.
    15. 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.
    16. Sriket, Hongsilp & Suen, Richard M.H., 2022. "Sources of economic growth in models with non-renewable resources," Journal of Macroeconomics, Elsevier, vol. 72(C).
    17. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Jakub Growiec, 2007. "Warunki zrównoważonego wzrostu gospodarczego," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 11-12, pages 1-16.
    3. Jones, C.I., 2016. "The Facts of Economic Growth," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 3-69, Elsevier.
    4. Attar, Mustafa A., 2008. "Science in the Third Dimension of R&D," MPRA Paper 9427, University Library of Munich, Germany.
    5. Di Bartolomeo, Giovanni & D'Imperio, Paolo & Felici, Francesco, 2022. "The fiscal response to the Italian COVID-19 crisis: A counterfactual analysis," Journal of Macroeconomics, Elsevier, vol. 73(C).
    6. Maemir, H. & Ziesemer, T., 2014. "Multinational production and trade in an endogenous growth model with heterogeneous firms," MERIT Working Papers 2014-038, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    7. Janos Varga & Werner Roeger & Jan in’t Veld, 2014. "Growth effects of structural reforms in Southern Europe: the case of Greece, Italy, Spain and Portugal," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 323-363, May.
    8. Michael Bar & Oksana Leukhina, 2010. "The role of mortality in the transmission of knowledge," Journal of Economic Growth, Springer, vol. 15(4), pages 291-321, December.
    9. Jerbashian Vahagn, 2016. "Knowledge licensing in a model of R&D-driven endogenous growth," The B.E. Journal of Macroeconomics, De Gruyter, vol. 16(2), pages 555-579, June.
    10. Marchese, Carla & Privileggi, Fabio, 2014. "A Competitive Idea-Based Growth Model with Shrinking Workers' Income," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201415, University of Turin.
    11. repec:got:cegedp:140 is not listed on IDEAS
    12. Emmanuel Bovari & Victor Court, 2019. "Energy, knowledge, and demo-economic development in the long run: a unified growth model," Working Papers hal-01698755, HAL.
    13. Alberto Bucci & Vladimir Matveenko, 2017. "Horizontal differentiation and economic growth under non-CES aggregate production function," Journal of Economics, Springer, vol. 120(1), pages 1-29, January.
    14. Carla Marchese & Fabio Privileggi, 2018. "Endogenous economic growth with disembodied knowledge," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(3), pages 437-449, June.
    15. Peter K. Kruse-Andersen, 2019. "Directed Technical Change, Environmental Sustainability, and Population Growth," Discussion Papers 19-12, University of Copenhagen. Department of Economics.
    16. Growiec Jakub, 2006. "Fertility Choice and Semi-Endogenous Growth: Where Becker Meets Jones," The B.E. Journal of Macroeconomics, De Gruyter, vol. 6(2), pages 1-25, September.
    17. Richard M. H. Suen, 2013. "Research Policy and U.S. Economic Growth," Working papers 2013-18, University of Connecticut, Department of Economics.
    18. Capolupo, Rosa, 2009. "The New Growth Theories and Their Empirics after Twenty Years," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-72.
    19. Sener, Fuat, 2008. "R&D policies, endogenous growth and scale effects," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3895-3916, December.
    20. Strulik, Holger & Prettner, Klaus & Prskawetz, Alexia, 2010. "R\&D-based Growth in the Post-modern Era," Hannover Economic Papers (HEP) dp-457, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    21. Klenow, Peter J. & Rodriguez-Clare, Andres, 2005. "Externalities and Growth," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 11, pages 817-861, Elsevier.

    More about this item

    Keywords

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpge:0505003. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.