IDEAS home Printed from https://ideas.repec.org/a/eee/jmacro/v32y2010i4p1143-1154.html
   My bibliography  Save this article

Knife-edge conditions in the modeling of long-run growth regularities

Author

Listed:
  • Growiec, Jakub

Abstract

Balanced (exponential) growth cannot be generalized to a concept which would not require knife-edge conditions to be imposed on dynamic models. Already the assumption that a solution to a dynamical system (i.e. time path of an economy) satisfies a given functional regularity (e.g. quasi-arithmetic, logistic, etc.) imposes at least one knife-edge assumption on the considered model. Furthermore, it is always possible to find divergent and qualitative changes in dynamic behavior of the model - strong enough to invalidate its long-run predictions - if a certain parameter is infinitesimally manipulated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmacro:v:32:y:2010:i:4:p:1143-1154
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0164-0704(10)00048-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    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. repec:ebl:ecbull:v:5:y:2006:i:6:p:1-5 is not listed on IDEAS
    3. Robert M. Solow, 1994. "Perspectives on Growth Theory," Journal of Economic Perspectives, American Economic Association, vol. 8(1), pages 45-54, Winter.
    4. 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.
    5. 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.
    6. 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.
    7. Charles I. Jones, "undated". "Population and Ideas: A Theory of Endogenous Growth," Working Papers 98014, Stanford University, Department of Economics.
    8. H. Uzawa, 1961. "Neutral Inventions and the Stability of Growth Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 117-124.
    9. Hendrik Hakenes & Andreas Irmen, 2007. "On the long-run evolution of technological knowledge," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 171-180, January.
    10. Joonkyung Ha & Peter Howitt, 2007. "Accounting for Trends in Productivity and R&D: A Schumpeterian Critique of Semi-Endogenous Growth Theory," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 733-774, June.
    11. Jakob Madsen, 2008. "Semi-endogenous versus Schumpeterian growth models: testing the knowledge production function using international data," Journal of Economic Growth, Springer, vol. 13(1), pages 1-26, March.
    12. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(2), pages 517-549.
    13. Larry E. Jones & Rodolfo Manuelli, 1990. "A Convex Model of Equilibrium Growth," NBER Working Papers 3241, National Bureau of Economic Research, Inc.
    14. Jakub Growiec, 2008. "A new class of production functions and an argument against purely labor‐augmenting technical change," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 483-502, December.
    15. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, March.
    16. Jones, Larry E & Manuelli, Rodolfo E, 1990. "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 1008-1038, October.
    17. Robert Axtell, 1999. "The Emergence of Firms in a Population of Agents," Working Papers 99-03-019, Santa Fe Institute.
    18. Jonathan Temple, 2003. "The Long‐Run implications of Growth Theories," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 497-510, July.
    19. Asheim, Geir B. & Buchholz, Wolfgang & Hartwick, John M. & Mitra, Tapan & Withagen, Cees, 2007. "Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints," Journal of Environmental Economics and Management, Elsevier, vol. 53(2), pages 213-229, March.
    20. Charles I. Jones & Dean Scrimgeour, 2008. "A New Proof of Uzawa's Steady-State Growth Theorem," The Review of Economics and Statistics, MIT Press, vol. 90(1), pages 180-182, February.
    21. Juan Gabriel Brida & Elvio Accinelli, 2007. "The Ramsey model with logistic population growth," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    22. Christiaans, Thomas, 2004. "Types of balanced growth," Economics Letters, Elsevier, vol. 82(2), pages 253-258, February.
    23. repec:awi:wpaper:0438 is not listed on IDEAS
    24. repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
    25. Alwyn Young, 1998. "Growth without Scale Effects," Journal of Political Economy, University of Chicago Press, vol. 106(1), pages 41-63, February.
    26. Mitra, Tapan, 1983. "Limits on Population Growth under Exhaustible Resource Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 155-168, February.
    27. Jakub Growiec, 2007. "Warunki zrównoważonego wzrostu gospodarczego," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 11-12, pages 1-16.
    28. Ekkehart Schlicht, 2006. "A Variant of Uzawa's Theorem," Economics Bulletin, AccessEcon, vol. 5(6), pages 1-5.
    29. 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.
    30. 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.
    31. Johansen, Anders & Sornette, Didier, 2001. "Finite-time singularity in the dynamics of the world population, economic and financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 465-502.
    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. LI, Defu & Bental, Benjamin, 2015. "Growth with Endogenous Direction of Technical Change," MPRA Paper 64124, University Library of Munich, Germany.
    3. Bugajewski, Dariusz & Maćkowiak, Piotr, 2015. "On knife-edge conditions with unbounded growth," Journal of Macroeconomics, Elsevier, vol. 45(C), pages 274-283.
    4. Mand, Matthias, 2016. "On the Cyclicality of R&D Activities," VfS Annual Conference 2016 (Augsburg): Demographic Change 145472, Verein für Socialpolitik / German Economic Association.
    5. Li, Defu & Huang, Jiuli & Zhou, Ying, 2013. "Revisting the Steady-State Equilibrium Conditions of Neoclassical Growth Models," MPRA Paper 55045, University Library of Munich, Germany, revised May 2013.
    6. Li, Defu & Bental, Benjamin, 2016. "What determines the direction of technological progress?," MPRA Paper 71517, University Library of Munich, Germany.

    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. Jakub Growiec, 2007. "Warunki zrównoważonego wzrostu gospodarczego," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 11-12, pages 1-16.
    2. 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.
    3. 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, Osaka University.
    4. 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.
    5. Jakub Growiec, 2019. "The Hardware–Software Model: A New Conceptual Framework of Production, R&D, and Growth with AI," Working Paper series 19-18, Rimini Centre for Economic Analysis.
    6. Christian Groth & Karl-Josef Koch & Thomas Steger, 2006. "Rethinking the Concept of Long-Run Economic Growth," CESifo Working Paper Series 1701, CESifo.
    7. 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.
    8. Gregory Casey, 2018. "Technology-Driven Unemployment," 2018 Meeting Papers 302, Society for Economic Dynamics.
    9. Bugajewski, Dariusz & Maćkowiak, Piotr, 2015. "On knife-edge conditions with unbounded growth," Journal of Macroeconomics, Elsevier, vol. 45(C), pages 274-283.
    10. Irmen, Andreas, 2011. "Steady-state growth and the elasticity of substitution," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1215-1228, August.
    11. Grossmann, Volker, 2009. "Entrepreneurial innovation and economic growth," Journal of Macroeconomics, Elsevier, vol. 31(4), pages 602-613, December.
    12. Grieben, Wolf-Heimo & Sener, Fuat, 2009. "Globalization, rent protection institutions, and going alone in freeing trade," European Economic Review, Elsevier, vol. 53(8), pages 1042-1065, November.
    13. Attar, Mustafa A., 2008. "Science in the Third Dimension of R&D," MPRA Paper 9427, University Library of Munich, Germany.
    14. Irmen, Andreas, 2018. "A Generalized Steady-State Growth Theorem," Macroeconomic Dynamics, Cambridge University Press, vol. 22(4), pages 779-804, June.
    15. Turnovsky, S., 2000. "Growth in an Open Economy: some Recent Developments," Papers 5, Warwick - Development Economics Research Centre.
    16. Armando Sánchez-Vargas & José Manuel Márquez-Estrada & Eric Hernández-Ramírez, 2023. "Uncovering the Link Between the Theoretical and Probabilistic Models of the Global Production Function: A Copula Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 289-315, June.
    17. Jakub Growiec, 2008. "A new class of production functions and an argument against purely labor‐augmenting technical change," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 483-502, December.
    18. Katsuhiko Hori & Katsunori Yamada, 2013. "Education, Innovation and Long-Run Growth," The Japanese Economic Review, Japanese Economic Association, vol. 64(3), pages 295-318, September.
    19. Cozzi, Guido, 2021. "Semi-Endogenous or Fully Endogenous Growth? A Simple Unified Theory," MPRA Paper 110681, University Library of Munich, Germany.
    20. Gene M. Grossman & Elhanan Helpman & Ezra Oberfield & Thomas Sampson, 2017. "Balanced Growth Despite Uzawa," American Economic Review, American Economic Association, vol. 107(4), pages 1293-1312, April.

    More about this item

    Keywords

    Knife-edge condition Balanced growth Regular growth Bifurcation Growth model Long-run dynamics;

    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:eee:jmacro:v:32:y:2010:i:4:p:1143-1154. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622617 .

    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.