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Knife-Edge Conditions in the Modeling of Long-Run Growth Regularities

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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

  • Jakub Growiec, 2009. "Knife-Edge Conditions in the Modeling of Long-Run Growth Regularities," NBP Working Papers 68, Narodowy Bank Polski, Economic Research Department.
  • Handle: RePEc:nbp:nbpmis:68
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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. 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.
    3. repec:ebl:ecbull:v:5:y:2006:i:6:p:1-5 is not listed on IDEAS
    4. Robert M. Solow, 1994. "Perspectives on Growth Theory," Journal of Economic Perspectives, American Economic Association, vol. 8(1), pages 45-54, Winter.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Charles I. Jones, "undated". "Population and Ideas: A Theory of Endogenous Growth," Working Papers 98014, Stanford University, Department of Economics.
    10. Juan Gabriel Brida & Elvio Accinelli, 2007. "The Ramsey model with logistic population growth," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    11. Christiaans, Thomas, 2004. "Types of balanced growth," Economics Letters, Elsevier, vol. 82(2), pages 253-258, February.
    12. Hendrik Hakenes & Andreas Irmen, 2007. "Long-Run Growth and the Evolution of Technological Knowledge," Working Papers 0438, University of Heidelberg, Department of Economics, revised Mar 2007.
    13. 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.
    14. repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
    15. H. Uzawa, 1961. "Neutral Inventions and the Stability of Growth Equilibrium," Review of Economic Studies, Oxford University Press, vol. 28(2), pages 117-124.
    16. Alwyn Young, 1998. "Growth without Scale Effects," Journal of Political Economy, University of Chicago Press, vol. 106(1), pages 41-63, February.
    17. 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.
    18. 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.
    19. Ekkehart Schlicht, 2006. "A Variant of Uzawa's Theorem," Economics Bulletin, AccessEcon, vol. 5(6), pages 1-5.
    20. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, March.
    21. 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.
    22. 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.
    23. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, Oxford University Press, vol. 120(2), pages 517-549.
    24. 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.
    25. 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.
    26. Robert Axtell, 1999. "The Emergence of Firms in a Population of Agents," Working Papers 99-03-019, Santa Fe Institute.
    27. 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.
    28. 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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    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. Mand, Matthias, 2016. "On the Cyclicality of R&D Activities," Annual Conference 2016 (Augsburg): Demographic Change 145472, Verein für Socialpolitik / German Economic Association.
    3. LI, Defu & Bental, Benjamin, 2015. "Growth with Endogenous Direction of Technical Change," MPRA Paper 64124, University Library of Munich, Germany.
    4. Bugajewski, Dariusz & Maćkowiak, Piotr, 2015. "On knife-edge conditions with unbounded growth," Journal of Macroeconomics, Elsevier, vol. 45(C), pages 274-283.
    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.

    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

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