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The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production


  • Kent Smetters


Despite being the standard growth model for several decades, little is actually known analytically about the dynamic properties of the neoclassical Ramsey-Cass-Koopmans growth model. This paper derives analytically the properties of the endogenous saving rate when technology takes the Constant Elasticity of Substitution (CES) form. For a factor substitution elasticity between capital and labor less than unity, the saving rate decreases along the transition path after the capital stock reaches a critical value identified analytically herein. But before reaching this critical value, the saving rate might increase and so, taken as a whole, the saving rate path might manifest overshooting.' Similarly, for a factor substitution elasticity greater than unity, the saving rate increases along the transition path after the capital stock reaches a critical value. Before reaching this critical value, the saving rate might decrease and so the saving rate path might manifest undershooting.' A simulation illustrating these interesting dynamics is presented.

Suggested Citation

  • Kent Smetters, 2003. "The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production," NBER Technical Working Papers 0290, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0290 Note: TWP

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    References listed on IDEAS

    1. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec..
    2. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
    3. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
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    Cited by:

    1. Farzin, Y. Hossein & Wendner, Ronald, 2014. "The Time Path of the Saving Rate: Hyperbolic Discounting and Short-Term Planning," MPRA Paper 54614, University Library of Munich, Germany.
    2. Jang-Ting Guo & Kevin J. Lansing, 2008. "Capital-Labor Substitution, Equilibrium Indeterminacy, and the Cyclical Behavior of Labor Income," Working Papers 200804, University of California at Riverside, Department of Economics, revised Apr 2008.
    3. Alberto Bucci & Chiara Del Bo, 2009. "On the interaction between public investment and private capital in economic growth," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1092, Universitá degli Studi di Milano.
    4. Alberto Bucci, 2012. "Public Capital, Private Capital and Economic Growth," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 120(2), pages 149-180.
    5. Chang Yongsung & Hornstein Andreas, 2015. "Transition dynamics in the neoclassical growth model: the case of South Korea," The B.E. Journal of Macroeconomics, De Gruyter, vol. 15(2), pages 649-676, July.
    6. Voß, Achim & Lingens, Jörg, 2014. "What's the damage? Environmental regulation with policy-motivated bureaucrats," CAWM Discussion Papers 67, University of Münster, Center of Applied Economic Research Münster (CAWM).
    7. Y. Hossein Farzin & Ronald Wendner, 2013. "Saving Rate Dynamics in the Neoclassical Growth Model — Hyperbolic Discounting and Observational Equivalence," Graz Economics Papers 2013-05, University of Graz, Department of Economics.
    8. Gómez, Manuel A., 2008. "Dynamics Of The Saving Rate In The Neoclassical Growth Model With Ces Production," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 195-210, April.
    9. Alberto Bucci & Chiara Del Bo, 2012. "On the interaction between public and private capital in economic growth," Journal of Economics, Springer, vol. 106(2), pages 133-152, June.
    10. Guo, Jang-Ting & Lansing, Kevin J., 2009. "Capital-labor substitution and equilibrium indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1991-2000, December.
    11. Huikang Ying, 2014. "Growth and Structural Change in a Dynamic Lagakos-Waugh Model," Bristol Economics Discussion Papers 14/639, Department of Economics, University of Bristol, UK.
    12. Alvarez-Cuadrado, Francisco, 2008. "Growth outside the stable path: Lessons from the European reconstruction," European Economic Review, Elsevier, vol. 52(3), pages 568-588, April.

    More about this item

    JEL classification:

    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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