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

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  • Kent Smetters

Abstract

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0290.

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Date of creation: Mar 2003
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Publication status: published as Smetters, Kent. "The (Interesting) Dynamic Properties Of The Neoclassical Growth Model With CES Production," Review of Economic Dynamics, 2003, v6(2,Apr), 697-707.
Handle: RePEc:nbr:nberte:0290

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  1. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec..
  2. Mulligan, C.B. & Sala-i-Martin, X., 1992. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," Papers, Yale - Economic Growth Center 651, Yale - Economic Growth Center.
  3. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 163, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Achim Voß & Jörg Lingens, 2014. "What’s the Damage? Environmental Regulation with Policy-Motivated Bureaucrats," Working Papers, Fondazione Eni Enrico Mattei 2014.66, Fondazione Eni Enrico Mattei.
  2. Alvarez-Cuadrado, Francisco, 2008. "Growth outside the stable path: Lessons from the European reconstruction," European Economic Review, Elsevier, Elsevier, vol. 52(3), pages 568-588, April.
  3. Yongsung Chang & Andreas Hornstein, 2011. "Transition dynamics in the neoclassical growth model : the case of South Korea," Working Paper, Federal Reserve Bank of Richmond 11-04, Federal Reserve Bank of Richmond.
  4. Y. Hossein Farzin & Ronald Wendner, 2013. "Saving Rate Dynamics in the Neoclassical Growth Model – Hyperbolic Discounting and Observational Equivalence," Working Papers, Fondazione Eni Enrico Mattei 2013.42, Fondazione Eni Enrico Mattei.
  5. 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.
  6. Y. Hossein Farzin & Ronald Wendner, 2014. "The Time Path of the Saving Rate: Hyperbolic Discounting and Short-Term Planning," Working Papers, Fondazione Eni Enrico Mattei 2014.63, Fondazione Eni Enrico Mattei.
  7. 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.
  8. 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.
  9. Debdulal Mallick, 2007. "Growth and Slowdown of Nations: What Role for the Elasticity of Substitution?," Economics Series 2007_02, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  10. Alberto Bucci & Chiara Del Bo, 2012. "On the interaction between public and private capital in economic growth," Journal of Economics, Springer, Springer, vol. 106(2), pages 133-152, June.
  11. Guo, Jang-Ting & Lansing, Kevin J., 2009. "Capital-labor substitution and equilibrium indeterminacy," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(12), pages 1991-2000, December.
  12. Gómez, Manuel A., 2008. "Dynamics Of The Saving Rate In The Neoclassical Growth Model With Ces Production," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 12(02), pages 195-210, April.

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