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

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Kent Smetters

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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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Handle: RePEc:nbr:nberte:0290

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Find related papers by JEL classification:
E20 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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  1. Mulligan, Casey B & Sala-i-Martin, Xavier, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, MIT Press, vol. 108(3), pages 739-73, August. [Downloadable!] (restricted)
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  2. 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.. [Downloadable!] (restricted)
  3. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation, Yale University. [Downloadable!]
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  1. 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. [Downloadable!]
  2. 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. [Downloadable!]
  3. Jang-Ting Guo & Kevin J. Lansing, 2008. "Capital-labor substitution, equilibrium indeterminacy, and the cyclical behavior of labor income," Working Paper Series 2008-06, Federal Reserve Bank of San Francisco. [Downloadable!]
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