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

Author

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  • Kent Smetters

    (University of Pennsylvania)

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 papers derives analytically the properties of the endogenous savings rate when technology takes the Constant Elesticity 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 transistion path after the capital stock reaches a critical value. Before reaching this critical value, the saving rate might decrease and the saving rate path might manifest 'undershooting.' A simulation illustrating these interesting dynamics is presented. (Copyright: Elsevier)

Suggested Citation

  • Kent Smetters, 2003. "The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(3), pages 697-707, July.
    • Handle: RePEc:red:issued:v:6:y:2003:i:3:p:697-707
    DOI: 10.1016/S1094-2025(03)00012-7
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    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. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 739-773.
    3. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. repec:grz:wpaper:2014-04 is not listed on IDEAS
    2. Farzin, Y. Hossein & Wendner, Ronald, 2013. "Saving Rate Dynamics in the Neoclassical Growth Model – Hyperbolic Discounting and Observational Equivalence," MPRA Paper 45518, University Library of Munich, Germany.
    3. Litina, Anastasia & Palivos, Theodore, 2010. "The Behavior Of The Saving Rate In The Neoclassical Optimal Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 14(4), pages 482-500, September.
    4. Gómez, Manuel A., 2008. "Dynamics Of The Saving Rate In The Neoclassical Growth Model With Ces Production," Macroeconomic Dynamics, Cambridge University Press, vol. 12(2), pages 195-210, April.
    5. Alberto BUCCI & Chiara DEL BO, 2009. "On the interaction between public investment and private capital in economic growth," Departmental Working Papers 2009-44, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    6. Huikang Ying, 2014. "Growth and Structural Change in a Dynamic Lagakos-Waugh Model," Bristol Economics Discussion Papers 14/639, School of Economics, University of Bristol, UK.
    7. Farzin, Y. Hossein & Wendner, Ronald, 2014. "The Time Path of the Saving Rate: Hyperbolic Discounting and Short-Term Planning," Climate Change and Sustainable Development 178243, Fondazione Eni Enrico Mattei (FEEM).
    8. 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.
    9. 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.
    10. Achim Voss & Jörg Lingens, 2018. "What's the damage? Environmental regulation with policy‐motivated bureaucrats," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(4), pages 613-633, August.
    11. Scott S. Condie & Richard W. Evans & Kerk L. Phillips, 2014. "When are There Natural Limits on Inequality?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-10, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    12. Manuel García‐Santana & Josep Pijoan‐Mas & Lucciano Villacorta, 2021. "Investment Demand and Structural Change," Econometrica, Econometric Society, vol. 89(6), pages 2751-2785, November.
    13. repec:grz:wpaper:2013-05 is not listed on IDEAS
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Nguyen Ngoc Thach, 2020. "The Variable Elasticity of Substitution Function and Endogenous Growth: An Empirical Evidence from Vietnam," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(1), pages 263-277.

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    More about this item

    Keywords

    The Ramsey-Cass-Koopmans model; saving; CES production;
    All these keywords.

    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
    • O10 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - General

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