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Econometric Estimation of the “Constant Elasticity of Substitution" Function in R: Package micEconCES

Author

Listed:
  • Arne Henningsen

    (Institute of Food and Resource Economics, University of Copenhagen)

  • Géraldine Henningsen

    (Risø National Laboratory for Sustainable Energy, Technical University of Denmark)

Abstract

The Constant Elasticity of Substitution (CES) function is popular in several areas of economics, but it is rarely used in econometric analysis because it cannot be estimated by standard linear regression techniques. We discuss several existing approaches and propose a new grid-search approach for estimating the traditional CES function with two inputs as well as nested CES functions with three and four inputs. Furthermore, we demonstrate how these approaches can be applied in R using the add-on package micEconCES and we describe how the various estimation approaches are implemented in the micEconCES package. Finally, we illustrate the usage of this package by replicating some estimations of CES functions that are reported in the literature.

Suggested Citation

  • Arne Henningsen & Géraldine Henningsen, 2011. "Econometric Estimation of the “Constant Elasticity of Substitution" Function in R: Package micEconCES," IFRO Working Paper 2011/9, University of Copenhagen, Department of Food and Resource Economics.
  • Handle: RePEc:foi:wpaper:2011_9
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    References listed on IDEAS

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    1. Mullen, Katharine M. & Ardia, David & Gil, David L. & Windover, Donald & Cline, James, 2011. "DEoptim: An R Package for Global Optimization by Differential Evolution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i06).
    2. James B Davies, 2009. "Combining microsimulation with CGE and macro modelling for distributional analysis in developing and transition countries," International Journal of Microsimulation, International Microsimulation Association, vol. 2(1), pages 49-56.
    3. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    4. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, October.
    5. Arto Luoma & Jani Luoto, 2010. "The Aggregate Production Function of the Finnish Economy in the Twentieth Century," Southern Economic Journal, John Wiley & Sons, vol. 76(3), pages 723-737, January.
    6. Daron Acemoglu, 1998. "Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 113(4), pages 1055-1089.
    7. Kemfert, Claudia, 1998. "Estimated substitution elasticities of a nested CES production function approach for Germany," Energy Economics, Elsevier, vol. 20(3), pages 249-264, June.
    8. Henningsen, Arne & Hamann, Jeff D., 2007. "systemfit: A Package for Estimating Systems of Simultaneous Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i04).
    9. Klump, Rainer & Papageorgiou, Chris, 2008. "Editorial introduction The CES production function in the theory and empirics of economic growth," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 599-600, June.
    10. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2010. "Identifying the Elasticity of Substitution with Biased Technical Change," American Economic Review, American Economic Association, vol. 100(4), pages 1330-1357, September.
    11. Mishra, SK, 2006. "A Note on Numerical Estimation of Sato’s Two-Level CES Production Function," MPRA Paper 1019, University Library of Munich, Germany, revised 02 Dec 2006.
    12. Rainer Klump & Peter McAdam & Alpo Willman, 2007. "Factor Substitution and Factor-Augmenting Technical Progress in the United States: A Normalized Supply-Side System Approach," The Review of Economics and Statistics, MIT Press, vol. 89(1), pages 183-192, February.
    13. K. Sato, 1967. "A Two-Level Constant-Elasticity-of-Substitution Production Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(2), pages 201-218.
    14. Richard Anderson & William Greene & B. D. McCullough & H. D. Vinod, 2008. "The role of data/code archives in the future of economic research," Journal of Economic Methodology, Taylor & Francis Journals, vol. 15(1), pages 99-119.
    15. Winford H. Masanjala & Chris Papageorgiou, 2004. "The Solow model with CES technology: nonlinearities and parameter heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 171-201.
    16. Chris Papageorgiou & Marianne Saam, 2008. "Two‐level CES Production Technology in the Solow and Diamond Growth Models," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(1), pages 119-143, March.
    17. Pandey, Manish, 2008. "Human capital aggregation and relative wages across countries," Journal of Macroeconomics, Elsevier, vol. 30(4), pages 1587-1601, December.
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    More about this item

    Keywords

    constant elasticity of substitution; CES; nested CES; R;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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