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


  • Arne Henningsen

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

  • Géraldine Henningsen

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


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

    1. Kemfert, Claudia, 1998. "Estimated substitution elasticities of a nested CES production function approach for Germany," Energy Economics, Elsevier, pages 249-264.
    2. 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, pages 99-119.
    3. 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.
    4. McAdam, Peter & Willman, Alpo & León-Ledesma, Miguel A., 2009. "Identifying the elasticity of substitution with biased technical change," Working Paper Series 1001, European Central Bank.
    5. Winford H. Masanjala & Chris Papageorgiou, 2004. "The Solow model with CES technology: nonlinearities and parameter heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 171-201.
    6. 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.
    7. 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.
    8. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2010. "Identifying the Elasticity of Substitution with Biased Technical Change," American Economic Review, American Economic Association, pages 1330-1357.
    9. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, December.
    10. Klump, Rainer & Papageorgiou, Chris, 2008. "Editorial introduction The CES production function in the theory and empirics of economic growth," Journal of Macroeconomics, Elsevier, pages 599-600.
    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. Pandey, Manish, 2008. "Human capital aggregation and relative wages across countries," Journal of Macroeconomics, Elsevier, pages 1587-1601.
    13. 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, pages 183-192.
    14. K. Sato, 1967. "A Two-Level Constant-Elasticity-of-Substitution Production Function," Review of Economic Studies, Oxford University Press, vol. 34(2), pages 201-218.
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    Cited by:

    1. Nowak, Thomas & Hofer, Vera, 2014. "On stabilizing volatile product returns," European Journal of Operational Research, Elsevier, vol. 234(3), pages 701-708.
    2. Zachlod-Jelec, Magdalena & Boratynski, Jakub, 2016. "How large and uncertain are costs of 2030 GHG emissions reduction target for the European countries? Sensitivity analysis in a global CGE model," MF Working Papers 26, Ministry of Finance in Poland.
    3. Glensk, Barbara & Madlener, Reinhard, 2017. "Evaluating the Enhanced Flexibility of Lignite-Fired Power Plants: A Real Options Analysis," FCN Working Papers 10/2016, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    4. repec:hur:ijarbs:v:7:y:2017:i:3:p:270-297 is not listed on IDEAS
    5. Koesler, Simon & Schymura, Michael, 2012. "Substitution elasticities in a CES production framework: An empirical analysis on the basis of non-linear least squares estimations," ZEW Discussion Papers 12-007, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    6. Matthew K. Heun & João Santos & Paul E. Brockway & Randall Pruim & Tiago Domingos & Marco Sakai, 2017. "From Theory to Econometrics to Energy Policy: Cautionary Tales for Policymaking Using Aggregate Production Functions," Energies, MDPI, Open Access Journal, vol. 10(2), pages 1-44, February.
    7. Becker, Sascha O. & Pfaff, Steven & Rubin, Jared, 2016. "Causes and consequences of the Protestant Reformation," Explorations in Economic History, Elsevier, vol. 62(C), pages 1-25.
    8. P. Capros & Denise Van Regemorter & Leonidas Paroussos & P. Karkatsoulis & C. Fragkiadakis & S. Tsani & I. Charalampidis & Tamas Revesz, 2013. "GEM-E3 Model Documentation," JRC Working Papers JRC83177, Joint Research Centre (Seville site).
    9. Idrovo Aguirre, Byron, 2012. "Inversión en infraestructura pública y crecimiento económico, evidencia para Chile
      [Public infrastructure, investment and economic growth in Chile]
      ," MPRA Paper 39857, University Library of Munich, Germany.
    10. Agata Sielska, 2015. "The impact of weights on the quality of agricultural producers' multicriteria decision models," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, pages 51-69.
    11. Andreas Voss and Reinhard Madlener, 2017. "Auction Schemes, Bidding Strategies and the Cost-Optimal Level of Promoting Renewable Electricity in Germany," The Energy Journal, International Association for Energy Economics, vol. 0(KAPSARC S).
    12. Keting Shen & John Whalley, 2013. "Capital-Labor-Energy Substitution in Nested CES Production Functions for China," NBER Working Papers 19104, National Bureau of Economic Research, Inc.
    13. DURAND-LASSERVE, Olivier & Pierru , Axel & SMEERS, Yves, 2012. "Sensitivity of policy simulation to benchmark scenarios in CGE models: illustration with carbon leakage," CORE Discussion Papers 2012063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Juan Aquino-Chávez & N.R. Ramírez-Rondán, 2017. "Estimating Factor Shares from Nonstationary Panel Data," Working Papers 2017-89, Peruvian Economic Association.
    15. Henningsen, Arne & Henningsen, Géraldine, 2012. "On estimation of the CES production function—Revisited," Economics Letters, Elsevier, vol. 115(1), pages 67-69.
    16. Paul E. Brockway & Harry Saunders & Matthew K. Heun & Timothy J. Foxon & Julia K. Steinberger & John R. Barrett & Steve Sorrell, 2017. "Energy Rebound as a Potential Threat to a Low-Carbon Future: Findings from a New Exergy-Based National-Level Rebound Approach," Energies, MDPI, Open Access Journal, vol. 10(1), pages 1-24, January.
    17. Simon Koesler & Michael Schymura, 2012. "Substitution Elasticities for CGE Models," EcoMod2012 4010, EcoMod.
    18. Antoszewski, Michal, 2017. "Panel estimation of sectoral substitution elasticities for CES production functions," MF Working Papers 28, Ministry of Finance in Poland.
    19. Paul E. Brockway & Matthew K. Heun & João Santos & John R. Barrett, 2017. "Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation," Energies, MDPI, Open Access Journal, vol. 10(2), pages 1-23, February.
    20. Bui, Linh & Hoang, Huyen & Bui, Hang, 2015. "Estimating the Constant Elasticity of Substitution Function of Rice Production.The case of Vietnam in 2012," MPRA Paper 71224, University Library of Munich, Germany.
    21. Magdalena Zachlod-Jelec & Jakub Boratyński, 2016. "How large and uncertain are costs of 2030 emission reduction target for the European countries? Sensitivity analysis in a global CGE model," EcoMod2016 9449, EcoMod.
    22. T.V.S.Ramamohan Rao, 2011. "Contemporary Relevance and Ongoing Controversies Related to the CES Production Function," Journal of Quantitative Economics, The Indian Econometric Society, vol. 9(2), pages 36-57, July.
    23. Keting Shen & Jing Wang & John Whalley, 2015. "Measuring Changes in the Bilateral Technology Gaps between China, India and the U.S. 1979 - 2008," NBER Working Papers 21657, National Bureau of Economic Research, Inc.
    24. Knoblach, Michael & Rößler, Martin & Zwerschke, Patrick, 2016. "The Elasticity of Factor Substitution Between Capital and Labor in the U.S. Economy: A Meta-Regression Analysis," CEPIE Working Papers 03/16, Technische Universität Dresden, Center of Public and International Economics (CEPIE).

    More about this item


    constant elasticity of substitution; CES; nested CES; R;

    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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