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On estimation of the CES production function—Revisited


  • Henningsen, Arne
  • Henningsen, Géraldine


Estimation of the non-linear Constant Elasticity of Scale (CES) function is generally considered problematic due to convergence problems and unstable and/or meaningless results. These problems often arise from a non-smooth objective function with large flat areas, the discontinuity of the CES function where the elasticity of substitution is one, and possibly significant rounding errors where the elasticity of substitution is close to one. We suggest three (combinable) solutions that alleviate these problems and improve the reliability and stability of the results.

Suggested Citation

  • Henningsen, Arne & Henningsen, Géraldine, 2012. "On estimation of the CES production function—Revisited," Economics Letters, Elsevier, vol. 115(1), pages 67-69.
  • Handle: RePEc:eee:ecolet:v:115:y:2012:i:1:p:67-69 DOI: 10.1016/j.econlet.2011.12.007

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    References listed on IDEAS

    1. Kai Sun & Daniel J. Henderson & Subal C. Kumbhakar, 2011. "Biases in approximating log production," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(4), pages 708-714, June.
    2. Lloyd, P. J. & MacLaren, D., 2002. "Measures of trade openness using CGE analysis," Journal of Policy Modeling, Elsevier, vol. 24(1), pages 67-81, March.
    3. McFarland, J. R. & Reilly, J. M. & Herzog, H. J., 2004. "Representing energy technologies in top-down economic models using bottom-up information," Energy Economics, Elsevier, vol. 26(4), pages 685-707, July.
    4. 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.
    5. Thursby, Jerry G & Lovell, C A Knox, 1978. "An Investigation of the Kmenta Approximation to the CES Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(2), pages 363-377, June.
    6. 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.
    7. 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.
    8. 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.
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    Cited by:

    1. Frieling, Julius & Madlener, Reinhard, 2017. "Fueling the US Economy: Energy as a Production Factor from the Great Depression until Today," FCN Working Papers 2/2017, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    2. Frieling, Julius & Madlener, Reinhard, 2017. "The Turning Tide: How Energy has Driven the Transformation of the British Economy Since the Industrial Revolution," FCN Working Papers 7/2017, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    3. Wu, Wei-Ming & Lin, Tsan-Hwan, 2015. "Selection behavior of the global container shipping industry for carrier-owned and leased containers," Transport Policy, Elsevier, vol. 37(C), pages 11-19.
    4. Sueyoshi, Toshiyuki & Yuan, Yan, 2016. "Marginal Rate of Transformation and Rate of Substitution measured by DEA environmental assessment: Comparison among European and North American nations," Energy Economics, Elsevier, vol. 56(C), pages 270-287.
    5. 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.
    6. 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.
    7. repec:eee:appene:v:204:y:2017:i:c:p:509-524 is not listed on IDEAS

    More about this item


    Constant elasticity of substitution; CES function; Estimation; Non-linear least squares;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production


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