IDEAS home Printed from https://ideas.repec.org/p/foi/wpaper/2011_9.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://okonomi.foi.dk/workingpapers/WPpdf/WP2011/WP_2011_9_econometric_estimation_CES.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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, vol. 15(1), pages 99-119.
    3. Daron Acemoglu, 1998. "Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality," The Quarterly Journal of Economics, Oxford University Press, vol. 113(4), pages 1055-1089.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    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. 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.
    10. 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.
    11. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    12. 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.
    13. 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.
    14. Pandey, Manish, 2008. "Human capital aggregation and relative wages across countries," Journal of Macroeconomics, Elsevier, vol. 30(4), pages 1587-1601, December.
    15. 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.
    16. 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.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(5), pages 769-799, December.
    2. Growiec, Jakub & Mućk, Jakub, 2020. "Isoelastic Elasticity Of Substitution Production Functions," Macroeconomic Dynamics, Cambridge University Press, vol. 24(7), pages 1597-1634, October.
    3. Zhu, Xuehong & Zeng, Anqi & Zhong, Meirui & Huang, Jianbai, 2021. "Elasticity of substitution and biased technical change in the CES production function for China's metal-intensive industries," Resources Policy, Elsevier, vol. 73(C).
    4. 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).
    5. Frieling, Julius & Madlener, Reinhard, 2016. "Estimation of Substitution Elasticities in Three-Factor Production Functions: Identifying the Role of Energy," FCN Working Papers 1/2016, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN), revised Sep 2016.
    6. Esteban Aucejo & Jonathan James, 2019. "The Path to College Education: The Role of Math and Verbal Skills," Working Papers 1901, California Polytechnic State University, Department of Economics.
    7. Lagomarsino, Elena, 2020. "Estimating elasticities of substitution with nested CES production functions: Where do we stand?," Energy Economics, Elsevier, vol. 88(C).
    8. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    9. Yazid Dissou & Lilia Karnizova & Qian Sun, 2015. "Industry-level Econometric Estimates of Energy-Capital-Labor Substitution with a Nested CES Production Function," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 43(1), pages 107-121, March.
    10. Ma, Chunbo & Stern, David I., 2016. "Long-run estimates of interfuel and interfactor elasticities," Resource and Energy Economics, Elsevier, vol. 46(C), pages 114-130.
    11. Michal Antoszewski, 2017. "Panel estimation of sectoral substitution elasticities for CES production functions," EcoMod2017 10160, EcoMod.
    12. Frédéric Reynès, 2017. "The Cobb-Douglas function as a flexible function. Analysing the substitution between capital, labor and energy," Documents de Travail de l'OFCE 2017-12, Observatoire Francais des Conjonctures Economiques (OFCE).
    13. Inoue, Emiko & Taniguchi, Hiroya & Yamada, Ken, 2022. "Measuring energy-saving technological change: International trends and differences," Journal of Environmental Economics and Management, Elsevier, vol. 115(C).
    14. 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.
    15. Ezra Oberfield & Devesh Raval, 2012. "Micro Data and the Macro Elasticity of Substitution," Working Papers 12-05, Center for Economic Studies, U.S. Census Bureau.
    16. Zha, Donglan & Kavuri, Anil Savio & Si, Songjian, 2018. "Energy-biased technical change in the Chinese industrial sector with CES production functions," Energy, Elsevier, vol. 148(C), pages 896-903.
    17. Michael Knoblach & Fabian Stöckl, 2020. "What Determines The Elasticity Of Substitution Between Capital And Labor? A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 847-875, September.
    18. Gerald Daniels & Venoo Kakar, 2017. "Economic Growth and the CES Production Function with Human Capital," Economics Bulletin, AccessEcon, vol. 37(2), pages 930-951.
    19. repec:hal:spmain:info:hdl:2441/1cpd872l2j8lb968d53pu5f30q is not listed on IDEAS
    20. Mallick, Debdulal, 2012. "The role of the elasticity of substitution in economic growth: A cross-country investigation," Labour Economics, Elsevier, vol. 19(5), pages 682-694.
    21. Frédéric Reynés, 2019. "The Cobb-Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities," SciencePo Working papers Main hal-03403639, HAL.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:foi:wpaper:2011_9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Geir Tveit (email available below). General contact details of provider: https://edirc.repec.org/data/foikudk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.