IDEAS home Printed from https://ideas.repec.org/p/bri/uobdis/08-606.html
   My bibliography  Save this paper

The Calibration of CES Production Functions

Author

Listed:
  • Jonathan R. W. Temple

    ()

Abstract

This note addresses some issues that arise when using 'normalized' CES production functions, an approach that has become popular in the literature. The results of Klump and de La Grandville (2000) provide a simple way to calibrate the parameters of the CES production function when the necessary data are available. But some of the other applications of normalized CES production functions appear problematic, especially when used to argue that productivity is increasing in the elasticity of substitution.

Suggested Citation

  • Jonathan R. W. Temple, 2008. "The Calibration of CES Production Functions," Bristol Economics Discussion Papers 08/606, School of Economics, University of Bristol, UK.
    • Handle: RePEc:bri:uobdis:08/606
    as

    Download full text from publisher

    File URL: http://www.bristol.ac.uk/efm/media/workingpapers/working_papers/pdffiles/dp08606.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Samuel S. Kortum, 1997. "Research, Patenting, and Technological Change," Econometrica, Econometric Society, vol. 65(6), pages 1389-1420, November.
    2. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521725200, December.
    3. Turnovsky, Stephen J., 2002. "Intertemporal and intratemporal substitution, and the speed of convergence in the neoclassical growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1765-1785, August.
    4. Aiyar, Shekhar & Dalgaard, Carl-Johan, 2009. "Accounting for productivity: Is it OK to assume that the world is Cobb-Douglas?," Journal of Macroeconomics, Elsevier, vol. 31(2), pages 290-303, June.
    5. Francesco Caselli & Wilbur John Coleman II, 2006. "The World Technology Frontier," American Economic Review, American Economic Association, vol. 96(3), pages 499-522, June.
    6. Wong, Tsz-Nga & Yip, Chong K., 2010. "Indeterminacy and the elasticity of substitution in one-sector models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 623-635, April.
    7. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
    8. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, Oxford University Press, vol. 120(2), pages 517-549.
    9. Irmen, Andreas, 2011. "Steady-state growth and the elasticity of substitution," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1215-1228, August.
    10. Cristiano Cantore & Miguel León-Ledesma & Peter McAdam & Alpo Willman, 2014. "Shocking Stuff: Technology, Hours, And Factor Substitution," Journal of the European Economic Association, European Economic Association, vol. 12(1), pages 108-128, February.
    11. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
    12. 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.
    13. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521898010, December.
    14. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
    15. Laitner, John, 1995. "Quantitative Evaluations of Efficient Tax Policies for Lucas' Supply Side Models," Oxford Economic Papers, Oxford University Press, vol. 47(3), pages 471-492, July.
    16. Miyagiwa, Kaz & Papageorgiou, Chris, 2007. "Endogenous aggregate elasticity of substitution," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 2899-2919, September.
    17. 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.
    18. Jürgen Antony, 2010. "A class of changing elasticity of substitution production functions," Journal of Economics, Springer, vol. 100(2), pages 165-183, June.
    19. Lucas, Robert E, Jr, 1990. "Supply-Side Economics: An Analytical Review," Oxford Economic Papers, Oxford University Press, vol. 42(2), pages 293-316, April.
    20. Jones, Ronald W., 2008. "The aggregate elasticity of factor substitution with middle products," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 633-640, June.
    21. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, March.
    22. Miyagiwa, Kaz, 2008. "Comment on "The endogenous aggregate elasticity of substitution for a small open economy"," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 641-644, June.
    23. Cantore, C. & Levine, P., 2012. "Getting normalization right: Dealing with ‘dimensional constants’ in macroeconomics," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1931-1949.
    24. Backus, David & Henriksen, Espen & Storesletten, Kjetil, 2008. "Taxes and the global allocation of capital," Journal of Monetary Economics, Elsevier, vol. 55(1), pages 48-61, January.
    25. Caselli, Francesco, 2005. "Accounting for cross-country income differences," LSE Research Online Documents on Economics 5266, London School of Economics and Political Science, LSE Library.
    26. Rainer Klump & Harald Preissler, 2000. "CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
    27. 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.
    28. Ronald W. Jones, 1965. "The Structure of Simple General Equilibrium Models," Journal of Political Economy, University of Chicago Press, vol. 73, pages 557-557.
    29. Olivier de La Grandville & Rainer Klump, 2000. "Economic Growth and the Elasticity of Substitution: Two Theorems and Some Suggestions," American Economic Review, American Economic Association, vol. 90(1), pages 282-291, March.
    30. 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.
    31. Nakamura, Hideki, 2009. "Micro-foundation for a constant elasticity of substitution production function through mechanization," Journal of Macroeconomics, Elsevier, vol. 31(3), pages 464-472, September.
    32. Caselli, Francesco, 2005. "Accounting for cross-country income differences," LSE Research Online Documents on Economics 3567, London School of Economics and Political Science, LSE Library.
    33. Atkinson, Anthony B & Stiglitz, Joseph E, 1969. "A New View of Technological Change," Economic Journal, Royal Economic Society, vol. 79(315), pages 573-578, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stiassny, Alfred & Uhl, Christina, 2014. "Does Elderly Employment have an Impact on Youth Employment? A General Equilibrium Approach," Department of Economics Working Paper Series 178, WU Vienna University of Economics and Business.
    2. Alfred Stiassny & Christina Uhl, 2014. "Does Elderly Employment have an Impact on Youth Employment? A General Equilibrium Approach," Department of Economics Working Papers wuwp178, Vienna University of Economics and Business, Department of Economics.
    3. Romain Houssa & Jolan Mohimont & Chris Otrok, 2019. "A Model for International Spillovers to Emerging Markets," CESifo Working Paper Series 7702, CESifo.
    4. Cantore, C. & Levine, P., 2012. "Getting normalization right: Dealing with ‘dimensional constants’ in macroeconomics," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1931-1949.
    5. Miguel A León-Ledesma & Peter McAdam & Alpo Willman, 2012. "Non-Balanced Growth and Production Technology Estimation," Studies in Economics 1204, School of Economics, University of Kent.
    6. Alvarez-Cuadrado, Francisco & Long, Ngo Van & Poschke, Markus, 2018. "Capital-labor substitution, structural change and the labor income share," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 206-231.
    7. Daan Steenkamp, 2018. "Factor Substitution and Productivity in New Zealand," The Economic Record, The Economic Society of Australia, vol. 94(304), pages 64-79, March.
    8. Gervas Huxley & Mike Peacey, 2014. "A Simple Model of Learning Styles," The Centre for Market and Public Organisation 14/322, The Centre for Market and Public Organisation, University of Bristol, UK.
    9. 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).
    10. Jürgen Antony, 2010. "A class of changing elasticity of substitution production functions," Journal of Economics, Springer, vol. 100(2), pages 165-183, June.
    11. Knoblach, Michael, 2019. "Skill-biased technological change, endogenous labor supply, and the skill premium," CEPIE Working Papers 03/19, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    12. Gervas Huxley & Mike Peacey, 2014. "An Economic Model of Learning Styles," The Centre for Market and Public Organisation 14/319, The Centre for Market and Public Organisation, University of Bristol, UK.
    13. Fabian Stöckl, 2020. "Is Substitutability the New Efficiency? Endogenous Investment in the Elasticity of Substitution between Clean and Dirty Energy," Discussion Papers of DIW Berlin 1886, DIW Berlin, German Institute for Economic Research.
    14. Jens J. Krüger, 2017. "Revisiting the world technology frontier: a directional distance function approach," Journal of Economic Growth, Springer, vol. 22(1), pages 67-95, March.
    15. 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.
    16. Michael Knoblach & Martin Roessler & Patrick Zwerschke, 2020. "The Elasticity of Substitution Between Capital and Labour in the US Economy: A Meta‐Regression Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(1), pages 62-82, February.
    17. 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.
    18. repec:bri:cmpowp:13/319 is not listed on IDEAS
    19. Sushanta K. MALLICK & Ricardo M. SOUSA, 2017. "The skill premium effect of technological change: New evidence from United States manufacturing," International Labour Review, International Labour Organization, vol. 156(1), pages 113-131, March.
    20. Romain Houssa & Jolan Mohimont & Chris Otrok, 2019. "A Model for International Spillovers to Emerging Markets," CESifo Working Paper Series 7702, CESifo.
    21. Ikizler, Burcin & Pehlivan, Ayse Ozgur, 2020. "New trade models, different distributions, same old results?," Economics Letters, Elsevier, vol. 187(C).
    22. De Lucia, Caterina & Bartlett, Mark, 2014. "Implementing a biofuel economy in the EU: Lessons from the SUSTOIL project and future perspectives for next generation biofuels," Renewable and Sustainable Energy Reviews, Elsevier, vol. 29(C), pages 22-30.
    23. 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.
    24. Antony, Jürgen, 2014. "Technical change and the elasticity of factor substitution," Beiträge der Hochschule Pforzheim 147, Pforzheim University.
    25. repec:bri:cmpowp:13/322 is not listed 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. 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.
    2. 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.
    3. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    4. 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.
    5. Cantore, Cristiano & Levine, Paul & Pearlman, Joseph & Yang, Bo, 2015. "CES technology and business cycle fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 133-151.
    6. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    7. Cantore, C. & Levine, P., 2012. "Getting normalization right: Dealing with ‘dimensional constants’ in macroeconomics," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1931-1949.
    8. Kemnitz, Alexander & Knoblach, Michael, 2020. "Endogenous sigma-augmenting technological change: An R&D-based approach," CEPIE Working Papers 02/20, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    9. Growiec, Jakub, 2013. "A microfoundation for normalized CES production functions with factor-augmenting technical change," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2336-2350.
    10. Mallick, Debdulal, 2010. "Capital-labor substitution and balanced growth," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1131-1142, December.
    11. Antony, Jürgen, 2014. "Technical change and the elasticity of factor substitution," Beiträge der Hochschule Pforzheim 147, Pforzheim University.
    12. Miguel A. Leon-Ledesma & Mathan Satchi, 2015. "Appropriate Technology and the Labour Share," Studies in Economics 1505, School of Economics, University of Kent, revised Nov 2016.
    13. Miguel A León-Ledesma & Mathan Satchi, 2019. "Appropriate Technology and Balanced Growth," Review of Economic Studies, Oxford University Press, vol. 86(2), pages 807-835.
    14. Robert S. Chirinko & Debdulal Mallick, 2014. "The Substitution Elasticity, Factor Shares, Long-Run Growth, and the Low-Frequency Panel Model," CESifo Working Paper Series 4895, CESifo.
    15. Miguel A León-Ledesma & Peter McAdam & Alpo Willman, 2012. "Non-Balanced Growth and Production Technology Estimation," Studies in Economics 1204, School of Economics, University of Kent.
    16. Federici, Daniela & Saltari, Enrico, 2018. "Elasticity Of Substitution And Technical Progress: Is There A Misspecification Problem?," Macroeconomic Dynamics, Cambridge University Press, vol. 22(1), pages 101-121, January.
    17. 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.
    18. Xue, Jianpo & Yip, Chong K., 2013. "Aggregate elasticity of substitution and economic growth: A synthesis," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 60-75.
    19. Fabian Stöckl, 2020. "Is Substitutability the New Efficiency? Endogenous Investment in the Elasticity of Substitution between Clean and Dirty Energy," Discussion Papers of DIW Berlin 1886, DIW Berlin, German Institute for Economic Research.
    20. Irmen, Andreas, 2011. "Steady-state growth and the elasticity of substitution," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1215-1228, August.

    More about this item

    Keywords

    CES production functions; elasticity of substitution; normalization;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

    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:bri:uobdis:08/606. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Vicky Jackson). General contact details of provider: http://edirc.repec.org/data/sebriuk.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.