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The Calibration of CES Production Functions

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  • Jonathan R. W. Temple

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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.

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File URL: http://www.efm.bris.ac.uk/economics/working_papers/pdffiles/dp08606.pdf
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Paper provided by Department of Economics, University of Bristol, UK in its series Bristol Economics Discussion Papers with number 08/606.

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Length: 16 pages
Date of creation: Sep 2008
Handle: RePEc:bri:uobdis:08/606
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Keywords: CES production functions; elasticity of substitution; normalization;

Other versions of this item:

Find related papers by 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

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  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, August.
  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, 02.
  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, August.
  14. Miyagiwa, Kaz & Papageorgiou, Chris, 2007. "Endogenous aggregate elasticity of substitution," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 2899-2919, September.
  15. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
  16. 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.
  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, 03.
  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. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  26. 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.
  27. Ronald W. Jones, 1965. "The Structure of Simple General Equilibrium Models," Journal of Political Economy, University of Chicago Press, vol. 73, pages 557-557.
  28. 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.
  29. 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, 03.
  30. 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.
  31. Francesco Caselli, 2005. "Accounting for cross-country income differences," LSE Research Online Documents on Economics 3567, London School of Economics and Political Science, LSE Library.
  32. 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.
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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 4246, WU Vienna University of Economics and Business.
  2. 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.
  3. Francisco ALVAREZ-CUADRADO & Ngo Van LONG & Markus POSCHKE, 2014. "Capital-Labor Substitution, Structural Change and the Labor Income Share," Cahiers de recherche 01-2014, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. 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.
  5. Gervas Huxley & Mike Peacey, 2014. "A Simple Model of Learning Styles," The Centre for Market and Public Organisation 14/322, Department of Economics, University of Bristol, UK.
  6. 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.
  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. 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.
  9. 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.
  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. 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.
  12. Antony, Jürgen, 2014. "Technical change and the elasticity of factor substitution," Beiträge der Hochschule Pforzheim 147, Pforzheim University.
  13. repec:bri:cmpowp:13/319 is not listed on IDEAS
  14. repec:bri:cmpowp:13/322 is not listed on IDEAS
  15. Gervas Huxley & Mike Peacey, 2014. "An Economic Model of Learning Styles," The Centre for Market and Public Organisation 14/319, Department of Economics, University of Bristol, UK.

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