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The Calibration of CES Production Functions

  • Jonathan R. W. Temple


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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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
Date of revision:
Handle: RePEc:bri:uobdis:08/606
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  1. 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.
  2. 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.
  3. Lucas, Robert E, Jr, 1990. "Supply-Side Economics: An Analytical Review," Oxford Economic Papers, Oxford University Press, vol. 42(2), pages 293-316, April.
  4. David Backus & Espen Henriksen & Kjetil Storesletten, 2007. "Taxes and the Global Allocation of Capital," NBER Working Papers 13624, National Bureau of Economic Research, Inc.
  5. Francesco Caselli & Wilbur John Coleman II, 2000. "The World Technology Frontier," NBER Working Papers 7904, National Bureau of Economic Research, Inc.
  6. Cristiano Cantore & Miguel A. Leon-Ledesma & Peter McAdam & Alpo Willman, 2013. "Shocking Stuff: Technology, Hours, and Factor Substitution," School of Economics Discussion Papers 0913, School of Economics, University of Surrey.
  7. 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.
  8. Kaz Miyagiwa & Chris Papageorgiou, 2007. "Endogenous Aggregate Elasticity of Substitution," Emory Economics 0707, Department of Economics, Emory University (Atlanta).
  9. 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.
  10. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521725200, September.
  11. Chris Papageorgiou & Marianne Saam, . "Two-Level CES Production Technology in the Solow and Diamond Growth Models," Departmental Working Papers 2005-07, Department of Economics, Louisiana State University.
  12. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  13. Atkinson, Anthony B & Stiglitz, Joseph E, 1969. "A New View of Technological Change," Economic Journal, Royal Economic Society, vol. 79(315), pages 573-78, September.
  14. Laitner, John, 1995. "Quantitative Evaluations of Efficient Tax Policies for Lucas' Supply Side Models," Oxford Economic Papers, Oxford University Press, vol. 47(3), pages 471-92, July.
  15. 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.
  16. Ronald W. Jones, 1965. "The Structure of Simple General Equilibrium Models," Journal of Political Economy, University of Chicago Press, vol. 73, pages 557.
  17. 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.
  18. 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.
  19. Jones, Ronald W., 2008. "The aggregate elasticity of factor substitution with middle products," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 633-640, June.
  20. Jürgen Antony, 2010. "A class of changing elasticity of substitution production functions," Journal of Economics, Springer, vol. 100(2), pages 165-183, June.
  21. Shekhar Aiyar & Carl-Johan Dalgaard, 2008. "Accounting for Productivity: Is it OK to Assume that the World is Cobb-Douglas?," Discussion Papers 08-14, University of Copenhagen. Department of Economics.
  22. León-Ledesma, Miguel A. & McAdam, Peter & Willman, Alpo, 2009. "Identifying the elasticity of substitution with biased technical change," Working Paper Series 1001, European Central Bank.
  23. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
  24. 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.
  25. 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.
  26. Samuel S. Kortum, 1997. "Research, Patenting, and Technological Change," Econometrica, Econometric Society, vol. 65(6), pages 1389-1420, November.
  27. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
  28. Daron Acemoglu, 2000. "Labor- and Capital- Augmenting Technical Change," NBER Working Papers 7544, National Bureau of Economic Research, Inc.
  29. 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.
  30. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521898010, September.
  31. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
  32. 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.
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