IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

Getting Normalization Right: Dealing with 'Dimensional Constants' in Macroeconomics

  • Cristiano Cantore

    (University of Surrey)

  • Paul Levine

    (University of Surrey)

We contribute to a recent literature on the normalization, calibration and estimation of CES production functions. The problem arises because CES 'share' parameters are not in fact shares, but depend on underlying dimensions - they are 'dimensional constants' in other words. It follows that such parameters cannot be calibrated, nor estimated unless the choice of units is made explicit. We use an RBC model to demonstrate two equivalent solutions. The standard one expresses the production function in deviation form about some reference point, usually the steady state of the model. Our alternative, 're-parametrization', expresses dimensional constants in terms of a new dimensionless (share) parameter and all remaining dimensionless ones. We show that our 're-parametrization' method is equivalent and arguably more straightforward than the standard normalization in deviation form. We then examine a similar problem of dimensional constants for CES utility functions in a two-sector model and in a small open economy model; then re-parametrization is the only solution to the problem, showing that our approach is in fact more general.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by School of Economics, University of Surrey in its series School of Economics Discussion Papers with number 0511.

in new window

Length: 38 pages
Date of creation: Jun 2011
Date of revision:
Handle: RePEc:sur:surrec:0511
Contact details of provider: Postal: Guildford, Surrey GU2 5XH
Phone: (01483) 259380
Fax: (01483) 259548
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. 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.
  2. McAdam, Peter & Willman, Alpo, 2013. "Medium Run Redux," Macroeconomic Dynamics, Cambridge University Press, vol. 17(04), pages 695-727, June.
  3. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
  4. Mark Gertler & Lars Svensson & Andrea Ferrero, 2008. "Current Account Dynamics and Monetary Policy," 2008 Meeting Papers 359, Society for Economic Dynamics.
  5. 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.
  6. Pierpaolo Benigno, 2008. "Price stability with imperfect financial integration," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  7. 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.
  8. Klump, Rainer & McAdam, Peter & Willman, Alpo, 2011. "The normalized CES production function: theory and empirics," Working Paper Series 1294, European Central Bank.
  9. Jonathan R. W. Temple, 2008. "The Calibration of CES Production Functions," Bristol Economics Discussion Papers 08/606, Department of Economics, University of Bristol, UK.
  10. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
  11. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521725200.
  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. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
  14. Guo, Jang-Ting & Lansing, Kevin J., 2009. "Capital-labor substitution and equilibrium indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1991-2000, December.
  15. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521898010.
  16. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
  17. Gabriel, Vasco & Levine, Paul & Pearlman, Joseph & Yang, Bo, 2011. "An Estimated DSGE Model of the Indian Economy," Working Papers 11/95, National Institute of Public Finance and Policy.
  18. Diamond, Peter & McFadden, Daniel & Rodriguez, Miguel, 1978. "Measurement of the Elasticity of Factor Substitution and Bias of Technical Change," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 2, chapter 5 McMaster University Archive for the History of Economic Thought.
  19. Miguel A. Leon-Ledesma & Mathan Satchi, 2010. "A Note on Balanced Growth with a less than unitary Elasticity of Substitution," Studies in Economics 1007, School of Economics, University of Kent.
  20. Miguel A. Leon-Ledesma & Mathan Satchi, 2011. "The Choice of CES Production Techniques and Balanced Growth," Studies in Economics 1113, School of Economics, University of Kent.
  21. 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.
Full references (including those not matched with items on IDEAS)

This item is featured on the following reading lists or Wikipedia pages:

  1. Wikipedia talk:WikiProject Economics/Archive 7 in Wikipedia English ne '')
  2. User talk:John Quiggin in Wikipedia English ne '')

When requesting a correction, please mention this item's handle: RePEc:sur:surrec:0511. 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: (Alex Mandilaras)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.