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Getting Normalization Right: Dealing with ‘Dimensional Constants’ in Macroeconomics

  • Cantore, Cristiano
  • Levine, Paul

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.

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Paper provided by CEPREMAP in its series Dynare Working Papers with number 9.

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Length: 38 pages
Date of creation: Jul 2011
Date of revision:
Handle: RePEc:cpm:dynare:009
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  1. Andrea Ferrero & Mark Gertler & Lars E. O. Svensson, 2007. "Current Account Dynamics and Monetary Policy," NBER Chapters, in: International Dimensions of Monetary Policy, pages 199-244 National Bureau of Economic Research, Inc.
  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. 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.
  4. Klump, Rainer & Saam, Marianne, 2006. "Calibration of normalised CES production functions in dynamic models," ZEW Discussion Papers 06-78, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  5. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
  6. Pierpaolo Benigno, 2008. "Price stability with imperfect financial integration," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  7. 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.
  8. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  9. Charles I. Jones, 2004. "The Shape of Production Function and the Direction of Technical Change," NBER Working Papers 10457, National Bureau of Economic Research, Inc.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
  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. 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.
  17. Miguel A. Le�n-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 1330-57, September.
  18. McAdam, Peter & Willman, Alpo, 2013. "Medium Run Redux," Macroeconomic Dynamics, Cambridge University Press, vol. 17(04), pages 695-727, June.
  19. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
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