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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
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Handle: RePEc:cpm:dynare:009
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  1. Vasco J. Gabriel & Paul Levine & Joseph Pearlman & Bo Yang, 2010. "An Estimated DSGE Model of the Indian Economy," NIPE Working Papers 29/2010, NIPE - Universidade do Minho.
  2. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
  3. Andrea Ferrero & Mark Gertler & Lars E.O. Svensson, 2008. "Current account dynamics and monetary policy," Working Paper Series 2008-26, Federal Reserve Bank of San Francisco.
  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. 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.
  6. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
  7. Jonathan R. W. Temple, 2008. "The Calibration of CES Production Functions," Bristol Economics Discussion Papers 08/606, Department of Economics, University of Bristol, UK.
  8. 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.
  9. 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.
  10. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  11. McAdam, Peter & Willman, Alpo, 2013. "Medium Run Redux," Macroeconomic Dynamics, Cambridge University Press, vol. 17(04), pages 695-727, June.
  12. Benigno, Pierpaolo, 2001. "Price Stability with Imperfect Financial Integration," CEPR Discussion Papers 2854, C.E.P.R. Discussion Papers.
  13. 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.
  14. 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.
  15. 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.
  16. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
  17. 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.
  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. 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.
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