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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.

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

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Length: 38 pages
Date of creation: Jun 2011
Date of revision:
Handle: RePEc:sur:surrec:0511
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  1. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, MIT Press, vol. 120(2), pages 517-549, May.
  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. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
  4. 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.
  5. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
  6. 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.
  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, 2010. "A Note on Balanced Growth with a less than unitary Elasticity of Substitution," Studies in Economics 1007, School of Economics, University of Kent.
  9. repec:cup:cbooks:9780521898010 is not listed on IDEAS
  10. 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.
  11. Cantore, Cristiano & León-Ledesma, Miguel A. & McAdam, Peter & Willman, Alpo, 2010. "Shocking stuff: technology, hours, and factor substitution," Working Paper Series 1278, European Central Bank.
  12. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
  13. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
  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. Pierpaolo Benigno, 2009. "Price Stability with Imperfect Financial Integration," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(s1), pages 121-149, 02.
  16. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  17. 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.
  18. repec:cup:cbooks:9780521725200 is not listed on IDEAS
  19. 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.
  20. 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.
  21. McAdam, Peter & Willman, Alpo, 2013. "Medium Run Redux," Macroeconomic Dynamics, Cambridge University Press, vol. 17(04), pages 695-727, June.
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