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

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  • Cristiano Cantore

    (University of Surrey)

  • Paul Levine

    (University of Surrey)

Abstract

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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Bibliographic Info

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. Mark Gertler & Lars Svensson & Andrea Ferrero, 2008. "Current Account Dynamics and Monetary Policy," 2008 Meeting Papers 359, Society for Economic Dynamics.
  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.
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  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. 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.
  8. 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.
  9. 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.
  10. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
  11. 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.
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  13. 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.
  14. 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.
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  16. Miguel A. Leon-Ledesma & Mathan Satchi, 2011. "The Choice of CES Production Techniques and Balanced Growth," Studies in Economics 1113, Department of Economics, University of Kent.
  17. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
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  19. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
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Citations

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Cited by:
  1. Konstantinos Angelopoulos & Stylianos Asimakopoulos & Jim Malley, 2013. "The Optimal Distribution of the Tax Burden over the Business Cycle," CESifo Working Paper Series 4468, CESifo Group Munich.
  2. Jonathan R. W. Temple, 2008. "The Calibration of CES Production Functions," Bristol Economics Discussion Papers 08/606, Department of Economics, University of Bristol, UK.
  3. Francisco Alvarez-Cuadrado & Ngo Van Long & Markus Poschke, 2014. "Capital Labor Substitution, Structural Change, and the Labor Income Share," CIRANO Working Papers 2014s-02, CIRANO.
  4. 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.
  5. Cristiano Cantore & Paul Levine & Giovanni Melina, 2013. "A Fiscal Stimulus and Jobless Recovery," IMF Working Papers 13/17, International Monetary Fund.
  6. Alfred Stiassny & Christina Uhl, 2014. "Does Elderly Employment have an Impact on Youth Employment? A General Equilibrium Approach," Department of Economics Working Papers wuwp178, Vienna University of Economics, Department of Economics.

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