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Getting normalization right: Dealing with ‘dimensional constants’ in macroeconomics

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  • Cantore, C.
  • Levine, P.

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—in other words they are ‘dimensional constants’. It follows that such parameters can neither be calibrated nor be 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-parameterization’, expresses dimensional constants in terms of a new dimensionless (share) parameter and all remaining dimensionless ones. We show that our ‘re-parameterization’ 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-parameterization is the only solution to the problem, showing that our approach is in fact more general.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 36 (2012)
Issue (Month): 12 ()
Pages: 1931-1949

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Handle: RePEc:eee:dyncon:v:36:y:2012:i:12:p:1931-1949

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Keywords: CES production function; Normalization; CES utility function;

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References

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  1. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
  2. 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.
  3. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
  4. Pierpaolo Benigno, 2009. "Price Stability with Imperfect Financial Integration," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(s1), pages 121-149, 02.
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  8. 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.
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  13. Miguel A. Leon-Ledesma & Mathan Satchi, 2010. "A Note on Balanced Growth with a less than unitary Elasticity of Substitution," Studies in Economics 1007, Department of Economics, University of Kent.
  14. 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.
  15. 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.
  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. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  18. Klump, Rainer & McAdam, Peter & Willman, Alpo, 2011. "The normalized CES production function: theory and empirics," Working Paper Series 1294, European Central Bank.
  19. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  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. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
  5. Cristiano Cantore & Paul Levine & Giovanni Melina, 2013. "A Fiscal Stimulus and Jobless Recovery," IMF Working Papers 13/17, International Monetary Fund.
  6. 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.

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