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

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  • Cantore, Cristiano
  • Levine, Paul

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 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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Keywords: CES production function; normalization; CES utility function;

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References

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  6. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
  7. 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.
  8. Pierpaolo Benigno, 2008. "Price stability with imperfect financial integration," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  9. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
  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. 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.
  12. McAdam, Peter & Willman, Alpo, 2013. "Medium Run Redux," Macroeconomic Dynamics, Cambridge University Press, vol. 17(04), pages 695-727, June.
  13. 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.
  14. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
  15. 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.
  16. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
  17. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
  18. 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.
  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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Citations

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Cited by:
  1. Cristiano Cantore & Paul Levine & Giovanni Melina, 2011. "A Fiscal Stimulus and Jobless Recovery," School of Economics Discussion Papers 1111, School of Economics, University of Surrey.
  2. 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.
  3. Angelopoulos, Konstantinos & Asimakopoulos, Stylianosulos & Malley, James, 2013. "The Optimal Distribution of the Tax Burden over the Business Cycle," SIRE Discussion Papers 2013-80, Scottish Institute for Research in Economics (SIRE).
  4. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
  5. Francisco Alvarez-Cuadrado & Ngo Van Long & Markus Poschke, 2014. "Capital-Labor Substitution, Structural Change and the Labor Income Share," CESifo Working Paper Series 4600, CESifo Group Munich.

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