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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. 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.
  3. Pierpaolo Benigno, 2009. "Price Stability with Imperfect Financial Integration," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(s1), pages 121-149, 02.
  4. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
  5. Gabriel, Vasco & Levine, Paul & Pearlman, Joseph & Yang, Bo, 2011. "An Estimated DSGE Model of the Indian Economy," Working Papers 11/95, National Institute of Public Finance and Policy.
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  7. Oliver J. Blanchard, 1997. "The Medium Run," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(2), pages 89-158.
  8. 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.
  9. 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.
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  13. 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.
  14. 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.
  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. 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. 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).
  2. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
  3. 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.
  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. 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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