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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.

Suggested Citation

  • Cantore, Cristiano & Levine, Paul, 2011. "Getting Normalization Right: Dealing with ‘Dimensional Constants’ in Macroeconomics," Dynare Working Papers 9, CEPREMAP.
  • Handle: RePEc:cpm:dynare:009
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    References listed on IDEAS

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    1. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521725200, December.
    2. Charles I. Jones, 2003. "Growth, capital shares, and a new perspective on production functions," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
    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, February.
    4. Klump, Rainer & Saam, Marianne, 2008. "Calibration of normalised CES production functions in dynamic models," Economics Letters, Elsevier, vol. 99(2), pages 256-259, May.
    5. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521898010, December.
    6. 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.
    7. Miguel A. León-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 1330-1357, September.
    8. Pierpaolo Benigno, 2009. "Price Stability with Imperfect Financial Integration," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(s1), pages 121-149, February.
    9. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
    10. 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.
    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.
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    Cited by:

    1. Simeon D. Alder, 2016. "In the Wrong Hands: Complementarities, Resource Allocation, and TFP," American Economic Journal: Macroeconomics, American Economic Association, vol. 8(1), pages 199-241, January.
    2. Stiassny, Alfred & Uhl, Christina, 2014. "Does Elderly Employment have an Impact on Youth Employment? A General Equilibrium Approach," Department of Economics Working Paper Series 4246, WU Vienna University of Economics and Business.
    3. Verónica Acurio Vásconez, 2015. "What if oil is less substitutable? A New-Keynesian Model with Oil, Price and Wage Stickiness including Capital Accumulation," Documents de travail du Centre d'Economie de la Sorbonne 15041, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Rankin Neil & Burger Rulof & Kreuser Friedrich, 2015. "The elasticity of substitution and labour-displacing technical change in post-apartheid South Africa," WIDER Working Paper Series 101, World Institute for Development Economic Research (UNU-WIDER).
    5. 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.
    6. Born, Benjamin & Pfeifer, Johannes, 2016. "Uncertainty-driven business cycles: assessing the markup channel," Annual Conference 2016 (Augsburg): Demographic Change 145608, Verein für Socialpolitik / German Economic Association.
    7. 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 and Business, Department of Economics.
    8. Verónica Acurio Vásconez, 2015. "Oil and Unemployment in a New-Keynesian Model," Documents de travail du Centre d'Economie de la Sorbonne 15043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. 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, February.
    10. Cristiano Cantore & Paul Levine & Giovanni Melina, 2014. "A Fiscal Stimulus and Jobless Recovery," Scandinavian Journal of Economics, Wiley Blackwell, vol. 116(3), pages 669-701, July.
    11. Cantore, Cristiano & Levine, Paul & Pearlman, Joseph & Yang, Bo, 2015. "CES technology and business cycle fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 133-151.
    12. Di Pace, Federico & Villa, Stefania, 2016. "Factor complementarity and labour market dynamics," European Economic Review, Elsevier, vol. 82(C), pages 70-112.
    13. Alvarez-Cuadrado, Francisco & Long, Ngo Van & Poschke, Markus, 2018. "Capital-labor substitution, structural change and the labor income share," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 206-231.
    14. Daan Steenkamp, 2018. "Factor Substitution and Productivity in New Zealand," The Economic Record, The Economic Society of Australia, vol. 94(304), pages 64-79, March.

    More about this item

    Keywords

    CES production function; normalization; CES utility function;

    JEL classification:

    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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