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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.

Suggested Citation

  • Cristiano Cantore & Paul Levine, 2011. "Getting Normalization Right: Dealing with 'Dimensional Constants' in Macroeconomics," School of Economics Discussion Papers 0511, School of Economics, University of Surrey.
  • Handle: RePEc:sur:surrec:0511
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    References listed on IDEAS

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    7. 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.
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    16. Stiassny, Alfred & Uhl, Christina, 2014. "Does Elderly Employment have an Impact on Youth Employment? A General Equilibrium Approach," Department of Economics Working Paper Series 178, WU Vienna University of Economics and Business.
    17. Verónica Acurio Vásconez, 2015. "What if oil is less substitutable? A New-Keynesian Model with Oil, Price and Wage Stickiness including Capital Accumulation," Post-Print halshs-01167027, HAL.
    18. Neil Rankin & Rulof Burger & Friedrich Kreuser, 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).
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    24. Temple, Jonathan, 2012. "The calibration of CES production functions," Journal of Macroeconomics, Elsevier, vol. 34(2), pages 294-303.
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    More about this item

    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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