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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.

Suggested Citation

  • Cantore, C. & Levine, P., 2012. "Getting normalization right: Dealing with ‘dimensional constants’ in macroeconomics," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1931-1949.
  • Handle: RePEc:eee:dyncon:v:36:y:2012:i:12:p:1931-1949
    DOI: 10.1016/j.jedc.2012.05.009
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    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.
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    16. 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.
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    More about this item

    Keywords

    CES production function; Normalization; CES utility function;
    All these keywords.

    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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