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Dimensions and logarithmic function in economics: A short critical analysis

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  • Mayumi, Kozo
  • Giampietro, Mario

Abstract

When dealing with sustainability, we are concerned with the biophysical and the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is paid to dimensional issues. However, many studies in economics, as well as in ecological economics, apply dimensional numbers to exponential or logarithmic functions. We show first that it is an analytical error to put a dimensional number x into exponential functions (ax) and logarithmic functions (log ax). We introduce several examples of this analytical error both in ecological economics and conventional economics. These observations are presented with the hope that they will orient future quantitative analyses toward more constructive ends. Since the empirical and theoretical studies in economics often adopt the logarithmic specification of the production and cost function, we derive a procedure or an algorithm, concerned with the given data set, by which we can examine whether or not a particular logarithmic specification is superior to the usual regression specification in terms of the least square norm.

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  • Mayumi, Kozo & Giampietro, Mario, 2010. "Dimensions and logarithmic function in economics: A short critical analysis," Ecological Economics, Elsevier, vol. 69(8), pages 1604-1609, June.
    • Handle: RePEc:eee:ecolec:v:69:y:2010:i:8:p:1604-1609
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    References listed on IDEAS

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    Cited by:

    1. Malghan, Deepak, 2011. "A dimensionally consistent aggregation framework for biophysical metrics," Ecological Economics, Elsevier, vol. 70(5), pages 900-909, March.
    2. Batabyal, Amitrajeet A. & Beladi, Hamid, 2021. "A game-theoretic model of water theft during a drought," Agricultural Water Management, Elsevier, vol. 255(C).
    3. Kozo Mayumi & Mario Giampietro & Jesus Ramos-Martin, 2012. "Reconsideration of Dimensions and Curve Fitting Practice in View of Georgescu-Roegen’s Epistemology in Economics," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 17-35, December.
    4. Reinout Heijungs & Arjan Koning, 2019. "Analyzing the effects of the choice of model in the context of marginal changes in final demand," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-22, December.
    5. Chilarescu, Constantin & Viasu, Ioana, 2012. "Dimensions and logarithmic function in economics: A comment," Ecological Economics, Elsevier, vol. 75(C), pages 10-11.
    6. Nicolae-Marius JULA, 2015. "Modelling loans and deposits during electoral years in Romania," Computational Methods in Social Sciences (CMSS), "Nicolae Titulescu" University of Bucharest, Faculty of Economic Sciences, vol. 3(1), pages 43-48, June.
    7. Baiocchi, Giovanni, 2012. "On dimensions of ecological economics," Ecological Economics, Elsevier, vol. 75(C), pages 1-9.
    8. Luzzati, T. & Parenti, A. & Rughi, T., 2018. "Economic Growth and Cancer Incidence," Ecological Economics, Elsevier, vol. 146(C), pages 381-396.

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