Dimensions and logarithmic function in economics: A short critical analysis
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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- Pindyck, Robert S, 1979. "Interfuel Substitution and the Industrial Demand for Energy: An International Comparison," The Review of Economics and Statistics, MIT Press, vol. 61(2), pages 169-79, May.
- Richmond, Amy K. & Kaufmann, Robert K., 2006. "Is there a turning point in the relationship between income and energy use and/or carbon emissions?," Ecological Economics, Elsevier, vol. 56(2), pages 176-189, February.
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- Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
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