On dimensions of ecological economics

a r t i c l e i n f o A recent paper (Ecological Economics 69, 2010, pp. 1604–1609) has addressed the issues of dimensional homo-geneity of equations and non-linear transformations of variables in economic and ecological economic models. The authors argued that logarithmic transformation cannot be used when variables are dimensional, presented several examples of purportedly incorrect use in applied economics and ecological economics publications, and concluded that these applications " make no sense. " In this paper we show that this view goes against well established theory and practice of many disciplines including physics, statistics, biology, and economics, and rests on an inadequate understanding of dimensional homogeneity and the nature of empirical modeling in applied sciences. We believe that it is important to clarify that the use of dimensional variables in transcendental functions is in fact in accordance with the established scientific consensus so as to prevent further confusion from arising in ecological economics where addressing complex problems requires the synthesis of insights from many diverse disciplines to further our understanding of the environment–economy interface. We also provide novel applications of dimensional methods to ecological economics and useful methodological references from several strands of scientific literature, not previously systematically consolidated, that should be of interest to every applied researcher. To further our understanding of the interdependence between the economy and the environment, ecological economics often seeks mathematical relationships among quantities that describe the phenomena under investigation. These quantities, variables and constants in our models, will often be dimensional in nature, i.e., their numerical value depends on the unit of measurement chosen. In a recent paper, pub-Mayumi and Giampietro, hereinafter referred to as M&G, using arguments based on the Taylor's theorem of calculus, argued that exponential and logarithmic functions can only be applied to dimensionless numbers. They then reviewed several economics and ecological economics papers published over the past 50 years where this precept is purportedly not followed, resulting in applications that, according to the authors, " make no sense, " and concluded that " it is unfortunate that many empirical and theoretical studies in economics, as well as in ecological economics, use dimensional numbers in exponential or logarithmic functions " and that " economists concerned with the biophysical and monetary aspects of ecological and economic interactions must understand the importance of dimensional homogeneity. " These are extraordinary claims that, if correct, would imply that most applications of …