Die Dimensionsanalyse und ihre Anwendung in der Ökonomik[Dimensional analysis and its application in economics]

The task of dimensional analysis is to check the formal correctness of formulas in a branch of empirical science and to explore the effects of a change in units of measurement on law-like formulas. Scale invariance is only a special case to ensure the neutrality of changes of units of measurement of independent variables on the variable to be explained. In general, mathematical functions and their applications in a discipline like economics are not scale-invariant. This alone should be a sufficient reason to deal more intensively with the question of the dependence of law-like formulations on the units of measurement of the variables integrated into them. There can be no dimensionless variables in an empirical scientific discipline. Even if there are numerous examples of variables that do not carry units of measurement, i.e. that are seemingly pure numbers, these variables do mean something special in observable reality. They capture a relationship which is important for the discipline and which is more than just a number. The dimension of an empirical quantity is anchored in a context that defines it. As a rule, these are the definitions of the system of national accounts, which show up to eight different dimensions even for simple aggregates such as GDP, investment or exports. Most of these dimensions are measured and reported in prices; they have the same unit of measurement, although they are different and are in need of a different treatment in an economic theory.