Econometrics Commons^™

Dimensional Analysis And Logarithmic Transformations In Applied Econometrics, Deepankar Basu

Economics Department Working Paper Series

In economics, it is common to use dimensioned variables, e.g. earn- ings (measured in dollars per year), as arguments in the logarithmic function. This is conceptually problematic because a logarithmic func- tion can only take dimensionless quantities as its argument. One way to avoid this conceptual error is to rewrite commonly used logarithmic regressions using an arbitrarily chosen reference unit so that ratios of dimensioned quantities are used in logarithmic functions. With the addition of a zero conditional mean assumption about the reference unit to the standard list of assumptions about asymptotic properties of ordinary least squares estimators, such a …