“Price-levels” regressions: “scale-effect” or “distribution effect”?

Abstract

Easton and Sommers (ES) (2003) document the existence of an overwhelming influence of large firms in ‘price-levels’ regressions on US data (as do Akbar and Stark (2003) on UK data). They refer to this overwhelming influence as the ‘scale effect’. ES argue that the scale effect is caused by non-linearlities in the relationship between market value and the accounting variables. But non-linearities are only one possibility. We posit that the scale effect documented by ES is a pure econometric phenomenon. Typical variables used in Market-based Accounting Research (i.e. market value, book value, total assets, positive earnings, losses….) follow distributions that are very strong skewed, that is, distributions with a single, long tail. We argue that the scale effect is related to the presence of this large tail. When we apply a logarithmic transformation (as recommended by the literature in the case of highly skewed distributions, tending to restore normality), the ‘scale effect’ disappears.

Keywords

• Scale-Effect
• ‘Price-levels’ Regressions
• Lognormal Distribution
• Logarithmic Transformation