Bounded variation and the asymmetric distribution of scaled earnings

This paper proposes a finite limits distribution for scaled accounting earnings. The probability density function of earnings has been the subject of a great deal of attention, indicating an apparent 'observational discontinuity' at zero. Paradoxically, the customary research design used in such studies is built on the implied assumption that the distribution of scaled accounting earnings should approximate a continuous normal variable at the population level. This paper shows that such assumptions may be unfounded, and, using large samples from both the US and the EU, the study provides alternative evidence of a consistently asymmetric frequency of profits and losses. This casts further doubt on the interpretation of the observed discontinuity in the distribution of earnings as prima facie evidence of earnings management. A particular innovation in this paper is to scale the earnings variable by the magnitude of its own components, restricting the standardised range to [-1,1]. Nonparametric descriptions are provided that improve upon the simple histogram, together with non-normal parametric probability estimates that are consistent with the scalar that is proposed. A notable advantage of this approach is that it avoids some of the statistical shortcomings of commonly used scalars, such as influential outliers and infinite variances.