Is the Pareto-Lévy law a good representation of income distributions?

Mandelbrot (1960) proposed using the so-called Pareto-Lévy class of distributions as a framework for representing income distributions. We argue in this paper that the Pareto-Lévy distribution is an interesting candidate for representing income distribution because its parameters are easy to interpret and it satisfies a specific invariance-under-aggregation property. We also demonstrate that the Gini coefficient can be expressed as a simple formula of the parameters of the Pareto-Lévy distribution. We subsequently use wage and income data for Norway and seven other OECD countries to fit the Pareto- Lévy distribution as well as the Generalized Beta type II (GB2) distribution. The results show that the Pareto-Lévy distribution fits the data better than the GB2 distribution for most countries, despite the fact that GB2 distribution has four parameters whereas the Pareto-Lévy distribution has only three. -- Stable distributions ; Pareto-Lévy distribution ; income distributions ; invariance principles ; Generalized Beta distributions