On Pareto’s law and the determinants of Pareto exponents

Abstract

A stochastic model for the generation of observed income distributions is used to provide an explanation for the Pareto law of incomes. The basic assumptions of the model are that the evolution of individual incomes follows Gibrat's law and that the population or workforce is growing at a fixed (probabilistic) rate. Analysis of the model suggests that Paretian behaviour can occur in either or both tails of an income distribution. It is shown that the magnitude of the upper-tail Pareto exponent depends on the interaction between the distribution of the growth in incomes and the growth in the size of the earning population. In particular a small Pareto exponent can be expected to occur for a population exhibiting fast or highly variable growth in incomes coupled with relatively slow population growth.