Generalized Pareto distribution and income inequality: an extension of Gibrat's law

Abstract

Motivated by empirical observations, we proposed a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution, we found that the income distribution is described by a generalized Pareto distribution (GPD) with three parameters. We observed that there is a parameter $ \eta $ in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically showed that, for typical market-economy countries, $ \eta $ is significantly close to 0, indicating that the income distribution is characterized by a two-class pattern: The bottom 90% of the population is approximated by an exponential distribution, while the richest 1%~3% is approximated by an asymptotic power law. However, we empirically found that in China during the period of the planned economy and the early stages of market reform (from 1978 to 1990), $ \eta $ deviated significantly from 0, indicating that the bottom of the population no longer conformed to an exponential distribution.

Keywords

• random growth theory
• kolmogorov forward equation
• generalized pareto distribution
• kolmogorov-smirnov test
• generalized double-pareto distribution