Growth and Fluctuations of Personal Income

TL;DR

This study analyzes the dynamics of personal income fluctuations among high-income taxpayers in Japan, revealing that income growth rates are independent of previous income and supporting Pareto's law as a consequence of economic stability.

Contribution

First empirical investigation of personal income dynamics showing independence of growth rates from previous income, explaining Pareto's law through income flow mechanisms.

Findings

Income growth rate distribution is independent of previous income.

Approximate time-reversal symmetry supports Pareto's law.

Derived scaling relation matches empirical data.

Abstract

Pareto's law states that the distribution of personal income obeys a power-law in the high-income range, and has been supported by international observations. Researchers have proposed models over a century since its discovery. However, the dynamical nature of personal income has been little studied hitherto, mostly due to the lack of empirical work. Here we report the first such study, an examination of the fluctuations in personal income of about 80,000 high-income taxpayers in Japan for two consecutive years, 1997 and 1998, when the economy was relatively stable. We find that the distribution of the growth rate in one year is independent of income in the previous year. This fact, combined with an approximate time-reversal symmetry, leads to the Pareto law, thereby explaining it as a consequence of a stable economy. We also derive a scaling relation between positive and negative growth rates, and show good agreement with the data. These findings provide the direct observation of the dynamical process of personal income flow not yet studied as much as for companies.