  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.
