  This paper develops a nonparametric statistical model of wealth distribution
that imposes little structure on the fluctuations of household wealth. In this
setting, we use new techniques to obtain a closed-form household-by-household
characterization of the stable distribution of wealth and show that this
distribution is shaped entirely by two factors - the reversion rates (a measure
of cross-sectional mean reversion) and idiosyncratic volatilities of wealth
across different ranked households. By estimating these factors, our model can
exactly match the U.S. wealth distribution. This provides information about the
current trajectory of inequality as well as estimates of the distributional
effects of progressive capital taxes. We find evidence that the U.S. wealth
distribution might be on a temporarily unstable trajectory, thus suggesting
that further increases in top wealth shares are likely in the near future. For
capital taxes, we find that a small tax levied on just 1% of households
substantially reshapes the distribution of wealth and reduces inequality.
