A Statistical Model of Inequality

Abstract: 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.