A Statistical Model of Inequality

TL;DR

This paper introduces a nonparametric statistical model of wealth distribution that captures the effects of reversion rates and volatilities, accurately matching U.S. wealth data and analyzing implications for inequality and taxation.

Contribution

It develops a novel nonparametric model that characterizes wealth distribution using reversion rates and volatilities, providing insights into inequality dynamics and tax policy impacts.

Findings

U.S. wealth distribution may be on an unstable trajectory.

Small capital taxes on 1% of households significantly reduce inequality.

Model accurately matches observed wealth distribution.

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.