Estimating Wealth Distribution: Top Tail and Inequality

TL;DR

This paper develops and compares mathematical methods to estimate the wealth share of the richest p percent, using Pareto models for the top-tail of wealth distribution, with applications to German data and rich lists.

Contribution

It introduces new criteria for parameter estimation in Pareto models and demonstrates the superiority of maximum-likelihood estimation through simulations.

Findings

Maximum-likelihood estimator outperforms other methods in simulations.

New criteria for parameter choice improve top-tail wealth estimates.

Applied methods to German data and rich lists with provided R scripts.

Abstract

This article describes mathematical methods for estimating the top-tail of the wealth distribution and therefrom the share of total wealth that the richest $p$ percent hold, which is an intuitive measure of inequality. As the data base for the top-tail of the wealth distribution is inevitably less complete than the data for lower wealth, the top-tail distribution is replaced by a parametric model based on a Pareto distribution. The different methods for estimating the parameters are compared and new simulations are presented which favor the maximum-likelihood estimator for the Pareto parameter $\alpha$. New criteria for the choice of other parameters are presented which have not yet been discussed in the literature before. The methods are applied to the 2012 data from the ECB Household and Consumption Survey (HFCS) for Germany and the corresponding rich list from the Manager Magazin. In addition to a presentation of all formulas, R scripts implementing them are provided by the author.