A multivariate extension of the Lorenz curve based on copulas and a related multivariate Gini coefficient

TL;DR

This paper introduces a multivariate extension of the Lorenz curve and Gini coefficient using copulas, enabling simultaneous measurement of inequality across multiple variables and dependence structures.

Contribution

It develops nonparametric estimators for multivariate inequality measures based on copulas, extending traditional univariate concepts to multiple variables.

Findings

Effective in measuring inequality in income and wealth data.

Captures dependence structure effects on inequality.

Applicable to cross-country data analysis.

Abstract

We propose an extension of the univariate Lorenz curve and of the Gini coefficient to the multivariate case, i.e., to simultaneously measure inequality in more than one variable. Our extensions are based on copulas and measure inequality stemming from inequality in every single variable as well as inequality stemming from the dependence structure of the variables. We derive simple nonparametric estimators for both instruments and apply them exemplary to data of individual income and wealth for various countries.