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

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 each single variable as well as inequality stemming from the dependence structure of the variables. We derive simple nonparametric estimators for both instruments and exemplary apply them to data of individual income and wealth for various countries.