Heavy tailed capital incomes: Zenga index, statistical inference, and ECHP data analysis

Abstract

Micro-data of European Union (EU) countries show that capital incomes account for a large part of disparity in populations and follow heavy-tailed distributions in many EU countries. Measuring and comparing the disparity requires incorporating the relative nature of ‘small’ and ‘large,’ and for this reason we employ the newly developed Zenga index of economic inequality. Its non-parametric estimator does not fall into any well known class of statistics. This makes the development of statistical inference a challenge even for light-tailed populations, let alone heavy-tailed ones, as is the case with capital incomes. In this paper we construct a heavy-tailed Zenga estimator, establish its asymptotic distribution, and derive confidence intervals. We explore the performance of the confidence intervals in a simulation study and draw conclusions about capital incomes in EU countries, based on the 2001 wave of the European Community Household Panel (ECHP) survey.