Graphical Measures Summarizing the Inequality of Income of Two Groups

Abstract

Recently, Gastwirth proposed two transformations $p^{\ast }(q)$and $m^{\ast }(q)$ of the Lorenz curve, which calculates the proportion of a population, cumulated from the poorest or middle, respectively, needed to have the same amount of income as top $100q\%$. Economists and policy makers are often interested in the comparative status of two groups, for example, females versus males or minority versus majority. This article adapts and extends the concept underlying the $p^{\ast }(q)$ and $m^{\ast }(q)$ curves to provide analogous curves comparing the relative status of two groups. Now one calculates the proportion of the minority group, cumulated from the bottom or middle needed to have the same total income as the top qth fraction of the majority group (after adjusting for sample size). The areas between these curves and the line of equality are analogous to the Gini index. The methodology is used to illustrate the change in the degree of inequality between males and females, as well as between black and white males, in the United States between 2000 and 2017, and can be used to examine disparities between the expenditures on health of minorities and white people.

Keywords:

• Black–White income inequality
• Gini Index
• Lorenz curve
• Male–female income inequality
• Transformations of the Lorenz curve