Title
A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries
Authors
Abstract
There is a vast literature on the selection of an appropriate index of income inequality and onwhat desirable properties such a measure (or index) should contain. The Gini index is the most
popular. There is a concurrent literature on the use of hypothetical statistical distributions to
approximate and describe an observed distribution of incomes. Pareto and others observed
early on that incomes tend to be heavily right-tailed in their distribution. These asymmetries
led to approximating the observed income distributions with extreme value hypothetical
statistical distributions. But these income distribution functions (IDFs) continue to be described
with a single index (such as the Gini) that poorly detect the extreme values present. This paper
introduces a new inequality measure to supplement the Gini (not to replace it) that better
measures the inherent asymmetries and extreme values that are present in observed income
distributions. The new measure is based on a third order term of a Legendre polynomial from
the logarithm of a share function (or Lorenz curve). We advocate using the two measures
together to provide a better description of inequality inherent in empirical income distributions
with extreme values. Using Current Population Survey data, we show we can better describe
the overall IDF and better detect changes in the tails of the empirical IDF using the two
measures concomitantly.
Keywords
Extreme income values, Distributional aspects missed by the Gini coefficient, Lorenz dominance effects, Orthonormal basis expansion, Legendre polynomials.
Classification-JEL
D31, D63
Pages
31-61