A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries

Michael McAleer, Hang Ryu and Daniel Slottje

No EI2017-28, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: There is a vast literature on the selection of an appropriate index of income inequality and on what desirable properties such a measure (or index) should contain. The Gini index is, of course, 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, such as the Pareto distribution. 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 in the underlying empirical IDF. This paper introduces a new inequality measure to supplement, but not to replace, the Gini that measures more accurately 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.

Keywords: Inequality Index; Extreme value distributions; Maximum entropy method; Orthonormal basis; Legendre polynomials (search for similar items in EconPapers)
JEL-codes: D31 D63 (search for similar items in EconPapers)
Pages: 34
Date: 2017-10-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries (2019)
Working Paper: A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries (2017)
Working Paper: A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries (2017)
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