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.

Additional Metadata
Keywords Inequality Index, Extreme value distributions, Maximum entropy method, Orthonormal basis, Legendre polynomials
JEL Personal Income, Wealth, and Their Distributions (jel D31), Equity, Justice, Inequality, and Other Normative Criteria and Measurement (jel D63)
Sponsor This research was supported by the National Research Foundation of Korea (2017S1A3A2066657), National Science Council, Ministry of Science and Technology (MOST), Taiwan, and the Australian Research Council
Persistent URL hdl.handle.net/1765/102548
Series Econometric Institute Research Papers
Citation
McAleer, M.J, Ryu, H.K, & Slottje, D.J. (2017). A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries. Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/102548