Gini Coefficient - Generalized Inequality Index

Generalized Inequality Index

See also: Generalized entropy index

The Gini coefficient and other standard inequality indices reduce to a common form. Perfect equality—the absence of inequality—exists when and only when the inequality ratio, equals 1 for all j units in some population; for example, there is perfect income equality when everyone’s income equals the mean income, so that for everyone). Measures of inequality, then, are measures of the average deviations of the from 1; the greater the average deviation, the greater the inequality. Based on these observations the inequality indices have this common form:

where pj weights the units by their population share, and f(rj) is a function of the deviation of each unit’s rj from 1, the point of equality. The insight of this generalised inequality index is that inequality indices differ because they employ different functions of the distance of the inequality ratios (the rj) from 1.

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