Common Income Inequality Metrics
Among the most common metrics used to measure inequality are the Gini index (also known as Gini coefficient), the Theil index, and the Hoover index. They have all four properties described above.
An additional property of an inequality metric that may be desirable from an empirical point of view is that of 'decomposability'. This means that if a particular economy is broken down into sub-regions, and an inequality metric is computed for each sub region separately, then the measure of inequality for the economy as a whole should be a weighted average of the regional inequalities (in a weaker form, it means that it should be an explicit function of sub-regional inequalities, though not necessarily linear). Of the above indexes, only the Theil index has this property.
Because these income inequality metrics are summary statistics that seek to aggregate an entire distribution of incomes into a single index, the information on the measured inequality is reduced. This information reduction of course is the goal of computing inequality measures, as it reduces complexity.
A weaker reduction of complexity is achieved if income distributions are described by shares of total income. Rather than to indicate a single measure, the society under investigation is split into segments, e.g. into quintiles (or any other percentage of population). Usually each segment contains the same share of income earners. In case of an unequal income distribution, the shares of income available in each segment are different. In many cases the inequality indices mentioned above are computed from such segment data without evaluating the inequalities within the segments. The higher the amount of segments (e.g. deciles instead of quintiles), the closer the measured inequality of distribution gets to the real inequality. (If the inequality within the segments is known, the total inequality can be determined by those inequality metrics which have the property of being "decomposable".)
Quintile measures of inequality satisfy the transfer principle only in its weak form because any changes in income distribution outside the relevant quintiles are not picked up by this measures; only the distribution of income between the very rich and the very poor matters while inequality in the middle plays no role.
Details of the three inequality measures are described in the respective Wikipedia articles. The following subsections cover them only briefly.
Read more about this topic: Income Inequality Metrics
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