Comparable Indicators of Inequality Across Countries
3. Measuring Income Inequality
In seeking to either investigate the evolution of income inequality itself or its impact on other economic and
social outcomes, a range of alternative ways of summarising the distribution are employed. Ranking recipients
from poorest to richest, it is common to present the overall distribution in terms of deciles levels or decile shares
- the (next-higher) level of income below which 10% of the population (bottom 10%, next 10%, etc. ... up to the
top 10%) is found or the share of the population’s total income accruing to that decile. Graphing the distribution in
various ways has proved a powerful tool, notably via the Lorenz curve which plots the cumulative share of income
going to the bottom x% of recipients, where x goes from 0 to 100%. This has allowed the circumstances in which
distributions can be robustly ranked as more or less equal in social welfare terms to be determined. If the Lorenz
curves of two distributions do not cross, then one can unambiguously conclude that inequality is lower in one dis-
tribution than another, without relying on any particular inequality measure to order the distributions.7
However, summary measures seeking to capture the level of inequality are particularly convenient, especially
when inequality is to be used as an explanatory variable; the problem is that there is a profusion of available meas-
ures. An extensive literature has teased out the properties of the available measures (see for example Cowell, 2003,
2011), and we briefly describe the most commonly-used ones.
1. Percentile ratios, taking for example the difference between the 90th and the 10th percentiles or the ratio
between them. Percentile ratios are also sometimes expressed vis-a-vis the median, allowing dispersion
towards the top and the bottom to be distinguished.
2. Income share ratios, expressing the share of total incomes held by the richest 20% (for example) versus
the poorest.
3. The Gini coefficient, which is half the relative mean difference — the average of the absolute values of
the differences between all pairs of incomes, relative to the mean. In Lorenz curve terms this is equal to
the ratio of the area enclosed by the Lorenz curve and the diagonal line of perfect equality to the total
area below the diagonal. It ranges from zero (perfect equality) to 1 (perfect inequality).
4. The class of Generalized Entropy measures of which prominent members are Theil’s index, the Mean
Logarithmic Deviation, and half the squared coefficient of variation. (A useful feature of these indices
is that they are additively decomposable by population subgroups.)
5. The closely related Atkinson inequality measure (Atkinson, 1970), which incorporates an explicit ine-
quality-aversion parameter.
7 Even when Lorenz curves intersect, if they cross only once Davies and Hoy (1995) show that they can be readily ranked.
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