KfW Development Research Development in Brief

Measuring inequality – Important statistics for describing income

No 21, 2 November 2017

Author: Jonas Petrenz Editor: Karla Henning

For a very long time, international de- measurement primarily reacts to chang- velopment policy has focused on the Graph 1: The Lorenz curve es at both extreme ends of the distribu- issue of combating extreme poverty. It is tion range, it is used increasingly often only in the past few years that the issue in the "poor and rich" inequality debate. of income inequality has increasingly However, statements concerning the come to the fore. Meanwhile, reducing middle range of distribution cannot be inequality has even become anchored described well by this type of ratio. as a universal objective in the 2030 e) The Hoover Index, also known as Agenda for Sustainable Development the Robin Hood Index, indicates the (SDG 10). portion of the unevenly distributed in- There is less international consensus come that would have to be redistributed about the best way to measure inequali- in order to create completely equal dis- ty. Analogous to poverty measurement, tribution. It can be deduced graphically most measures of inequality concern the from the maximum vertical distance monetary dimension (income and developments at both extremes tend to between the Lorenz curve and the 45° distribution). The most important meas- be poorly registered. line of perfectly equal distribution (see urements of inequality for income distri- Graphic 1). Corresponding to the Gini bution, including their respective bene- b) Building on the Gini Index, the , the value 0 represents perfectly fits and drawbacks, will be briefly pre- Index introduces weighting of individu- equal distribution and 1 represents ab- sented in the following: als/groups based on their income. It is thus more sensitive to changes in the solute income inequality. It is both easy a) The Gini Index is the most wide- upper distribution range (highest per- to calculate and to understand. spread measurement of income inequal- centages of income). Because the Theil ity in the field of due to its Index is not capped, it cannot be easily Conclusion: Many measurements of easy interpretability, among other things. interpreted as an absolute value and inequality with different strengths/ It is based on the Lorenz curve: to do thus tends to be more suitable for eval- weaknesses this, all income earners are first sorted uating changes over time. The curve contains a on the x-axis according to individual great amount of information that can income amounts in ascending order; on c) The Atkinson Index is subject to the only be reduced to an individual statistic the y-axis is the percentage of all people assumption of diminishing marginal with significant loss of information. This with individual incomes lower than or utility. That means that the benefit of an is why there are a number of alternative equal to those incomes of the aggregat- additional unit of income is higher for measurements of distribution. Each ed total income (Graphic 1). If income those who have a lower income. The measures a different aspect or focuses equality is perfect, the Lorenz curve is a Atkinson Index measures the welfare on different parts of the distribution line at a 45° angle (blue line). loss of a society by calculating "lost curve. But no one can say that one The Gini Index now describes the rela- utility" that arises from unequal distribu- measurement is better than another tionship of the (shaded) area between tion of income (in comparison with bene- measurement per se. Rather, the selec- fit-optimised distribution). The Atkinson the Lorenz curve and the line at the 45° tion should depend on the question to angle to the whole triangle area under- Index is relatively complex to calculate. be examined and what sections of dis- neath the 45° line. If there is completely It is sensitive to changes in the lower tribution are therefore of particular inter- equal distribution, the Gini Index has a range of distribution. est. However, one should also consider value of 0; if distribution is completely d) Relational measurements place the fact that information about income unequal (one person owns everything) cer tain income groups in relation to each distribution is often based on rough the value is 1. The Gini Index takes the other. For example, the Palma Ratio is estimates and often-used distribution overall distribution into account but measurements thus do not necessarily the ratio of the richest 10% of the popu- reacts more sensitively to changes in lation's share of income divided by the yield more reliable results.■ the middle range of distribution, while share of the poorest 40%. Because this

Note: This paper reflects the opinion of the authors and does not necessarily represent the position of KfW.