How is income inequality calculated

Concepts for measuring income inequalities

Dr Bernhard Payk

Income inequality can be measured and calculated empirically in very different ways. Studies on income disparities use different reference values ​​and measures of inequality depending on the objective and the object of investigation. The most common are presented in this paper with the help of actual examples. It is intended as a methodological supplement to the title article in this issue. That is why the analysis concept of the OECD report "Devided We Stand" is explained, which the title article follows in major parts.

Monetary inequality1 can basically be determined for assets and for income. In the following, only the income perspective is discussed. Here, too, different reference values ​​are used depending on the objective and the subject of the investigation.

The distribution of income can be determined independently of the person, for example in relation to collectively agreed wages, or at an individual level. The decisive factor for the perceived inequality, however, is not the income of the individual, but the disposable income of the households, the differences of which can be mitigated by non-monetary benefits from the state, such as education and care or health services.

Most studies present inequality on the basis of weighted disposable household incomes, the so-called net equivalised income. It is assumed that multi-person households have lower expenditures per person due to synergy effects in order to achieve the same level of prosperity as single-person households. The net equivalent income is the attempt to generate an income that is as comparable as possible. To calculate this income, the head of the household receives the weight 1 - according to the modified OECD scale - each additional adult household member receives the value 0.5 and each child receives the value 0.3.2 These weights have largely become established for the calculation of net equivalent income. It is also used by the OECD and the other studies discussed in the title post to describe inequality between countries.

Income disparities in relation to net equivalent income are important for the perceived inequality in societies. They stand at the end of the wealth distribution and arise from various sources. The multi-level analysis concept of the OECD integrates the most important components. The overview illustrates which these are and how they are interrelated.

The three areas of politics, globalization and technological change are considered as independent variables in the OECD study (orange area). It is assumed that these influence (collectively agreed) wages as well as employment behavior and unemployment (light blue and green areas). In the transition from the green to the purple area, the individual income is translated into household income. In addition to wages, these are also influenced by the number of employees in the household and their workload. Other income, for example from assets, is also taken into account. Household incomes are reduced through taxes, and if necessary increased through social transfers. At the end there is the disposable household income, which is weighted with the household size to increase comparability and is then referred to as net equivalent income. If care, education and health services have to be financed from this income, this ultimately leads to even greater inequality, since households with low incomes are then excluded from these services. If these services are equally available free of charge to all strata of the population, however, this will reduce inequality. However, since these factors are difficult to quantify, they are not considered further, which is why this area is shown with a dashed line. Even this complex analysis scheme hides many other influencing factors and interactions, but it is a good basis for gradually working out the central relationships. On this basis, the empirical results on income inequality are presented in the title article of this issue.3

To calculate inequality, people or households are sorted according to the level of income considered. One way of describing the distribution of income is to look at the proportions of total income earned by groups of the same size. For this purpose, the people or households are divided into five groups (quintiles) or, for a more precise analysis, into ten groups (deciles).

The differences are most evident when looking at the 10% of households with the lowest income (bottom decile) and the 10% with the highest income (top decile). For example, in 2008 the top 10% of households in Germany earned around eight times as much as the bottom 10%. The income disparity is thus only slightly below the OECD average of 9 to 1. In the 1990s, this factor in Germany was 6 to 1 and well below the OECD average.4

On average for 27 OECD countries, net equivalent income grew faster in the top decile than in the bottom decile. From the mid-1980s to 2008, low incomes rose by only 1.3% per year, adjusted for price, while the incomes of the highest incomes rose by 1.9%. In Germany, incomes stagnated in the bottom decile (+ 0.1%), and in the top decile, incomes grew by an average of 1.6%. At 1.5 percentage points, the differences in growth in Germany were more than twice as strong as the OECD average. In eight countries, the income gap between the top 10% and the bottom 10% actually narrowed between the mid-1980s and 2008. Including the euro crisis countries Portugal, Spain, Greece and Ireland.5

A disadvantage of this approach is that it only describes the extremes of income distribution. However, there is also a measure that takes into account inequality across the range of incomes, the Gini coefficient.

The Gini coefficient ranges from 0 to 1. The coefficient assumes the value 0 if all persons in a population have the same income, and the value 1 if one person has all the income and the rest of the people have none. The higher it is, the higher the inequality.

The Gini coefficient can be calculated for different income concepts: hourly or monthly wages, depending on the scope of employment or calculated on full-time equivalents, gross or net income, personal, household or net equivalent income.

Depending on the data available, the calculation is carried out differently. It is also possible to calculate a Gini coefficient if there is no individual data but only data for groups, for example the lowest income 10% of households get 2.7% of the income, the next 10% get 4% and so on. However, the Gini coefficients can only be directly compared with one another if they are based on the same data and were calculated using the same method. A group formation, for example, always leads to lower Gini values, since an equal distribution of income is assumed within the group.

For a graphical illustration of the Gini coefficient, the cumulative income is shown on the y-axis of a diagram and the cumulative income earners on the x-axis. If the points are connected to one another, a curve results which is referred to as the Lorenz curve. The Gini coefficient is the proportion of the area between the diagonal that would result if the distribution were uniform and the Lorenz curve (gray area) of the total area under the straight line of uniform distribution.

The diagram shows the Lorenz curves and Gini coefficients of the gross household income (Gini = 0.37) and the disposable household income6 (Gini = 0.34) according to the results of the income and expenditure sample for Germany (EVS) 2008. The points reflect the proportions of total income achieved up to a certain household income (first point up to 900 euros). Almost 9% of households earn up to 900 euros. They have 1.8% of gross income and 2.1% of disposable income. The last size class ranges from 5,000 to 18,000 euros per month. The roughly 13% of households in this income size class generate over 31% of total net income and 32% of gross income. The small Gini difference of just 0.02, which results from the proximity of the two curves over the entire income range, shows that inequality is only marginally reduced by income tax, church tax, solidarity surcharge and social security contributions. This representation does not provide any information about the absolute amount of the income reduction, since the income is shown as a percentage of the total.

1 Monetary inequality is an important component of social inequality, which also includes cultural and educational disparities, cf. for example Werner Fuchs-Heinritz et al. 2008: Lexicon for Sociology, VS-Verlag, p. 686.

2 For example, for a four-person household with two children, divide the disposable household income by (1 + 0.5 + 0.3 + 0.3) = 2.1. See WHAT ARE EQUIVALENCE SCALES? (As of March 23, 2012).

3 Cf. Payk, Bernhard, Freiheit - Inequality - Fraternity? On the development of income distribution in the OECD countries over the past 25 years, see p. 3ff in this issue.

4 See German-language press release on “Divided We Stand” from December 5, 2011 (as of May 10, 2012).

5 The growth figures have been corrected with the development of consumer prices. The complete table is available online (as of April 19, 2012). It should be noted that the results relate to 2008 and therefore do not reflect current developments.

6 Deviating from the EVS concept, not only income taxes and compulsory social insurance contributions but also voluntary health and pension insurance contributions were deducted from gross income.