Income inequality metrics

A Ungleichverteilungsmaß describes the degree of unequal distribution of a quantity with respect to another variable. In the social sciences, these quantities on the one hand often resources such as income or wealth, and on the other hand, the number of those who have income and asset shares. With unequal distribution measurements indicated the degree to which different allocation of resources to people from a uniform distribution. The following is a brief overview of the main inequality dimensions is given.

Overview

Hoover inequality

As the simplest Ungleichverteilungsmaß the Hoover inequality is based on a distribution in which an unequal distribution into a uniform distribution at any time is transferred fully informed. The Hoover inequality is 0 (or 0%) in complete uniform distribution and 1 ( or 100 % ) at maximum inequality. It indicates directly what proportion example of a non- distributed total income would have to be moved in order to achieve full equality of distribution.

Theil index

In contrast, the Theil index, the distribution model of a completely unregulated economy based in the redistribution takes place in a purely stochastic process. At no time have any information about the current distribution of resources are evaluated in this model of the acting therein actors and processes. The Theil index is a derived from information theory Ungleichverteilungsmaß. It belongs to the family of Entropiemaße.

Gini coefficient

Although the Theil index is increasingly frequently used, however, the Gini coefficient is still most commonly used. It is an evaluation of the Lorenz curve and thus acts although clearly than other inequality measures, but it was his development no distribution model is based. The Gini coefficient is 0 (or 0%) in complete uniform distribution and 1 ( or 100 % ) at maximum inequality. Its calculation can be very clearly represent the geometric means; However, what a measured Gini coefficient means the social sciences, can not convey geometric. However, the long -term and frequent use of the Gini coefficient led to an empirical understanding of the importance of the Gini coefficient. Also, there are empirical studies that explore the relationship between subjective ratings of unequal distributions and the associated inequality measures.

Hoover inequality

The Hoover inequality is the simplest of all inequality measures. In English, this Ungleichverteilungsmaß is known inter alia as the " Robin Hood Index". The Hoover inequality is 0 (or 0%) in complete uniform distribution and 1 ( or 100 % ) at maximum inequality. It indicates directly what proportion example of a non- distributed total income would have to be moved in order to achieve full equality of distribution.

One can measure the effect of tax progression directly to the Hoover Index: In 2001, a Hoover unequal distribution of gross income to the taxpayers of 0,332 showed. With a flat tax without allowance would be the unequal distribution of net income at 0,332. In fact, there was a Hoover unequal distribution of 0.300. It was by progressive tax 3.2% of net income redistributed "top to bottom".

The Hoover - uniform distribution is 1 (or 100%) minus the Hoover inequality. A calculated for a national income with the Hoover equipartition welfare function is obtained when the national income is multiplied by the Hoover - uniform distribution. This welfare function has a specific meaning: it is the proportion of the national income, which would remain untouched if you would redistribute the national income so that would result in a complete uniform distribution.

If the national income multiplied by the Hoover inequality or will be deducted from the national income, the welfare function, then there is the share of national income that would have to be moved as a whole when a full uniform distribution should be carried out with minimal effort. To this end a perfect planning under the assumption of complete knowledge would be required.

Theil index

The Theil index is a derived from information theory Ungleichverteilungsmaß. It belongs to the family of Entropiemaße. The Theil index is sometimes mistakenly referred to as Theil entropy. Yet, in fact, this is a redundancy, because it is the difference between a uniform distribution at adjusting maximum entropy and a resulting from an unequal distribution entropy current.

The Theil index is 0 for perfect equality and 1 for distribution of unequal distribution in which 17.6 % of the resource owners about 82.4 % of the total resources and conversely 82.4 % of the resource owners have 17.6 % of the resources. As a memory aid can be used here is that this unequal distribution is for a part - index of 1 are quite close to the 80:20 distribution, which is known as the " Pareto Principle ". At a higher unequal distribution of the Theil index is greater than 1

In contrast to the Hoover inequality not only disparities are aggregated when calculating the Theil index, but these disparities are weighted by their information content. This yields a measure that not only describes the percentage of umzuverteilnden a balance resources, but also the attention that causes the imbalance.

The Theil index is available in two versions. The Theil- L index describes the distribution of resources to people, the Theil- T index describes the distribution of people to resources. The average of the two indices is a channel balanced Theil index, which is structurally very similar to the simple Hoover inequality (see main article).

In the calculation of inequality measures today both Theil indexes are often reported, sometimes in addition to the Gini coefficient.

The normalization of the Theil indices in the range between 0 and 1 ( or between 0% and 100 %) is with surgery.

Is the Theil- L- uniform distribution. A calculated for a national income with the Theil- L- uniform distribution of welfare function is obtained when the national income is multiplied by the Theil L- uniform distribution. In the article, the Theil- index the application of the Theil- L index is explained on the calculation of the welfare function in more detail. A per-capita welfare function can be interpreted as a " perceived average income 'and using as an alternative to the median.

If the national income multiplied by the Theil L index, or will be deducted from the national income calculated using the Theil- L index welfare function, then there is the share of national income, which would be moved as a whole when a full uniform distribution of the condition should be obtained from a planning point of view exclusively subject to the laws of chance distribution. The distribution model would correspond to the free-market model. This would require the system in which the distribution takes place, completely cut off from its environment and be left to themselves. ( If no income moves, then an equal distribution by movement of income earners in a randomly subjected distribution process is conceivable. The total number of moving recipients would in this case the product of the Theil- T index and the number of income earners. ) In high inequality arises with the Theil index is a redistribution volume, as calculated with the Hoover unequal distribution volume exceeds. For small inequalities, the calculated volume redistribution is initially below the calculated with the Hoover unequal distribution volume, a balance seems not to have taken place. However arise during the leveling process theoretically assumed new values ​​for the Theil index, approaching near zero values ​​of the Hoover inequality again.

In real economies, there is always a mixture of a randomly surrendered and the planning of subject distribution. In (only theoretically possible ) closed economic system, this distribution leads to balance, in an open system, however, can also increase the inequality, for example, by time and place unequally distributed access to resources in the environment of the system. For this reason, both the Hoover inequality as well as the Theil index are relevant dimensions. The difference between the two unequal distribution measurements is smaller for most of the economies than 0.1 (see "Comparison of the Theil index with the Hoover inequality " in the main article Theil index).

Gini coefficient

The Gini coefficient is the Ungleichverteilungsmaß used in the social sciences most often. He is 0 (or 0%) in complete uniform distribution and 1 ( or 100 % ) at maximum inequality. Its calculation can be very clearly represent the geometric means; However, what a measured Gini coefficient means the social sciences, can not convey geometric.

However, the long -term and frequent use of the Gini coefficient led to an empirical understanding of the importance of the Gini coefficient. Also, there are empirical studies that explore the relationship between subjective ratings of unequal distributions and the associated inequality measures. The Gini coefficient is used, at least when research should be continued, in which was already worked with this Ungleichverteilungsmaß.

Other inequality measures

• Atkinson measure
• Kakwani index
• Measure of concentration by the Herfindahl
• Rosenbluth index
• Lerner index