Gini coefficient Totally Explained

Everything about The Gini Coefficient totally explained

The Gini coefficient is a measure of statistical dispersion most prominently used as a measure of inequality of income distribution or inequality of wealth distribution. It is defined as a ratio with values between 0 and 1: A low Gini coefficient indicates more equal income or wealth distribution, while a high Gini coefficient indicates more unequal distribution. 0 corresponds to perfect equality (everyone having exactly the same income) and 1 corresponds to perfect inequality (where one person has all the income, while everyone else has zero income). The Gini coefficient requires that no one have a negative net income or wealth. Worldwide, Gini coefficients range from approximately 0.249 in Japan to 0.707 in Namibia.
   As opposed to the Gini coefficient, the Gini index is the Gini coefficient expressed as a percentage, and is equal to the Gini coefficient multiplied by 100. The Gini index is more widely used, for example in country listings in Wikipedia.
   The Gini coefficient was developed by the Italian statistician Corrado Gini and published in his 1912 paper "Variability and Mutability" .
   The Gini coefficient is also commonly used for the measurement of the discriminatory power of rating systems in credit risk management. Since gini coefficient addresses wealth inequality it may be important to understand what a transformative asset is. Transformative assets increase the gini coefficient as they provide a family or individual with a wealth advantage over most persons.

Calculation

The Gini coefficient is defined as a ratio of the areas on the Lorenz curve diagram. If the area between the line of perfect equality and Lorenz curve is A, and the area under the Lorenz curve is B, then the Gini coefficient is A/(A+B). Since A+B = 0.5, the Gini coefficient, G = A/(0.5) = 2A = 1-2B. If the Lorenz curve is represented by the function Y = L(X), the value of B can be found with integration and: ť

G = 1 - 2,int_0^1 L(X) dX

In some cases, this equation can be applied to calculate the Gini coefficient without direct reference to the Lorenz curve. For example:

For a population uniform on the values y_i, i = 1 to n, indexed in non-decreasing order (y_i ≤ y_i+1): ť $G = frac$ into a inequality coefficient) averts such problems.

The Lorenz curve may understate the actual amount of inequality if richer households are able to use income more efficiently than lower income households. From another point of view, measured inequality may be the result of more or less efficient use of household incomes.

Economies with similar incomes and Gini coefficients can still have very different income distributions. This is because the Lorenz curves can have different shapes and yet still yield the same Gini coefficient.

It measures current income rather than lifetime income. A society in which everyone earned the same over a lifetime would appear unequal because of people at different stages in their life; a society in which students study rather than save can never have a coefficient of 0.

Problems in using the Gini coefficient

Gini coefficients do include income gained from wealth; however, the Gini coefficient is used to measure net income more than net worth, which can be misinterpreted. For example, Sweden has a low Gini coefficient for income distribution and a higher Gini coefficient for wealth (the wealth inequality is low by international standards, but still significant: 5% of Swedish household shareholders hold 77% of the share value owned by households). In other words and as a normative statement: the Gini income coefficient shouldn't be interpreted as measuring effective egalitarianism; and distribution of stock ownership doesn't appear to correlate to many recognized indicators of egalitarianism.

Too often only the Gini coefficient is quoted without describing the proportions of the quantiles used for measurement. As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements. For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) taken from the same distribution. This is an often encountered problem with measurements.

Care should be taken in using the Gini coefficient as a measure of egalitarianism, as it's properly a measure of income dispersion. Two equally egalitarian countries with different immigration policies may have different Gini coefficients.

General problems of measurement

Comparing income distributions among countries may be difficult because benefits systems may differ. For example, some countries give benefits in the form of money while others give food stamps, which might not be counted by some economists and researchers as income in the Lorenz curve and therefore not taken into account in the Gini coefficient. US counts income before benefits, while France counts it after benefits, making US appear more unequal vis-a-vis France than it is.

The measure will give different results when applied to individuals instead of households. When different populations are not measured with consistent definitions, comparison isn't meaningful.

As for all statistics, there may be systematic and random errors in the data. The meaning of the Gini coefficient decreases as the data become less accurate. Also, countries may collect data differently, making it difficult to compare statistics between countries. As one result of this criticism, in addition to or in competition with the Gini coefficient entropy measures are frequently used (for example the Theil Index and the index of Atkinson). These measures attempt to compare the distribution of resources by intelligent agents in the market with a maximum entropy random distribution, which would occur if these agents acted like non-intelligent particles in a closed system following the laws of statistical physics.

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