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The Gini coefficient is a measure of inequality developed by the Italian statistician
Corrado Gini and published in his 1912 paper "Variabilità e mutabilità". It is usually used
to measure income inequality, but can be used to measure any form of uneven
distribution. The Gini coefficient is a number between 0 and 1, where 0 corresponds with
perfect equality (where everyone has the same income) and 1 corresponds with perfect
inequality (where one person has all the income, and everyone else has zero income). The
Gini index is the Gini coefficient expressed in percentage form, and is equal to the Gini
coefficient multiplied by 100.
While the Gini coefficient is mostly used to measure income inequality, it can also be
used to measure wealth inequality. This use requires that no one has a negative net
wealth.
Contents
[hide]

1 Calculation

2 Gini coefficients in the world
o
[edit]
Calculation
2.1 Development of Gini coefficients in the
US over time

3 Advantages of the Gini coefficient as a measure
of inequality

4 Disadvantages of the Gini coefficient as a
measure of inequality

5 References

6 See also

7 External links
Graphical representation of the Gini coefficient
The small sample variance properties of G are not known, and large sample
approximations to the variance of G are poor. In order for G to be an unbiased estimate of
the true population value, it should be multiplied by n/(n-1).
The Gini coefficient is calculated 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
underneath the Lorenz curve is B, then the Gini coefficient is A/(A+B). This ratio is
expressed as a percentage or as the numerical equivalent of that percentage, which is
always a number between 0 and 1.
The Gini coefficient is often calculated with the more practical Brown Formula shown
below:
G: Gini coefficient
Xk: cumulated proportion of the population variable, for k = 0,...,n, with X0 = 0, Xn = 1
Yk: cumulated proportion of the income variable, for k = 0,...,n, with Y0 = 0, Yn = 1
[edit]
Gini coefficients in the world
See complete listing in list of countries by income equality.
Gini coefficient, by countries
While most developed European nations tend to have Gini coefficients between 0.24 and
0.36, the United States Gini coefficient is above 0.4, indicating that the United States has
greater inequality. Using the Gini can help quantify differences in welfare and
compensation policies and philosophies. However it should be borne in mind that the
Gini coefficient can be misleading when used to make political comparisons between
large and small countries (see criticisms section).
Note: The calculation of the index for the United States was changed in 1992, resulting in
an upwards shift. Comparisons before and after that period may be misleading.
Gini coefficients over time for selected countries
[edit]
Development of Gini coefficients in the US over time
Gini coefficients for the United States at various times, according to the US Census
Bureau:

1970: 0.394

1980: 0.403

1990: 0.428

2000: 0.462
[edit]
Advantages of the Gini coefficient as a measure of
inequality

The Gini coefficient's main advantage is that it is a measure of inequality, not a
measure of average income or some other variable which is unrepresentative of most
of the population, such as gross domestic product.

Gini coefficients can be used to compare income distributions across different
population sectors as well as countries, for example the Gini coefficient for urban
areas differs from that of rural areas in many countries (though the United States'
urban and rural Gini coefficients are nearly identical).

The Gini coefficient is sufficiently simple that it can be compared across countries
and be easily interpreted. GDP statistics are often criticised as they do not represent
changes for the whole population, the Gini coefficient demonstrates how income has
changed for poor and rich. If the Gini coefficient is rising as well as GDP, poverty
may not be improving for the vast majority of the population.

The Gini coefficient can be used to indicate how the distribution of income has
changed within a country over a period of time, thus it is possible to see if inequality is
increasing or decreasing.

The Gini coefficient satisfies four important principles:
Anonymity: it doesn’t matter who the high and low earners are.
o
o
Scale independence: the Gini coefficient does not consider the size of the
economy, the way it is measured, or whether it is a rich or poor country on average.
o
Population independence: it does not matter how large the population of
the country is.
o
Transfer principle: if income (less than the difference), is transferred from
a rich person to a poor person the resulting distribution is more equal.
[edit]
Disadvantages of the Gini coefficient as a measure of
inequality

The Gini coefficient measured for a large geographically diverse country will
generally result in a much higher coefficient than each of its regions has individually.
For this reason the scores calculated for individual countries within the E.U. are
difficult to compare with the score of the entire U.S.

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 use food stamps, which may not be counted as income in the
Lorenz curve and therefore not taken into account in the Gini coefficient.

The measure will give different results when applied to individuals instead of
households. When different populations are not measured with consistent definitions,
comparison is not meaningful.

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.

As for all statistics, there will 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.

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. As an extreme example, an economy where
half the households have no income, and the other half share income equally has a
Gini coefficient of ½; but an economy with complete income equality, except for one
wealthy household that has half the total income, also has a Gini coefficient of ½.

It is claimed that the Gini coefficient is more sensitive to the income of the middle
classes than to that of the extremes.

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 yield a lower Gini coefficient than twenty 5%
quantiles (high granularity) taken from the same distribution.
As one result of this criticism, additionally to or in competition with the Gini
coefficient entropy measures are frequently used (e.g. the Atkinson and Theil indices).
These measures attempt to compare the distribution of resources by intelligent players
in the market with a maximum entropy random distribution, which would occur if
these players acted like non-intelligent particles in a closed system following the laws
of statistical physics.
[edit]
References
Dixon, PM, Weiner J., Mitchell-Olds T, Woodley R. Boot-strapping the Gini
coefficient of inequality. Ecology 1987;68:1548-1551.
Gini C. "Variabilità e mutabilità" (1912) Reprinted in Memorie di metodologica
statistica (Ed. Pizetti E, Salvemini, T). Rome: Libreria Eredi Virgilio Veschi (1955).
[edit]
See also

List of countries by income equality

List of countries by Human Development Index

Welfare economics

Income inequality metrics

ROC analysis

Social welfare (political science)

Pareto distribution

Robin Hood index
[edit]
External links


Measuring income inequality: a new database, with link to dataset
UN Human Development Report 2004, p50-53: Gini Index calculated for all
countries.

[1] Comparison of Urban and Rural Areas' Gini Coefficients Within States

[2] World Income Inequality Database

[3], Forbes Article, In praise of inequality

Gini index map from WorldPolicy.org

Software:
o
Free Online Calculator computes the Gini Coefficient, plots the Lorenz
curve, and computes many other measures of concentration for any dataset
o
Free Calculator: Online and downloadable scripts (Python and Lua) for
Atkinson, Gini, Hoover and Kullback-Leibler inequalities
o
Users of the R data analysis software can install the "ineq" package which
allows for computation of a variety of inequality indices including Gini, Atkinson,
Theil.
Retrieved from "http://en.wikipedia.org/wiki/Gini_coefficient"
Categories: Welfare economics | Socioeconomics | Economic indicators
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This page was last modified 08:22, 30 January 2006.
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