### Robin Hood Index of inequality

January 30, 2008

I participated in a cool conference call meeting this morning which mentioned the Robin Hood Index and Ted was wonderful enough to send some info along.

The Robin Hood index is typically used in applications related to socio-economic class (SES) and health. It is conceptually the simplest inequality index used in econometrics.

It is based on the Lorenz Curve

Every point on the Lorenz curve represents a statement like "the bottom 20% of all households have 10% of the total income". A perfectly equal income distribution would be one in which every person has the same income. In this case, the bottom N% of society would always have N% of the income. This can be depicted by the straight line y = x; called the line of perfect equality or the 45° line.

By contrast, a perfectly unequal distribution would be one in which one person has all the income and everyone else has none. In that case, the curve would be at y = 0 for all x < 100%, and y = 100% when x = 100%. This curve is called the line of perfect inequality.

The Gini coefficient is the area between the line of perfect equality and the observed Lorenz curve, as a percentage of the area between the line of perfect equality and the line of perfect inequality. This equals two times the area between the line of perfect equality and the observed Lorenz curve.

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: the numerator is the area between the Lorenz curve of the distribution and the uniform distribution line; the denominator is the area under the uniform distribution line. Thus, 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.

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.

It is however not easy to fini GINI indicator maps! There is a good one on wikipedia but surely it must be part of most international indicator programs!

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