The genius behind the Gini index

December 20, 2013

By Ireti Adesanya

The Lorenz curve is used to calculate the Gini index. Photo Credit: significancemagazine.org

The Lorenz curve is used to calculate the Gini index.
Photo Credit: significancemagazine.org

Italian statistician Corrado Gini created the Gini coefficient or index in 1912. It is the most commonly used instrument of measurement for income inequality.

The index is used by organizations like the World Bank and the United Nations to measure income inequality between and within countries.

In the U.S., the Gini index is used by the Census Bureau to measure household income inequality. The bureau calculates the Gini index using income data collected in its annual American Community Survey.

The Census Bureau uses the index to measure inequality at the state, county and neighborhood levels (census tracts). Inequality is measured with a range from zero to one. Zero denotes perfect equality; one denotes maximum inequality.

To determine the Gini coefficient of an area, a Lorenz curve is used. The Lorenz curve is a mathematical line plot that measures the total income of the population on the vertical axis (X-axis) against the distribution of income to the population on the horizontal axis (Y-axis). A straight line at 45 degrees denotes perfect equality.

To calculate the Gini coefficient, the sum of the Lorenz curve and the line of equality is divided by the area between the line of equality and the Lorenz curve. If an area had maximum inequality, the Lorenz curve would mirror the line of equality and be straight.

Although the Gini coefficient has been useful in measuring inequality, it has been criticized because:

¶ It measures only relative wealth — not the absolute wealth of an area.

¶ It does not take into account change in population growth as a factor for income inequality.

¶ Trying to measure income inequality at an individual level instead of at a household level yields different results. Inconsistent definitions render comparisons meaningless.

¶ A state’s index does not correlate with the sum of its counties’ index and the same goes for census tracts.

Alternatives to the Gini coefficient are the Theil index and the Atkinson measures; both can be used in conjunction with the Gini index to measure income inequality.

Main story: Income Inequality in Richmond