# Gini coefficient

The Gini coefficient is a measure of income inequality within a country. It is usually expressed as a percentage or index where either 1 or 100% indicates "perfect" inequality and 0 or 0% indicates "perfect" equality of income distribution. The compiling of the Index requires that costly surveys be undertaken. Neither the IMF nor the World Bank computes Gini coefficients as part of their country missions and programs. Thus, the Gini coefficient has a rather sparse coverage in terms of countries and years available. Scandinavian countries have Gini coefficients of around 25%, continental European countries of around 30%, Anglo-Saxon countries of around 40%, many Latin American Countries of around 50-60%, and some African countries reach Gini coefficients of 60-70%.

## Technical definition

The Gini coefficient is a measure of statistical dispersion developed by the Italian statistician Corrado Gini and published in his 1912 paper "Variability and Mutability" (Italian: Variabilità e mutabilità). It is commonly used as a measure of inequality of income or wealth. It has, however, also found application in the study of inequalities in disciplines as diverse as health science, ecology, and chemistry.

The Gini coefficient is usually defined mathematically based on the Lorenz curve, which plots the proportion of the total income of the population (y axis) that is cumulatively earned by the bottom x% of the population (see diagram). The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked 'A' in the diagram) over the total area under the line of equality (marked 'A' and 'B' in the diagram); i.e., G=A/(A+B). The Gini coefficient can range from 0 to 1; it is sometimes multiplied by 100 to range between 0 and 100. A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality, while higher Gini coefficients indicate more unequal distribution, with 1 corresponding to complete inequality. To be validly computed, no negative goods can be distributed. Thus, if the Gini coefficient is being used to describe household income inequality, then no household can have a negative income. When used as a measure of income inequality, the most unequal society will be one in which a single person receives 100% of the total income and the remaining people receive none (G=1); and the most equal society will be one in which every person receives the same percentage of the total income (G=0). Some find it more intuitive (and it is mathematically equivalent) to think of the Gini coefficient as half of the Relative mean difference. The mean difference is the average absolute difference between two items selected randomly from a population, and the relative mean difference is the mean difference divided by the average, to normalize for scale. Worldwide, Gini coefficients for income range from approximately 0.25 (Denmark) to 0.70 (Namibia) although not every country has been assessed. As a mathematical measure of inequality, the Gini coefficient does not necessarily entail any value judgement, i.e. the "rightness" or "wrongness" of a particular level of equality.

## External links

- Wikipedia article
- Travis Hale, University of Texas Inequality Project:The Theoretical Basics of Popular Inequality Measures, online computation of examples: 1A, 1B
- United States Census Bureau List of Gini Coefficients by State for Families and Households
- Article from The Guardian analysing inequality in the UK 1974 - 2006
- World Income Inequality Database
- Income Distribution and Poverty in OECD Countries
- Software:
- A Matlab Inequality Package, including code for computing Gini, Atkinson, Theil indexes and for plotting the Lorenz Curve. Many examples are available.
- Free Online Calculator computes the Gini Coefficient, plots the Lorenz curve, and computes many other measures of concentration for any dataset
- Free Calculator: Online and downloadable scripts ((Python) and (Lua) for Atkinson, Gini, and Hoover inequalities