The Gini coefficient, or Gini index, is the most commonly used measure of inequality. It was developed by Italian statistician Corrado Gini (1884–1965) and is named after him.
It is typically used as a measure of income inequality, but it can be used to measure the inequality of any distribution – such as the distribution of wealth, or even life expectancy.1
It measures inequality on a scale from 0 to 1, where higher values indicate higher inequality. This can sometimes be shown as a percentage from 0 to 100%, this is then called the ‘Gini Index’.
A value of 0 indicates perfect equality – where everyone has the same income. A value of 1 indicates perfect inequality – where one person receives all the income, and everyone else receives nothing.
How is the Gini coefficient calculated?
There are two main ways of calculating the Gini coefficient. Both arrive at the same value, but they provide us with two different angles for understanding what it measures.
Method 1: The Gini tells us the difference we expect to find between any two people’s incomes, relative to the mean
The first method can be illustrated with the following thought experiment.
Imagine two people bumping into each other in the street at random. They compare their incomes and find out how much richer one person is than the other. How big a gap would we expect there to be?
This expected gap between two randomly chosen people is what the Gini coefficient measures. It is calculated by taking the average gap between all pairs of people.
Where incomes are distributed equally, we would expect the gap between two randomly selected people to be small. Where inequality is high, we would expect the gap to be large.
If measured in absolute terms, however, this will also depend on how rich or poor the population is generally. Where even the most well-off in society have a low income, the absolute gap between people’s incomes cannot be high. Conversely, where incomes are generally high, even very small relative differences between people’s incomes can result in large absolute gaps.
For this reason, the Gini coefficient expresses the expected absolute gap between people’s incomes relative to the mean income in the population.
In particular, it is calculated as the expected gap as a share of twice the mean income. Twice the mean income is the highest possible value for the average gap – a situation of perfect inequality, where one person has all the income and everyone else has none.2 So in this case of maximum inequality, the Gini coefficient is 1.
The lowest possible value for the average gap between all pairs of people is zero – a situation of perfect equality, where there are no gaps between any two people’s income because everyone earns the same. In this case, the Gini coefficient is 0.
Method 2: The Gini tells us how far the ‘Lorenz curve’ falls from perfect equality
The figure illustrates a second, visual definition of the Gini coefficient.
The left panel shows the share of income received by each fifth of a hypothetical population. The right panel shows this data plotted cumulatively. This is known as a ‘Lorenz curve’.
In a population where income is shared perfectly equally, the Lorenz curve would be a straight diagonal line: 10% of the population would earn 10% of the total income, 20% would earn 20% of the total income, and so on. This is shown in the chart as the ‘line of equality’.
In the hypothetical population shown in the chart, though, incomes are not distributed equally. The bottom 60% of the population earns 30% of the total income.
The Gini coefficient captures how far the Lorenz curve falls from the ‘line of equality’ by comparing the areas A and B, as calculated in the following way:
Gini coefficient = A / (A + B)
Where incomes are shared perfectly equally, the Lorenz curve is just the ‘line of equality’. The area A is 0, and hence so is the Gini coefficient. Where one person has all income and all others receive no income, the Lorenz curve will run along the bottom axis of the chart – the cumulative share of income is zero until the very last person. The area B will be zero, and the Gini coefficient will equal 1.