Teaching Notes · Economic Development and Growth

Measuring Inequality: The Lorenz Curve and the Gini Coefficient

Saying that a country has unequal income distribution is easy. Measuring exactly how unequal, in a way that lets you compare one country or one year to another, takes a bit more structure. Two tools, developed more than a century ago and still the standard today, do most of the work: the Lorenz curve and the Gini coefficient that summarizes it.

Building the Lorenz curve

The construction is simpler than it sounds. Line every individual up in ascending order of personal income, then divide the population into equal groups, typically quintiles, five groups of twenty percent each, or deciles, ten groups of ten percent each. For each group, calculate its share of total national income, and accumulate both the population share and the income share as you move from the poorest group to the richest.

Plot the cumulative population share on the horizontal axis and the cumulative income share on the vertical axis, and you get the Lorenz curve. A straight diagonal line represents perfect equality: the poorest twenty percent of the population holding exactly twenty percent of national income, the poorest forty percent holding exactly forty percent, and so on. The actual Lorenz curve for any real economy bows away from that diagonal, because the poorest fifth of a population essentially never holds a fifth of national income. The further the curve bows away from the equality line, the more unequal the distribution.

From a curve to a single number

A curve is useful for visualizing inequality within one country, but it becomes awkward for comparison once curves from different countries start to cross, which happens often enough that you cannot always simply eyeball which distribution is worse. That is the problem the Gini coefficient solves, by converting the whole curve into a single number between 0 and 1.

Gini coefficient = (area between the equality line and the Lorenz curve) ÷ (total area under the equality line)

A coefficient of 0 means perfect equality, every group holding exactly its proportional share of income. A coefficient of 1 means perfect inequality, all income concentrated in a single hand. In practice, no real economy sits at either extreme. As a rough guide, countries with relatively equitable income distribution tend to post Gini coefficients in roughly the 0.2 to 0.35 range, while countries with highly unequal distribution tend to run from about 0.5 up to 0.7. The coefficient makes it possible to rank countries, or to track a single country over time, in a way that a visual comparison of curves cannot always do cleanly.

What can actually be done about it

Once inequality is measured, the policy conversation usually settles around three broad approaches, each targeting a different part of the problem.

• Progressive taxation. Taxing higher incomes at a higher rate, aimed at the upper end of the distribution. It is a standard tool, though its effectiveness in developing countries is often limited in practice, since the poor can end up paying a disproportionately large share of their limited income through indirect taxes even while formal income tax rates look progressive on paper.
• A social safety net. Transfers aimed at the lower end of the distribution, cash payments to poor households with no production requirement attached, or free access to services such as education, designed to raise the floor rather than lower the ceiling.
• Redistributing the underlying assets. An older and today much less commonly used approach, aimed directly at the source of the gap rather than at the income it generates. Physical assets, land and capital, can in principle be redistributed through land reform that limits how much any one owner can hold, or through nationalization, in which the state buys productive firms outright. Human assets, the workforce itself, can be addressed by expanding equal access to education, which is really a redistribution of future earning capacity rather than of an existing asset. Most contemporary policy has shifted toward redistributing income rather than the underlying wealth or asset base, since asset redistribution tends to be far more disruptive and politically contested.

None of these three tools works in isolation, and most countries use some blend of all three, with the mix shaped as much by politics as by economics.