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# Gini says: measuring income inequality

### an LBO report, October 18, 1993

There are several ways to express the degree of income inequality
in a society. The simplest way is to arrange whatever units you
choose persons, families, or households in rank order, from poorest
to richest; divide the hierarchy into fifths (quintiles) or tenths
(deciles); and compute either the average income by decile or
quintile or the share that each grouping has of the society's
total income. Then, the shares or averages of rich and poor can
be compared.

Here are examples for the U.S. for two important years 1968, when
the U.S. income distribution was the most equal it has been in
modern times, and 1992, when it was the most unequal (so far!).
The five columns on the left show the share of pretax income earned
by each quintile of households, from the poorest to the richest;
columns six through nine show the ratios of those shares for the
richest to poorest, the middle to the poorest, and the richest
to the middle. Note that from 1968 to 1992, the increase in inequality
was almost entirely the result of the rich getting richer at the
expense of the lower-middle and middle ranks.

This technique is simple and revealing, but not without awkwardness:
which comparison to choose? Economists have devised several ways
of making such comparisons with a single index number. The most
popular of these is the Gini index (or coefficient or ratio or
number). While it simplifies com parisons, however, the Gini is
not easy to explain. Here's an attempt to do so.

### Plotting distribution: Lorenz curves

We can start with the nearby graph, derived from the numbers
in the table. The horizontal axis shows the quintiles; the vertical,
the cumulative share of income earned by the plotted quintile
and the ones below it. For example, for 1968, the cumulative value
for quintile 1 is the share earned by quintile 1, or 4.2%; that
for quintile 2, 11.1%+4.2%, or 15.3%; and so on, up to quintile
5, when the sum is 100%. The graph plots these values for 1968
and 1992. These lines are called Lorenz curves.

In a society with perfectly equal income distribution, the cu