A Tool for Measuring Income Inequality

Article excerpt

Income inequality -- that gap between the haves and have-nots -- is a topic that begs the use of databased reporting. Because the gap grows slowly and unevenly, no one has the same perception of it. If you live in Washington and witness dark-glassed, stretch limousines zipping past down-trodden homeless folks, the gap seems to be huge and growing every day. But if you live in Hot Springs, Ark., where the differences are more on the line of Cadillacs sharing the roads with years-old Chevy pick-ups, inequality may seem less daunting.

Listening to the various opinions and forecasts on the topic issued by politicians, economists and social philosophers often does little to clarify the issue for the average Joe or Jane Public. So data-based journalists, once armed with a formula for the Gini coefficient of inequality and the appropriate income data, can provide a real service by telling their readers if income inequality is growing in their area and if it is better or worse there than elsewhere. What's more, they can do it in away that is both easy to understand and quite precise.

Why is using the Gini coefficient easy? Several reasons. One, the formula -- named for its italian developer -- is pretty simple for journalists to plug right into a spreadsheet program such as Excel. Two, the computed results are even easier to compare and explain because the coefficient is a single number between 0 and 1, with 0 representing complete equality of incomes and 1 signifying complete inequality. Three, income data at any level can be used, from country on down to county or even census track. I analyzed county level data for the state of North Carolina; USA Today looked at county level data for the entire United States for its September 1996 series on the income gap.

The Gini formula's precision also gives it a huge advantage over other common methods of talking about income inequality. For instance, some efforts have tried to explain income inequality with a comparison of median incomes, a number that can be misleading because it ignores specific information about top and bottom incomes. Others have looked at changes in income in the top and bottom quintiles of a population. While explaining it this way is valuable for describing changes in income distribution, it is a bit unwieldy for measuring and especially comparing inequality. Because the Gini formula involves cumulative proportion of income earned by cumulative proportion of the population, it does a much better job of detecting changes in distribution in the middle as well as at the ends of the income ladder.

The formula for the Gini coefficient of inequality is:

Gini coefficient = 1 - SUM(Xi-Xi)(Yi+Yj)

where:

X is the cumulative proportion of households;

Y is the cumulative proportion of income;

i is a particular income category;

j is i - 1, or the preceding income category.

The easiest way to conceptualize what is being measured is to picture a graph in which the final points on the X and Y axes are 100 percent, or 1.0. Points are graphed based on cumulative numbers; therefore, in a completely "income-equal" county, 10 percent of households would take in 10 percent of that county's income, 20 percent of households would take in 20 percent of income, and on up to 100 percent of households, which would account for 100 percent of income. The points in this unusual county would form a straight, diagonal line from 0,0 to 1,1 -- think of it as the "line of equality."

In reality, however, 10 percent of the overall households may account for only two percent of income; 20 percent of households only five percent of income and so forth, so that the points would form a curve below the line of equality. …