# Relationship between lorenz curve gini coefficient by country

### Lorenz curve - Wikipedia

The Lorenz curve offers an intuitively clear picture of inequality. The Gini coefficient, which is based on the curve, offers a way of measuring of Wealth," appeared in Publications of the American Statistical Association, Vol. 9, No. . and Informal Learning · What if Country Size Was Relative to Population?. Shown is the simple cross-country average of Gini coefficients—as per the estimates In fact, as Piketty and co-authors point out, in the US the relationship used to be .. The 'Lorenz curve' shows the income distribution in a population where. If the actual relationship between the two variables were to follow a path where G is the Gini coefficient; X is the area between the Lorenz curve and the of the statistics office for the country where you live to try to find Gini coefficient data.

## Ask Gini: How to Measure Inequality

Census Bureau usually reports Gini coefficients based on pretax numbers, whereas many calculations for foreign countries use posttax numbers, which often include redistribution of wealth from rich to poor and tend to lower the Gini coefficient. Comparing the pretax number in one country with the posttax number in another is somewhat meaningless. To understand what the Gini coefficient can and cannot explain, and how to interpret articles about economic inequality, a deeper look at this statistic is required.

The Gini coefficient compares the income or wealth distribution of a population to a perfectly equal distribution—in which every citizen of a city or country has equal wealth. To compute the Gini coefficient, economists first find the Lorenz curve for the population.

### Ask Gini: How to Measure Inequality - Scientific American

The curve is a graphical representation of the distribution of income or wealth in a society. The x-axis is the proportion of the population, from lowest to highest income, and the y-axis is the cumulative percentage of income or wealth owned. So the point 0. The Gini coefficient measures how far the actual Lorenz curve for a society's income or wealth is from the line of equality. Both the Lorenz curve and the line of equality are plotted on a graph. Then the area between the two graphs is computed.

The Gini coefficient is the area between the two graphs divided by the total area under the line of inequality. In the picture at the top right of this article, it is the area of the region labeled A divided by the combined areas for A and B. This yields a number between 0 and 1, sometimes reported as a percentage—for example, 0.

Enter a set of incomes to find out what the Gini coefficient of the group is and what the distribution looks like. Cowell says that the Gini coefficient is useful, particularly because it allows negative values for income and wealth, unlike some other measures of inequality.

If some amount of the population has negative wealth owes moneythe Lorenz curve will dip below the x-axis. But the Gini coefficient also has limitations. For one, it takes all the data from the Lorenz curve and converts it to a single number. Two different income distributions can have the same Gini coefficient, and a lot of information is lost in the conversion to a graph.

Cowell asks, "Why not just look at the Lorenz curve?

### CONVERSABLE ECONOMIST: Lorenz curves and Gini coefficients: CBO #3.

It samples people at random points of their lives, which means that it can't separate those whose financial futures are reasonably secure from those who do not have prospects. Its results are also sensitive to outliers—a few very wealthy or very poor individuals can change the statistic significantly, even in a large sample.

Cowell says that the Gini coefficient should not be used as the sole measure of economic inequality. He suggests two ways to handle the number: The other is to consider whether it might be useful to use a model of the upper tail of the distribution, so you get a clearer picture. To mitigate this problem, Cowell studies better ways to model income and wealth distribution in the most well-off.

• Lorenz curve
• Macroeconomics

One option is to "patch in" an assumed distribution specifically a Pareto distribution for the top 5 or 10 percent of the population.

In effect, this means assuming that the distribution of wealth takes a certain form, and using that model, rather than sparse data, to calculate the Gini coefficient.

The study of income and wealth inequality are of course fertile ground for many questions and controversies. At the other extreme, if the highest income group earned all the income, the Lorenz curve would be flat across the vast majority of the income range,following the bottom edge of the figure, and then jump to the top of the figure at the very right-hand edge.

Lorenz curves for actual income distributions fall between those two hypothetical extremes. Typically, they intersect the diagonal line only at the very first and last points. Between those points, the curves are bow-shaped below the degree line. The Lorenz curve of market income falls to the right and below the curve for after-tax income, reflecting its greater inequality.

Both curves fall to the right and below the line of equality, reflecting the inequality in both market income and after-tax income. The intuition is straightforward although the mathematical formula will look a little messier. On a Lorenz curve, greater equality means that the line based on actual data is closer to the degree line that shows a perfectly equal distribution.

Greater inequality means that the line based on actual data will be more "bowed" away from the degree line.

The Gini coefficient is based on the area between the degree line and the actual data line. As the CBO writes: Once again, the extreme cases of complete equality and complete inequality bound the measure.