# How is a Lorenz Curve used in Social Research

The Lorenz curve is a graphical representation of the inequality in any particular society. Before considering the use of the curve you need to understand how the curve is generated, and some of the pitfalls with this generation.

The Lorenz curve has two linear perpendicular axes. The x-axis measures the cumulative percent of the society under consideration, starting from the poorest segment and ending with the richest segment. The y-axis represents the cumulative percent of wealth owned by that society. It is important to remember that both axes represent cumulative values.

As an example, consider a society where the poorest 10% own 0% of the total wealth, the next 10% own 3% of the total wealth, the next 10% own 7 percent of the total wealth, and so on. Under this scenario the wealthiest 10% would own far more that 10% of the total wealth of the society.

To generate the curve, plot the cumulative values. As 10% of the population (x-axis) owns no wealth, the y-axis shows a value of 0% for when the x-axis shows a value of 10%. The bottom 20% of the population owns 3% of the total wealth (0% for the first 10%, 3% for the second 10%), so for an x value of 20% you have a y value of 3%. The poorest 30% owns 10% of the wealth (0%+3%+7%) so for an x value of 30 you have a y value of 10.

You know the total population owns 100% of the wealth, so for 100 on the x axis you have 100 on the y axis. A little thought will indicate that a perfectly equal society will generate a straight line from 0 to 100 on both axes (as each 10% of the population will own 10% of the wealth), and that in practice the curve will always be concave (the poorest 10% will always own less that 10 % of the total wealth, and each successive 10% of the population will own a greater percentage).

A series of graphs comparing societies, or even the same society over time, while useful, does not provide a meaningful statistic for comparison purposes. The Gini coefficient, based on the Lorenz curve provides such a statistic. It is the ratio of the area between the Lorenz Curve and the curve generated in a perfectly equal society (straight line) to the area under the straight line curve. A perfectly equal society will therefore have a Gini coefficient of 0 (there is no area between the curves), while a perfectly unequal society (where all the wealth is owned by 1 person) would have a coefficient of 1.

One of the pitfalls with both these representations is the reliability of the statistics from varying countries, and even varying organizations within one country. As an example Wikipedia provides a listing of Gini coefficients based on statistics by differing organizations which illustrate the problems. Note also that Wikipedia also provides the Gini coefficient as a figure between 0 and 100(%), and not 1 and 1

This pitfall notwithstanding, while a single Gini or curve may be misleading, a series provided by the same source will provide a good estimation of the progress of a society over years, or even of the relative equality between societies. It is here that the social researcher can utilize the curves or coefficients to compare and contrast societies.

Sources:

World Bank discussion on poverty and inequality: http://go.worldbank.org/3SLYUTVY00

Some statistics on poverty, including cumulative figures by the World Bank: http://go.worldbank.org/JIO7WY61V0

Gini Coefficient:

GORDON MARSHALL. “Gini coefficient.” A Dictionary of Sociology. 1998. Retrieved July 28, 2011 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O88-Ginicoefficient.html

Lorenz Curve:

GORDON MARSHALL. “Lorenz curve.” A Dictionary of Sociology. 1998. Retrieved July 28, 2011 from Encyclopedia.com:http://www.encyclopedia.com/doc/1O88-Lorenzcurve.html