LORENZ CURVE

Sociologyindex, Sociology Books 2009, Lorenz Curve, Gini Coefficent

Lorenz Curve was developed by Max O. Lorenz in order to describe the extent of inequality in a society.

Imagine a graph in which the cummulated income (expressed as a percentage) is placed on the vertical axis and the cumulated number of households (expressed as a percentage) is placed on the horizontal axis.

If there was perfect equality (so that the first 10 per cent of the households received 10% of the income and 20% of the households received 20% of the income, etc.) a diagonal line would be drawn across the graph.

When actual income distributions are depicted on this graph the line ( a 'Lorenz' curve) departs from the line of perfect equality.

For example, the bottom 20 per cent of households may receive only 4.5% of the total income. This line is the Lorenz curve and can be expressed mathematically.

The Gini coefficient is an expression of the ratio of the amount of the graph located between the line of perfect inequality and the Lorenz curve to the total area of the graph below the line of equality.

The Lorenz curve is a graphical representation of the proportionality of a distribution (the cumulative percentage of the values). To build the Lorenz curve, all the elements of a distribution must be ordered from the most important to the least important. Then, each element is plotted according to their cumulative percentage of X and Y, X being the cumulative percentage of elements. For instance, out of a distribution of 10 elements (N), the first element would represent 10% of X and whatever percentage of Y it represents (this percentage must be the highest in the distribution). The second element would cumulatively represent 20% of X (its 10% plus the 10% of the first element) and its percentage of Y plus the percentage of Y of the first element.

The Lorenz curve is compared with the perfect equality line, which is a linear relationships that plots a distribution where each element has an equal value in its shares of X and Y. For instance, in a distribution of 10 elements, if there is perfect equality, the 5th element would have a cumulative percentage of 50% for X and Y. The perfect equality line forms an angle of 45 degrees with a slope of 100/N. The perfect inequality line represents a distribution where one element has the total cumulative percentage of Y while the others have none.
The Gini coefficient is defined graphically as a ratio of two surfaces involving the summation of all vertical deviations between the Lorenz curve and the perfect equality line (A) divided by the difference between the perfect equality and perfect inequality lines (A+B).

Lorenz curve provides a fuller grasp of how the coefficient is determined.

Gini coefficent was developed by Italian statistician Corrodo Gini to provide a mathematical expression of the degree of concentration of wealth or income. For measurements of income inequality at a given point in time, the most widely-used measure is the Gini coefficient. 

Gini coefficent has been criticized over the years, but Gini coefficent continues to be used by social scientists describing inequality or comparing inequality among nations. Gini coefficient is superior for comparative analysis. But different researchers can and do obtain different values of the Gini coefficient for the same country.

In a completely equal society, the Gini coefficient is zero, no inequality, and in a society in which one person has all the income it is 100. So the higher the value, the more unequal the society. A Gini coefficent of approximately 0.400 is normal for most developed economies.

As with many concepts in the social sciences, translating it into practice is not straightforward. The economy and society are not physical systems which we can put on a pair of scales and measure exactly. We have to rely on estimates. The result is that different researchers can and do obtain different values of the Gini coefficient for the same country. 
But however measured, its value in Britain and America is now higher than it was 20 years ago. Deininger and Squire reported for the World Bank in 1996 some 693 calculations of Gini coefficients since the war in different countries around the world. For most of the postwar period, the US Gini coefficient was in the low to mid-30s; it now seems to be in the low to mid-40s. Britain is more egalitarian, with a Gini in the mid-20s for many years, now in the low to mid-30s. 
But the degree of inequality in the Anglo-Saxon societies must be placed in global context. Taking the world as a whole, the 1996 World Bank study found a minimum value of 18 and a maximum of 63, and offered the following generalisation: “Income inequality is much greater in Latin America and sub-Saharan Africa, which have Gini coefficients in the upper 40s, than in east and south Asia, which have Gini coefficients in the middle-to-upper 30s. The OECD countries, in general, have relatively egalitarian distributions of income, with Gini coefficients around 30, while the eastern European countries have historically had very low Gini coefficients.” 
The recent experience of inequality in countries such as South Korea and China mirror the evolution of global inequality over the past two centuries. In the 1950s, Korea was a poor but very egalitarian society. During its phase of phenomenal growth, inequalities opened up and its Gini coefficient approached 40. Now that Korean income is close to the average income levels of the west, prosperity is being more widely shared, and the Gini has dropped back to the low 30s.