Measuring inequality: Using the Lorenz Curve and Gini Coefficient
Almost thirty years ago, the author of this brief attended a lecture addressing the economics of inequality. At the start, the class was invited to imagine the implications of individual wealth being reflected in our personal height. Assume that by government decree, everyone has to march past a fixed point over the period of one hour, starting with the smallest people and ending with the largest. The parade would begin with all the people who owed money. They would march underground. Even after 20 minutes, marchers would be invisible since they had no wealth.
At the half way point, the parade would comprise of dwarves, little more than a few centimetres in height. Only 12 minutes before the end of the parade would people start to be of an average height and hence, of average wealth. In the last few minutes of the parade, marchers would evolve rapidly into giants, assuming heights of several metres. The heads of the last few participants would be invisible since their height would be measured in kilometres rather than metres.
The moral, of what seems to be a trivial example, is that despite increases in living standards, wealth is not distributed evenly through society. The vast majority is owned by the very few.
The degree to which the inequality depicted in the parade of dwarves and giants is undesirable is a normative issue. Commentators concerned with poverty levels in society will argue that one of the major roles of government should involve some degree of re-distribution. If a government is to play a role in such a process, then it needs to be informed about the distribution of wealth (which is a stock and can include a range of assets that include shares, land, houses as well as money) and the distribution of national income (which is a flow since it is paid per week, month, year etc).
The terms wealth and income should not be used interchangeably. The distribution of the stock of wealth will be much more unequal than the flow of income in a given year. As we have already seen in the case of the parade of dwarves and giants, many people have substantial negative wealth. Furthermore, studies based on wealth are a lot less common since it is harder to measure wealth than it is income.
The aim of this case study is to introduce readers to two interlinked methods of measuring inequality: the Lorenz Curve and the Gini Coefficient. Both originate from the early years of the twentieth century: in 1905, Max Otto Lorenz published a paper in an American statistical journal outlining the technique which was to bear his name. Corrado Gini’s index of income inequality was published shortly afterwards in 1914. However, it was the work on poverty and income inequality by Sir Tony Atkinson during the 1970s that led to the popular dissemination and development of the original work of Lorenz and Gini.
2. The Lorenz Curve
Let us assume that we wish to construct a Lorenz Curve to measure wealth inequality. The standard framework can be built up in four stages. First, we draw a set of axes in which the cumulative percentage of wealth is measured along the y-axis while the cumulative percentage of households is measured along the x-axis. Usually, the graph’s axes are closed off to form a box.
The second stage requires us to order the distribution from the smallest through to the largest, thereby enabling us to answer the following sequential questions: (a) what proportion of wealth is owned by the poorest 10 percent of the population? (b) what proportion of wealth is owned by the poorest 20 percent of the population? (c) what proportion of wealth is owned by the poorest 30 percent of the population?
This process continues until we reach the point where 100 per cent of wealth is owned by 100 per cent of the population. The third step is to assume that we live in a truly equal society. If this were to be the case,...
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