There are several ways to measure inequalities, from straightforward to more complex strategies, including graphical and mathematical ones. All of them may be utilized to give a thorough picture of the income concentration, to compare and order various income distributions, and to analyze the effects of different policy alternatives. A function that assigns a value to a particular income distribution to facilitate direct and accurate comparisons between distributions is known as an inequality measure. One can use several ways to measure inequalities, including the standard deviation, coefficient of variation, relative mean deviation, and Gini coefficient. Theil’s Index of Entropy, Atkinson’s Measure, and other less popular metrics are also utilized. The note discusses the Lorentz curve and Ginni Index as a measure of inequality.
Lorentz Curve #
Max O. Lorentz, for whom the curve is called, was the first to employ it as a graph showing the distribution of wealth. The Lorentz curve represents observed income distributions by showing the proportion of households on the x-axis and the percentage of incomes on the y-axis. It contrasts this with a state of complete income equality. To achieve this, it compares the cumulative proportion of total income received to the cumulative percentage of persons or households getting incomes, starting with the lowest-income individual or family and working its way up. The Lorentz curve is now widely used to represent social inequality and is not just associated with income inequality measurement.
Since the Lorentz curve compares total income to total people, the first step involves ranking people or families by wealth. Following this step, all of these people or families are classified into either five quintiles of 20% each or ten quintiles of 10% each, depending on the level of income inequality sought from the graph. After categorizing individuals and households, the aggregate share of all five quintiles is plotted against the cumulative percentage of individuals and households receiving income. This process is repeated until the aggregate share of all five quintiles is plotted against the cumulative percentage of individuals and households receiving income (see Figure).
In a scenario of complete economic parity, the Lorentz curve would be a straight diagonal line, also known as the line of equality, indicating that the poorest 20% of persons or families get 20% of the income. A fully unequal distribution would be one in which one person receives all the income and everyone else has zero. In contrast, if there is any discrepancy in size, the Lorentz curve will fall below the line of equality.
The Gini Coefficient #
A measure of inequality, the Gini coefficient2 (or “G”), is derived from the Lorentz curve and is written as a percentage. Calculates the fraction of space lying between the line of mathematical equality and the Lorentz curve. If we suppose that the area between the perfectly equal line and the Lorentz curve is x and the area under the Lorentz curve is y, then the Gini coefficient for the distribution represented by the Lorentz curve is
x/(x+y)
It can be anything from 0 to 1, inclusive. When the Gini index is 0, everyone is on equal footing. The Lorentz curve is parallel to the straight line when there is complete equality. Everyone is unequal when the Gini index is one, and the Lorentz curve is parallel to the x-axis.
Regardless of the sizes of the two populations, the coefficient enables a direct comparison of the income distribution between them. The Gini’s biggest drawback is that it is difficult to break down or add to. Additionally, it reacts differently to income transfers between individuals at the opposing tails of the income distribution than it does to transfers in the center. Furthermore, the same Gini coefficient might appear in widely distinct income distributions.
Other popular measures of inequality #
The other most often used welfare-based measure of inequality is Atkinson’s inequality measure, also known as Atkinson’s index. It displays the proportion of total revenue that a society would have to sacrifice to achieve more equitable income distribution among its members.
Measures of General Entropy (GE) and the Theil index are also used for measuring inequality. The GE class of measures has values ranging from zero to infinity. These metrics may be fully decomposed—that is, demographic groupings can break them down, providing vital information.
