Gini coefficient

In economics, the Gini coefficient ( JEE-nee), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality within a nation or a social group. It was developed by Italian statistician and sociologist Corrado Gini. The Gini coefficient measures the inequality among the values of a frequency distribution, such as income levels. A Gini coefficient of 0 reflects perfect equality, where all income or wealth values are the same. In contrast, a Gini coefficient of 1 (or 100%) reflects maximal inequality among values, where a single individual has all of the income while all others have none. Corrado Gini proposed the Gini coefficient as a measure of inequality of income or wealth. For OECD countries in the late 20th century, considering the effect of taxes and transfer payments, the income Gini coefficient ranged between 0.24 and 0.49, with Slovakia being the lowest and Mexico the highest. African countries had the highest pre-tax Gini coefficients in 2008–2009, with South Africa having the world's highest, estimated to be 0.63 to 0.7. However, this figure drops to 0.52 after social assistance is taken into account and drops again to 0.47 after taxation. Slovakia has the lowest Gini coefficient, with a Gini coefficient of 0.232. Various sources have estimated the Gini coefficient of the global income in 2005 to be between 0.61 and 0.68. There are multiple issues in interpreting a Gini coefficient, as the same value may result from many different distribution curves. The demographic structure should be taken into account to mitigate this. Countries with an aging population or those with an increased birth rate experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Over a dozen variants of the Gini coefficient exist, devised by various scholars.

History The Italian statistician Corrado Gini developed the Gini coefficient and published it in his 1912 paper Variabilità e mutabilità (English: variability and mutability). Building on the work of economist Max Lorenz, Gini proposed using the difference between the hypothetical straight line depicting perfect equality and the actual line depicting people's incomes as a measure of inequality. In this paper, he introduced the concept of simple mean difference as a measure of variability. He then applied the simple mean difference of observed variables to income and wealth inequality in his work On the measurement of concentration and variability of characters in 1914. Here, he presented the concentration ratio, which further developed into today's Gini coefficient. Secondly, Gini observed that improving methods introduced by Lorenz, Chatelain, or Séailles could also achieve his proposed ratio. In 1915, Gaetano Pietra introduced a geometrical interpretation between Gini's proposed ratio and between the observed area of concentration and maximum concentration. This altered version of the Gini coefficient became the most commonly used inequality index in upcoming years. According to data from the OECD, the Gini coefficient was first officially used country-wide in Canada in the 1970s. Canadian index of income inequality ranged from 0.303 to 0.284 from 1976 to the end of the 1980s. The OECD has published more data on countries since the start of the 21st century. The Central European countries of Slovenia, Czechia, and Slovakia have had the lowest inequality index of all OECD countries ever since the 2000s. Scandinavian countries also frequently appeared at the top of the equality list in recent decades.

Definition

The Gini coefficient is an index for the degree of inequality in the distribution of income/wealth, used to estimate how far a country's wealth or income distribution deviates from an equal distribution. The Gini coefficient is usually defined mathematically based on the Lorenz curve, which plots the proportion of the total income of the population (y-axis) that is cumulatively earned by the bottom x of the population (see diagram). The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked A in the diagram) over the total area under the line of equality (marked A and B in the diagram); i.e., G = A/(A + B). If there are no negative incomes, it is also equal to 2A and 1 − 2B due to the fact that A + B = 0.5. Assuming non-negative income or wealth for all, the Gini coefficient's theoretical range is from 0 (total equality) to 1 (absolute inequality). This measure is often rendered as a percentage, spanning 0 to 100. However, if negative values are factored in, as in cases of debt, the Gini index could exceed 1. Typically, we presuppose a positive mean or total, precluding a Gini coefficient below zero. An alternative approach is to define the Gini coefficient as half of the relative mean absolute difference, which is equivalent to the definition based on the Lorenz curve. The mean absolute difference is the average absolute difference of all pairs of items of the population, and the relative mean absolute difference is the mean absolute difference divided by the average, x ¯ {\displaystyle {\bar {x}}} , to normalize for scale. If xi is the wealth or income of person i, and there are n persons, then the Gini coefficient G is given by:

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