The Italian ideologist and statistician Corrado Gini (1884-1965), author of The Scientific Basis of Fascism (1927), developed in 1912 a method to measure inequality of a distribution in your work Variability and mutability. In it he introduced the value of 0 to express total equality and the value of 1 for maximum inequality.
This method is applied in the study of the distribution of inequality in Health Sciences, engineering, ecology, chemistry, transportation, etc. But perhaps where it has its most characteristic use is in the study of income inequality that is done in Economics. About him Gini coefficient and its advantages as a measure of inequality compared to other indicators, we speak today in the Concepts of Economics.
Gini coefficient calculation
The Gini coefficient is based on the Curva de Lorenz, which is a graphical representation of a cumulative distribution function, and is mathematically defined as the cumulative proportion of total income (y-axis), obtained by the cumulative proportions of the population (x-axis). The diagonal line represents the perfect equality of income: all receive the same income (20% of the population receives 20% of the income; 40% of the population 40% of the income, etc.).
In the situation of maximum equality or distributive equity, the Gini coefficient is equal to zero (area A disappears): as inequality increases, the Gini coefficient approaches the value of 1. This coefficient can be considered as the proportion between the area that is located between the line of equality and the Lorenz curve (marked “A” in the diagram) over the total area under the equality line. That is, G = A / (A + B). It is also equal to A * 2, since A + B = 0.5.
The Gini coefficient is calculated as the quotient between the area between the diagonal of perfect equality and the Curva de Lorenz (area A in the graph, over the area A + B). As equity improves, area A decreases and the Lorenz Curve (red line) approaches the 45% diagonal (green line). If the Lorenz Curve moves away from the diagonal, the inequality increases at the same rate as area “A” increases.
If the inequality is total, area B disappears and only area A remains, indicating that a single family keeps the total income (blue line). In the example of the graph, the first quintile (20% of the population) keeps 4% of the income; 40% of the population, with 12% (increases by 8% in relation to the first), 60% with 22% of income and 80% of the population with 42% of accumulated income. In this case the Gini Coefficient is 0.48.
Gini coefficient in the world
According to the 2009 Human Development Report, the Gini Coefficient for Namibia is 0.707 (situation of maximum inequality), while that of Denmark is 0.247 (situation of maximum equal distribution. According to this report, the Gini Coefficient of Brazil is 0.571; Chile 0.557; Mexico 0.546; Argentina 0.542; Venezuela 0.471; China 0.447, United States 0.445; Russia 0.391; Portugal 0.385; Italy 0.36; France 0.327; Spain 0.325; Germany 0.283; Sweden 0.25; Japan 0.249.According to the graph, the areas that have green colors (Canada, Europe and Australia) have a more equal distribution while as the colors intensify: blue, lilac, orange or red (situation of Latin America and Africa ), distribution becomes more uneven.
The Gini Coefficient measures the global distributional terms without separating what corresponds to the urban population and the rural population. This data is very valuable to consider because you cannot compare a country like China, which has 60% of the rural population, with a country like USA which has less than 10% rural population. In this sense, when the comparison is made without taking into account the other variable, we can confuse the results.
In The Salmon Blog | There are more poor people in the world, you just have to measure them, The origins of inequality