LAC Equity Lab: Income Inequality - Income Distribution

This dashboard shows the distribution of income at a country and regional level for different years. The horizontal axis denotes the percentage of the population, while the vertical axis shows the share of income. The colored bars show the share of income that each centile (portion) of the population earns, while the black dashed curve measures the accumulated share of income earned.

Gini coefficient: The most common measure of inequality is the Gini coefficient. It is based on the Lorenz curve, a cumulative frequency curve that compares the distribution of a specific variable (for example, income) with the uniform distribution that represents equality. To construct the Gini coefficient, graph the cumulative percentage of households (from poor to rich) on the horizontal axis and the cumulative percentage of income (or expenditure) on the vertical axis. The Gini captures the area between this curve and a completely equal distribution. If there is no difference between these two, the Gini coefficient becomes 0, equivalent to perfect equality, while if they are very far apart, the Gini coefficient becomes 1, which corresponds to complete inequality.

Decile Dispersion Ratio: A simple and popular measure of inequality is the decile dispersion ratio, which presents the ratio of the average income or consumption of the richest 10 percent (for instance, the 90th percentile) by that of the poorest 10 percent (the 10th percentile). This ratio is readily interpretable by expressing the income of the rich as multiples of that of the poor. However, it ignores information about incomes in the middle of the income distribution and doesn’t use information about the distribution of income within the top and bottom deciles or percentiles.

Generalized Entropy Measures: Among the most widely used are the Theil indexes and the mean log deviation measure. Both belong to the family of generalized entropy (GE) inequality measures. The values of GE measures vary between zero and infinity, with zero representing an equal distribution and higher values representing higher levels of inequality. The parameter α in the class represents the weight given to distances between incomes at different parts of the income distribution, and can take any real value. For GE(0), GE is more sensitive to changes in the lower tail of the distribution, and for higher values like GE(2), the measure is more sensitive to changes that affect the upper tail. The most common are GE(0), GE(1) and GE(2). GE(1) is Theil’s index.

Atkinson's Inequality Measures: Atkinson (1970) has proposed another class of inequality measures that are used from time to time. This class also has a weighting parameter ε that measures aversion to inequality. As ε rises, the index becomes more sensitive to transfers at the lower end of the distribution and less sensitive to transfers at the top. In the limit case, ε→ 0, the index reflects the Function of Rawls which only takes into account transfers to the very lowest income group; at the other extreme, when ε=0, we obtain the linear utility function. This ranks distributions solely according to total income.