unequal than the inequality in a system to which the "80:20 Pareto principle" applies1. The Theil index can. 1 A Theil index of 0.5 characterizes systems which ...
SOME INCOME INEQUALITY INDEXES 20/20 Ratio The 20/20 ratio compares how much richer the top 20% of populations are to the bottom 20% of a given population. This can be more revealing of the actual impact of inequality in a population, as it reduces the effect of outliers. The measure is used for the United Nations Development Programme Human Development Indicators. Some believe that the 20/20 ratio is a more useful measure as it correlates well with measures of human development and social stability (including the index of child well-being, index of health and social problems, population in prison, physical health, mental health).
Palma ratio It is defined as the ratio of the richest 10% of the population's share of gross national income divided by the poorest 40%'s share. It is based on the work of the Chilean economist Gabriel Palma who found that middle class incomes almost always represent about half of gross national income while the other half is split between the richest 10% and poorest 40%, but the share of those two groups varies considerably across countries.
Hoover index This index is
where N are the quantiles with different widths A, Ei is the income in the quantile i, Ai is the number of earners in the quantile i, Etotal is the sum of income of all N quantiles, Atotal is the sum of earners of all N quantiles. The Hoover index is the proportion of income which would have to be redistributed to achieve a state of perfect equality. In a perfectly equal world, no resources would need to be redistributed to achieve equal distribution (a Hoover index of 0). It ranges between 0 and 1.
Theil index This index is
where is the mean of , and N is the number of individuals. If everyone has the same income, then TT gives 0. If one person has all the income, then TT gives the result ln(N), which is maximum order. Dividing TT by ln(N) can normalize the equation to range from 0 to 1. A Theil index of 0 indicates perfect equality. A Theil index of 1 indicates that the distributional entropy of the system under investigation is almost similar to a system with an 82:18 distribution. This is slightly more unequal than the inequality in a system to which the "80:20 Pareto principle" applies1. The Theil index can 1
A Theil index of 0.5 characterizes systems which are close to a 74:26 distribution. A 92:8 distribution would yield a Theil index of 2 and 98:2 would yield 4. For an 80:20 distribution (Pareto principle) the Theil index is 0.83. For 73:27 the Theil index and the Hoover index are identical: Both are 0.46. For 62:38 the difference between the Theil index (representing stochastic distribution) and the Hoover index (representing a perfectly planned distribution) reaches a minimum of -0.12.
be transformed into an Atkinson index, which has a range between 0 and 1, where 0 indicates perfect equality and 1 indicates maximum inequality. The Theil index is an entropy measure. As for any resource distribution and with reference to information theory, "maximum entropy" occurs once income earners cannot be distinguished by their resources, i.e. when there is perfect equality. In real societies people can be distinguished by their different resources, with the resources being incomes. The more "distinguishable" they are, the lower is the "actual entropy" of a system consisting of income and income earners. Also based on information theory, the gap between these two entropies can be called "redundancy".
