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The formula for general entropy for real values of is: = {() = [(¯)],,, = ¯ ¯, =, = ¯, = where N is the number of cases (e.g., households or families), is the income for case i and is a parameter which regulates the weight given to distances between incomes at different parts of the income distribution.
Income inequality and income mobility trends have been different for men and women workers between 1937 and the 2000s. When men and women are considered together, the Gini coefficient-based Shorrocks index trends imply long-term income inequality has been substantially reduced among all workers, in recent decades for the United States. [67]
The MLD of household income has been defined as [1] = = ¯ where N is the number of households, is the income of household i, and ¯ is the mean of .Naturally the same formula can be used for positive variables other than income and for units of observation other than households.
The inequality income metric should be independent of the aggregate level of income. This may be stated as: = where α is a positive real number. Population independence Similarly, the income inequality metric should not depend on whether an economy has a large or small population.
Income inequality is a discussion that’s been surfacing off and on for years now, but thanks to presidential politics, it’s once again in the headlines.
The most commonly used index from the family, FGT 2, puts higher weight on the poverty of the poorest individuals, making it a combined measure of poverty and income inequality and a popular choice within development economics. The indices were introduced in a 1984 paper by economists Erik Thorbecke, Joel Greer, and James Foster. [1] [2]
The growth in income was much higher for families at the top end than for middle and lower earners. In other words, the rich have gotten richer much faster than everyone else.
The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and is the mean income.. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean).