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« October 23, 2008 | Main | October 26, 2008 »
25 October 2008
A General Inequality Parameter
There is an interesting paper by Guillermina Jasso and Samuel Kotz in Sociological methods and Research in which they analyzed the mathematical connections between two kinds of inequality: inequality between persons and inequality between subgroups. They showed that a general inequality parameter (a shape parameter c of a two-parameter continuous univariate distribution), or a deep structure of inequality, governs both types of inequality. More concretely, they demonstrated convenient measures of personal inequality like Gini coefficient, Arkinson's measure, Theil's MLD and Pearson's coefficient of variation, and measures of inequality between subgroup are nothing but functions of this general inequality parameter c. The c parameter, according to the authors, also governs the shape of Lorenz curve, a conventional graph tool to express inequality.
Given the unitary operation of this inequality parameter, the authors concluded there is a monotonic connection between personal inequality and between-group inequality, namely, as personal inequality increases, so does between-group inequality. This conclusion is kind of surprising and even contradictory to our intuition that it is very plausible, if not usual, that personal inequality can change due to within-group transfers while between-group inequality still keeps the same. The authors admitted that their conclusion hold only under certain set of conditions. For example, the derived relation between the two types of inequality assumes two-parameter distribution and non-intersecting Lorenz curves. You may consult the full article to obtain more technical details if interested.
Source:
Jasso, Guillermina and Samuel Kotz. 2008. "Two Types of Inequality: Inequality Between Persons and Inequality Between Subgroups." Sociological Methods & Research 37: 31-74.
click here to get a working paper version of that from IDEAS