J-divergence measurements of economic inequality

摘要

Income inequality among individuals has many implications on socio-economic problems and thus it is important for economists to understand the dynamics behind the wealth distribution in the society. There are many indices proposed to indicate economic inequality and are based on strong axiomatic foundations. They are capable of analyzing within and between group inequalities. Another measure is the distance between two distributions, one the egalitarian distribution which is the reference distribution and the other that has been derived from the income data. The degree of divergence between these two distributions can be taken as a measure of economic inequality. There are many statistical indices that can quantify these differences and it will be useful to examine their merits and demerits as indices. This paper used the statistical classification known as J-divergence that belong to the entropy class of measures. The J-divergence can be considered as the average of n generalized distances from the mean. This allows one way of decomposition in to different subgroups within the population so that in can highlight the subgroups that are in the extremes of the income distribution. This will provide the reasons for the inequality in the income that is present among individuals. This approach was considered in 1950s but did not gain ground due to the reason that they are not transfer consistent. However if it is combined with a well-functioning measure, it may be useful in providing meaningful insights in to the income distribution. This study establishes the properties of the J-divergence and uses its decomposition properties to examine the income inequality in the USA, Germany and Britain. (55 refs.)