D. Theil index and General Entropy (GE) measures

The values of the GE class of measures vary between zero (perfect equality) and infinity (or one, if normalized). A key feature of these measures is that they are fully decomposable, i.e. inequality may be broken down by population groups or income sources or using other dimensions, which can prove useful to policy makers. Another key feature is that researchers can choose a parameter α that assigns a weight to distances between incomes in different parts of the income distribution. For lower values of α, the measure is more sensitive to changes in the lower tail of the distribution and, for higher values, it is more sensitive to changes that affect the upper tail. The most common values for α are 0, 1, and 2. When α=0, the index is called “Theil’s L” or the “mean log deviation” measure. When α=1, the index is called “Theil’s T” index or, more commonly, “Theil index”. When α=2, the index is called “coefficient of variation”. Similarly to the Gini coefficient, when income redistribution happens, change in the indices depends on the level of individual incomes involved in the redistribution and the population size.

 Ratios

Ratios constitute the most basic inequality measures available. They are simple, direct, easy to understand, and they offer few data and computation challenges. Accordingly, they do not provide as much information as the complex measures described above.