Chapter 3: How to Interpret ADePT Results
The solid line represents the Lorenz curve for 2003, while the dotted line corresponds to 2006. It is evident that the dotted curve lies nowhere to the left of the solid curve. This implies that the inequality in urban Georgia unambiguously increased in 2006 compared with 2003. If these two curves had crossed, then the reported inequality measures would not have necessarily agreed with each other. Standardized General Mean Curve Dominance in terms of the Lorenz curves is not very common. Therefore, for inequality comparisons, we need to rely on various measures we covered earlier. We reported the Atkinson measures and generalized entropy measures in addition to the Gini coefficient. The Gini coefficient is not subgroup consistent, which means that if inequality in one region increases but remains the same in another region, the overall inequality may fall. We also showed in chapter 2 that each generalized entropy for a < 1 is a monotonic transformation of the Atkinson inequality measures, and for a ≠ 1 it is a monotonic transformation of the general means. However, we report the Atkinson measures and the generalized entropy measures for only certain values of parameter a. This exercise should be understood as a dominance analysis of the Atkinson measures and the generalized entropy measures. Figure 3.8 graphs the standardized general mean curve of Georgia’s per capita expenditure for 2003 and 2006. The vertical axis reports the standardized general mean of per capita expenditure, where standardization is done by dividing the general mean of per capita expenditures by their mean. The horizontal axis reports parameter a, which is the degree of generalized mean and also known as the degree of a society’s aversion toward inequality. The general mean of a distribution tends toward the maximum and the minimum per capita expenditure in the distribution when a tends to ∞ and – ∞, respectively. Given that the largest per capita expenditure in any distribution is usually several times larger than the mean per capita expenditure, allowing a to be very large prevents meaningful analysis. Therefore, we restrict a to between – 5 and 5, which we consider large enough. The height of a standardized general mean curve for a particular value of parameter a is the general mean per capita expenditure divided by the mean per capita expenditure. The height of any standardized general mean curve is 1 at a = 1.
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