Index
income elasticity of poverty line, 42 four-person vector, 106 gap ratio, 164–65 individual’s, 46–47 mean and median per capita growth and, 171–72 permutation of, 55 share of the top 1 percent, 16 source decomposition of generalized entropy measure, 284–86, 284t variable, 4 vectors, 4–5, 113, 128–30, 134–35 income distributions. See also Gini coefficient base of, 26–27 cdf, 5, 50, 52–53, 52f data collection, 4–5 degenerate, 65 density function, 50–52, 51f generalized Lorenz curve and, 72–73, 73f nonpoverty censored, 106 poverty measures, 134–35 poverty measures and, 26–27 size of, 5–6 skewness of, 51–52 vector of incomes, 50, 113 income standards. See also Sen means, income standards anonymity standards, 54 applications for, 9 arithmetic means, 63 calibration property, 54 censored, 273–75, 273t comparisons of, 10–12 definition of, 6, 54 desirable properties, 54–58 dominance relation, 69–70 Euclidean means, 17, 64 general means, 66f, 143 general means as normative family of, 62–64 geometric means, 63 growth curves, 12–13, 26 harmonic means, 63 inequality and, 271–73 inequality measures and, 87 invariance properties, 54
298
linear homogeneity, 6, 54, 57 monotonicity, 55–56 normalization property, 54 partial means, 60–62, 62f population invariance property, 54, 55 poverty measures and, 32–34, 113 progressive transfer, 56 quantile function, 62f quantile incomes, 58–60, 59f regressive transfer, 56 robustness of, 10–12 Sen means, 8, 66–69 subgroup consistency property, 57–58 symmetry properties, 54–55 transfer principle property, 56–57 types of, 7–8 unanimous relation, 69–70 weak monotonicity, 54, 55–56 weak transfer principle, 54 welfare functions as, 35 independent, path, 237 inequality aversion parameter, 91 decomposition using second Theil measure, 282–84, 283t income standards and, 271–73 origins of, 19 standard of living and, 158–59, 171–72, 171t, 183–84, 184t Inequality-Adjusted Human Development Index (IA-HDI), 237 inequality-based approach, 43, 142–43 inequality measures. See also Gini coefficient; measures applications of, 18–21 Atkinson by geographic regions, 204–7, 205t Atkinson’s class of, 16–17, 91–93 between-group, 20, 21 decomposition of, 21–22 desirable properties, 81–87 dominance and unanimity, 101–3 dominance properties, 81 examples of, 15–18 generalized entropy measures, 96–100 group, 238–40 group-based, 19 growth and, 103–5