Chapter 2: Income Standards, Inequality, and Poverty
15. Previously, Sen (1976b) proposed the index PS(x; z) = PH[PIG + (1 − PIG)IGini(xq)], where xq is the income distribution of the poor only. This measure was modified later by Thon (1979) and Shorrocks (1995). 16. For a more elaborated discussion on various formulations of the SST index, see Xu and Osberg (2003). 17. Rawls’s welfare function maximizes the welfare of society’s worse-off member. “Social and economic inequalities are to be arranged ... to the greatest benefit of the least advantaged...” (Rawls 1971, 302). 18. For an in-depth discussion on poverty ordering, see Atkinson (1987), Foster and Shorrocks (1988), and Ravallion (1994). 19. Note that the poverty deficit curve and the generalized Lorenz curve have an interesting relationship. They are based on the area underneath the cdf and the quantile function, where a quantile function is an inverse of a cdf. See figure 2.7. 20. For various approaches to measuring pro-poor growth for a fixed poverty line, see Kakwani and Son (2008). 21. For a discussion on the poverty-growth-inequality triangle, see Bourguignon (2003). 22. The growth-redistribution decomposition becomes a bit more complicated when there is interregional migration. For such decomposition with change in population, see Huppi and Ravallion (1991). An application of their method can be found in table 30 of chapter 3.
References Atkinson, A. B. 1970. “On the Measurement of Inequality.” Journal of Economic Theory 2 (1970): 244–63. ———. 1987. “On the Measurement of Poverty.” Econometrica 55 (4): 749–64. Atkinson, A. B., and J. Micklewright. 1983. “On the Reliability of Income Data in the Family Expenditure Survey 1970–1977.” Journal of the Royal Statistical Society, Series A (146): 33–61. Bourguignon, F. 2003. “The Growth Elasticity of Poverty Reduction: Explaining Heterogeneity across Countries and Time Periods.” In Inequality and Growth: Theory and Policy Implications, edited by T. Eicher and S. Turnovsky, 3–26. Cambridge, MA: Massachusetts Institute of Technology. Chakravarty, S. R. 1983. “A New Index of Poverty.” Mathematical Social Sciences 6: 307–13.
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