Chapter 4: Frontiers of Poverty Measurement
and the within-group inequality (as measured by the Gini coefficient) times the ratio of mean to median (where the ratio of mean to median is a measure of skewness of the distribution). Foster and Wolfson (1992, 2010) also propose dominance orderings based on polarization curves that can determine whether unambiguous increases in polarization have taken place. First-order polarization occurs when there are first-order stochastic dominant movements away from the median. Second-order polarization occurs when there are second-order dominant movements away from the median. The Foster-Wolfson polarization measure is related to the area below the second-order polarization curve. This approach has been extended by Zhang and Kanbur (2001) and Chakravarty and D’Ambrosio (2010). In contrast to the Foster-Wolfson approach, in which two groups of observations are endogenously defined using the median as the dividing line, Esteban and Ray (1994) assume that several groups of observations are exogenously given, each around its own pole. Their polarization measure rises when the groups pull apart from one another, or when observations within a group become more tightly clustered together. The measure is challenging to implement in practice because no clear way is given for dividing an overall distribution into relevant clusters. These and other practical problems of implementation are addressed in Duclos, Esteban, and Ray (2004).
References Alkire, S., and J. E. Foster. 2007. “Counting and Multidimensional Poverty Measurement.” Working Paper 7, Oxford Poverty and Human Development Initiative, University of Oxford. ———. 2010. “Designing the Inequality-Adjusted Human Development Index (HDI).” Working Paper 37, Oxford Poverty and Human Development Initiative, University of Oxford. ———. 2011. “Counting and Multidimensional Poverty Measurement.” Journal of Public Economics 95 (7–8): 476–87. Alkire, S., J. E. Foster, and M. E. Santos. 2011. “Where Did Identification Go?” Journal of Economic Inequality 9 (3): 501–5. Allison, R. A., and J. E. Foster. 2004. “Measuring Health Inequality Using Qualitative Data.” Journal of Health Economics 23 (3): 505–24.
241