Chapter 1: Introduction
discuss several other poverty measures that share this structure but use different income standards in constructing the gap standard. Common Examples The first general form of poverty measures uses an income standard applied to the censored distribution. An income standard that puts progressively greater weight on lower incomes will yield a poverty measure that is sensitive to the distribution of income among the poor. The Sen-Shorrocks-Thon (SST) index is given by (b â&#x2C6;&#x2019; a)/b, where a is the Sen mean applied to x*and b is the poverty line. This measure inherits its characteristics from the Sen mean: it satisfies all six basic properties and monotonicity and the transfer property. Increments and progressive transfers among the poor are reflected in a strictly higher poor income standard a, and hence a lower poverty level. The next measure is based on another income standard that emphasizes lower incomes. The Watts index is defined as ln(b/a), where a is the geometric mean applied to the censored distribution and b is the poverty line z. It likewise satisfies the six basic axioms and the strict forms of monotonicity and the transfer principle. Additionally, the geometric mean has the property that a given-sized transfer among the poor has a greater effect at lower income levels, so the poverty measure satisfies transfer sensitivity. The Watts index can be expanded to an entire class of measures, each of which uses a general mean to evaluate the censored distribution. The Clark-Hemming-Ulph-Chakravarty (CHUC) family of indices compares the poor income standard a = ma (x*) for a â&#x2030;¤ 1 and the poverty line b = z. There are two forms of the measure: the original form (b â&#x2C6;&#x2019; a)/b and a decomposable form obtained by a simple transformation. The measure becomes the poverty gap at a = 1 and the Watts index (or a transformation) at a = 0. The properties of the general means ensure that the CHUC measures satisfy all six basic properties for poverty measures, for monotonicity, and for a < 1 the transfer principle as well as transfer sensitivity. The second general form of poverty measures uses an income standard applied to the gap distribution. The key family of measures has a traditional decomposable version and an alternative version that is only subgroup consistent. The FGT family of decomposable poverty indices was defined above as the mean of the a-gap distribution and includes the headcount ratio for
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