Abstract
In this chapter the further development of indexes of poverty which aim to counter many of the criticisms and limitations of simpler indexes but which seek to retain their tractability, is outlined. The first section describes the development of indexes based on the income gap measure. The development of a range of indexes with varying properties lead to the search for encompassing classifications of these indexes and to theories of orderings which identified the circumstances in which classes of indexes produced consistent results. These classifications and orderings are described in the second section. The final section introduces a new index which has desirable properties yet is consistent with everyday definitions of poverty.
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The index is more precisely written as Ps = PI + (PH-P,)IG[q/(q+1)] which for large q (the number of poor) reverts to 4.2.
The derivation of equation 4.4 from equation 4.2 is shown in Appendix A4.1 of this chapter.
With some further rearrangement the Sen index can be expressed in a form similar to the poverty gap index shown in equation 4.1
Ng (1983, p4–7) and Deaton and Muellbauer (1980, p217–220) provide further explanation of utilitarian welfare functions in the context of alternatives.
However, the circumstances under which this will be true are quite restrictive. It can be seen from the version of the Sen index given in footnote 3 than Ps will be equal to equation 4.6 only when
Setting z equal to some fraction of mean income such as 0.5 (or 0.56 in the case of the Henderson poverty lines used in Australia) presents no problem for the theory presented here. Just define z* = 4•z where 4) is the fraction and use z* for z in 4.12 and following equations.
The assignation of poverty lines unique to each income unit is a major generalisation of previous poverty lines.
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© 1996 Springer-Verlag Berlin Heidelberg
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Johnson, D.T. (1996). Development of Indexes of Poverty. In: Poverty, Inequality and Social Welfare in Australia. Contributions to Economics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12729-2_4
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DOI: https://doi.org/10.1007/978-3-662-12729-2_4
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0942-8
Online ISBN: 978-3-662-12729-2
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