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Social Choice and Welfare

Erschienen in:

01.10.2013 | Original Paper

On intertemporal poverty measures: the role of affluence and want

verfasst von: Indranil Dutta, Laurence Roope, Horst Zank

Erschienen in: Social Choice and Welfare | Ausgabe 4/2013

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Abstract

This paper proposes classes of intertemporal poverty measures which take into account both the debilitating impact of prolonged spells in poverty and the mitigating effect of periods of affluence on subsequent poverty. The weight assigned to the level of poverty in each time period depends on the length of the preceding spell of poverty or of non-poverty. The proposed classes of intertemporal poverty measures are quite general and allow for a range of possible judgements as to the overall impact on a poor period of preceding spells of poverty or affluence. We discuss the properties of the proposed classes of measures and axiomatically characterize these measures.

Vorheriger Artikel Vulnerability to individual and aggregate poverty

Nächster Artikel On the generalization and decomposition of the Bonferroni index

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See also Cruces (2005), Calvo and Dercon (2009), Grab and Grimm (2007), Carter and Ikegami (2007), Porter and Quinn (2008), Foster and Santos (2012) and Gradín et al. (2012).

Hoy and Zheng (2011) would rank these cases differently. However, the motivation for doing so is very different from that here. They explicitly consider poverty early in life to be more damaging than poverty later on. We have no such assumption here.

Zheng (2011) proposes several classes of measures. Here, and for the rest of the paper, we are concerned mainly with his Newtonian poverty measure (p. 10).

Our notion of income smoothing is based on (Morduch (1995), p. 104) where households can smooth income by “making conservative production and employment choices and diversifying economic activities.”

Note that here, and throughout the paper, we are referring to Foster (2009)’s total intertemporal poverty measure, not his chronic poverty measure. Foster (2009) defines a poverty duration cut-off line as the minimum proportion of time periods a person must be poor in order to be deemed chronically poor; individuals who are in poverty for a proportion of periods less than this threshold are considered transiently poor. Foster (2009)’s total intertemporal poverty measure is obtained by choosing a poverty duration cut-off line of zero.

Net income can be thought of as consumption, but then our interpretation of the measure has to change in line with this. If we assume consumption as our primitive, then the mitigating impact of affluent periods reflects non-consumption smoothing mechanisms since presumably any consumption smoothing is already reflected in the consumption vector.

For example, \(p_{t}\) could be any static poverty measure from the literature, such as a normalized poverty gap. In fact, with some minor amendments, our results will go through for a more general definition, where \(p_{t}\in \mathbb R _{+}.\)

If both \(\alpha =0\) and \(\beta =0\), provided \(p_{t}\) is a normalized poverty gap, the measure reduces to the simple average of static poverty measures advocated by Foster (2009).

The approach of effectively censoring the income in each time period at the poverty line is common in the literature on intertemporal poverty measurement and is also adopted by Bossert et al. (2012) and Mendola et al. (2011), among others. However, this leads to a discontinuity in the measure at the poverty line. For a continuous measure see Hoy and Zheng (2011).

See Dutta et al. (2011) for a more general stucture for poverty mitigation.

Note that explictly incorporating the non-income dimensions is not feasible in this context, since all we observe is the ex-post income distribution for the individual across time.

A natural counter-argument of course is that the proportion of poverty which is mitigated remains the same, regardless of the poverty level. This possible criticism is somewhat reminiscent of the charge often made against relative inequality measures, which register no change in inequality when all incomes are increased by the same proportion. Those who regard absolute differences in income to be important with respect to inequality would reject such measures.

Note that the summation in \(P_{A}\) is over only those periods where \( p_{t}\ne 0\). This is a technical requirement since in our paper \(n_{t}\) (the number of immediately preceding affluent periods) is not defined when \( p_{t}=0\).

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Titel: On intertemporal poverty measures: the role of affluence and want
verfasst von: Indranil Dutta
Laurence Roope
Horst Zank
Publikationsdatum: 01.10.2013
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 4/2013
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-012-0709-8

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