An Impossibility Theorem on Poverty Indices

Kundu, Amitabh; Smith, Tony

doi:10.2307/2648756

Cited by 76 publications

(32 citation statements)

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“…This is a weakened version (see Subramanian 2002 andHassoun andSubramanian 2011) of a similar axiom, with the same name, proposed by Kundu and Smith (1983).…”

Section: Focus and The Possibility Of Coherent Aggregationmentioning

confidence: 81%

The Focus Axiom and Poverty: On the Co-Existence of Precise Language and Ambiguous Meaning in Economic Measurement

Subramanian¹

2011

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Despite the formal rigour that attends social and economic measurement, the substantive meaning of particular measures could be compromised in the absence of a clear and coherent conceptualization of the phenomenon being measured. A case in point is afforded by the status of a 'focus axiom' in the measurement of poverty. 'Focus' requires that a measure of poverty ought to be sensitive only to changes in the income-distribution of the poor population of any society. In practice, most poverty indices advanced in the literature satisfy an 'income-focus' but not a 'populationfocus' axiom. This, it is argued in the present paper, makes for an incoherent underlying conception of poverty. The paper provides examples of poverty measures which either satisfy both income and population focus or violate both, or which effectively do not recognize a clear dichotomization of a population into its poor and non-poor components, and suggests that such measures possess a virtue of consistency, and coherent meaning, lacking in most extant measures of poverty available in the literature. Terms of use: Documents inPaper submitted to the special issue The Measurement of Inequality and Well-Being: New Perspectives JEL B40, D31, D63, I32, O15

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“…This is a weakened version (see Subramanian 2002 andHassoun andSubramanian 2011) of a similar axiom, with the same name, proposed by Kundu and Smith (1983).…”

Section: Focus and The Possibility Of Coherent Aggregationmentioning

confidence: 81%

The Focus Axiom and Poverty: On the Co-Existence of Precise Language and Ambiguous Meaning in Economic Measurement

Subramanian¹

2011

SSRN Journal

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“…In moving from x to y, it is hard to see how the addition of one non-poor person to the population makes a difference to one's perception of poverty; however, in moving from x to u, the potential for relieving poverty through redistribution increases so considerably through an expansion in the size of the non-poor population that it is not immediately unreasonable to pronounce x to be poverty-wise worse than u. This also is the view that would be upheld by Kundu and Smith's (1983) Nonpoverty Growth Axiom; further, a monotonic and replication invariant poverty index would also support the notion that x displays more poverty than y. The population focus axiom is less persuasive when we consider the transition from x to u than when we consider the transition from x to y.…”

Section: Appendix Focus: Pro or Con?mentioning

confidence: 85%

“…It may be mentioned here that Axiom PF is diametrically opposed in spirit to what Kundu and Smith (1983) call the 'Nonpoverty Growth Axiom', which is the requirement that poverty should decline with an increase in the non-poor population. Population Focus, clearly, takes a 'quantity of poverty in a society' view of a poverty measure, while the Nonpoverty Growth property takes a 'how poor is a society' view of a poverty measure.…”

Section: Focus and The Possibility Of Coherent Aggregationmentioning

confidence: 99%

“…In particular, a vague approach to reckoning poverty is compatible with postulating a 'fuzzy membership function', which assigns a 'poverty status' in the interval [0,1] to each individual income in a distribution. On fuzzy poverty measurement, the reader is referred to, among others, Kundu and Smith (1983), Shorrocks and Subramanian (1994), Chiappero-Martinetti (2000), Qizilbash (2003), and Subramanian (2009b). (It should be noted that the fuzzy approach described in this paper corresponds to what Qizilbash 2003 calls the 'degree' approach, and which he distinguishes from 'epistemic' and 'supervaluationist' approaches to accounting for vague predicates.…”

Section: Where Focus Is Irrelevant: Further Examples Of Measures Whicmentioning

confidence: 99%

“…P z = x ) 1 Finally, the Poverty Growth axiom requires that in a situation where there is at least one non-poor person and where all the poor have the same income, the addition of another person to the population with this income should cause measured poverty to rise. This is a weakened version (see Subramanian 2002 andHassoun andSubramanian 2011) of a similar axiom, with the same name, proposed by Kundu and Smith (1983).…”

Section: Focus and The Possibility Of Coherent Aggregationmentioning

confidence: 99%

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The Focus Axiom and Poverty: On the Co-existence of Precise Language and Ambiguous Meaning in Economic Measurement

Subramanian

2012

Economics

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Despite the formal rigour that attends social and economic measurement, the substantive meaning of particular measures could be compromised in the absence of a clear and coherent conceptualization of the phenomenon being measured. A case in point is afforded by the status of a 'focus axiom' in the measurement of poverty. 'Focus' requires that a measure of poverty ought to be sensitive only to changes in the income-distribution of the poor population of any society. In practice, most poverty indices advanced in the literature satisfy an 'incomefocus' but not a 'population-focus' axiom. This, it is argued in the present paper, makes for an incoherent underlying conception of poverty. The paper provides examples of poverty measures which either satisfy both income and population focus or violate both, or which effectively do not recognize a clear dichotomization of a population into its poor and non-poor components, and suggests that such measures possess a virtue of consistency, and coherent meaning, lacking in most extant measures of poverty available in the literature.Paper submitted to the special issue The Measurement of Inequality and Well-Being: New Perspectives JEL B40, D31, D63, I32, O15

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