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

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 '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

Variable Populations and the Measurement of Poverty and Inequality: A Selective Overview

“…The proof follows, given Proposition 3, from the fact that Axioms T and PF together imply Axiom M. To see this, imagine a situation in which z is the poverty line, n is a positive integer, Δ is a positive scalar, and -which, precisely, is what is dictated by Axiom M. We have shown that Axioms T and PF in conjunction imply Axiom M; from Proposition 3, we know that there exists no anonymous poverty measure R S → × X : P which simultaneously satisfies Axioms M, RI and PF; it follows that there exists no anonymous poverty measure R S → × X : P which simultaneously satisfies Axioms T, RI and PF. ■ Propositions 1 and 2 are based on results available in Subramanian (2002b) and Subramanian (2011b) respectively, while Propositions 3 and 4 are available in Hassoun (2010) and Hassoun and Subramanian (2011). The impossibility results stated and proved above are fairly straightforward ones, and require little in the way of complicated reasoning to comprehend.…”

“…It would appear to be inconsistent to find merit in the income focus axiom and none in the population focus axiom; when this inconsistency is sought to be rectified by requiring poverty indices to also satisfy population focus, then we find-unsurprisingly perhaps, but also disquietingly-that Population Focus in conjunction with other axioms which traditionally emphasize a headcount ratio view of poverty leads to incoherence and impossibility. This section-which relies heavily on Subramanian (2002bSubramanian ( , 2011b, Hassoun (2010) and Hassoun and Subramanian (2011)-presents a small set of very elementary impossibility theorems which point to the difficulties inherent in variable population poverty comparisons. Proposition 1.…”

“…What is attempted is an overview of the subject, but one which is selectively biased toward earlier work in which the present writer (either individually or in collaboration) has himself been involved. The paper on offer unsurprisingly draws heavily-and often enough quite directly-on the author's own work, notably Subramanian (2000Subramanian ( , 2002bSubramanian ( , 2005aSubramanian ( , 2005bSubramanian ( , 2006Subramanian ( , 2010Subramanian ( , 2011aSubramanian ( , 2011b, and Hassoun and Subramanian (2011). Of related interest are the essays by, among others, Kundu and Smith (1983), Bossert (1990), Paxton (2003), Chakravarty, Kanbur and Mukherjee (2006), Kanbur and Mukherjee (2007), and Hassoun (2010).…”

Welfare Poverty Measurement

“…The precedent analysis can be readily extended to the case of multidimensional poverty measurement (see Dardadoni (1995) When there is a single dimension involved we can define who are the poor independently on the way of measuring the incidence of poverty (see however Subramanian (2012)). The literature on multidimensional poverty has kept the tradition of determining who are the poor as a separate issue of the choice of the poverty index.…”