The Capability Approach and Fuzzy Poverty Measures: An Application to the South. African Context. By Mozaffar Qizilbash* and David A.

The Capability Approach and Fuzzy Poverty Measures: An Application to the South African Context. By Mozaffar Qizilbash* and David A. Clark** Paper Prepared For the Special Issue of Social Indicators Research
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The Capability Approach and Fuzzy Poverty Measures: An Application to the South African Context. By Mozaffar Qizilbash* and David A. Clark** Paper Prepared For the Special Issue of Social Indicators Research on Capability and the Quality of Life. Abstract One way of making the capability approach (CA) operational uses fuzzy poverty measures. In this paper, we present a new approach to applying these measures in the South African context using responses to a questionnaire on The Essentials of Life in conjunction with a methodology for dealing with the vagueness of poverty. Our results suggest very low cut-offs for people or households to classify as definitely poor for some social indicators. These cut-offs are far lower than those Klasen used in his application of the CA. The attempt to apply the CA using Cheli and Lemmi s totally fuzzy and relative poverty measure in conjunction with our approach to specifying cut-offs can lead to incoherence. This measure can, nonetheless, be useful when social indicators have a relativist component. While the Cerioli and Zani measure does not lead to such incoherence, it also has a serious weakness. Keywords : capability, well-being, poverty, fuzzy sets, South Africa. Version of the 12 th of December * School of Economics, University of East Anglia, Norwich, NR4 7TJ. Tel: ; Fax: ; and and ** Global Poverty Research Group (GPRG) and Institute for Development Policy Management (IDPM), University of Manchester, Harold Hankins Building, Precinct Centre, Oxford Road, Manchester, M13 9QH, UK; Visiting Scholar, Department of Development Studies, University of Cambridge, UK; and Southern Africa Labour and Development Research Unit (SALDRU), University of Cape Town, South Africa; Tel: ++ 44(0) ; and Corresponding Author: Mozaffar Qizilbash Acknowledgements: Related work was presented at a seminar in Bath, at the Poverty Study Group and Queen Elizabeth House conference in London, the International Association for Research on Income and Wealth Conference in Stockholm and the Chronic Poverty Conference in Manchester. We are very grateful to those who commented on these occasions as well as to many others who commented at various stages. We are also grateful to two anonymous referees for their comments. This paper is based on research which was funded by the Department of International Development. The UK Department for International Development (DfID) supports policies, programmes and projects to promote international development. DfID provided funds for this study as part of that objective, but the views and opinions expressed are those of the authors alone. Any errors or omissions are our own. 1 THE CAPABILITY APPROACH AND FUZZY POVERTY MEASURES: AN APPLICATION TO THE SOUTH AFRICAN CONTEXT INTRODUCTION Amartya Sen s capability approach (CA) has generated a great deal of conceptual literature about how we ought to think about the quality of life, development and poverty inter alia. It has also been applied in a variety of contexts. Issues remain, nonetheless, about how the approach is best applied and about the relationship between some of the conceptual insights of the CA and its application. In this paper, we are concerned with one particular method of operationalisation. This involves the use of fuzzy set theoretic poverty measures (henceforth, fuzzy poverty measures for short). The motivation for the use of these measures is that - as Sen (1981, p.13; 1993, pp. 48-9) has pointed out - notions such as wellbeing and poverty can be inexact or vague. Furthermore, the cut-off between the poor and the non-poor might be imprecise. Sen (1989, pp ) has also suggested that fuzzy set theory and incomplete orderings are useful techniques for approaching inexactness or vagueness. Enrica Chiappero-Martinetti (1994; 1996; 2000) has pursued this line of thought and has used fuzzy poverty measures in conjunction with the CA in the Italian context. Mozaffar Qizilbash (2002) has applied such measures in the South African context. Both Chiappero-Martinetti and Qizilbash use non-income social indicators - alongside income or expenditure measures - in their applications of fuzzy poverty measures. They show that there is considerable difference between the picture of poverty that emerges from examining income or expenditure alone to that which emerges from the use of social indicators which can be motivated by the CA and other related accounts of the quality of life (such as that developed by Griffin, 1986; 1996). There is, however, a well-known problem with the use of fuzzy measures in the poverty context. Even if such measures allow for an imprecise borderline between the poor 1 and the non-poor, they can involve quite exact and arbitrary specifications of the boundaries of this imprecise borderline. Bruno Cheli and Achille Lemmi (1995) have attempted to deal with this problem by examining the functional distribution of the relevant variable(s) in terms of which someone may be judged to be poor. They proposed a simple solution to the problem in which the limits of the rough borderline were data driven. Nonetheless, serious issues remain. The Cheli and Lemmi methodology for specifying the upper and lower limits of the imprecise borderline is relativist whereas Sen s work on the CA suggests that poverty has an absolutist core (Sen, 1983; 1985). Consequently, alternative approaches to specifying the upper and lower levels that define the boundaries of imprecision need to be explored in the context of applications of the CA and related views of well-being. In this paper, we present one such approach in the South African context. Our approach involved a questionnaire on The Essentials of Life which was carried out in collaboration with the Southern Africa Labour and Development Research Unit (SALDRU) in Responses to this questionnaire can be used to define the upper and lower boundaries of the imprecise borderline. In presenting this approach using social indicators, we took as our starting point Stephan Klasen s attempt (Klasen, 1997; 2000) to apply the CA to the South African context. While Klasen s work does not use fuzzy poverty measures, his ordering of various levels of disadvantage in terms of different indicators can be used to apply such measures. We use questionnaire responses to identify the cut-offs involving indicators which were either used, or are very similar to those used, in Klasen s application. The paper is structured as follows: the second section introduces the CA and two fuzzy poverty measures; issues relating to the identification of cut-offs are discussed and our approach is explained in the third section; implications for the use of fuzzy poverty measures in the South African context are discussed in the fourth section; and the final section concludes. 2 THE CA, IMPRECISION AND FUZZY POVERTY MEASURES Amartya Sen has argued that in judging a person s quality of life we should focus on the capability to achieve various (valuable) beings and doings, or functionings. Here the idea is that flourishing lives are constituted by various valuable beings and doings or functionings (Sen, 1993, p. 31). Capability refers to the range of lives - constituted by valuable functionings - from which a person can choose. To this degree, a person s capability is related to her opportunities or positive freedom. Poverty, on Sen s account, involves not being able to do certain basic things, or basic capability failure. The basic things Sen has in mind involve achieving certain crucially important functionings up to certain minimally adequate levels (Sen, 1993, p. 41). On Sen s view the relevant functionings can include being well-nourished, being adequately clothed and sheltered, as well as being able to appear in public without shame (Sen, 1984, p. 337). While Sen gives examples of such crucially important functionings, he does not give any definitive list of capabilities or functionings which are relevant to evaluating the quality of life. 1 Sen (1983; 1985) also argues that poverty is relative in the evaluative spaces of income and resources - inasmuch as it can depend on how much one has as compared to others. However, he suggests that poverty is absolute in the spaces of capability and functioning, inasmuch as it has to do with being incapable of doing and being certain basic things such as being minimally adequately nourished, which do not depend on one s position vis-à-vis others in these spaces. So Sen s view allows for relativity in some spaces, and insists on an absolutist core of poverty in terms of basic capability failure. If, for example, achieving self-respect is a crucially important functioning, and the capability to achieve it up to some minimally adequate level depends on one s relative position in the income distribution, then one can suffer from basic capability failure because of one s position in the income distribution. 2 3 The imprecision or vagueness of poverty relates to the idea that there is no clear-cut borderline between the poor and the non-poor. This vagueness is not specific to any particular focal variable and is relevant whether one is working in the income space or in some other space, such as capability or well-being (Qizilbash, 2003). Significant attempts have been made to analyse such imprecision using fuzzy set theory. There are now a number of fuzzy poverty measures which are in use (see Lelli, 2001). In this paper, we focus on two of these. In both measures there is some cut-off at or above which people are definitely not poor, and do not belong to the set of poor people. There is another cut-off at or below which people are definitely poor, and do belong to the set of poor people. In between these cut-offs there is ambiguity and people belong to the set of the poor to some degree. Cerioli and Zani (1990) developed the first and most simple fuzzy poverty measure. In their work, they write the set of poor people as A. : A is the degree of membership of A and belongs to the [0,1] interval. If someone is definitely poor, : A = 1. If she is definitely not poor, then : A = 0. If, however, someone belongs to, or is a member of, the set of the poor to some degree, then 0 : A 1. Cerioli and Zani develop their approach for both income and multi-dimensional cases. We focus here on the multi-dimensional case which can be used in conjunction with social indicators. In this case, Cerioli and Zani develop a number of measures. Of the measures that they suggest, the one used in this paper involves an ordinal method of scoring. The reason for the choice of this measure relates to Klasen s work - discussed in the next section - which also involves ordering levels of disadvantage in various dimensions. Cerioli and Zani s ordinal method works so that if there are two individuals, and one has a higher level of deprivation, that person gets assigned a lower number. The lowest score is, thus, assigned to the highest level of deprivation. If we write R for rank order score, then R j is the score at or below which someone is definitely poor in dimension j. R j is the best score for deprivation in dimension j, in the sense that anyone at or above it is definitely 4 non-poor in dimension j. R ij gives the score of individual i in dimension j. Individual i s degree of membership of the set of the poor in dimension j is written z ij. It is set to 1 if R ij # R j, and to 0 if R ij $ R j. If R j R ij R j, then: (1) z ij = (R j -R ij )/(R j -R j ) The degree to which someone belongs to the set of the poor, : A, is a weighted average of the z ij. By contrast, Cheli and Lelli (1995) developed a totally fuzzy and relative poverty measure. They were motivated, in part, by the potential arbitrariness of the cut-offs used to define someone as definitely poor or definitely not poor in the Cerioli and Zani approach. After all, Cerioli and Zani give us no criterion for deciding these cut-offs. In the income space, the Cheli and Lemmi (henceforth CL) measure is relative inasmuch as the cut-offs and the way in which membership of the set of the poor varies with income, depend on the sampling distribution of income. Their framework is, nonetheless, multi-dimensional. To show how the multi-dimensional version of the CL measure is constructed, we write variable x for dimension j as x j. Suppose that people are ranked according to their achievement in terms of this variable. k gives the rank order of the level of, or class of, achievement in terms of x, and is set to one for the highest ranking class or level, to two for the second highest class or level, and so on. CL write the degree of membership of the set of the poor for someone ranked, or someone in the class ranked, k in terms of x j as g(x (k) j ). They set g(x (k) j ) = 0 for k=1. Writing the sampling distribution of x j arranged in increasing order according to k as H(x j ), then for k 1, the degree of membership is given by: (2) g(x j (k) ) = g(x j (k-1) ) + {H(x j (k) ) - H(x j (k-1) )}/(1-H(x j (1) )) 5 g(x (k) j ) falls on the [0,1] interval and is a measure for dimension j only. It can be used with different ways of aggregating across the dimensions. In this formulation, clearly the group or individual that is doing best in terms of the sampling distribution of some relevant variable is definitely not poor as regards that variable. By construction, furthermore, the group or individual that is doing worst is definitely poor. The choice of upper and lower cut-offs used in the CL methodology is, in this sense, relative. It is derived directly from the data, with no further judgement(s) by the researcher. To this degree, this methodology removes the worry of arbitrariness. Chiappero Martinetti (1994; 1996; 2000) has used this methodology in the Italian context. A recurrent worry about fuzzy poverty measures has to do with the interpretation of a degree of membership of the set of the poor. One way of interpreting these measures adopted by Qizilbash (2003, pp. 52-3) involves seeing them as measures of vulnerability, where this relates to the possibility of being classified as poor. It is worth emphasising that if this interpretation is adopted, vulnerability is not interpreted as the probability of becoming poor given some (possibly exact) specification(s) of the cut-off between the poor and the non-poor. This interpretation is consistent with the discussion in this paper, though we do not insist on it. In this paper, we treat these measures throughout as measures of the degree of membership of the set of the poor in terms of specific indicators. We make no attempt to aggregate across indicators to arrive at some sort of overall evaluation across the dimensions of poverty. It is also worth mentioning a common misunderstanding of fuzzy poverty measures. The degree to which someone belongs to the set of the poor is sometimes mistakenly interpreted in terms of the intensity of poverty. It should be clear that fuzzy poverty measures are not measures of intensity. They address vagueness or imprecision about poverty rather than its depth or intensity. 6 As was mentioned earlier, Sen has argued that poverty is absolute in the capability space even if it can be relative in the income or commodity space. That suggests that the CL methodology may be inappropriate when used in conjunction with social indicators, if use of such indicators is motivated by the CA (or related approaches which imply an absolutist core of poverty). Yet not all social indicators that might be used in applications of the CA are straightforwardly related to an absolutist core. The distinction between absolute and relative poverty which Sen himself uses in making his conceptual points may not relate straightforwardly to the contrast between income and non-income social indicators. Yet at the level of application, the main contrast between income-based approaches and the CA is that non-income social indicators are used in the application of the latter. 3 Qizilbash (2002, pp ) makes this point using one of Sen s own examples. Sen writes that: the absolute advantage of a person to enjoy a lonely beach may depend upon his relative advantage in the space of knowledge regarding the existence [of] and access to such beaches (Sen, 1984, p. 333). Here knowledge is central and the relevant capability has to do with enjoying a beach. Knowledge may be seen as valuable in itself, and can be related to certain valuable functionings and capabilities. However, it is also a resource which can be useful for other purposes. In his discussion, Sen follows this example with a passage from Adam Smith about the relationship between the ability to appear in public without shame and the commodities which are indispensably necessary for the support of life (Sen, 1984, p. 333). In discussing Sen s example, Qizilbash argues that one s relative position in terms of knowledge might be important even when it comes to poverty. One s relative position in terms of the amount of knowledge one has might matter, for example, to one s ability to achieve self-respect, or to participate in social life, which might be basic functionings. So social indicators relating to knowledge - indicators relating to schooling, and educational attainment, for example - might be important, in part, in the same relativist manner that 7 income is. To this degree, social indicators and measures based on them may have a relativist component to them (Qizilbash, 2002, p.759). This argument might look as if it conflicts with Sen s views but it actually follows directly from them. 4 Knowledge can be a resource, and studies of poverty which use a measure of educational attainment - such as years of schooling - through a concern with functioning or capability ought to take this into account. The same might be said about other social indicators. To this degree, there remains a case for using the CL measure, even if it is used with an alternative approach for specifying the upper and lower limits of the imprecise borderline. DEFINING CUT-OFFS FOR SOCIAL INDICATORS IN THE SOUTH AFRICAN CONTEXT. Qizilbash (2002) has applied the CL and Cerioli and Zani measures in the South African context using data from the 1996 South African Census. In that application, the cutoffs used for both fuzzy poverty measures are in line with the CL methodology. The worstoff (best-off) category in the sample is thus defined as definitely poor (definitely not poor) in each relevant dimension of the quality of life. As was just noted, worries might be expressed about this way of defining cut-offs, particularly when one approaches the issue starting from Sen s discussion of the absolutist core of poverty. In his attempt to apply Sen s CA to the South African context, Stephan Klasen (1997; 2000) uses various indices as proxies for fourteen components of his composite measure of deprivation. Each component is thought of as relating to some specific capability, 5 with levels of achievement in terms of these components associated with a rank order number. Klasen includes income as a component in his study. 6 His choice of indices is motivated by data from the 1993 Project for Statistics on Living Standards and Development (PSLSD) undertaken by SALDRU. The indices and rank order numbers Klasen (2000, p. 41) uses are presented in Table 1. For illustrative purposes, consider the first row in Table 1 which relates to the average 8 educational attainment of household members. In this case, rank orders are assigned so that: less than two years of education is given a rank order of 1; between 3 and 5 years of education is given a rank order of 2; and so on. Similar exercises are carried out for the other indicators. While Klasen notes difficulties with ranking some categories, he suggests that the scoring is quite intuitive and unlikely to stir much debate (Klasen, 2000, p. 39). Each household is assigned a rank order score on the basis of its achievements in each indicator. Klasen
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