Assessing individuals' deprivation in a multidimensional framework

Highlights

• Poverty indices do not allow tradeoffs between meager and non-meager attributes.

• We present new multidimensional poverty indices allowing for such tradeoffs.

• The new poverty indices are characterized axiomatically.

• Poverty assessments differ dramatically when introducing our new indices.

Abstract

In the context of multidimensional poverty measurement, it seems plausible to assume that when individuals are deprived in some dimensions and non-deprived in the remaining ones, the latter can be allowed to play a non-trivial role in the assessment of those individuals' poverty levels. Yet, this simple and attractive property is violated by virtually all multidimensional poverty indices proposed in the literature so far because they stick to the so-called ‘Strong Focus’ axiom. This paper characterizes a class of multidimensional poverty indices that allows for certain trade-offs between deprived and non-deprived attributes when measuring individuals' deprivation. The empirical results based on ‘Demographic and Health Surveys’ from 54 countries suggest that our assessments of multidimensional poverty can differ dramatically when the overly restrictive Strong Focus is abandoned in favor of weaker versions of the axiom.

Introduction

At the beginning of the 21st century, poverty reduction continues to be one of the greatest challenges faced by policy makers in most parts of the world. Not surprisingly, the United Nations' Millennium Development Goal #1 prompts countries to halve the proportion of population living in poverty by the year 2015. Therefore, the targeting of poor individuals and the measurement of poverty levels are a high-priority topic of research with enormous policy implications. In the last years it is becoming increasingly acknowledged that poverty is a multidimensional phenomenon, and many authors have insisted on the necessity of defining multidimensional poverty rather than relying on income or consumption expenditures alone (see, for instance, Bourguignon and Chakravarty, 2003:26). This line of research is particularly pertinent at this moment given the fact that international institutions like the European Commission or the United Nations are implementing the multidimensional approach to complement official income poverty measures. Following the definition adopted by the Europe 2020 strategy, Eurostat publishes since 2009 the values of the multidimensional AROPE index (people at-risk-of-poverty rate or social exclusion), and since 2010 the United Nations' Human Development Report publishes the values of the so-called ‘Multidimensional Poverty Index’ for over a hundred countries all over the world (see Alkire and Santos, 2010). These publications have renewed the interest and invigorated the debate on multidimensional poverty measurement (see Alkire and Foster, 2011b, Alkire et al., 2011, Ravallion, 2011, Silber, 2011). As will be clear later, this paper addresses some of the issues raised in such debate.

After the seminal contribution of Sen (1976), the measurement of poverty is commonly divided in two different but interconnected steps: the ‘identification step’ (i.e.: decide who is ‘poor’ and who is not) and the ‘aggregation step’ (i.e.: summarizing information about ‘the poor’ into a single number). While the identification step is relatively straightforward in the single dimensional case (an income poverty line defines who is poor and who is not), the problem becomes more complicated in a multidimensional framework, and different well-known approaches have been proposed in the literature. In the cases where it is meaningful to aggregate the different attainments into an overall welfare indicator, individuals are identified as ‘poor’ whenever their aggregate well-being level falls below a given poverty threshold. This approach – also known as the ‘poverty frontier’ approach – has implicitly been used by Duclos et al. (2006) and has been advocated by Ravallion (2011) as long as the different attributes that are being taken into account are commensurable. Alternatively, whenever aggregation is not meaningful in the attainment space, many authors have suggested considering the deprivation space – which, according to Alkire et al. (2011:502) “is arguably as salient as attainment space for poverty measurement” – to identify the poverty status of individuals. Implicit in this argument we have the idea that each deprivation is essential when determining the poverty status of individuals (Tsui, 2002:74). In this context, and assuming that one is able to define dimension-specific poverty thresholds that allow determining whether individuals are deprived or not in the corresponding dimensions, one can define the well-known ‘union’, ‘intersection’ and ‘intermediate’ approaches – which basically identify an individual as being ‘poor’ depending on the number of dimensions in which s/he is deprived.¹ While Ravallion (2011) argues that aggregating in the attainment space might be conducive to poverty measures in which tradeoffs between dimensions are explicitly controlled for so that they are consistent with certain welfare criteria, Alkire and Foster (2011b) emphasize that aggregating in the deprivation space allows identifying the multiply deprived individuals – something which is not feasible when aggregating in the attainment space. Even if the debate is far from being settled, most of the multidimensional poverty indices presented so far have been defined in the deprivation space (see Alkire and Foster, 2011a, Bossert et al., 2013, Bourguignon and Chakravarty, 2003, Chakravarty et al., 2008, Tsui, 2002). In this paper, we introduce a methodology that is also framed in the deprivation space but which goes some way towards addressing Ravallion's (2011) concerns.

Once the identification step is over, one must typically assess the extent of poverty of those individuals that are deemed ‘poor’ via the ‘aggregation step’. For the sake of clarity, it might be useful to think of the latter as a two-stage procedure. Initially, a ‘deprivation assessment’ stage determines how poor ‘poor’ individuals are. After that, the ‘aggregation step’ summarizes individuals' poverty levels into a single number. This subtle but important distinction is motivated by the fact that in a multiattribute framework, the problem of assessing individuals' deprivation levels (i.e.: the first stage in the ‘aggregation step’) is a non-trivial matter which, as will be shown below, has received insufficient attention from the literature and will be the main concern of this paper. For the ‘deprivation assessment’ stage, there are different axioms regulating and mediating the extent to which individuals' poverty levels are affected by their achievements in the different dimensions that are being taken into account. Among these, the so-called ‘Focus Axiom’ can be considered as one of the cornerstones of poverty measurement. In its single-dimensional version, the axiom precludes the possibility that incomes above the poverty line affect our assessment of the poverty levels in a given population. When it comes to define that axiom in a multidimensional setting there are basically two alternatives with essentially different ethical implications: the Strong and Weak Focus axioms. Assuming one is able to define dimension-specific poverty thresholds to determine whether individuals are deprived or not in the corresponding dimensions, the Strong Focus axiom demands that poverty measures should be insensitive to any change occurring above the different poverty lines. This axiom rules out any possible trade-off between achievements below and above the poverty lines for any given individual. Even if it is a quite stringent requirement that is insensitive to many situations in which the over-achievements in certain dimensions could somehow compensate the low achievements in other dimensions, up to now it has been imposed on virtually all poverty measures proposed in the literature (e.g. Alkire and Foster, 2011a, Bossert et al., 2013, Bourguignon and Chakravarty, 2003, Chakravarty et al., 2008, Tsui, 2002). On the other hand, Weak Focus is a less stringent requirement stating that a poverty measure should be insensitive to increases of non-poor individuals' attributes only, therefore leaving room for certain trade-offs between achievements above and below the poverty lines of poor individuals. In this context, Dutta et al. (2003:205) support the reasonableness of that axiom when they state: “One can argue that there is no reason why, other things remaining the same, a change in the level of over-achievement of an individual in terms of an attribute should not be allowed to affect the assessment of the overall deprivation of that individual”. More generally, the existence of trade-offs between attributes in the assessment of deprivation levels has been a topic of major concern since the times of the ‘Basic Needs’ approach (see Hicks and Streeten, 1979, Streeten, 1977) up until the present day (see, among many others, Dowrick et al., 2003 or Ravallion, 2012).

The fact that virtually all multidimensional poverty measures proposed in the literature so far satisfy the Strong Focus axiom is truly remarkable, since there are many circumstances in which one might want to allow over-achievements to exert some kind of influence when assessing individuals' overall deprivation levels. Consider a stylized setting in which poverty levels are assessed through the dimensions of health and income. Using the union approach (see footnote #1), an individual A with poor health and an income on the corresponding poverty line (typically a very low income) can be reasonably considered as a ‘poor’ person. Another individual B with the same poor health but with a moderate income level could also be considered to be poor according to the union approach but not as poor as individual A, because her higher income level might allow her to somehow compensate for her poor health status and enjoy a better standard of living. Interestingly, since virtually all multidimensional poverty indices that have been proposed in the literature so far are insensitive to this kind of interaction between dimensions, they would –somewhat surprisingly– consider individual A to be exactly as poor as individual B (see Fig. 1).²

The main goal of this paper is to propose a new conceptualization of multidimensional poverty in such a way that achievements above the poverty line are allowed to play a non-trivial role in the assessment of individuals' deprivation levels. More specifically, we will generalize the existing multidimensional poverty measures in such a way that they will be allowed to violate the Strong Focus axiom while satisfying its Weak version. In terms of the stylized setting presented in Fig. 1, we want to extend the family of multidimensional poverty measures in such a way that the poverty level of individual B can be considered to be the same as the poverty level of an individual C which is situated somewhere to the right of individual A, or – if deemed appropriate – as the poverty level of individual A itself.

While there are many compelling reasons to allow over-achievements playing a non-trivial role in the assessment of individuals' deprivation levels, it is not straightforward to specify the extent to which a certain attribute should be traded-off by another one. Among other things, this would require determining empirically the extent to which these attributes are complements or substitutes, an issue for which there does not seem to be a standard procedure (Alkire and Foster, 2011a:486).³ In other words: there are widely varying degrees in which the Strong Focus axiom can be relaxed in favor of its weak version. In face of such a daunting task, a decision maker might be uncertain and could prefer to introduce a certain degree of underspecification: rather than arbitrarily fixing the values of parameters governing trade-offs between deprived and non-deprived attributes, she might prefer to let them freely move within certain regions of those parameters' space denoted as ‘admissible sets’ (call them Λ).⁴ This paper introduces different tools to assess the extent to which the set of admissible rankings derived from the choice of Λ differs with respect to the ‘status quo’ ranking derived from the Strong Focus axiom – so the reliability and robustness of the later can be fully explored. In particular, we will investigate the pace at which the dissimilarity between the rankings associated to the Strong and Weak Focus assumptions increases as we gradually enlarge the size of the admissible sets (i.e.: as we increasingly weaken the Strong Focus axiom). Interestingly, the methodology presented in this paper allows modeling different degrees of complementarity/substitutability for alternative couples of attributes – an improvement with respect to the current state of the literature, that requires attributes to be all complements or all substitutes with a strength that is uniform across all pairs – therefore opening the possibility of eventually choosing “reasonable” tradeoffs between dimensions as advocated by Ravallion, 2011, Ravallion, 2012.

Using the same 54 Demographic and Health Surveys that were used in the calculation of UNDP's Multidimensional Poverty Index, we show an application of our methodology to test the robustness of ‘Strong Focus poverty rankings’ to alternative implementations of the Weak Focus axiom. Inter alia, the results shown in this paper suggest that our assessments of multidimensional poverty levels can differ dramatically when making some room for trade-offs between deprived and non-deprived attributes.

The paper is structured as follows. Section 2 will present some basic definitions and notation that will be used throughout the paper. Our methodology and its axiomatic characterization will be presented in Section 3. Section 4 presents some sensitivity analysis tools that will be used in the empirical application. In Section 5 we turn to our empirical application and in Section 6 we present some substantive comments on the implications of our results. The proofs are relegated to the Appendix A.