WPS5580 Policy Research Working Paper 5580 On Multidimensional Indices of Poverty Martin Ravallion The World Bank Development Research Group Director's office February 2011 Policy Research Working Paper 5580 Abstract There has been a growing interest in what have come for, should it be done in the space of "attainments," to be termed "multidimensional indices of poverty." using prices when appropriate, or that of "deprivations," Advocates for these new indices correctly point out that using weights set by the analyst? The paper argues that command over market goods is not all that matters to the goal for future poverty monitoring efforts should be peoples' well-being, and that other factors need to be to develop a credible set of multiple indices, spanning considered when quantifying the extent of poverty and the dimensions of poverty most relevant to a specific informing policy making for fighting poverty. However, setting, rather than a single multidimensional index. the author argues that there are two poorly understood When weights are needed, they shouldn't be set solely by issues in assessing these indices. First, does one believe an analyst measuring poverty. Rather, they should be, as that any single index can ever be a sufficient statistic for much as possible, consistent with well-informed choices poverty assessments? Second, when aggregation is called made by poor people. This paper is a product of the Director's office, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at mravallion@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team On Multidimensional Indices of Poverty Martin Ravallion1 1 The author is Director of the Development Research Group, World Bank, 1818 H Street NW, Washington DC, 20433, USA. For helpful discussions on this topic and comments on this paper the author is grateful to Sabina Alkire, Kathleen Beegle, Gabriel Demombynes, Quy-Toan Do, Jean-Yves Duclos, Francisco Ferreira, James Foster, Garance Genicot, Stephan Klasen, Peter Lanjouw, Michael Lokshin, Nora Lustig, Branko Milanovic, Mead Over, Dominique van de Walle, Roy Van der Weide and Hassan Zaman. These are the views of the author, and need not reflect those of the World Bank or any affiliated organization. 1. Introduction There has been a growing interest in what have come to be termed "multidimensional indices of poverty." There are many issues one might discuss related to these indices, including the choice of the functional form, the choice of poverty lines, and the robustness of the implied rankings to those choices.2 However, these issues are essentially generic to all poverty measures (though with some more technical differences). The present discussion will focus instead on how multidimensional indices differ from more familiar approaches. This is a logical starting point for potential users trying to understand and apply these new measures; to assess their contribution we must first understand how they differ from standard measures. Multidimensionality per se cannot be what distinguishes a multidimensional index of poverty (MIP). There is an obvious sense in which almost every poverty measure found in practice is "multidimensional." Indeed, to my knowledge, the only truly one-dimensional indices are the rice-based measures once found in some countries in Asia, but no longer used.3 The main measures now found in practice use a composite measure of consumption or income with many components, relying heavily on market prices in aggregation. Nor does the difference lie in the recognition of the fact that poverty is not just about low consumption of market commodities. It is widely agreed that there are also important non-market goods relevant to welfare, such as access to public services. Poverty is multidimensional. However, that does not imply that one needs a MIP. It is one thing to recognize that something is missing from a given measure, and needs to be considered, and quite another to create a single composite index. The more common approach is to collect multiple indicators of the various dimensions of poverty, invariably including an index of command over market goods, but also including indicators for health and education attainments and access to services. A well-known example is the United Nations' Millennium Development Goals, which span multiple 2 For example, in the case of poverty measurement, where there is almost always a degree of arbitrariness about the poverty line, best practice tests the robustness of poverty comparisons to the choices made, invoking the theory of stochastic dominance. For expositions in the standard "unidimensional" case see Atkinson (1987) and Ravallion (1994). Duclos et al. (2006) provide dominance tests for "multidimensional poverty." 3 For example, the government of Vietnam measured poverty by rice consumption prior to the early 1990s. This was in part at least because of high inflation in the 1980s, and inadequate price indices. More standard multi-commodity poverty measures emerged soon after. 2 dimensions, but without forming a single composite index. At the country level, the World Bank's Poverty Assessments and the Poverty Reduction Strategy Papers of individual governments have typically drawn on multiple indicators (though naturally with varying emphasis), without forming a single composite index.4 This paper argues that the real differences between the recent measures that are called "multidimensional" and standard approaches lie elsewhere. The first difference is in whether one believes that a single index of poverty could ever be a sufficient statistic, or whether multiple indices are required, each measuring different things using the best data available for that task-- presenting us with a "large and eclectic dashboard" (Stiglitz et al., 2009, p.62). A second difference is also evident on closer inspection, namely how the analyst chooses to collapse multiple dimensions into one, recognizing that some degree of aggregation will probably be called for even in the "dashboard" approach. In elaborating these two differences I will illustrate the arguments using the most well- developed and broadly applied MIP to date, namely that developed by Alkire and Santos (2010a), which is a special case of the class of measures proposed by Alkire and Foster (2007). The following section discusses the Alkire-Santos index, and whether it can be considered sufficient for measuring poverty and informing policy making. Section 3 turns to the issue of how one can go about aggregating across multiple dimensions when a degree of aggregation is called for to reduce the dimensionality. Section 4 concludes. 2. Can we measure poverty adequately with any single index? There are countless possibilities for forming composite indices by some form of essentially ad hoc aggregation--giving what I term elsewhere "mashup indices" (Ravallion, 2010a). The issue in this section is not how this can be done but whether it is useful to do so. One can easily imagine situations in which one would not want a mashup index. Imagine you go for your annual medical checkup. Your doctor does all the usual tests, but tells you that she will base her assessment solely on a single composite index--rescaling and averaging all the test 4 The Bank's Poverty Assessments (significant analytic reports covering virtually all developing countries) typically cover education, health and nutrition and access to infrastructure, in addition to income poverty. 3 results. You would be well advised to get a new doctor!5 Or imagine that a new car comes on the market that collapses all those dials on the dashboard into just one composite index, on which you are supposed to decide what to do (slow down or get fuel). You would surely not buy this car! Essentially the same point applies to the task of prioritizing policies for fighting poverty in a given country (or other geographic area). We will naturally want to look at the country's attainments in various dimensions, rather than focusing on its performance with respect to a single composite index. Should we be focus on promoting job creation (say) or better health and education services? Such an approach does not deny that poverty is "multidimensional." Rather it says that forming a single (uni-dimensional) index may not be particularly useful for sound development policy making. Consider now the MIP developed by Alkire and Santos (2010a) for the 2010 Human Development Report (UNDP, 2010). They choose 10 variables for their MIP under the same three headings--health, education and living standards--as the UNDP's Human Development Index (HDI). There are two variables for health (malnutrition, and child mortality), two for education (years of schooling and school enrolment), and six for deprivation in "living standards" (namely cooking with wood, charcoal or dung; not having a conventional toilet; lack of easy access to safe drinking water; no electricity; dirt, sand or dung flooring and not owning at least one of a radio, TV, telephone, bike or car). Poverty is measured separately in each of these 10 dimensions. The equally-weighted aggregate poverty measures for each of these three main headings are then weighted equally (one-third each) to form the composite index, also echoing the HDI. A household is identified as being poor if it is deprived across at least 30% of the weighted indicators. While the HDI uses aggregate country-level data, the Alkire-Santos MIP uses household-level data, which are then aggregated to the country level. Alkire and Santos construct their index for more than 100 countries. 5 In certain emergency situations (such as on the battle field), treatment decisions often require a prioritization of patients ("triage") and it appears that this is typically based on the probability of survival, which is a single index. But then one is not creating a "maship index" since the variables and weights are entirely determined by their ability to predict that probability. There is nothing analogous to this probability in a MIP. As Mead Over points out in a blog comment: "In the physical examination example, where the situation is not life threatening, both the doctor and the patient presume that the patient's valuation of the information deserves priority, since presuming otherwise would be unnecessarily paternalistic." 4 The Alkire-Santos MIP is a special case of the theoretical measure proposed in an elegant formulation of the problem by Alkire and Foster (2007). This fact helps in understanding the Alkire-Santos MIP, but does not really get us very far since the theoretical formulation in Alkire and Foster (in common with other papers in this literature) takes virtually all the elements of the measure as given (determined outside the measure), notably the dimensions of poverty, the dimension-specific cutoffs, the weights on deprivations and the minimum number of deprivations needed to be deemed "poor." As we will see, the devil is in these details. What dimensions? A key step in implementing any multidimensional measure is to select a set of dimensions. There is, of course, ample scope for debate here. There is a (rather poorly- understood) issue about what dimensions are intrinsically, versus instrumentally, important. For example, we can probably all agree that "health" is valued intrinsically, independently of command over commodities. However, it is more contentious that education has such an intrinsic value--as implicitly assumed by the Alkire-Santos MIP--rather than being (very) important to income and (hence) command over commodities (and health too). And even if we agree that education is to be valued intrinsically, it is far from clear that "education poverty" should have the same weight as "health poverty." The data requirements of the Alkire-Foster index entail that relevant dimensions of poverty must invariably be left out in practice. Consider first the material goods entering the Alkire-Santos MIP. This is a rather narrow set of goods, leaving out a great many things that people do in fact consume. The consumption measure formed from a modern household budget or living-standards survey will aggregate (actual or imputed) expenditures on literarily 100's of consumption items (1,000 or more items in some surveys). Yet the Alkire-Santos MIP only identifies six factors for "living standards" (as described above). So their measure leaves out a great many of the multiple dimensions poverty--indeed, their MIP has far fewer dimensions of living standards than those included in a standard ("unidimensional") consumption-based measure. Nor does the index appear to span the relevant "non-income" dimensions. In a blog comment, Duncan Green criticized the Alkire-Santos MIP for leaving out "conflict, personal security, domestic and social violence, issues of power/empowerment" and "intra-household dynamics." 5 Why is so much left out? In practice, the choice of dimensions for measuring poverty will naturally be constrained by the data. When following the Alkire-Foster approach, the options are constrained further by the fact that one must obtain all the data for the same sampled household. So they must all come from the same survey.6 Yet most surveys do not cover all the things one would like to know in a comprehensive assessment of poverty. This restricts the set of dimensions that can be included in the MIP. Nor can it be presumed that the dimensions that can be measured this way are representative of some subset of dimensions, within some seemingly reasonable taxonomy (such as "consumption poverty," "health poverty" or "education poverty"). There will often be other data available on the selected dimensions, and other data on other relevant dimensions, but only from different surveys. This aspect of the Alkire-Foster approach suggests that we will inevitably fall back in practice on the standard approach I described at the outset in which we use multiple indices rather than a single index. If one chooses not to form the composite at household level but to look instead at the separate dimensions of poverty then one is in a better position to span the relevant dimensions and to choose the best available data on each. While this aspect of the Alkire-Foster methodology comes at a cost in terms of the coverage of the relevant dimensions of poverty, it can be acknowledged that it has an advantage too in that one can get some idea of the joint distribution of the multiple dimensions of poverty-- to what extent the different dimensions of poverty that can be identified are shared by the same people. This adds something that cannot be easily identified when using multiple surveys (though simulation methods are sometimes used for that purpose). When a survey for a specific country does span multiple dimensions there can be much interest in exploring their joint distribution, though a MIP is not the only tool available for that purpose.7 Another data constraint also points to the need for multiple measures in practice, namely that the data we typically use in measuring poverty do not tell us much about consumption within the household. To use such data we need to make assumptions about intra-household 6 Unique identifiers can in principle link households across two or more surveys, but this is relatively rare in practice, especially in developing countries. 7 See, for example, the study by Lokshin and Ravallion (2005) of the joint distribution of wealth and power. Lokshin and Ravallion use standard statistical tools for this purpose, including correlation and regression methods and contingency tables and related statistics for ordinal categorical data. 6 distribution, such as the seemingly strong assumption of welfare equality within the household (Haddad and Kanbur, 1990). This data constraint points to the desirability of supplementary indicators of individual attainments. Data on child health and mortality has understandably been given high priority in looking for such indicators. So why aggregate in the form of a MIP? Alkire and Santos (2010b, p.7) argue that their index "... goes beyond previous international measures of poverty to identify the poorest people and aspects in which they are deprived. Such information is vital to allocate resources where they are likely to be most effective." But is it the MIP or its components that matter for this purpose? Following Alkire and Foster (2007), the Alkire-Santos MIP has a neat decomposability; we can reverse the aggregation. This is useful, for only then will we have any idea how to go about addressing the poverty problem in that specific setting. But the question remains: why do we need the aggregation in the first place? Consider the following stylized example of a policy problem. Suppose that there are two dimensions of welfare, "income" and "access to services." Assume that an "income-poor" but "services-rich" household attaches a high value to extra income but a low value to extra services, while the opposite holds for an "income-rich" but "services-poor" household.8 There are two policy instruments, a transfer payment and service provision. The economy is divided into geographic areas (which could be countries) and a given area gets either the service or the transfer. We then calculate a composite index like the Alkire-Santos MIP based on survey data on incomes and access to services. There is bound to be a positive correlation between average income and service provision, but (nonetheless) some places have high income poverty but adequate services, while others have low income poverty but poor services. The policy maker then decides whether each area gets the transfer or the service. Plainly, the policy maker should not be using the aggregate MIP for this purpose, for then some income-poor but service-rich households will get even better services, while some income-rich but service poor households will get the transfer. The total impact on (multidimensional) poverty would be lower if one based the allocation on the MIP rather than the separate poverty measures--one for incomes and one 8 Sufficient conditions are that there is declining marginal utility to both income and services and that the marginal utility of income (services) is non-decreasing in services (income). 7 for access to services. It is not the aggregate index that we need for this purpose but its components. Once we recognize that not even the Alkire-Santos MIP can be considered a sufficient statistic for poverty assessments, and that it will need to be complemented by other measures for those things left out, we are essentially back to the standard approach of using multiple measures. Whether that still leaves a role for the MIP depends on whether we think that it captures an important subset of the relevant dimensions of poverty. Here the ambition to be "multidimensional" is in such marked tension with the need to obtain all dimensions for each surveyed household that one must question what role such an index can usefully play. Arguably it would be better to derive the best measure possible for each of a logically defensible set of grouped dimensions--such as "income poverty," "health poverty" and "education poverty". Clearly that task will still require some degree of aggregation. How should that be done? Here too there is an important, but poorly understood, distinction between the approach taken by recent MIPs and standard approaches to measuring poverty. 3. How should we aggregate? One can distinguish two approaches to forming an aggregate poverty index. The first is to use prices (actual or imputed) to form a composite index for aggregate consumption, to be compared to a poverty line defined in the same space.9 Ideally this is not just consumption of market goods and services, but should include imputed values for non-market commodities. For market goods, either their market prices or appropriate shadow prices can be used. For non- market goods the missing "prices" will need to be assigned on a priori grounds or estimated. In practice, most poverty measures require imputations for missing prices, so this approach is a natural extension of prevailing practices. In principle we can broaden this approach to allow for non-commodity dimensions of welfare. The space defined by all primary dimensions of welfare (including commodities) can be called the "attainment space" (though the term "achievements" is also used in the literature), and the aggregation can be called "attainment aggregation." The weights on attainments can be called "prices," understood to include imputed prices. 9 Household consumption is typically normalized for differences in household size and the prices faced; equivalently the poverty line is so differentiated. 8 A simple example of a poverty measure using attainment-aggregation is the usual headcount index of poverty:10 (1) where Fy is the distribution function for aggregate consumption y and z is the poverty line in that space. To keep things simple for expository purposes (including graphing), suppose that there are two attainments in amounts x1 and x2, with prices p1 and p2, so y=p1x1+p2x2. The second approach measures poverty in each of the dimensions separately and then aggregates the dimension-specific "deprivations" into a composite index. Formal treatments of this approach can be found in Tsui (2002), Bourguignon and Chakravarty (2003), Duclos et al. (2006) and Alkire and Foster (2007). The Alkire-Santos MIP is an example. I shall call this "deprivation aggregation." To see more clearly how this second approach works, consider again the two continuous attainments, x1 and x2, with distribution functions F1 and F2 respectively. Poverty lines, denoted z1 and z2, are defined in each space and the weights on deprivations are w1 and w2 (w1+w2=1). Then a simple example of a poverty measure using deprivation-aggregation is the weighted incidence of poverty across the two dimensions:11 (2) This is only one possible way of aggregating deprivations. Alternatively one can focus on the joint distribution, and ask what proportion of the population is poor in at least one of the two dimensions (Bourguignon and Chakravarty, 2003). Letting F12 denote the joint distribution function, the poverty measure is then . Alternatively, one might ask what proportion is poor in both dimensions, i.e., . The measure proposed by Alkire and Foster (2007) goes further in introducing an extra parameter, such that a household is 10 The headcount index has a number of well-known limitations, and there is a large literature on alternative measures; Atkinson (1987) lists a number of these. But the headcount index is all we need for the present expository purpose. 11 Higher-order measures can also be defined, such as based on the Watts (1968) index (see Chakravarty et al., 2008) and the Foster, Greer and Thorbecke (1984) measure (Alkire and Foster, 2008). Tsui (2002) provides a general formulation of subgroup-consistent poverty measures based on deprivation aggregation. However, I will confine attention to the simple form in (2). 9 deemed to be poor if its weighted deprivation exceeds a critical value.12 However, all these measures are essentially some weighted aggregation of deprivations, and (implicitly) a nonlinear function of the cut-offs z1 and z2. This discussion will focus on the analytically convenient form in (2), though this simplification does not appear to come at much loss. It is evident that these two approaches will not, in general, give the same measure, even when the poverty lines are consistent in that z=p1z1+p2z2. This is clear from Figure 1. Attainment aggregation identifies as poor all those people whose consumption of the two goods is within the triangle with vertices, z/p1, 0 and z/p2; instead, the deprivation approach identifies some subset of those with x1< z1 or x2< z2 (the two unbounded rectangles of width z1 and z2 in Figure 1). Without knowing the weights and data one cannot say which will give the larger count of who is poor. If deprivation-aggregation measure focuses on those who are poor in both dimensions (x1< z1 and x2< z2) then the "deprivation poor" will never outnumber the "attainment poor" (y