Robust multidimensional spatial poverty comparisons in Ghana, Madagascar, and Uganda

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Spatial poverty comparisons are investigated in three African countries using multidimensional indicators of well-being. The work is analogous to the univariate stochastic dominance literature in that it seeks poverty orderings that are robust to the choice of multidimensional poverty lines and indices. In addition, the study seeks to ensure that the comparisons are robust to aggregation procedures for multiple welfare variables. In contrast to earlier work, the methodology applies equally well to what can be defined as union, intersection, and intermediate approaches to dealing with multidimensional indicators of well-being. Furthermore, unlike much of the stochastic dominance literature, this work computes the sampling distributions of the poverty estimators to perform statistical tests of the difference in poverty measures. The methods are applied to two measures of well-being, the log of household expenditures per capita and children's height-forage z scores, using data from the 1988 Ghana Living Standards Study survey, the 1993 National Household Survey in Madagascar, and the 1999 National Household Survey in Uganda. Bivariate poverty comparisons are at odds with univariate comparisons in several interesting ways. Most important, it cannot always be concluded that poverty is lower in urban areas in one region compared with that in rural areas in another, even though univariate comparisons based on household expenditures per capita almost always lead to that conclusion.
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 77512 Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda Jean-Yves Duclos, David Sahn, and Stephen D. Younger Spatial poverty comparisons are investigated in three African countries using multi- dimensional indicators of well-being. The work is analogous to the univariate stochastic dominance literature in that it seeks poverty orderings that are robust to the choice of multidimensional poverty lines and indices. In addition, the study seeks to ensure that the comparisons are robust to aggregation procedures for multiple welfare variables. In contrast to earlier work, the methodology applies equally well to what can be defined as ‘‘union,’’ ‘‘intersection,’’ and ‘‘intermediate’’ approaches to dealing with multidimensional indicators of well-being. Furthermore, unlike much of the stochastic dominance literature, this work computes the sam- pling distributions of the poverty estimators to perform statistical tests of the difference in poverty measures. The methods are applied to two measures of well-being, the log of household expenditures per capita and children’s height-for- age z scores, using data from the 1988 Ghana Living Standards Study survey, the 1993 National Household Survey in Madagascar, and the 1999 National Household Survey in Uganda. Bivariate poverty comparisons are at odds with univariate compar- isons in several interesting ways. Most important, it cannot always be concluded that poverty is lower in urban areas in one region compared with that in rural areas in another, even though univariate comparisons based on household expenditures per capita almost always lead to that conclusion. It is common to assert that poverty is a multidimensional phenomenon, yet most empirical work on poverty, including spatial poverty, uses a unidimensional yardstick to judge a person’s well-being, usually household expenditures or income per capita or per adult equivalent. When studies use more than one indicator of well-being, poverty comparisons are either made independently for Jean-Yves Duclos is a professor of economics and director of the Inter-University Center on Risk, Economic Policies, and Employment (CIRPE ´ Laval; his email address is jyves@ecn.ulaval.ca. ´ E) at Universite David Sahn is a professor of economics and director of the Food and Nutrition Policy Program at Cornell University; his email address is des16@cornell.edu. Stephen D. Younger is an associate director of the Food and Nutrition Policy Program at Cornell University; his email address is sdy1@cornell.edu. The authors are grateful to three anonymous referees and the editor for comments on a previous draft. The research for this study is supported by the Strategies and Analysis for Growth and Access project, funded by a U.S. Agency for International Development cooperative agreement with Cornell University and Clark-Atlanta University and by the Poverty and Economic Policy network of the International Develop- ment Research Centre. For more information, see http://www.saga.cornell.edu and www.pep-net.org/. THE WORLD BANK ECONOMIC REVIEW, VOL. 20, NO. 1, pp. 91–113 doi:10.1093/wber/lhj005 Advance Access publication April 6, 2006 Ó The Author 2006. Published by Oxford University Press on behalf of the International Bank for Reconstruction and Development / THE WORLD BANK. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org. 91 92 THE WORLD BANK ECONOMIC REVIEW, VOL. 20, NO. 1 each indicator1 or made using an arbitrarily defined aggregation of the multiple indicators into a single index.2 In either case, aggregation across multiple welfare indicators and across the welfare statuses of individuals or households requires specific aggregation rules that are necessarily arbitrary.3 Multidimensional pov- erty comparisons also require the estimation of multidimensional poverty lines, a procedure that is problematic even in a unidimensional setting. Taking as a starting point the conviction that multidimensional poverty comparisons are ethically and theoretically attractive, the purpose here is to apply quite general methods for multidimensional poverty comparisons to the particular question of spatial poverty in three African countries—Ghana, Madagascar, and Uganda. The relevant welfare theory and accompanying statistics are developed elsewhere (Duclos, Sahn, and Younger 2003). The purpose here is to give an intuitive explanation of the methods and to show that they are both tractable and useful when applied to spatial poverty in Africa. The poverty comparisons use the dominance approach initially developed by Atkinson (1987) and Foster and Shorrocks (1988a, 1988b, 1988c) in a unidi- mensional context.4 In a review of this literature, Zheng (2000) distinguishes between poverty comparisons that are robust to the choice of a poverty line and those that are robust to the choice of a poverty measure or index. Both are attractive features of the dominance approach because they enable the analyst to avoid relying on ethically arbitrary choices of a poverty line and a poverty measure. The poverty comparisons used here are robust to the selection of both a poverty line and a poverty measure. In the multidimensional context, this includes robustness over the manner in which multiple indicators interact to generate overall individual well-being. Section I briefly presents the data and provides an intuitive discussion of multidimensional poverty comparisons. In addition to the stochastic dominance conditions that are familiar from the univariate literature, it discusses two concepts that arise only in a multivariate context. First, it distinguishes between intersection and union definitions of poverty.5 By the well-known focus axiom used in poverty measurement (see, for instance, Foster 1984), these definitions 1. This would involve, say, comparing incomes across regions and then comparing mortality rates across regions and so on. 2. The best-known example is the human development index of the United Nations Development Programme (UNDP 1990), which uses a weighted average of life expectancy, literacy, and GDP per capita across the population. 3. Such rules have been the focus of some of the recent literature. See, for instance, Tsui (2002) and Bourguignon and Chakravarty (2003). Bourguignon and Chakravarty (2002) also give several interesting examples in which poverty orderings vary with the choice of aggregation rules. 4. Atkinson and Bourguignon (1982, 1987) first used this approach in the context of multidimen- sional social welfare. See also Crawford (1999). 5. For further recent discussion, see Bourguignon and Chakravarty (2002, 2003), Atkinson (2003), and Tsui (2002). Duclos, Sahn, and Younger 93 identify the individual poverty statuses to be aggregated to obtain poverty indices. If well-being is measured in the dimensions of income and height, say, then a person whose income falls below an income poverty line or whose height falls below a height poverty line could be considered poor. This is a union definition of multidimensional poverty. By an intersection definition, however, a person would have to fall below both poverty lines to be considered poor. In contrast to earlier work, the tests used here are valid for both definitions—or for any choice of intermediate definitions for which the poverty line in one dimen- sion is a function of well-being measured in the other dimension. A second key concept that arises only in the context of multivariate poverty comparisons is that, roughly speaking, the correlation between individual measures of well-being matters. If two populations have the same univariate distributions for two measures of well-being, but one has a higher correlation between these measures, then it should not have lower poverty.6 This is because a person’s deprivation in one dimension of well- being should matter more if the person is also poorer in the other dimension. The dimensions of well-being are substitutes in the poverty measure. While this is apparently intuitive, counterexamples are also presented, although the poverty comparisons are valid only for the case in which the dimensions are substitutes. Section I concludes with examples of why the poverty comparisons here are more general than comparisons of indices such as the United Nations Develop- ment Programme’s human development index (UNDP 1990) and comparisons that consider each dimension of well-being independently. Section II applies these methods to spatial poverty comparisons in Ghana, Madagascar, and Uganda, comparing poverty across regions and areas (urban and rural) in the dimensions of household expenditures per capita and nutri- tional status for children under the age of 5. Univariate comparisons based on expenditures or nutritional status alone almost always show greater poverty in rural areas in any one region than in urban areas in any other region. Bivariate comparisons, however, are less likely to draw this conclusion for a variety of reasons. For this particular application, all of the interesting deviations from the generally accepted conclusion that poverty is higher in rural areas result from the fact that the correlation between these two dimensions of well-being is often higher in urban areas. Previous work on multidimensional poverty comparisons has ignored sam- pling variability, yet this is fundamental if the study of multidimensional poverty comparisons is to have any practical application. The poverty comparisons here are all statistical, using consistent, distribution-free estimators of the sampling distributions of the statistics of each poverty comparison. 6. Bourguignon and Chakravarty (2003, p. 31) refer to this as a ‘‘correlation increasing switch’’ and discuss it in detail. It is closely related to Tsui’s (1999) concept of correlation increasing majorization. 94 THE WORLD BANK ECONOMIC REVIEW, VOL. 20, NO. 1 I. METHODS TO COMPARE POVERTY WITH MULTIPLE INDICATORS OF WELL-BEING This section discusses the data and provides an intuitive presentation of multi- dimensional poverty comparisons. Data The data for this study come from the 1988 Ghana Living Standards Survey, the 1993 National Household Survey (Enque ˆ te Permanente aupre` s des Me ´nages) in Madagascar, and the 1999 National Household Survey in Uganda. All are nationally representative multipurpose household surveys. The first measure of well-being is household expenditures per capita, the standard variable for empirical poverty analysis in developing economies. The second is children’s height-for-age z score (HAZ) that measures how a child’s height compares with the median of the World Health Organization reference sample of healthy children (WHO 1983). In particular, the z scores standardize a child’s height by age and gender as ðxi À xmedian Þ=x , where xi is a child’s height, xmedian the median height of children in a healthy and well-nourished reference population of the same age and gender, and sx the standard deviation from the mean of the reference population. Thus, the z-score measures the number of standard deviations that a child’s height is above or below the median for a reference population of healthy children of the same age and gender. The nutrition literature includes a wealth of studies showing that in poor countries children’s height is a particularly good summary measure of children’s general health status (Cole and Parkin 1977; Mosley and Chen 1984; WHO 1995). As summarized by Beaton and others (1990, p. 2), growth failure is ‘‘the best general proxy for constraints to human welfare of the poorest, includ- ing dietary inadequacy, infectious diseases and other environmental health risks.’’ They go on to point out that the usefulness of stature is that it captures the ‘‘multiple dimensions of individual health and development and their socio- economic and environmental determinants.’’ In addition, HAZ is an interesting variable to consider with expenditures per capita because the two are, surpris- ingly, not highly correlated, so that they capture different dimensions of well- being (Haddad and others 2003).7 Univariate Poverty Dominance Methods The theoretical and statistical bases for the methods used here are developed in Duclos, Sahn, and Younger (2003). This section provides only an intuitive presentation; the formal argument is presented in the appendix. Even though the goal is to make multidimensional poverty comparisons, it is easier to grasp the intuition with a unidimensional example. 7. Pradhan, Sahn, and Younger (2003) give a more thorough defense of using children’s height as a welfare measure. Duclos, Sahn, and Younger 95 Consider the question: Is poverty greater in urban or rural areas? The dom- inance approach to poverty analysis addresses this question by making poverty comparisons that are valid for a wide range of poverty lines and a broad class of poverty measures. Figure 1 displays the cumulative density functions—or distribution functions—for real household expenditures per capita in urban and rural areas of Uganda in 1999. If the values on the x axis are thought of as potential poverty lines—the amount that a household has to spend per capita in order not to be poor—then the corresponding value on the y axis would be the headcount poverty rate—the share of people whose expenditure is below that particular poverty line. Note that this particular cumulative density function is sometimes called a poverty incidence curve. The graph makes clear that no matter which poverty line one chooses, the headcount poverty index (the share of the sample that is poor) will always be lower for urban areas than for rural. Thus, this sort of poverty comparison is robust to the choice of a poverty line. What is less obvious is that this type of comparison also permits drawing conclusions about poverty according to a very broad class of poverty measures. In particular, if the poverty incidence curve for one sample is everywhere below the poverty incidence curve for another sample over a bottom range of poverty lines, then poverty will be lower in the first sample for all those poverty lines and for all additive poverty measures that obey two conditions: they are nondecreas- ing and anonymous. Nondecreasing means that if any one person’s income increases, the poverty measure cannot increase as well. Anonymous means that F I G U R E 1 . Poverty Incidence Curves, Urban and Rural Areas of Uganda 1999 1.0 0.9 0.8 0.7 Poverty incidence 0.6 0.5 0.4 0.3 Rural 0.2 Urban 0.1 0.0 7.5 8.0 8.5 9.0 9.5 10.0 Log of household expenditures per capita Source: Authors’ analysis based on data from the Uganda 1999 National Household Survey. 96 THE WORLD BANK ECONOMIC REVIEW, VOL. 20, NO. 1 it does not matter which person occupies which position or rank in the income distribution. It is helpful to denote as Å1 the class of all poverty measures that have these characteristics. Å1 includes virtually every standard poverty measure. It should be clear that the nondecreasing and anonymous characteristics of the class Å1 are entirely unobjectionable. Additivity is perhaps less benign, but it is a standard feature of the poverty measures because it allows subgroup decomposi- tion (Foster, Greer, and Thorbecke 1984). Comparing cumulative density curves as in figure 1 thus enables making a very general statement about poverty in urban and rural Uganda: for any reason- able poverty line and for the class of poverty measures Å1, poverty is lower in urban areas than in rural areas. This is called first-order poverty dominance. The generality of such conclusions makes poverty dominance methods attractive. However, such generality comes at a cost. If the cumulative density functions cross one or more times, there is no clear ordering—it cannot be said whether poverty is lower in one group or the other. There are two ways to deal with this problem, both reasonably general. First, it is possible to conclude that poverty is lower in one sample than in another for the same large class of poverty measures, but only for poverty lines up to the first point at which the cumulative density functions cross (for a recent treatment of this, see Duclos and Makdissi 2005). If reasonable people agree that this crossing point is at a level of well-being safely beyond any sensible poverty line, this conclusion may be sufficient. Second, it is possible to make comparisons over a smaller class of poverty measures. For example, if the condition is added that the poverty measure respects the Pigou–Dalton transfer principle,8 it turns out that the areas under the crossing poverty incidence curves can be compared. If the area under one curve is less than the area under another for a bottom range of reasonable poverty lines, poverty will be lower for the first sample for all additive poverty measures that are nondecreasing, are anonymous, and obey the Pigou–Dalton transfer principle. This is called second-order poverty dom- inance, and the associated class of poverty measures is called Å2. While not as general as first-order dominance, it is still a quite general conclusion.9 Bivariate Poverty Dominance Methods Bivariate poverty dominance comparisons extend the univariate methods dis- cussed above. If there are two measures of well-being rather than one, figure 1 becomes a three-dimensional graph, with one measure of well-being on the x axis, a second on the y axis, and the bivariate cumulative density function 8. The Pigou–Dalton transfer principle says that a marginal transfer from a richer person to a poorer person should decrease (or not increase) the poverty measure. Again, this seems entirely sensible, but note that it does not work for the headcount whenever a richer person located initially just above the poverty line falls below the poverty line because of the transfer to the poorer person. 9. If second-order poverty dominance cannot be established, it is possible to integrate once again and check for poverty dominance for a still smaller class of poverty indices and so on. See Zheng (2000) and Davidson and Duclos (2000) for more detailed discussions.
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