wps a-1 45 POLICY RESEARCH WORKING PAPER 2765 Inequality Aversion, Health This paper shows how value judgments can be explicitly Inequalities, and Health recognized in measuring Achievem ent health inequalities between the poor and the better-off, and how such inequalities Adam Wagstaff can be included in assessments of countries' health indicators- The World Bank Development Research Group Public Services and Human Development Network Health, Nutrition, and Population Team January 2002 | POLICY RESEARCH WORKING PAPER 2765 Summary findings Wagstaff addresses two issues. First, how can health relevant distribution to obtain an overall measure of inequalities be measured so as to take into account health "achievement?" Applying the approach developed policymakers' attitudes toward inequality? The Gini by Wagstaff shows how much worse some countries coefficient and the related concentration index embody perform when the focus switches from average health to one particular set of value judgments. Generalizing these an achievement index that also reflects the health gap indexes allows alternative sets of value judgments to be between the poor and the better-off. reflected. And second, how can information on health inequality be combined with information on the mean of the This paper-a joint product of Public Services, Development Research Group, and the Health, Nutrition, and Population Team, Human Development Network-is part of a larger effort in the Bank to investigate the links between poverty and health. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Hedy Sladovich, room MC3-311, telephone 202-473-7698, fax 202-522-1154, email address hsladovich@worldbank.org. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at awagstaff@worldbank.org. January 2002. (21 pages) The Policy Researcb Working Paper Sedes disseminates the findings of work in progress to encourage the excange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fuly polished. The papers car?y 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 view of the World Bank, its Executive Directors, or the countries they represent. Produced by the Policy Research Dissemination Center Inequality Aversion, Health Inequalities, and Health Achievement Adam Wagstaff Development Research Group and Human Development Network, The World Bank, Washington DC, USA and School of Social Sciences, The University of Sussex, Brighton, UK awagstaffl(aworldbank.org Without wishing to incriminate them in any way, I am grateful to Eddy van Doorslaer, and two anonymous referees for comments on an earlier version of this paper. Keywords: Health inequality, inequality aversion, equity-efficiency tradeoffs. 1. Introduction The literature on health inequality measurement has benefited substantially from cross-fertilization, both within the discipline of economics (principally from the literature on income inequality measurement to the literature on health inequality measurement) and between the disciplines of economics, epidemiology, and public health (see e.g., Wagstaff, Paci, and van Doorslaer 1991; Mackenbach and Kunst 1997). This paper extends the literature on health inequality measurement in two directions, borrowing heavily on the income inequality literature. The first is to allow for the fact that commonly used summary measures of health inequality have ethical judgments about inequality aversion built into them-albeit implicitly. This is true, for example, of the Gini coefficient, which has been used to measure pure health inequality (Le Grand 1987, 1989). But it is also true of the concentration index' (Wagstaff, Paci, and van Doorslaer 1991; Kakwani, Wagstaff, and Van Doorlsaer 1997), which has been used to measure socioeconomic inequalities in health-i.e., health inequalities by income or by some other measure of socioeconomic ' Sirnilar remarks apply to the slope index of inequality used by epidemniologists ( see e.g., Kunst, Geurts, and van den Berg 1995; Pamuk 1985, 1988; Schalick and others 2000). This is closely related to the concentration index (cf. e.g., Wagstaff, Paci, and van Doorslaer 1991; Kakwani, Wagstaff, and Van Doorlsaer 1997), and implicitly involves the same ethical judgements about inequality aversion. 2 2 status. The implicit ethical judgements have been recognized in the measurement of pure health inequality, where Atkinson's (1970) index has been used to allow attitudes to inequality to be varied (cf. Le Grand 1987, 1989). But varying attitudes to inequality have not been allowed for up to now in the measurement of socioeconomic inequalities in health. To allow for varying attitudes to inequality aversion, this paper develops the concentration index analogue of the Yitzhaki's (1983) extended Gini coefficient. While the aim is primarily to extend the literature on the measurement of socioeconomic health inequalities, the paper also contributes to the literature on the measurement of pure inequality, since, from a formal point of view, the latter can be thought of a special case of the measurement of socioeconomic inequality in health, where what matters is the individual's rank in the health distribution rather than their rank in the income distribution. The approach suggested here, when used in the measurement of pure health inequality, is a natural alternative to Atkinson's index. The second direction in which the paper extends the literature on the measurement of health inequality is to recognize that policymakers are unlikely to be concerned only about health inequalities, either of the pure variety or the socioeconomic. Rather they are likely to be willing to trade off increases in inequality against improvements in the mean of the distribution (cf. e.g., Wagstaff 1991). This paper shows how, as in the income inequality literature (see e.g., Lambert 1993), a single summary measure can be computed that reflects both average health and inequality in its distribution. This index is termed here an index of "achievement," but is in effect an abbreviated social welfare function-albeit in the health domain. Again, the exposition is for the case where the interest is in socioeconomic inequalities, but the application to the case of pure inequality is immediate. The plan of the paper is as follows. The first part of section II generalizes the concentration index to allow the degree of inequality aversion to be specified. The second part of section II proposes the achievement index that combines information on inequality 2 There has been a lively debate over which of these approaches makes more sense and squares better with policymakers' views. See, for example, Alleyne and others (2000), Bravernan and others (2001), 3 with information on the average level of health. Section III presents some empirical illustrations of these two measurement tools using data for 44 developing countries on socioeconomic inequalities in and average levels of three health indicators: under-five mortality, child malnutrition, and fertility. 2. Measurement issues The starting point is the measurement of health inequalities. To make the discussion more applicable to typical health indicators, it is assumed that the health variable measures ill health. It might be an index based on, say, a self-assessed health question (Wagstaff and Van Doorslaer 1994; Gerdtham and others 1999; Humphries and van Doorslaer 2000). Or it might be an anthropometric measure of malnutrition (Wagstaff and Watanabe 2000; Wagstaff, van Doorslaer, and Watanabe 2001). Or it might be a binary variable capturing death prior to a certain age (Wagstaff 2000). The approach is easily modified for health measures that are increasing in good health. This section summarizes the basics of the concentration curve and concentration index, and then shows how the concentration index has underlying it an implicit value judgement concerning the weights to be attached to people in different points in the income distribution. The section then shows how the index can be extended to make explicit differing attitudes to inequality. Finally, the section shows how information on the average and on the degree of inequality can be combined into a single summary measure of health achievement that is linked to extended concentration index. 2.]. The concentration curve and concentration index Suppose we want to measure inequalities in health by income, or some other measure of socioeconomic status (SES). (The case of pure inequality is easily handled, and is discussed briefly below.) We rank individuals by their household's income (or whatever measure of SES we are using), starting with the most disadvantaged. Let p be the cumulative proportion of people, so ranked. The curve labelled L(p) in Figure 1 is an Evans and others (2001), Gakidou and others (2000), Le Grand (1987), Wagstaff (2001) and Whitehead (1992). 4 ill-health concentration curve. It plots the cumulative proportion of ill health (on the y- axis) against the cumulative proportion of individuals (on the x-axis), ranked by living standards. If the curve L(p) coincides with the diagonal, everyone, irrespective of their economic status, enjoys the same level of ill health. If, as is more likely, L(p) lies above the diagonal, inequalities in ill health favor the better-off; we will call such inequalities prorich. If L(p) lies below the diagonal, we have propoor inequalities in ill health (inequalities to the disadvantage of the better-off). The further L(p) lies from the diagonal, the greater the degree of inequality in ill health between the poor and better-off. If L(p) of country X is everywhere closer to the diagonal than that of country Y, then countryXs concentration curve is said to dominate that of country Y It seems reasonable in such cases to conclude that there is unambiguously less inequality in ill health in country Xthan in country Y. Fig 1: III health concentration curve 1009- L L(p) 0%W 0% 100% cumulative % of persons, ranked by economic status Where concentration curves cross, the literature to date has used the concentration index as a tiebreaker. This index, denoted below by C, is defined as twice the area between L(p) and the diagonal, or equivalently one minus twice the area underneath the concentration curve: 5 C takes a value of zero when L(p) coincides with the diagonal and is negative (positive) when L(p) lies above (below) the diagonal. For individual-level data, C is equal to (Kakwani, Wagstaff, and Van Doorlsaer 1997) (2) C =-2En R-1 where n is the sample size, yi is the ill-health indicator for person i, ,u is the mean level of ill health, and R, is the fractional rank in the living-standards distribution of the ith person (i.e., the empirical analogue ofp). In the case where one wants to measure pure inequalities, the only change one has to make in the above is that one ranks by health (or ill health), beginning with the most healthy (or least healthy in the case where the health measure is a measure of ill health). The resultant index is, of course, the Gini coefficient. 2.2. Attitudes to inequality Like the Gini coefficient, the concentration index implicitly embodies a particular view about where in the income distribution reductions in health inequality matter most. One way to see this clearly is to rewrite eqn (2) slightly differently:3 (3) C =l 1- E" Iyi(I -Ri) The two expressions are equivalent. The quantity (yi/np) is the share of health (or ill health) enjoyed (or suffered by) person i. This is then weighted in the summation by twice the complement of the person's fractional rank. Thus the poorest person gets their health share weighted by a number close to two. The weights decline in a stepwise fashion, reaching a number close to zero for the richest person. The concentration index is simply one minus the sum of these weighted health shares. 3 Replace -I in eqn (2) by [1-2(Zyi/n1u)] and then rearrange terms. 6 In the income inequality literature, a variety of indices have been proposed that allow the analyst to specify explicitly the degree of aversion to inequality and then to experiment to see how sensitive the rankings of countries are to the value judgements. Of these indices, the most useful in the present context is Yitzhaki's (1983) extended Gini coefficient. Like the approach proposed by Atkinson (1970), this involves a parameter capturing the extent of aversion to inequality. The extended concentration index is equal to: (4) C(v) 1 -v(v 1) I (I1 p)v- L(p)dp, v>l . Setting v=-2 gives the standard concentration index. One way of seeing clearly the ethical judgements underlying the extended concentration index4 is to write it down along the lines of eqn (3), namely5 C(v)_=1 V n yi (1 Ri) (5) nfl,u = = 1-1L. (yi /n ASi (Ri, v), where wi(Ri, v)= v(l -R1)(>) is the weight attached to the ith person's health share, (y,lnu). Whatever the value of v, the average value of wi is one.6 When i-, wi= and everyone's health is weighted equally. This is the case where the investigator is indifferent to inequality, and C(1)=0 however unequal the distribution of health is across the income distribution. As v is raised above 1 toward 4 (see Figure 2), the weight attached to the health of persons in the top four quintiles falls, while the weight attached to the health of persons in the bottom two deciles rises. For people in the middle four quintiles, the precise effect on wi of raising v above 1 toward 4 depends on their location in the income distribution and on the values of v in question. The general conclusion, though, is clear: as v is raised above 1, the weight attached to the health of a very poor person rises, while the weight attached to the health of people who are above the 55th percentile decreases. 4There are other ways of showing the implied value judgements-see e.g., Yitzhaki (1994). 5 See Appendix for derivation of eqn (5). 7 As can be seen, for v=6 the weight attached to the health of persons in the top two quintiles is virtually zero. When v is raised to 8, the weight attached to the health of those in the top ha/f of the income distribution is virtually zero. Fig 2: Weighting scheme for extended concentration index-eqn (5) 4.0 - -_ _ . 3.5 _ _ 3.0- 2.5 - -+v=I .'2.0 v_2 _ X_ 1.5- 0.0 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 rank 2.3. Measuring achievement Overall "achievement" in health can be thought of as reflecting the average level of health and the inequality in health between the poor and better-off. In the context of the above index, the obvious way of thinking about achievement is as a weighted average of the health levels of the members of the community, where higher weights are attached to poorer people than to better-off people. Thus achievement might be measured by the index: (6) I(v) =- 1 yiv(1 - R ) (V-I) 6 This is true when individual-level data are used. The situation where grouped data are used is a little more complex. See the appendix on this issue. 8 which is a weighted average of health levels, where the weights are as graphed in Fig 2 and average to one. It turns out7 that this index is simply equal to: (7) I(v) = ' f(- C(v)) . Consider the case where the health indicator is a measure of ill health (so high values of I(v) are considered bad) and C(v)<0 (ill health is higher amongst the poor). Inequality serves to raise the value of I(v) above the mean (making achievement seem worse than it seems when looking just at the mean). So, for example, two countries might have the same value of I(v), but one might have a high mean but an equal distribution across income groups while the other might have a lower mean but an unequal distribution across income groups to the disadvantage of the poor. Or suppose that the mean stays unchanged over time but the distribution of health becomes more prorich. In this case, even though ,u has not changed, I(v) rises, assuming that v>l. If ill-health declines monotonically with income, the greater the degree of inequality aversion, the greater the wedge between the mean and the value of the index I(v). 3. Empirical illustrations In this section, these methods are illustrated for three health indicators-under- five mortality, child malnutrition, and fertility. The computations are based on grouped data from 44 developing countries, taken from tabulations by Gawtkin and others (2000) on data from the Demographic and Health Survey (DHS). The tabulations show average values for each of five "wealth" quintiles. 3.1. Data and methods Three indicators have been selected. The first is under-five mortality (U5MR), which is simply the proportion of children dying before they reach their fifth birthday. The second is child malnutrition, as measured by the proportion of under-five children who are classified as underweight, based on anthropometric measures (Alderman 2000). 7 ThS is most simply seen by substituting eqn (5) into eqn (7) and rearranging to get eqn (6). 9 The third indicator is the adult total fertility rate (TFR), defined as the total number of children a woman would have by the end of her reproductive period if she experienced the currently prevailing age-specific fertility rates throughout her childbearing life. All three indicators feature in the international development targets (International Monetary Fund and others 2000), and there are specific targets for the first two.8 There is, however, a concern (Gwatkin 2000) that progress toward population-based targets could mask uneven progress across socio-economic groups. Indeed, there is evidence that in some countries progress in reducing child mortality and malnutrition has been slower amongst the poor (Victora and others 2000; Stecklov, Bommier, and Boerma 1999; Vega and others 2001; Wagstaff, van Doorslaer, and Watanabe 2001). Households were ranked in the production of the tables in Gwatkin and others (2000) using an index of wealth obtained from a principal components analysis (PCA) of questions on housing characteristics (e.g., the material from which the floor is made of) and ownership of household durables (e.g., bicycle, refrigerator, etc.) (Filmer and Pritchett 1999). These methods along with the factor score matrices are reported elsewhere (Gwatkin and others 2000). The data are in grouped form, based on quintiles of households. The denominators relevant for computation of the concentration indices are the sample at risk (e.g., children under the age of five in the case of child malnutrition) so that the groups are not necessarily quintiles of the sample at risk. In the case where grouped data are used to compute the extended concentration indices, certain modifications need to be made to the equations in the previous section. These and other computational issues are discussed in the Appendix. 3.2. Poor-nonpoor inequalities Inequalities to the disadvantage of the poor are evident in all three health indicators (see Tables 1-3). They are especially pronounced for malnutrition, where the average value of C(2) is equal to -0.1475. The extent of prorich inequalities varies across countries, the values of C(2) ranging from -0.2590 (Brazil) to 0.0020 (Kazakhstan) in the 8 The targets are to reduce the under-five mortality rate by two-thirds between 1990 and 2015, to halve the percentage of children suffering from malnutrition between 1995 and 2015, and to reduce child 10 case of the under-five mortality rate, from -0.4167 (Dominican Republic) to -0.0487 (Niger) in the case of malnutrition, and from -0.2530 (Peru) to -0.0048 (Central African Republic) in the case of the TFR. The concern here is not so much with inequalities per se (important as these are) but rather with the extent to which measured inequality varies according to the weight attached to the poor in the computation of the inequality index. As expected, raising the value of v above 2 results in more prorich inequality. Thus, for example, for malnutrition the average value of C(8) is -0.3375 while the average value of C(2) is only -0.1475. Interestingly, the impact of raising v varies across countries. For example, raising the value of v from 2 to 8 causes the extended concentration index for TFR in Chad to fall from -0.0157 to -0.0777-a fourfold change. By contrast in Cameroon, the change is far smaller-from -0.0627 to -0.0843. This reflects the fact that in Chad, the TFR amongst the poorest group differs quite dramatically from the rest of the sample while in Cameroon the poorest group actually has a lower TFR than the second poorest group. Another country whose extended concentration index is highly sensitive to the choice of v is Brazil. In the case of the TFR, for example, raising the value of v from 2 to 8 causes the extended concentration index to fall from -0.1197 to -0.6593. This is a smaller percentage change than the change in the case of Chad, but the absolute change is much larger. This reflects the fact that the TFR amongst the poorest quintile in Brazil is much higher than that amongst the other four quintiles. The heavy concentration of high fertility in the poorest group in Brazil is reflected in that county's dramatic change of rank in the TFR inequality "league table" as v is raised above 2. For v=2, Brazil is ranked 34 out of 43. When v reaches 8, Brazil is almost bottom (number 42). Namibia, by contrast, where the poorest group has a somewhat lower TFR than the second poorest group, sees its rank position improve from 25 to 17. While these are just examples, they serve to illustrate the point that both measured inequality and the rankings of countries by inequality can be quite sensitive to the decision of whether to depart from the implicit weighting scheme of the standard concentration index and of so by how much. malnutrition to under 15 percent by 2015 (International Monetary Fund and others 2000). 11 3.3. Health achievement The need to take into account inequality as well as the average level of health is also evident from Tables 1-3. Many countries that do well on one dimension (e.g., the average) do badly on the other (e.g., inequality). Brazil, for example, has low average levels of under-five mortality, child malnutrition and fertility, but the inequalities between the poor and the better off are very large. By contrast, Niger has fairly small gaps between the poor and the better off on all three indicators, but the average values of the indicator are extremely high. It is important is assessing achievement to think not just about the mean, nor just about inequality, but about both. Moving from a focus on the mean to a focus on the achievement index produces some interesting results, especially for the TFR indicator. In the average TFR league table, for example, Mozambique comes 23rd out of 43. If achievement is measured using the index I and v is set at 2, Mozambique's position improves to 22 (the inequality in Mozambique is very low). If v is raised from 2 to 8, Mozambique moves up another eight places in the TFR achievement league table to number 14. A counterexarnple is Guatemala. In the average TFR league table, Guatemala is ranked 29 with a TFR of 5.08. By contrast, in the achievement league table with v set at 2, Guatemala is ranked 32. If v is raised from 2 to 8, its position slips to 41 with an achievement score of 7.54. 4. Summary and conclusions To recap briefly, the concentration index has embedded in it a particular set of value judgements about the weights to be attached to the health of people at different points in the income distribution. The standard concentration index can be shown to be equal to the complement of a weighted sum of the health shares of the individuals in the sample. The weights decline in a stepwise fashion, starting with a weight close to two for the poorest person, declining by equal steps for each one-person move upward through the income distribution, and reaching a number close to zero at the top end of the distribution. The extended concentration index allows different weightings to be used and hence the value judgements built into the calculations to be made explicit. By setting the 12 inequality aversion parameter v equal to 2, the extended concentration index reverts to the standard concentration index. By setting a value of v above 2, the analyst raises the weight attached to the poor (compared to the weight in the standard concentration index) and reduces the weight attached to the better off. Reducing the parameter v below 2 has the opposite effect. The paper also showed how inequality, as measured by the extended concentration index, can be combined with information on the average to measure overall health achievement. It was shown that by measuring achievement as a weighted average of health levels, where the weights are the same as used in the extended concentration index, the resultant index is in fact simply equal to the product of the average and the complement of the extended concentration index. In the case where the measure of health is a measure of ill health, and ill health is higher amongst the poor and hence the concentration index is negative, pro-rich inequality raises the level of achievement (or "disachievement") above the mean, by a percentage that is equal to the value of the extended concentration index. The methods were illustrated using distributional data on under-five mortality, child malnutrition and adult fertility for 44 developing countries. The results illustrate two important points, each of which has an important implication. First, levels of inequality and the rankings of countries can both be sensitive to how far one deviates from the implicit value judgements underlying the concentration index. In countries where the health of the poor is very much worse than that of the rest of the population, the increase in measured inequality when one weights more highly the health of the poor can be quite marked. This suggests that in future empirical work on health inequalities, especially in contexts where there is a specific concern with the health of the poor, more attention should be paid to the sensitivity of results-including country rankings-to the weighting scheme used in the health inequality measure. The second important point to emerge is that noteworthy changes-including major rank changes-result when one moves from an assessment of achievement based solely on the average to an index of achievement that captures both the average and the extent of inequality between the poor and better-off. These changes are especially pronounced when the weight attached to the 13 poor is increased substantially above the weight implied by the standard concentration index, and when ill health is highly concentrated amongst the poor. This suggests that if it is indeed a concern of the international development community to ensure that improvements in health are disproportionately concentrated amongst the world's poor, it would make sense to move away from the use of population averages toward the use of an index of achievement such as that proposed here that captures both average health levels and the often large inequalities in health between the poor and better off. Appendix Derivation of eqn (5) Lerman and Yitzhaki (1984) show that the extended Gini coefficient (the same logic applies to an extended concentration index) can be written as: (Al) C=--cov(yi,(l-Ri)v-1) Like the standard concentration index, this can be written as a convenient regression (Jenkins 1988; Kakwani, Wagstaff, and Van Doorlsaer 1997). In this case the regression is: (A2) - vvar[(I -Ri) ]- [yi /p] = a, +,B, (1 -R, )v- ui, where ,BI is the extended concentration index. Denoting the LHS variable by Yi and the RHS variable by Xi, the OLS estimate of /l is equal to EXi Yi - n YXY Xi £XY; YX- (A3) A- 2 2 2 ncx no-x ax From the definition of Yi, we have (A4) Y=- vcrx _vox n Substituting this and the definition of Y' into (A3), and using the definition of Xi, yields: 14 EAOXivc (Y,/p) + VU' 2 2 nax ax (A5) =-,, £Y(I - Ri)v- +-E (1-R )"-1 n for large n. Computation of C(v) on grouped data From eqn (A5), it is clear that the analog of eqn (5) is equal to: (A6) ~C(V) =S2T A (R (V-I) v ST (1R)v) wheref is the sample proportion in the tth group, yt is the average level of ill health of the tth group, and R, is its fractional rank, defined as (A7) R, t lr 2 tt and indicating the cumulative proportion of the population up to the midpoint of each group interval. Typically, the first term will not equal one on grouped data. 1s Table 1: Under-five mortality levels and inequalities 'LO -4 0 v=6.0 -8 0 R..k I(V) Rar- -f(v) RaW -Rank IT() Rank CI(v) TR 1() Rank CI(V) Rank f(v) Rak CI( Ra Cl() I ak Bangladesh 24 0.0553 13 134 93 24 -0.0841 14 I3&61 23 --OA085 11 141.74 23 -0.1043 - 9 141.20 23 -0 0966 9 14012 23 -00534 12 N4.90 3 38 -0 1106 Benin 184.38 36 19422 37 -0.0814 13 199-39 36 -0.1 1 13 12 9- -0.-1143 10- 44 12 204 79 38 Boji,ja 99 40 19 -o 1351 41 12,83 19 .2218 41 I 21.44 1 9 -0 3593 39 135.12 2 1 -b.3895 39 138 11 20 -0.3825 38 137.42 20 9 4 65 44 9 11 - 8 -0 1441 46- 5 10 o 2590 44 7 63 8 0 5056 44 95 66 10 0 5786 -4 89 81 10 733 - 8 51 - - - - - 112 99 39 0 1243 14 .1173 11 155 92 26 -0.1062 10 15438 261 Yurkina Faso 40 0 0624 18 148,26 27 0 0398 3 15 26 -0 -- - - -- Car ner. 143.38 29 -00938 32 156,83 32 -0 1594 33 166 24 31 -0 2783 35- 183.29 34 03180 35 188.98 36 -0.3296 36 190.64 37 -6--- - 2 1 7 35 -0 1850 23 87 76 35 34 -0 067i5 20 915 35 -0.1103 C75.92 34 -0 1742 22 IM04 35 -o H& 22 Igm ihad 201 01 39 -0.0095 2 202,92 39 0.0069 2 202.38 37 0 0383 2 193 31 37 O0763 2 185 68 34 0.0980 1 181.30 32 Colombia 37 36 1 -0 0752 40.17 -0.1306 28 42.24 1 -0 2547 9 2 -03016 33 48.63 2 _-0.3086 34 _48 89 2 -21 --12 - - -F 112.49 -0.0577 1 7 118 97 2 1 -0 6955 1 8 123 2 1 0 1438 6 1 8 -0 1416 1 8 28.41 1 8 -61305 14 127.16 9. 068 - 166 0 1930 33 2153 26 82 29 Cote d1voie 14 99 32 -0. 9 22 -33 33 - - 22 167 17 32 - --- - --- 33 O.:ZI73 29 182 33 Do. Re, 61 04 9 -0-1237 38 68,59 9 -0.2079 38 73.73 9 -0,3524 82,56 8 -0.3890 _ 38 _ 84.79 9 -0 3875 39 84.70 9 95.78 Is -0 1357 42 108.79 IS -0.2311 42 117 92 18 0 4006 42 134.16 20 -0.4435 42 138.27 21 -0 4402 42 137.95 Kg Y::P:l Q _ 21 Gbma L32 96 25 0 0834 29 14193 25 -0.1346 30 1'. 7 26 -0 1945 27 159 70 29 -0 1913 24 158 27 28 -0.1780 22 156.50 28 Guataniala 79A2 1 4 28 85,60 14 -0 1188 25 88A5 14 -0 1484 20 9121 1 2 -0 1326 1 5 89.95 1 1 -0.1147 1 3 88.52 1 0 Haiti -T40,63 29 -0.0432 9 -0.009 1 0 150 61 15 :10_11110 0 I17 21 2S -0 I314 I4 - - - -0- 1323 15 156 25 N 694 - - -T5 H - 36 139 05 24 -0.2619 33 15004 24 -0.2726 fndia 18 91 22 1038 36 131 25 23 0 1 32 1 33 25 -6 2627 3 1 150 15 25 Indonesia 7051 1 1 -0.1240 39 79 25 1 2 -0.2102 3 9 85.33 1 3 -j3731 4 1 96.81 1 3 -04274 4 1 100.64 1 3 -0.4356 4 1 101.22 1 4 49.22 4 40079 1 4&60 2 0.0020 1 48.12 2 0.0555 1 45.54 1 0.0792 1 44 45 1 0 0840 2 44 17 1 105.14 20 -0.0895 3 1 20 121.63 2 0 -0,290-0 36 13563 22 -0.3205 3 6 138.83 22 -0,3124 3 5 -137.98 22 75 93 1 2 .6 92 23 81 19 1 3 -0.1151 84 67 I 1 -0.1942 26 90 67 1 1 -01159 27 92.32 12 -0 2147 27 92 24 12 Madagascar 164 24 35 -0 06833 21 175,47 36 -0 1094 20 182 21 35 -0.1611 21 190 36 -0.1634 20 191.08 371 -0.1531 191 18939 36 239.90 42 -00319 5 247 44 419 42 42 8 -40515 5 252.14 4 1 -0.0497 5-2-51.72 411 -9.0481 5 251 34 41 43 -0 0556 14 6.16 43 -0.0901 17 274.85 43 -0 1422 1 9 287 99 43 -0.1550 19 291 20 43 -0 1551 20 291 24 43 84 06 1 6 O 0940 33 91 96 16 -0 1537 3 1 96 98 16 -0 2500 30 10509 1 -0.2 106 98 161 -0.2690 32 106.67 16 Mozarnbique 218.14 4 1 .0.0703 241 233 47 4 1 -0 1184 24 243 97 4 1 -0 2015 28 262 09 42 -0 2168 28 265 42 42 -0.2047 26 262.79 4 Narnibia 91.96 17 -0 0311 4 94.72 17 -0.0532 7 96.751 15 -0 1067 10 101.66 -0.1373 16 104.47 1 5 -0.1515 18 105.78 15 -T39.55 26 -0.0624 18 48 26 27 -0.0960 15195 28 -0.1243 14 15690 26 4 1 173 H 155,92 26 -0.1062 Repal 10 154 38 26 Niewagua 56 25 7 -0 0773 27 60 59 6 -0.1241 26 63.23 6, -0.1897 24 66.91 6 -0.1964 25 67.29 6 -0 1861 25 66 71 6 3 44 -0.0252 3 310 59 44 0.0 293.84 44 Niger --iO2 95 44 0 0406 8 15 26 44 -(W537 8-1-9 21 - 088 3300.29 44 0 0301 3 191 56 37 O 0767 26 2C6.26 40 -0.1275 27 215 99 40 -0.2061 29 231 04 40 -0-2201 29 233 72 40 -0.2157 28 232 98 40 ---b - -- - ---! I 9 -0.0626 127 24 19 862 15 130.07 22 0981 7 13 1 A9 1 9 (Y0795 6 129.26 119 74 23 .0 0569 16 126. 22 -0 0 6 -Ag""Y 46.59 3 -0 08 30 5059 4 -0 1334 29 52 80 3 -0.1852 23 55 21 3 -0,1910 23 55A8 3 --0.1853 24 55.22 3 Feru 68 70 43 78 21 10 -0.2357 43 84.89 12 0 4247 43 97 97 14 0 4759 43 TOI 39 14 -0 4674 43 100 80 13 - -T54 o i if -0 1636 -0.2550 32 175.76 31 -0.2666 30 177.39 31 se-neg.i - -T4o o5 - 27 -0 0997 35 35 162.97 30 -0.2584 30 17624 31 Tanzania --1444 69 3 1 -0.0367 6 150.01 29 -0.0513 6 152.11 27 -0.0398i 4 150.45 2 -0.0160 4 147 00 24 0 0010 4 144 54 24 - u- 61 24 7 - .3556 37 74.64 Th Phhp.,, 55 07 5 0 122 37 75.14 7 7 Togo 144.37 30 -0.0557 15 152-41 30 -0 0987 1 6 157,17 29 -0 1317 16 163 39 30 -0 1383 17 164 33 _ 30 --:70.1349 16 163.84 30 T.rkey 80.66 15 -OiZ61 40 90 83 15 -0.2104 40 9T63 17 -0,3664 40 110.21 17 -OA216 40 114.66 17 -0 4322 40 115.52 17 Ug.da, 156.28 331 -0.0476 11 163 71 34 -0.0786 12 168.55 33 -0.1373 17 177.73 32 -0.1646 21 182.01 32 -0.1756 21 18172 34 Uzbekistan ---- -i-- - - --7 55M 6F-00 59 3 6 69 5 -0 466 5 5T83 5 0 OW4 8 %76 5 -0 1291 1 3 62 34 5 -0,1388 1 7 62 9 Victnarn 46 03 2 -0.09 6 34 50 43 3 -1.1595 34 5337 4 -0,2730 34 58.59 4 -0445 60.05 - .3042 33 606 bia  92 31 8 0.04651 10 -0.0733 06.401 39 -OA026 9 212 04 39 8 _r WWI IOj -0 08721 8163 7 6 01 1 3 -0 04017 '79 05 1 , _0 61 8 Y ba I 1 -6.0137 9 -0.0971 7 83.39 8 -0 0954 24 33 40740 1 131.061 --105 L43= 1 I - I43 41 jkyrage 4 192 144 +6 16 Table 2: Child malnutrition levels and inequalities V~ .0 V=-1. 5 v-2.0 __ ___ v=4.0v60v80 1()Rank CI(y) Rank I (v)I Rank _I(v) Rank 1(v) Rank QIv) Ranki 1(v) Rank CI (v) Rank*jv) RanklCI (v) Rank Rn Bangladesh 47.66 38 -0.0741 141 51.191 39 -0.1213 14 53.44 39 -0.1961 13 57.01 39 -0.21681 14 57.99 39 -0.2196 141 58.13 39 Baiin 29.26 29 -0.0778 171 31.54 2 -0.1312 17 33.10 29 -0.2228 18 35.78 29 -0.242 L1 36.36 28 -0.2397_ 161 36.27 28 Bolivia 8.99 7 -0.1781 351 10.59 7 -0.3125 35 11.-80 ___ 7 -0b.5-964 -36 14.36 8 -0.6890 __36 15.19 8 -0.6957 361 15.25 _ 8 Brazil 5.3 2 -0.1868 36 6.80 2 -0.3398 37 7.67 _21 -0.6812 37 9.3 2-0.7843 37 10.22 2 -076 371.7_ 2 Burkina Faso 46.88 36 -0.0561 6 49.51 36 -0.0867 4 50.95 36 -0.1206 4 52.54 37 -0.1222" _ 4 52.61 37 -0.1162- 4 52.33 37 Can~~zoun 15.11 1 3 -0.1257 3 1 17.01 141 -0.2127 311 18.33 14 -0.36451 31 20.62 1i4 -048 22.9 1 04677 32 22.18 1 CAR 27.08 251 -0.06321 9 28.79, 22 -0.1091 9 30.03 22 -0.2033 15 32.59 '22 -0.2462 _ 19 33.75 23 -0.2658 _ 19 34.28 25 Chad 38.76 321 -0.05431 5 40.861 32 -0.0924 8 42.34 33 -0.1687 9 45.30 33 -0.2018 _ 13 46.58 34 -0.2151 13 47.09 34 Colonmbia 8.36 6-0.16951 34 9.78 6 -0.2931 34 10.81 6 -0.5345 34 12.83 6 -0.6040 34 13.41 61 -0.-6024 -34 13.4-0 -6 Comoma 25.84 211 -0.08901 22 28.14 21 -0. 1572 23 29.90 2 1-0.2935 27 33.43 25 -0.3299 28 34.37 26 -0.3298 27 34.37 26 Co-te cTlvoire 23.84 18 -0.0862 21 25.89 18-06.-14-10 -19 27.20 171 -0.2242 19 29.18 16 -0.2435 __18 29.64 161 -0.2436 17 29.64 16 DotRep 6.03 3 -0.2362 40 7.45 3 -0.4167 40 8.54 31 -0.7916, 40 10.80 3 -0.9019 40 -11.46 41 -0.8949 40 11.42 4 E&p 12.48 12 -0.0831 18 13.51 1 1-0.14541 22 14.29 1 1-0.2727 24 15.88 10 -0.3149 25 16.41 101 -0.3211 26 16.48 10 Ghana ~~27.17 26-.89 23 29.61 25 -0.1420 20 31.02 26 -0.1983 1 325 21 -0.20181_ 12 32.65 211 -0.1979 113.4 2 Guatan-1a 26.66 24 -0.1174 29 29.79 27 -0.1857 28 31.61 27 -0.2725 23 33.93 26 -0.2793 22 34.11 25 -0.2662 20 33.76 23 Haiti 27.47 27 -0.1035 27 30.31 28 -0.1693 26 32.12 28 -0.2873 26 35.36 28 -0.3270 27 36.45 29 -0.3336 28 36.63 29 Inda 5.91 40-.55 8 5. 90 40 -0.0920 7 56.68 40 -0.1351 6 89 0 -.32 6 59. 13 40 -0.1345 __6 58.89 40 Kazakhatan 8.32 5 -0.1205 30 9.32 4 -0.1973 30 9.961 4, -0.3093 29 10.89 4 -0.3234 26 11.01 3 -0.3124 25 10.92 3 Kenya 22.08 1 6 -0.1109 28 24.53 16 -0.1865, 29 26.20 16 -0.3232 30 29.22 1 7-0.3609 30 30.05 17 -0.3573 30 29.917 1 7 KyrgRep 11.03 1 0 -0.0688 1 011.79 9 -0.1120 10 1i2-.27 -8 -0.1585 8 12.78 5 -0.1543 8 -12.73 5 -0.1435 __7 12.61 __5 b4adaguscar 40.10 34 -0.0311 1 41.341 33 -0.0508 2 42.14 32 -0.0880 2 43.63 32 -0.0997 _ 2 44.10 32 -0.0991 2 44.07 32 Nalawi 27.75 28 -.0701 1 297 26 -0.1151 1 1 30.94 25 -0.1835 1 1 32.84 23 -0.1987 1 1 33.26 22 -0.1983 12 33.25 22 Mali 140.08 33 -0.0531 3 42.20 34 -0.0871 6 43.56 34 -0. 14-06 -7 45.71, 34 -0.1539 7 46.'25 33, -0.1544 8 46.26, 33 Mon,cco 9.49 81 -0.1925 37 11.32 8 -0.3308 36 12.63 9 -0.5901 35 15.101 9 -0.6632 35 15.79 9 -0.6640 35 15.801 9, Mozarmbiu 26.12 22 -0.1026 26 28.80 24 -0.1759 271 30.72 241 -0.3086 28 34.19 27 -0.3475 29 35.20 27 -0.3515 29 35.31 27 Nanilbia 26.21 23 -0-.0-988 25 28.80 23 -0.16261 241 30.47 231 -0.2612 22 33.06 24 -0.2897 23 33.80 24 -02967 24 33.98i 241 Nepal 46.88 36 -0.0561 6 49.51 36 -0.08671 4 50.95 36 -0.1206 4 52.54 37 -0. 17'222_ 4 52.61 37 -0.1162 4 52.331 37 Nicaragua 12.16 1 1 -0.1404 32 13.871 1 2-0.2336 32 15.01 -12 -0.3893 32 16.90 1 1-0.42201 3 1 17.30 1 1-0.4104 3 1 17.161 1 1 Niger 49.48 39-0.0327 2 51.101 38 -0.0487 1 51.89 38 -0.0584 1 52.37 36 -0.0552 _ 1 52.21 36, -0.0515 1 52.03 36 Nigeria 35.64 -31 -0O034 4 37.551 3 1-0.0822 3 3-8.57 31I -0.1112 3 39.61 31 -0.1134 _ 3 39.69 311 -0.1101 3 39.57 31 Pakistan 40.21 351 -0.0768 15 43.30 35 -0.1306 16 45.46 _35 -0.2273 20 49.35 35 4-02622 -20 50.76 351 -0.2758 22 51.30 35 Para9iY 3.66 11 -0.1669 33 4.28 1 -0.2790 33 4.69 1 -0.4631 33 5.36 __1 -0.5011 33 5.50 __1 -0.4876 33 5.45 _ 1 Peru 17.75 4-0.2238 39 9.48 5 -0.3934 39 10.80 5, -0.7552 39 13.60 7 -0.8709 __39 14.50 7 -0.8730 38 14.52 _71 Tanzania 30.6 30-0.0771 16 33.03 30 0 127 15 3.9 0-024 16 7.25 30 -0.2413 1 380 30 0245 18 38.16 301 Lop~ 25.10 1 005 20 27.25 1 -0.13871 181 28.58 20 -0.2197 17 30.61 201 -0.2359 15 31.02 20 -0.23051 15 30.88 201 Turkey 10.40_ 9 -0.1972 38 12.45 10 -0.3505 381 14.04 10 -0.6981 38 17.66 121 -0.84081 38 19.14 13 -0.8826 39 19.57 13 Uganda 25.53 20-.78 12 27.34 20 -0.1154 228.48 19 -0.1797 103.2 9-.90 10 041 9-.87 10 031 9 LJzbekistan 1.8 15 -0.0832 192.5 15 -0.142 2 1 21.46 1 5-0.2539 21 23.55 1 5-0.2784 2 1 24.01 1 5 6-02711 21 2388 -15 Zambia 23.44 17 -0.0982 24 25.74 -17 -0.1654- 25 27.32 18 -0.2755 25 29.90 18 -0.2959- 24 30.3~7 18 -0.2861 23 30.14 -18 iZimb.b. I 15..52 14 -0.07-39 131.7 13 -0.1205 13 17.39 13 -0.1854 12 18.4 13 -0.1901 9184 12-.75 9 830 2 [Average - 24.64 - -0.-1-033 I__ 266 -0.1745 - 279-030 3.1-031 3.0 - -0353.2 - 1 7 Table 3: Levels of and inequalities in total fertility rates V--1.0 v--1.5 v--2.0 ___ w40 __ _ v=6.0 ___ _ 80 1(v) Rank CIv) Rank 1(v)Rank CI(y) Rank T(5 an CI(vVF Rak 1()Rank ON() Rak ()Rnk Cv) ak 1() ak Bangladesh 3.28 9 -0.0590 13 3.48 9 -0.0952 12 3.60 8 -0.1404 11 3.75 6 -0.1452 11 3.76 5 -0.1414 11 3.75 5 Benin 596 35 -0.0718 ~~~16 6.39 36 -0.1185 1567 38 -0.1838 15 7.06 36 -0.1957 15 713 37 -01950 15 712 34 Bolivia ____ 4.2 16 -.17 42 4.78 1 7 -.2452 42 5.23 19 -0.4748 41 6.20 25 -0.5 70 40 660- 29 -0.12 40 .7 29 BnIzi 2.51 4 -0.1074 34 2.78 -4 -0.1997 34 3.01 _ 5 -0.4455 40 3.63 5 -0.5829 41 3.98 7 -0.6593 42 4.17 7 BiurIdnaFaso 4.67 19 -0.0733 19 5.02 20 -0.1228 18 5.25 20 -0.2144 19 5.67 19 -0.2498 9 8 19 0.60 85.9 7 Came~roun - 5.78 -34 -0.36 1 6.00 32 -0.0627 _106.15 30 -0.0946 10 6.33 27 -0.0925 9 6.2 25 4043 86.7 2 CA~R ___ 5.06 -25 -06.0-031 -1 5.08 22 -0.0048 1 5.09 18 -0. 0079 2 5.10 13 -.08 .1 3 -008 5.10 13 Chad 6~~-.-36 -39 -0.0080 2 6.41- 37 -.0157 335 -0 35 3 6.64 3 004 .7 3 007 .6 3 Col-ombia - 2.93 -6 -06.11-73 -35 -3.27 6 -0.21-12 -37 3.55 ___7 -0.:4279 3 4.18 10 -0.5336 38 4.49 It -0.5889 39 4.65 11 ~~omoros _ 4.60 18 -0.0825 26 4.98 19 -0.1432 27 5.26 23 -02617 2858 2 -.00_2 .1 21 -0312 2 60-8 -21 (oted'1lvoire -5.29 30 -.64 14 5.2 2 01024 14 5.83 28 -0.1649 13 6.17 24 -0.1798 12 6.2 24 -0.1815 12 6.25 2 DornRep 3.1TI7 -8 -0.04 30 -3.47 8 -0.1694 31 3.70 9 -0.3378 33 4.24~ 1 -0.19 34 4.49 10 -0.4597 34 4.62 10 Ghlana 5.14 27 -0.073 21 5.52 27 -0.1249 21 5.7-8 -27 -0.21-21 17 6,23 26 -0.2405 1 6 6.38 26 -0.2511 1 6 6.43 26 Guatamala 5.08 ~26 -029 40 5.74 30 -0.2259 40 6.23 32 -0.-4052 -35 7.14 40 -0.4650 35 7.45 41 -0.48401 35 7.54 41 Haiti 4.~-T73 -23 -0.6-1181 -37 -5.2-8 -26 -0.20-25 - 35 5.-6-8 -25 0-03481 34 -6.3-7 28 4)63-925 -33 6.58 -28 --0.4069 32 6.65 28 Ind-ia 309 7 -0.0727 17 3.32 7 -0.1249 20 3.48 6 -0.2213 21 3.77 7 -0.2560 22 3.88 6 0.86 23 3.92- 6 Indon-esia 2T66 --5 -0.0525 11 2.0 5-0.0893 1 1 2.90 4 -0.1597 12 3.09 2 -0.1859 14 3.16 3 0941 14, 3.18 3 Kaakstn .4 -.082 32270 3 -.146 30286 3 0.59 273.0 -.27 2 314 2-0272 4181 References Alderman, H. 2000. 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Nyairo Adult Time: Evidence from the Peru 34635 LSMS Panel Data WPS2745 Children's Work and Schooling: Nadeem llahi December 2001 S. Nyairo Does Gender Matter? Evidence 34635 from the Peru LSMS Panel Data WPS2746 Complementarity between Multilateral Dilip Ratha December 2001 S. Crow Lending and Private Flows to Developing 30763 Countries: Some Empirical Results WPS2747 Are Public Sector Workers Underpaid? Sarah Bales December 2001 H. Sladovich Appropriate Comparators in a Martin Rama 37698 Developing Country WPS2748 Deposit Dollarization and the Financial Patrick Honohan December 2001 A. Yaptenco Sector in Emerging Economies Anqing Shi 38526 WPS2749 Loan Loss Provisioning and Economic Luc Laeven December 2001 R. Vo Slowdowns: Too Much, Too Late? Giovanni Majnoni 33722 WPS2750 The Political Economy of Commodity Masanori Kondo December 2001 D. Umali-Deininger Export Policy: A Case Study of India 30419 WPS2751 Contractual Savings Institutions Gregorio Impavido December 2001 P. Braxton and Banks' Stability and Efficiency Alberto R. Musalem 32720 Thierry Tressel WPS2752 Investment and Income Effects of Klaus Deininger January 2002 M. Fernandez Land Regularization: The Case of Juan Sebastian Chamorro 44766 Nicaragua WPS2753 Unemployment, Skills, and Incentives: Carolina Sanchez-Paramo January 2002 C. Sanchez-Paramo An Overview of the Safety Net System 32583 in the Slovak Republic Policy Research Working Paper Series Contact Title Author Date for paper WPS2754 Revealed Preference and Abigail Barr January 2002 T. Packard Self-Insurance: Can We Learn from Truman Packard 89078 the Self-Employed in Chile? WPS2755 A Framework for Regulating Joselito Gallardo January 2002 T. Ishibe Microfinance Institutions: The 38968 Experience in Ghana and the Philippines WPS2756 Incomeplete Enforcement of Pollution Hua Wang January 2002 H. Wang Regulation: Bargaining Power of Nlandu Mamingi 33255 Chinese Factories Benoit Laplante Susmita Dasgupta WPS2757 Strengthening the Global Trade Bernard Hoekman January 2002 P. Flewitt Architecture for Development 32724 WPS2758 Inequality, the Price of Nontradables, Hong-Ghi Min January 2002 E. Hernandez and the Real Exchange Rate: Theory 33721 and Cross-Country Evidence WPS2759 Product Quality, Productive Aart Kraay January 2002 R. Bonfield Efficiency, and International Isidro Soloaga 31248 Technology Diffusion: Evidence from James Tybout Plant-Level Panel Data WPS2760 Bank Lending to Small Businesses George R. G. Clarke January 2002 P. Sintim-Aboagye in Latin America: Does Bank Origin Robert Cull 37644 Matter? Maria Soledad Martinez Peria Susana M. Sanchez WPS2761 Precautionary Saving from Different Richard H. Adams Jr. January 2002 N. Obias Sources of Income: Evidence from 31986 Rural Pakistan WPS2762 The (Positive) Effect of Norbert R. Schady January 2002 T. Gomez Macroeconomic Crises on the 32127 Schooling and Employment Decisions Of Children in a Middle-Income Country WPS2763 Capacity Building in Economics: Boris Pleskovic January 2002 B. Pleskovic Education and Research in Transition Anders Aslund 31062 Economies William Bader Robert Campbell WPS2764 What Determines the Quality Roumeen Islam January 2002 R. Islam of Institutions? Claudio E. Montenegro 32628