_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ W PS 291L,E POLICY RESEARCH WORKING PAPER 2714 On Decomposing the Causes Amethodfordecomposing inequalities in the health of Health Sector Inequalities sector into their causes is developed and applied to with an Application to data on child malnutrition in Malnutrition Inequalities Vietnam in Vietnam Adam Wagstaff Eddy van Doorslaer Naoko Watanabe The World Bank Development Research Group Public Services for Human Development and Development Data Group November 2001 PoLIcY RESEARCH WORKING PAPER 2714 Summary findings Wagstaff, van Doorslaer, and Watanabe propose a largely by inequalities in household consumption and by method for decomposing inequalities in the health sector unobserved influences at the commune level. And they into their causes, by coupling the concentration index find that an increase in such inequalities is accounted for with a regression framework. They also show how largely by changes in these two influences. changes in inequality over time, and differences across In the case of household consumption, rising countries, can be decomposed into the following: inequalities play a part, but more important have been * Changes due to changing inequalities in the the inequality-increasing effects of rising averat - determinants of the variable of interest. consumption and the increased protective effect of * Changes in the means of the determinants. consumption on nutritional status. In the case of * Changes in the effects of the determinants on the unobserved commune-level influences, rising inequality variable of interest. and general improvements seem to have been roughly The authors illustrate the method using data on child equally important in accounting for rising inequLality in malnutrition in Vietnam. They find that inequalities in malnutrition. height-for-age in 1993 and 1998 are accounted for This paper-a joint product of Public Services for Human Development, Development Research Grouw, and the Development Data Group-is part of a larger effort in the Bank to investigate the links between health and poverty. Copies of tht paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please co-itact Hedy Sladovich, room MC3-607, 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 authors may be contacted at awagstaffCkworldbank.org, vandoorslaer@econ.bmg.eur.nl, or nwatanabe(aworldbank.org. November 2001. (19 pages) 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 polishea'. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed ili this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, Ot the countries they represent. Produced by the Policy Research Dissemination Center On Decomposing the Causes of Health Sector Inequalities with an Application to Malnutrition Inequalities in Vietnam Adam Wagstaff Development Research Group, The World Bank 1818 H St. NW, Washington, DC, 20433, USA and University of Sussex, Brighton, BN1 6HG, UK awagstaff@worldbank.org. Eddy van Doorslaer Erasmus University, 3000 DR Rotterdam, The Netherlands Naoko Watanabe Development Data Group, The World Bank 1818 H St. NW, Washington, DC, 20433, USA Without wishing to implicate them in any way, we are grateful to the following for the helpful comments on an earlier version of the paper or research leading up to it: three anonymous referees; Anne Case, Angus Deaton, Christina Paxson and other participants at a seminar at Princeton; participants at the 2001 International Health Economics Association Meeting in York; Harold Alderman, Alok Bhargava, Deon Filmer, Berk Ozler, Martin Ravallion, Tom Van Ourti. 1. Introduction The large inequalities that exist in the health sector-between the poor and better- off-continue to be a cause for concern, in both the industrialized and the developing worlds. These inequalities are manifest in health outcomes, the utilization of health services, and in the benefits received from public expenditures on health services (Van Doorslaer et al. 1997; Castro-Leal et al. 1999; Castro-Leal et al. 2000; Gwatkin et al. 2000; Sahn and Younger 2000; Wagstaff 2000). With many national governments, international organizations and bilateral aid agencies firmly committed to reducing poor- nonpoor inequalities in the health sector (World Bank 1997; Department for International Development 1999; World Health Organization 1999), a good deal of attention is now being paid to the causes of these inequalities and to the impacts of policies and programs on them. In this paper, we present and apply some decomposition methods relevant to addressing three types of question. The first concerns the causes of health sector inequalities at a point in time. These stem from inequalities in the determinants of the variable of interest. For example, inequality in health sector subsidies presumably reflects inequalities in determinants of health service utilization (e.g. the quality of local health facilities, access to them, opportunity costs, etc.) and inequalities in the per unit subsidy (e.g. because of inequalities in liability for user fees). The issue arises: what is the relative contribution of each of these various inequalities in explaining subsidy inequalities? The second type of question concerns differences and changes in health sector inequalities. Countries vary substantially in the degree of inequality in different health sector outcomes, and there is evidence that these inequalities have changed over time (Schalick et al. 2000; Victora et al. 2000). The obvious question is why these differences exist and why these changes have occurred. The third type of question in which we are interested concerns the impacts of policies and programs. The fact that inequalities appear to have widened over time in some countries does not mean necessarily that policies have been ineffective, let alone that they have caused the growth of inequality. The decomposition we present below can be useful in situations like this where one wants to separate out the effects on inequality of various changes, including the effects associated with programs that-inadvertently or otherwise-have effects on health sector inequalities. In addition to presenting methods for unraveling the causes of health inequalities, we illustrate their use by analyzing the causes of levels of and changes in inequalities in child malnutrition in Vietnam over the period 1993-98. Whilst its child mortality figures are low by the standards of East Asia, Vietnam has a relatively high incidence of child malnutrition-albeit one that is falling (World Bank 1999). By contrast, malnutrition inequalities were fairly small in Vietnam in 1993 by international standards (Wagstaff and Watanabe 2000), but they have been rising: during the 1990s, the largest declines in malnutrition were in the higher income groups, particularly the top quintile (World Bank 1999). The two empirical questions we seek to address, therefore are: What accounts for I the inequality in child malnutrition in Vietnam? And why did the degree of inequality in child malnutrition rise between 1993 and 1998? The plan of the paper is as follows. In section 2 we present the methods fo:r decomposing the causes of health sector inequalities, focusing initially on levels an(d subsequently analyzing changes in inequality. In section 3 we outline the empirical model and data we use to decompose the causes of levels of and changes in malnutriticn inequalities in Vietnam. Section 4 presents and discusses our decomposition results, and section 5 contains our conclusions. 2. Decomposing health sector inequalities: methods Measuring health sector inequalities Let us denote by y the variable in whose distribution by socioeconomic status we are interested. This could be health or ill health, or health service utilization, or the subsidy received through public expenditure on health, or out-of-pocket payments, o:r some other variable of interest. Suppose too we have a measure of socioeconomic status. Without loss of generality, we will assume this to be income-the extension to other measures of socioeconomic status is immediate.' We measure inequalities (by income) in y using a concentration index (Wagstaff et al. 1991; Kakwani et al. 1997). The curve labeled L in Figure 1 is a concentration curve. It plots the cumulative proportion of y (cIl the vertical axis) against the cumulative proportion of the sample (on the horizontal axis), ranked by income, beginning with the most disadvantaged person. If the curve L coincides with the diagonal, all individuals, irrespective of their income, have the same value of y. If, on the other hand, L lies above the diagonal, as in Figure 1, y is typically larger amongst the worse-off, while if L lies below the diagonal, y is typically larger amongst the better-off. The further L lies from the diagonal, the greater the degree of inequality in y across income groups. The concentration index, denoted below by C, is defined as twice the area between L and the diagonal. C can be written in various ways, one (Kakwani et al. 1997) being (1) c=- 2 Y iRi-1 The approach as developed here is intended for cases where one wants to analyze inequality in a health sector variable across the distribution of another cardinal or ordinal variable, but could be used for the case where one warts to look at pure health inequality, in which case R would be the rank in the health distribution. The issues of which approach is more appropriate, and which second variable one should use to assess health inequalities across, are ethical ones and beyond the scope of this paper. 2 where ,u is the mean of y, Ri is the fractional rank of the ith person in the income distribution. C, like the Gini coefficient, is a measure of relative inequality, so that a doubling of everyone's health leaves C unchanged. C takes a value of zero when L coincides with the diagonal, and is negative (positive) when L lies above (below) the diagonal.2 In the case where y is a "bad"-like ill health or malnutrition-inequalities to the disadvantage of the poor (higher rates amongst the poor) push L above the diagonal and C below zero. Decomposing health sector inequalities Our aim is to explain health sector inequalities by income, as measured by C. Suppose we have a linear regression model linking our variable of interest, y, to a set of K determinants, xk: (2) yi =a+y,k/3kxkx + £i' where the 1k are coefficients and ei is an error term. We assume that everyone in the selected sample or subsample-irrespective of their income-faces the same coefficient vector, /k. Interpersonal variations in y are thus assumed to derive from systematic variations across income groups in the determinants of y, i.e. the xk. We have the following result, which owes much to Rao's (1969) theorem in the income inequality literature (Podder 1993), and which is proved in the Appendix: Result 1. Given the relationship between yi and Xik in eqn (2), the concentration index fory, C, can be written as: (3) C= Sk(I3kjEk I P)Ck +GC, I, where ,u is the mean of y, xk is the mean of Xk, and Ck is the concentration index for Xk (defined analogously to C). In the last term (which can be computed as a residual), GC, is a generalized concentration index for ei, defined as: (4) GC, =-2In, R which is analogous to the Gini coefficient corresponding to the generalized Lorenz curve (Shorrocks 1983). Eqn (2) shows that C can be thought of as being made up of two components. The first is the deterministic component, equal to a weighted sum of the concentration indices of the k regressors, where the weight or "share" for Xk, is simply the elasticity of y with respect to xk (evaluated at the sample mean). The second is a residual 2 C could be zero if L crosses the diagonal. This does not happen in our empirical illustration, but even if it did, C still provides a measure of the extent to which health is, on balance, concentrated amongst the poor (or better-off). 3 component, captured by the last term-this reflects the inequality in health that cannot bte explained by systematic variation across income groups in the xk. Thus eqn (3) shows, that by coupling regression analysis with distributional data, we can partition the causes of inequality into inequalities in each of the xk. Of course, the population means, coefficients and residuals are unknown, but can be replaced by their sample estimates. Decomposing changes in health sector inequalities The most general approach to unraveling the causes of changes in inequalities would be to allow for the possibility that all the components of the decomposition in eqn (3) have changed. Changes in the averages of the x's, may have been accompanied by changes in their impact on y, and the degree of inequality by income in the x's may have changed too. Allowing for all such changes, the simplest approach would be to take thLe difference of eqn (3): (5) AC = Sk (8iktXk' U ,)Ckt -Zk (hk-1jkt-l1 1XUk-1 )Ckt l + A(GC,, /u,), where the results would allow one to see how far changes concerning, say, the kth determinant were responsible for change in health inequality. The difficulty with eqn (5) is that it is relatively uninformative. One might, for example, want to know how far changes in inequality in health were attributable to changes in inequalities in the determinants of health rather than to changes in the other influences on health inequality. Furthermore, some changes (for example, changes in the mean of Xk) might be offset by other changes (for example, changes in the extent of inequality in xk). A slightly more illuminating approach would be to apply an Oaxaca- type decomposition (Oaxaca 1973) to eqn (3). If we denote by qkt the elasticity of y with respect to Xk at time t, and apply Oaxaca's method, we get: (6) AC= Sk 77kt (Ck, - Ckt-l ) + Yk Ckt-I (5kt - qkt-l) + A(GC/, p) with the alternative being: (7) AC Zk t7-1 (Ckt - Ckt-l ) + k Ck (7kt - )7k-i + A(GC. /p,) This approach allows us to see-for each xk in turn or for all xk combined-the extent to which changes in health inequalities are due to changes in inequality in the determinants of health, rather than to changes in their elasticities. Whilst more illuminating than eqn (5), eqns (6) and (7) still conceal a lot. One. cannot disentangle changes going on within the elasticity qk,. For example, it may be that the change in C owes far more to changes in 8k than to changes in the mean of xk, or vice versa. Indeed, the components of i7kt may change in different directions, possibly having 4 exactly offsetting effects. This would be especially worrisome if one's interest lay in the effects of a program thought to have influenced only one component of qk (e.g. one of the 18k) at a time when one of the other components of ilk (e.g. the mean of xk) was also changing. Ideally one would like to be able to distinguish between the various possible program-induced changes, as well as to be able to separate these changes from changes or differences attributable to things other than the program. A third possibility, then, is to take the total differential of eqn (3), allowing for changes in turn in each of the following: a, the /k, the Yk, and the Ck. We allow these changes to alter C directly and indirectly through ,u. Doing this, we obtain the following result, which is also proved in the Appendix: Result 2. The change in C, AC, can be approximated by: dC = C da + E-dCdk + L-dCxk + E-dC dC GC (8) da dIJ k dx-k dCk J1 =--{da + k-X(Ck -C)d/k + EkL-k(Ck -C)k + Ek fkkdCk + d u. From eqn (8), it emerges that although a does not enter the decomposition for levels, i.e. eqn (3), changes in a do produce changes in C. Take the case where y is a measure of good health, and has a positive mean and a positive C (good health is concentrated amongst the better off). In this case, dC/daO) amounts to an equal increase in everyone's health, and (relative) inequality in health falls, in just the same way as an equal increase in income for everyone reduces relative income inequality (Podder 1993). The reduction in inequality is larger the larger is C and the smaller is ,u. The case we consider in the empirical analysis is somewhat different-we look at inequality in ill health, our y-variable being an increasing function of child malnutrition. We have a positive mean (average malnutrition is positive) and a negative value of C (levels of malnutrition are higher amongst the poor). In this case, dC/da>O. Suppose there is a reduction in a (da0). The direct effect of an increase in xk is to raise inequality (C becomes more positive), since the existing inequality in Xk generates more inequality in y. But the rise in xk raises the mean of y which, all else constant, lowers inequality in y. Whether the net effect of the rise in Yk is to raise or lower inequality in y depends on whether xk is more unequally distributed than y itself (i.e. whether Ck-C is positive or negative). Similar remarks apply to the case of a change in IJk. Finally, and more straightforwardly, an increase (decrease) in inequality in Xk (i.e. Ck) will increase (reduce) the degree of inequality in y. The impact is an increasing function of /k and xk, and a decreasing function of p. So, for example, if y is increasina in ill health, C