_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 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
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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
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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