WPS3662
Micro-level Estimation of Child Malnutrition
Indicators and Its Application in Cambodia
Tomoki Fujii*
JEL classification code: C15, I12, I32, O15
Key words: Cambodia, Concentration curve, Decomposition, Health inequality,
Malnutrition,
Small-area estimation, Targeting
World Bank Policy Research Working Paper 3662, July 2005
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the
exchange of ideas about development issues. An objective of the series is to get the findings out quickly,
even if the presentations are less than fully polished. The papers carry the names of the authors and should
be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely
those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors,
or the countries they represent. Policy Research Working Papers are available online at
http://econ.worldbank.org.
*Singapore Management University and the World Bank. email:fujii@are.berkeley.edu. I am
deeply indebted to Chris Elbers, Jean Olson Lanjouw and Peter Lanjouw for their advice from the
beginning of this research. I also thank Alain de Janvry, Livia Montana, Mahadevan
Ramachandran, Martin Ravallion, H. E. Kim Saysamalen, Elisabeth Sadoulet, Boreak Sik and
H.E. San Sythan. I also thank the Government of Japan under the Millenium PHRD grant for
financial support. Of course, all the remaining mistakes are
mine.
1 Introduction
Malnutrition remains a major public health concern in most developing countries. The World
Health Organization (2002) estimates that about 3.7 million deaths among young children
worldwide were related to malnutrition in 2000. Similarly, Pelletier et al. (1994) estimate
that about one-half of childhood deaths in developing countries are caused by undernutrition.
Malnutrition has also been associated with mortality and morbidity in later life, delayed
mental development, decreased cognitive and behavioral functioning throughout childhood
and adolescence and poorer performance in school (de Onis et al., 2000; Galler and Barrett,
2001; Glewwe et al., 2001; Shariff et al., 2000).
In Cambodia, almost half of the children under five are malnourished as measured by
the height-for-age or weight-for-age indicator (National Institute of Statistics et al., 2001).
Given the grave consequences of malnutrition, the issue deserves serious attention. However,
as with many other developing countries, the resources available for improving children's
nutritional status are severely limited in Cambodia. Hence, efforts must be made to allocate
the available resources in an efficient manner. In particular, geographic targeting, or targeting
according to locational information, is often easy to administer and implement, and can be
quite effective when malnourished children are concentrated in certain locations. However,
the formulation of an effective geographic targeting policy requires knowledge of the location
of malnourished children, information which is often not readily available. The Cambodia
Demographic and Health Survey (CDHS) 2000 data provide information on child nutritional
status at the level of 17 strata, a level that is more aggregated than the provincial level.1
Hence, this information is too aggregated to be useful for formulating targeting policies.
Such informational constraints are among the central issues concerning the formulation
of targeting policies (Ravallion and Chao, 1989; Kanbur, 1987). This study aims to overcome
1In Cambodia, there are four administrative divisions, which are province, district, commune and village
in descending order of aggregation. On average, they have about 89,000, 12,000, 1,300 and 160 households
respectively. Each stratum has on average 125,000 households.
1
the problem by producing commune-level estimates of the prevalence of malnutrition in
Cambodia. The estimates can be projected onto maps, which allow policy-makers to visually
identify areas of severe child malnutrition, analyze the current situation of malnutrition and
formulate geographic targeting policies aimed at assisting the neediest people in a more
efficient and transparent manner.
To derive the commune-level estimates, we combine the CDHS 2000 dataset with indi-
vidual level Cambodian Population Census data for 1998. The former includes information
on child nutrition status but has a limited number of observations, while the latter covers
virtually everyone in Cambodia but lacks any specific information on child nutrition status.
The approach we take builds on the small-area estimation technique developed by Elbers,
Lanjouw and Lanjouw (2000; 2002; 2003a, hereafter ELL). We extend their methodology to
jointly estimate multiple indicators and allow for a richer structure of error terms, a critical
step to address issues unique to nutrition indicators.
While the commune-level estimates of the prevalence of malnutrition are in themselves of
interest for policy-makers, we take the analysis one step further and illustrate three distinct
but related applications of the methodology. First, we investigate the relationship between
consumption poverty, inequality and health at the commune level. While we find no simple re-
lationship, we find that non-linear effects of consumption on the nutritional status of children
are important for understanding the relationship. Second, we decompose health inequality
indicators into between group and within group components by geographic information. This
application is useful for elucidating the significance of the geographic information in explain-
ing overall inequality. We propose two decomposable inequality indicators that are useful
for this purpose. One is based on the analysis of variance. The other uses the concentration
curve, which is similar to the Lorenz curve but orders individuals on the horizontal axis ac-
cording to the group they belong to instead of the individual ranking. Concentration curves
have been used to analyze the health inequality across different socioeconomic groups and
2
the effect of taxation on income distribution (e.g. Kakwani (1977); Kakwani et al. (1997);
Mahalanobis (1960); Wagstaff and van Doorslaer (2004); Yitzhaki and Slemrod (1991)).
Third, we evaluate the potential gains from geographic targeting in the presence of
commune-level estimates. We show that the concentration curve is useful for this purpose as
well. We assume that we can target resources only at the stratum level with the DHS alone.
Given a fixed budget, we can compare reductions in child malnutrition with stratum-level and
commune-level targeting. Alternatively, we can calculate the reduction in resource needs to
achieve the same goal if targeting is carried out at a smaller geographic level. In general, the
efficiency gain depends on the spatial distribution of malnourished children. We find that the
savings in the cost of nutrition programs from commune-level targeting is on average at least
two to three times higher than that from stratum-level targeting when the per capita cost of
the program is fixed. The efficiency gains can be much higher under alternative assumptions.
This paper is structured as follows: Section 2 reviews the measurement and prediction of
nutritional status of children. Section 3 develops the methodology of nutrition mapping. We
then discuss the data in Section 4, followed by the results in Section 5. Section 6 discusses
the applications of the methodology, and Section 7 concludes.
2 Measurement and prediction of child nutrition status
To measure malnutrition in a non-invasive and inexpensive manner, anthropometry has been
widely used among nutritionists and epidemiologists. Among the most commonly used
anthropometric measures are weight-for-height, weight-for-age and height-for-age Z-scores.
Z-scores measure the number of standard deviations between an individual's value of the
anthropometric indicator and the median of the National Center for Health Statistics (NCHS)
growth reference population of the same sex, and in the same age or height group. Deficiency
in weight-for-height, weight-for-age and height-for-age Z-scores is respectively called "wast-
3
ing", "underweight", and "stunting." We use the conventional cut-off point of negative two
to calculate the prevalence of malnutrition. For example, the prevalence of stunting is defined
as the number of children with a height-for-age Z-score below negative two over the total
number of children. (See Dibley et al. (1987a,b); Waterlow et al. (1977); WHO Working
Group (1986, 1995) for further discussion on Z-scores.)
As WHO Working Group (1986) points out, there are several obvious differences among
these measures. First, one can lose weight but not height. Second, linear growth is a slower
process than growth in body mass. Third, catch-up in height is possible, but takes a relatively
long time even with a favorable environment. Thus, wasting reflects `acute', or short-term,
malnutrition whereas stunting reflects `chronic', or long-term, malnutrition with underweight
somewhere in between. Given these differences, it should not be surprising if patterns of
wasting and stunting are different. In fact, Victora (1992) finds no systematic pattern that
holds for an international population between levels of stunting and wasting.
As with Pradhan et al. (2003), we use standardized height and weight, which are the Z-
scores converted back to the corresponding height and weight of the reference age-sex group
of 24-month-old girls. The standardized height and weight are an affine transformation of
Z-scores and preserve all the desirable properties that the original Z-scores possess. The
additional merit of the standardized height and weight is that they are always positive for
practically possible values of Z-scores, and that we can compute inequality measures in
terms of height or weight. We chose the reference group of 24-month-old girls in order to
make the inequality decomposition analysis in this study comparable to the world inequality
decomposition by Pradhan et al. (2003).
The standardized height and weight corresponding to a negative two Z-score is analogous
to the "poverty line" z, a cut-off point below which an individual is considered poor. We can,
therefore, define the FGT measure (Foster, Greer and Thorbecke, 1984) of malnutrition by
simply replacing the consumption by the standardized height or weight. Hence, letting yi (1)
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and yi be individual i's standardized height and weight, and z(1) and z(2) be the standardized
(2)
height and weight corresponding to negative two Z-score, the FGT measure of malnutrition
with parameter can be written as follows:
P, (k)= Ind(yi < z( ) ·
(k) k) z( - yi
k) (k)
(k = 1,2)
z(k)
i
where Ind(·) denotes the indicator function. P0 ,(1)and P0 ,(2)are the prevalence of stunting
and underweight respectively.
The methodology we develop below is built on the association between anthropometric
indicators and other socio-economic and geographic indicators. It is, therefore, instructive to
briefly overview the previous studies on the relationship between anthropometric indicators
and other indicators.2 We report on the prevalence of stunting and underweight, but not
wasting. The primary reason for this is that we were unable to construct a regression model
for weight-for-height with sufficient explanatory power.3 Interestingly, this seems to be the
case in other countries. Alderman (2000) creates regression models of various anthropometric
indicators for Vietnam, South Africa, Pakistan and Morocco, and the variability of weight-
for-height is least well-captured among all the anthropometric indicators. His regression
results suggest that community level effects are of great importance. We also found that
the commune-level variables are important for explaining the variation of anthropometric
indicators.
Li et al. (1999) investigate the issue of malnutrition with various anthropometric indices
and examine its correlates in a large sample of poor rural minority children in China. In
this study, age, maternal height, water sources, maternal education and very low income
were significant correlates. In a study for Vietnam, similar factors were found to be relevant.
Height-for-age Z-scores were significantly correlated with the age of the child, maternal weight
2Note also that our model is a predictive one and not intended to describe causal relationship.
3It is possible to estimate weight-for-height from weight-for-age, height-for-age and age. This is a straight-
forward extension of this research.
5
and height, parental education, and some indicator variables on access to water sources
(Haughton and Haughton, 1997). In West Africa, residence in a dry zone was found to
be associated with wasting, but not with stunting once other variables are introduced as
controls (Curtis and Hossain, 1998). Frongillo et al. (1997) make a cross-country comparison
and find that higher energy availability, female literacy and gross domestic product were the
most important factors associated with lower prevalence of stunting.
Monteiro et al. (1997) investigate the patterns of intra-familiar distributions of under-
nutrition in Brazil. They analyze data for four income strata separately and find that under-
nutrition is significantly associated among household members for the 25 percent poorest
families. Khorshed Alam Mozumder et al. (2000) look into the effects of the length of the
interval between children on malnutrition in two districts in Bangladesh. They conclude
that the results indicate the potential importance of longer birth intervals in reducing child
malnutrition. Zeini and Casterline (2002) explore the importance of different levels of geo-
graphic clustering in Egypt, including regional level, governorate-level, local level, household
level and individual level, using the 2000 Egypt Demographic and Health Survey. They find
that spatial clustering does seem to be important in that country. They also find that, even
after controlling for socioeconomic factors, significant household-level clustering remained
and, interestingly, that individual clustering (i.e. across indicators) was also important. Fur-
thermore, they find that underweight was correlated with stunting and/or wasting in some,
but not all, governorates of Egypt.
3 Methodology
Overview We describe in this section the methodology used to estimate the indicators
of malnutrition at the level of small geographic areas. The methodology developed here is
similar to the small area estimation procedure developed by ELL (2000; 2002; 2003a) for
6
estimating consumption poverty and inequality in that we also combine survey data with
unit record census data in order to obtain estimates at a lower level of aggregation than the
survey permits. Their small area estimation approach was first applied to Ecuador (Hentschel
et al., 2000) and has subsequently been applied to poverty and inequality measures in many
countries, including Cambodia (Alderman et al., 2002; Demombynes et al., 2002; Fujii, 2004)).
We first provide a general overview of the methodology, and then describe it more formally.
The basic idea is straightforward. We first construct a prediction model of anthropometric
indicators using only the variables that are common between the census and the survey, along
with geographic indicators available for the entire country at the village or commune level.
The geographic indicators include the remotely-sensed data as well as village-level statistics
derived from the census data. Common geographic codes in all data sets allow these to be
linked to both the survey and the census data.
The parameters of the model are estimated with the survey dataset. An important
feature of our study and of the ELL approach is the explicit treatment of the error terms.
We estimate regression coefficients and the associated variance-covariance matrix, and also
scrutinize the distribution of the disturbance terms in order to carry out simulation. In
each round of simulation, we randomly draw regression coefficients and disturbance terms in
accordance with their estimated distribution and we impute the anthropometric indicators to
each census record. By geographically aggregating the imputed anthropometric indicators,
we can estimate the prevalence of malnutrition.
There are four major differences between this study and earlier work by ELL. The first
and most obvious difference concerns the type of the survey dataset used for estimation. ELL
have focused on consumption or income taken from a socio-economic survey, while we have
anthropometric measures taken from a Demographic and Health Survey (DHS). A second
difference stems from different units of analysis. Consumption data are usually produced
at the household level, whereas anthropometric measures are at the individual level. In the
7
ELL approach, disturbance terms are decomposed into a location-specific effect (usually at
the cluster-level) and a household-specific effect. However, in our study, it is important
to allow as well for an unobserved individual-specific effect in addition to location- and
household-specific effects.
The third difference is related to the second point. The number of children under five
in a household is very limited, with no more than two for most of the households. Hence,
we cannot rely on large-sample properties when estimating the parameters or distribution
of the individual-specific effect. Thus, unlike the ELL approach, we make finite-sample
corrections. The fourth point is the number of left-hand-side variables used in this study.
In the ELL approach, only a single consumption or income measure is considered, but we
consider multiple indicators. Because the unobserved parts of the different indicators may
be correlated, this must be taken into account when computing the parameter estimates.
We call correlation across indicators the intra-personal effect, and allow for it in the model.
Given that weight-for-age is a medium-term indicator of nutritional status, which is partly
affected by height-for-age, it would be natural to assume that intra-personal effect may exist.
Consequently, our approach involves simultaneous estimation of several models, unlike the
single-model procedure applied by ELL (2002; 2003a).
Parameter Estimation We denote the set of all clusters by C, the set of all households
in cluster c( C) by Hc and the set of all the children under five in household h( Hc) by
Ich. Let ychi be the k-th (1 k K) anthropometric indicator of interest for the individual
(k)
i in cluster c and household h.4 In our particular application, K = 2, with k = 1 and
k = 2 being the standardized height and weight respectively, but in general K could be
larger. Our goal is to find an estimate of an aggregate index W(V W({yi }i ) such as
k) (k)
V
the prevalence of malnutrition for a set of individuals V. ychi is related to a d( -vector of
(k) k)
4A cluster is the primary sampling unit for the survey, which is a village for CDHS 2000.
8
observable characteristics, x(chi, through the following anthropometric model.
k)
T
ychi = x(chi ( + u(chi
(k) k) k) k)
where ( k) is a d( -vector of parameters and u(chi is a disturbance term. u(chi satisfies
k) k) k)
E[u(chi|xchi] = 0 for all c, h, i and k. Let C #(C), Hc #(Hc), and Ich #(Ich), where
k) (k)
#(·) is the counting measure. The total number of observations is N
cC hHc Ich
and each cluster has a weight wc which is normalized so that cwc = 1. Recall here that
the number of children under five in one household is usually small and can be 1 for some
households.
As with the ELL study, we allow for location, or cluster-specific, effect and heteroskedas-
tic household-specific effect. In addition, we have multiple indicators and the individual
effect correlated across the indicators. Hence, u(chi = c +
k) (k) (k) (k) (k) (k), and
ch + chi, where c , ch
chi are respectively the location, household and individual effect. In principle, each of the
(k)
three components of u(chi could be heteroskedastic and correlated across the indicators. The
k)
particular choice we make is driven by the insights from previous studies and also by the
limitation imposed by the data. For example, given that Ich = 1 for many households in the
CDHS data, it is extremely difficult to distinguish household effects from individual effects if
both are heteroskedastic. Cluster-level heteroskedasticity is also difficult to estimate because
of the limited number of clusters. We allow for flexibility in the correlational structure of the
disturbance terms where such flexibility seems most crucial.
We shall hereafter denote (u(1),··· ,u( ) by u, and use similar notation for other vari-
K) T
ables. We assume that c, ch and chi are uncorrelated and satisfy E[c] = E[ ch] = E[chi] =
OK, where the last term is the K-vector of zeros. For l,k {1,2,...,K} with l = k, we
assume E[c c ] = E[
(k) (l) (k) (l)] = 0. We denote the variance of each component of the dis-
ch ch
turbance term as ( )2 E[c · c ], ((,ch)2 E[
(k) (k) (k) k) (k)· (k) (k) (k) (k)
ch ch ], and ( )2 E[chi · chi].
Note that we need subscripts ch to express the heteroskedasticity of the household effect.
9
We also assume that the intra-personal effect is (l,k) = (k,l) E[chi · chi] so that the
(l) (k)
(l,k)
intra-personal correlation is ( l,k) = . We shall denote simple means by dots such as
(k) (l)
u(ch =
k) 1 k) k) 1 u( .
k)
· u( and u(c =
Ich iIch chi ·· Hc hHc ch·
As discussed above, we estimate the distribution parameters of the estimate of the re-
gression coefficients and disturbance term. To do so, we run an ordinary least squares (OLS)
regression for indicator k, and get the residual u^(chi. Letting Hc {h Hc|Ich > 1},
k) ~
Hc #{Hc}, C~ {c C|Hc > 0}, and wc
~ ~ ~ ~ P wc , straightforward calculations give
c C~ c
w
w~c k) k)
E (u(chi - u(ch )2
· = ( )2(k)
Hc
~
~ iIch Ich - 1
cC~ hHc
and
w~c k) k) l) l)
E (u(chi - u(ch ) · (u(chi - u(ch )
· · = .
(k,l)
Hc
~
~ iIch Ich - 1
cC~ hHc
We obtain consistent estimators (^ )2 and
( k) ^( k,l) by taking out the expectations operator
on the left-hand-side and replacing u by u^ in the respective equation. In the same manner,
we obtain a consistent estimator (^ )2 of the variance of location effect using the following
(k)
formula (proof in the Appendix).
k) wc k)
cC wcHc(u(c )2 -
·· (u(ch )2
E cC Hc hHc · = ( )
(k) 2 (1)
cC wc(Hc - 1)
There is no guarantee that the estimated variance of the location effect is non-negative, and
hence we censor (^ )2 at zero.
( k)
The household and individual effects are difficult to separate from each other because Ich is
small for a majority of households. To estimate the distribution parameters of the household
effect, it is useful to work with the sum (s(ch )2( ((,ch)2 + ( )2) of the household and
k) k) (k)
individual effects. Note that the heteroskedasticity of (s(ch )2 comes only from the household
k)
effect. We can show the following formula (proof in Appendix) for c C { C|H > 2}:
10
E Hc · (u(ch - u(c )2
k) k)
· ·· - h Hc (u(ch - u(c )2
k) k)
· ·· + Ich - 1(
Hc - 2 (Hc - 1)(Hc - 2) Ich )2 = (s(ch )2
(k) k) (2)
We let s^2ch be the left hand side of the equation above with the expectation operator
removed and with u and replaced by u^ and respectively.5 For the heteroskedastic
^
model, we propose the following logistic heteroskedastic model similar to the one in ELL
(2003a):
ln (^(ch )2 - B(
s k) k)
A( + B( - (^(ch )2 = [z(ch ]T( + ch
k) k) (k)
k) k) k)
s
where A( and B( are the maximum and minimum of (s(ch )2, and z(ch is vector of household
k) k) k) k)
characteristics, ( heteroskedastic regression coefficient and ch the residual term. The
k) (k)
feature of this formulation is that (^( ) is both upper- and lower-bounded. Using B =
s k) 2 (k)
min{0,1.05 · minch{(^(ch )2}} and A( = 1.05 · (maxch{(^(ch )2}- B ), we run OLS to obtain
s k) k) s k) (k)
( . The use of the delta method suggests the following estimate of ((,ch)2:
^ k) k)
(^(,ch)2 = max 0, D( k) D( (1 - D( )(^ )2
k) k) ( k)
k) + k) (k) ( k) (3)
1 + D( k) 2(1 + D( ) k) 3 A( + B - (^ )2
where D( exp([z(ch ]T( ), and (^ )2 is the estimated variance of ch. The max{·,·}
k) k) ^k) ( k)
function is introduced to ensure the non-negativity of (^(,ch)2. The consequence of this is
k)
that ((,ch)2 may be upward-biased. Hence, the standard errors for the estimates of nutrition
k)
measures at the level of small geographic areas are conservative. We can now estimate the
variance-covariance matrix , and carry out a (feasible) generalized least squares (GLS)
regression to obtain the regression coefficients ^ and V ar[^] for all the indicators at once.
5When (^ )2 = 0, we use E[(u(ch )2] = ((,ch) +
( k) k) k) ( )2
(k)
instead.
· Ich
11
We then find the empirical distributions of each disturbance component. We approximate
the distributions of c, ch, and chi respectively by the distributions of uc , (uch - uc ), and
·· · ··
(uchi - uch ) standardized to have mean zero and a unit standard error.
·
Simulation We explicitly take into account the model and idiosyncratic errors using Monte-
Carlo simulation, where the model error is the error associated with the estimation of model
parameters and , and the idiosyncratic error is the variations of the anthropometric
indicators that remain unexplained by the model. Now, let R be the number of simulations,
which must be sufficiently large in order to make the computational errors small enough.
In our study, we set R = 100. In r-th simulation where r {1,2,...,R}, we need the
following parameters: ~( , ( , (~, )2, (~, )2, (~, )2, (~, )2, A( , B for k = l.
(k) k) k) k,l) ( k) k) (k)
r) ~(r) (r) ( (r) ( ( r) (r) ,(r) ,(r)
We randomly draw ( and ~( from the normal distribution with mean and ^, and
~ r) r) ^
variance-covariance matrix V ar[^] and V ar[^] respectively. For the rest of the parameters,
we create a two-stage bootstrapping sample of u^ in each round of simulation, and compute
the parameters using the bootstrapping sample.6 It is straightforward to calculate (~(,ch, )2 k)
(r)
from (~, )2, A( , B from Eq(3).
k) (k)
(r) ,(r) ,(r)
For each census record, we draw the standardized cluster, household and individual effects.
Each of these disturbance components is drawn jointly for multiple indicators to capture the
intra-personal effect. Letting the standardized components of disturbance terms drawn in
the r-th simulation be ~c, , ~(ch, , and ~chi respectively, the k-th imputed anthropometric
(k) k) (k)
(r) (r)
indicator for the individual in the census in r-th simulation is7:
y~chi, = x(chi ~( + ~c, · , + ~(ch, ·
(k) k) (k) (k) ~ k) ~ (k) ~
(r) r) (r) (r) (r) ,ch,(r)+ ~chi · , (r)
6Another possible implementation is to draw and ~ from the bootstrapping sample.
~
7To eliminate extreme values, we drop census observations for which the point estimate x(chi^( is not
k) k)
in the range of y( for at least one indicator. In each simulation, we censored y~chi,
k) (k) at the minimum and
(r)
maximum observed in the survey. We also censored D( at the minimum and maximum.
k)
12
This allows us to calculate the aggregate indicator of interest as W( ~ (k) (k)
r),V= W({y~i, }i )
(r)V
in r-th simulation. The point estimate and its associated standard error are estimated as
the mean and standard deviation of W( taken over the simulation. For example, the point
~ (k)
r)
estimate of the prevalence of stunting for commune is as follows:
^0,(1) 1 R
P = · y(1)
R ·
cC hHc Ich Ind(~chi, < z(1))
(r)
r=1 cC hHc iIch
4 Data
Our basic building blocks comprise a survey dataset, a census dataset and a dataset of
geographic variables. The survey dataset we used is CDHS 2000, which was designed to collect
health and demographic information for the Cambodian population with a particular focus
on women of childbearing age and young children. The sample covered 12,236 households
in 17 strata across the country. Data collection took place over a six-month period between
February and July in 2000. In addition to detailed information about each household, its
members, and housing characteristics, one-quarter of these households were systematically
selected to participate in the anthropometric data collection. All children under 60 months of
age in the sub-sampled households were weighed and measured. After excluding children for
which information on height or weight is missing or implausible, 3,596 observations were used
for this analysis (for further details, see National Institute of Statistics et al. (2001)). We first
derived the height-for-age and weight-for-age Z-score measures, which were then converted
to the height and weight for 24 month-old females with the same Z-score measures.
The second source of data is the Cambodian National Population Census, the first popula-
tion census to be conducted in Cambodia since 1962. The census covered virtually all persons
staying in Cambodia at the reference time of midnight of March 3, 1998.8 The census data
8Due to military operations, about 0.5 percent of the population was not covered.
13
contain information on housing characteristics as well as information on each usual household
member and visitors present on the reference night, including the relationship to the head
of household, sex, age, marital status, migration, literacy, education and employment. The
census also contained questions on fertility of females aged 15 and over, and infant mortality.
The census dataset contains about 1.4 million records of children under five.
A set of geographic indicators is also used in this analysis. Because Cambodia has a rich
collection of geographic data, indicators on a range of characteristics could be generated.
These indicators included distance calculations, land use and land cover information, climate
indicators, vegetation, agricultural production and flooding. A number of datasets from
various sources were compiled into a GIS and these indicators were generated for all villages
and communes in Cambodia. Very coarse resolution data were summarized at the commune
level, while high resolution data were attributed to individual villages. Distances from villages
to roads, other towns, health facilities, and major rivers were calculated from the center of
the villages. Indicators based on satellite data with varying temporal resolutions included
land use within the commune (agricultural, urban, forested, and so forth), the Normalized
Difference Vegetation Index (NDVI) to proxy agricultural productivity, and the degree to
which the area was lit by nighttime lights as a proxy of urbanization. Relatively stable
indicators including soil quality, elevation, and various 30-year average climate variables were
derived from other composite datasets. We have also generated the village-level means from
the census data. It should be noted that the village-level means do not have to be taken from
the variables that also exist in the CDHS dataset. This is because the village-level means, as
with other geographic variables, can be linked to both the census and the survey datasets.
Inclusion of these geographic variables and their cross terms with other individual-level and
household-level variables has improved substantially the ability to explain the variation of
anthropometric indicators.
14
5 Results
We constructed an anthropometric model in each of the five zones ("ecozones") of Urban,
Plain, Tonlesap, Coastal and Plateau. We combined provinces that are similar in agro-
climatic and socio-cultural characteristics because some of the strata had too few observations
to carry out meaningful analysis.9 We ran regressions in each ecozone separately. While
individual-level and household-level variables explain only 20 to 30 percent of the variation
in the standardized height and weight, we were able to increase the explanatory power of the
model to about 40 to 60 percent by including geographic variables and interaction terms. This
is consistent with Curtis and Hossain (1998). We checked the robustness of the regression
coefficients by randomly dropping some households or clusters as was done in ELL (2002).
The GLS regression results for the Coastal ecozone are presented in Table 1 and Table 2.10
The point estimate of the variance of the location effect was zero in all strata, even though
in some rounds of the simulation (~, )2 was strictly positive because of bootstrapping. The
( k)
(r)
average proportion of individual effect to the sum of all the disturbance components was
found very high with the ratio of individual effect to the overall residuals (^ )2
(1) ranging from
(^u )2
(1)
0.81 to 0.99 and (^ )2
(2) ranging from 0.66 to 0.92. This in turn means that the household effect
(^u )2
(2)
is relatively small, though it is in general not negligible. In all the ecozones, the magnitudes
of intra-personal correlations as measured by ^(1 ,2)were found high, ranging from 0.44 to
0.53. This strongly suggests the importance of the inclusion of intra-personal correlation.
After the predictions for standardized height and weight for each child in the census were
made in each round of simulation, they were aggregated to the commune level in Cambodia
to arrive at the prevalence of stunting and underweight. Because of missing data in the
census and geographic datasets for a small number of communes, we obtained commune-
level estimates for a total of 1,594 communes out of the 1,616 communes in Cambodia.
9We followed the definition of the ecozones previously used by WFP (2001).
10Other regression results are available from the author upon request.
15
To evaluate the reliability of the estimates, the ecozone-level CDHS prevalence of stunting
and underweight were compared with the ecozone-level estimates in this study. Table 3
summarizes these results. The differences between the CDHS estimates and this study are
within two standard errors of the CDHS estimates, suggesting that the differences can be
attributed to the random errors. It should also be noted from Table 3 that the standard
errors estimated with the CDHS alone are higher than those for this study except for the
underweight model in Tonlesap. The standard errors from Coastal ecozone in the survey are
quite high, and our methodology improved the ecozone level estimates quite substantially.
We also arrive at the same conclusion when comparisons are made at the level of 17 strata.
We also checked the magnitude of standard errors associated with commune-level esti-
mates of malnutrition prevalence. The simple means of the standard errors are 9.0 percent
for stunting and 10.1 percent for underweight, while the simple means of the coefficient of
variation are 3.8 percent for stunting and 4.2 percent for underweight. They are reasonably
small as they are about the same magnitude as the standard errors in the survey at the
ecozone level. We should note, however, that there are communes for which the standard
errors are quite high, as the maximum standard error was 22.7 percent for stunting and 18.5
percent for underweight. Overall, the accuracy of commune-level estimates for stunting and
underweight is about the same. It should be noted that, as the number of communes included
in a nutrition program increases, the idiosyncratic component of the error tends to decrease.
Hence, if a proposed nutrition intervention delivers assistance to a relatively large number of
communes, high levels of standard errors for each commune are not necessarily worrisome.
Using a GIS, we converted the commune-level estimates into maps. Figures 1 and 2 are
the maps of stunting and underweight at the commune level. These maps show the point
estimates of the prevalence of malnutrition as of the census year 1998 at the commune level,
and the orange and red areas represent bad situations.
As shown in Figure 3(a), stunting and underweight exhibit by and large similar patterns,
16
even though there is no simple geographic pattern of malnutrition. At the commune-level,
the correlation between the estimates of prevalence of stunting and underweight is 0.33. Red
areas are the communes where the prevalence of stunting and underweight is both over 45
percent, which is approximately the national average for both stunting and underweight.
Green areas have on the other hand prevalence of stunting and underweight both less than
45 percent. In terms of the number of communes, the green and red communes account for
about 65 percent of all the communes.
The prevalence of both stunting and underweight is high in the most densely populated
parts of Cambodia surrounding Phnom Penh, the provinces of Kandal, Prey Veng, Svay
Rieng, Kampong Cham, and Kampong Chhnang as shown red in Figure 3(b). While these
provinces are geographically close to each other, the causes of malnutrition may be quite
different. Inspection of possible causes elucidates this point. For example, the prevalence of
diarrhea for children under five is 29.7 percent in Kandal whereas it is only 3.1 percent in
Prey Veng. Similarly, the prevalence of fever, which is a primary manifestation of malaria
and other acute infections in children, is 46.8 percent in Kandal and 4.0 percent in Prey Veng
(National Institute of Statistics et al., 2001). On the other hand, the poverty rates in Kandal
and Prey Veng are estimated at 18.4 percent and 53.1 percent (Fujii, 2004). This suggests
that malnutrition in Prey Veng is likely to be driven mainly by poverty, or more specifically
lack of caloric intake, whereas infectious diseases seem important causes of malnutrition in
Kandal.
Figure 3(b) also shows some noticeable differences between stunting and underweight.
For example, most areas of Kampong Speu shown in pink have high levels of stunting but
not underweight. This suggests that the nutritional status has improved recently, which
is perhaps partly because of the recent improvement in road access in this province. Low
levels of stunting and high levels of underweight as shown orange in Figure 3 reflect recent
aggravation of nutritional status. Possible causes of aggravation include increased incidence
17
of malaria and diarrhea and acute food shortage due to natural disaster.
While these maps are presented in a user friendly format, they do not take into account
the fact that the commune-level estimates are subject to statistical errors. We can also
present the maps in terms of the difference between the commune-level estimate and a refer-
ence level such as the national average divided by the standard error of the commune-level
estimate. Figure 4(a) shows how significantly different the prevalence of stunting in each
commune is from the national average (NA). The point estimate in red areas are more than
two standard deviations higher than the NA. Orange areas have a point estimate between
one and two standard deviations higher than the NA. Green and yellowish green areas are
similarly defined. In yellow areas, the absolute value of the difference is less than one stan-
dard deviation. This representation would be useful to identify a small number of communes
for a nutrition program.
Another useful way to present the results would be to depict the density of malnourished
children as shown in Figure 4(b). This picture is completely different from Figure 1 because
the population density is very high in Phnom Penh and surrounding provinces. This rep-
resentation would be most relevant when a proposed policy intervention is likely to benefit
the target location as a whole. Construction of health clinics might be an example of such a
project. Health clinics are likely to help improve the nutrition status of children in areas like
Kandal, where infectious disease is likely to be a cause of the problem and the distance to
health facility is problem. In fact, 60.1 percent of women in Kandal reported that distance
to health facility is a big problem in accessing health care for themselves. This contrasts
with 12.9 percent in Prey Veng. Different representations shed light on different aspects
of malnutrition, and most appropriate format would depend on the purpose and intended
audience of the map.
The maps are in themselves useful, but the estimates we derived have a number of appli-
cations. We illustrate three applications of the estimates in the next section.
18
6 Applications
6.1 Consumption Poverty and Inequality as Correlates
of Malnutrition
The first application we illustrate in this paper is the analysis of the relationship between
consumption poverty, inequality and malnutrition. We utilize the estimates of consumption
poverty and inequality derived by Fujii (2004) using the standard ELL approach. One way to
look at the relationship is to overlay maps. Figure 5(a) and Figure 5(b) are the stunting and
underweight maps overlaid with the poverty map. Table 6 gives the number of communes by
poverty rate and prevalence of underweight. While there is not an obvious pattern between
poverty and malnutrition, there are at least two notable features on these maps. First, the
northern part of Siem Reap and southern part of Prey Veng have high levels of stunting,
underweight and poverty. These places have food security problems because many people
lack means of production there. Southern Prey Veng has been repeatedly hit by drought
and flood. Second, the northeastern provinces of Kratie, Stueng Treng and Ratanakiri have
low levels of poverty and high levels of malnutrition. This may be partly because of diseases
and poor child care in this region (See Hardy and Health Unlimited Ratanakiri Team (2001)
for the case of Ratanakiri), both of which are not direct results of poverty. By overlaying
nutrition map with other maps, we can investigate the plausible causes of malnutrition in
different parts of the country.
To analyze the correlational structure of aggregate indicators, we first regressed estimates
of malnutrition indicators on the estimates of the logarithm of the commune-level mean con-
sumption Y¯ and the generalized entropy inequality measure with parameter 0 (GE(0)).11
Table 4 shows the results.12 Not surprisingly, we found that the logarithmic mean consump-
11GE(0) is also known as the Theil's L index. See Shorrocks (1980) for the discussion of generalized entropy
measures.
12The standard errors in Table 4 are underestimated because they do not take into account the fact that
19
tion has a negative and significant coefficient. However, the significance goes away once
provincial-level dummies are included. The coefficient on inequality (GE(0)) is also negative
and significant in both specifications. The negative relationship between the prevalence of
malnutrition and inequality also holds for the Gini index. This is a surprising result because
inequality has been associated with poor health outcomes in various geographic locations and
at various level of aggregation (See, for example, Wilkinson (1996); Kawachi et al. (1997)),
even though a majority of the studies use mortality as a health indicator and relatively few
studies are done in developing countries.
What we found from this analysis has an important implication for the current debate on
the significance of inequality on health outcomes. Some researchers in public health, including
Wilkinson (1996), have argued that higher income inequality leads to worse health outcomes
partly because income inequality leads to higher levels of psychosocial stress. Economists
have been skeptical about this line of argument because of omission of factors other than
income inequality (Deaton, 2003; Wagstaff and van Doorslaer, 2000). We also argue that the
psychosocial explanation is unattractive because it fails to explain the negative correlation
between the prevalence of malnutrition and poverty rate.
We can explain the negative correlation between the rate of malnutrition and consumption
with Figure 6. The horizontal axis measures consumption and the vertical axis measures
the probability density of consumption within the commune. Let us consider a situation
where consumption has positive and non-linear effects on the status of child nutrition. For
simplicity assume that a child is malnourished if and only if the consumption of the child
falls short of a threshold X. Let the solid line A be the graph of the probability density
function for the reference population. A mean-preserving spread would make the graph look
like the dashed line B, and an increase in the mean consumption would correspond to the
Y¯ and GE(0) are estimates, while the point estimate is likely to be unbiased ELL (2004a). The correction
requires the correlation of model errors between poverty and nutrition models, which we do not know because
they were estimated from different data sets. This point also applies to Table 5.
20
dotted line C. The prevalence of malnutrition for B is the smallest followed by C and A.
This argument is consistent with Deaton (2003). It is also similar to the argument made by
Ravallion (1988) and Haddad and Kanbur (1990), though they dealt with welfare risk and
intra-familiar distribution respectively.
To see if Figure 6 is reasonable, we also regressed average severity of malnutrition among
malnourished children (i.e. P2) on Y¯ and GE(0) as well as provincial-level dummies. We
P0
found that the coefficient on GE(0) was neither significant for stunting nor underweight.
Once we include the prevalence of malnutrition P0 on the right hand side, GE(0) has a
positive and significant coefficient for both malnutrition indicators as shown in Table 5. This
means that, given the prevalence of malnutrition and the logarithmic mean of consumption,
the average severity of malnutrition among malnourished children within the same province
tends to be higher in communes with higher inequality. This is consistent with Figure 6,
because the average severity among malnourished children tends to increase with increased
level of inequality regardless of the location of the threshold X on the horizontal axis.
If the effect of consumption on the prevalence of malnutrition is linear, inequality should
have no effect on P0 of malnutrition. Hence, non-linear effects of consumption on nutrition
are extremely important in understanding the relationship between consumption and mal-
nutrition. This is particularly the case when we have only aggregate data. Prevalence is an
important indicator, but we also need to look at the FGT measures with higher parameter
values. DHS estimates are typically too aggregated to meaningfully investigate aggregate
relationships. The small-area estimates of consumption and health are very helpful for ex-
ploring the relationship between poverty, inequality and malnutrition.
6.2 Decomposition analysis of health inequality
While the relationship between consumption poverty, inequality and the prevalence of mal-
nutrition is important, inequality of child health, as measured by nutrition outcomes, is also
21
a matter of interest on its own. Health is an important aspect of human welfare, and health
inequality is relevant to the equity of health, a broader notion (Sen, 2002). Given that child
health indicators are important in predicting the future social standing of the child (Nys-
trom Peck, 1992; Montgomery et al., 1996), the existence of child health inequality in itself
is indeed a concern.
In what follows, we shall focus on the decomposition analysis of inequality indicators. The
analysis we carry out is different from most other studies on health inequality decomposition
in at least three respects. First, despite the growing literature on health inequality, there
have been relatively few studies carried out at a spatially disaggregated level, especially in
developing countries. The methodology we developed in this study allows us to analyze
health inequality at a level of small geographic areas even in the absence of a large number
of observations of health indicators collected at that level.
Second, while the majority of health inequality literature uses mortality data, we use
the standardized height and weight. Because death is a rare event, it may not be the best
indicator at a very disaggregated level. Also, the probability of death is influenced by the
individual's experiences over the course of his/her life. This makes it difficult to compare
populations with different demographic groups. Standardized height and weight for children
have some advantages here. Moreover, anthropometric indicators are likely to be more reliable
than mortality data in countries like Cambodia where vital records are not fully maintained.
Pradhan et al. (2003) discusses additional advantages of the standardized height measure.13
Third, we emphasize direct policy implications of inequality for targeting. Geographic
targeting is meaningful only when there exists spatial heterogeneity in malnutrition or con-
sumption. Hence, the between-location component of overall inequality is relevant to po-
tential gains from geographic targeting. In many of the health inequality studies, the focus
13Pradhan et al. (2003) prefer height to weight because too much weight is obviously not good for health.
Given that less than 1 percent of the children under five is overweight in Cambodia, this is a minor concern
in this study.
22
is placed on the different health outcomes for different groups defined by the socioeconomic
status (SES) or income groups (e.g. Kunst et al. (1998); van Doorslaer et al. (1997)). Such
analyses provides us with a valuable description of the difference in health outcome among
various groups in society. However, they are of little use for the purpose of targeting health
programs, unless we can target resources on the basis of the SES or income. Even if such
targeting is possible, it is still useful to combine it with geographic targeting.
Let us now proceed to the decomposition of health inequality. We present the results
based on three decomposable indices. We begin with the approach proposed by Pradhan et al.
(2003). We then propose two other decomposable measures of health inequality. One of them
is the variance of FGT measures, and the other uses concentration curves for decomposition of
the Gini index. Pradhan et al. (2003) apply GE(0) to the standardized height to decompose
world health inequality into the between-country component and the within-country compo-
nent. They adjust the proportion of between-group component by replacing the denominator
(i.e. GEWorld(0)) with inequality in the reference population due to natural variation in height
subtracted from the world health inequality (i.e. GEWorld(0) - GENatural(0)). They find that
around 30 percent of total inequality is due to the between-country component. In a similar
way, Table 7 provides the proportion of between-group inequality to total inequality adjusted
for the natural inequality. Compared with global health inequality, the share of the between-
group inequality is small in Cambodia. Table 7 also compares the share of between-group
inequality for anthropometric indicators and consumption. Consumption is much more un-
evenly distributed across space than anthropometric indicators.14 For the parameter values
of the generalized entropy measure between -1 and 1, the share of the between-group com-
14Even though this point still holds, one should note that consumption does not capture intra-household
inequality because the unit record of consumption data is a household. We can subtract within-household
GE(0) from the denominator when calculating the share of between-group inequality in order to adjust for
intra-household inequality. The numbers except for the last column in Table 7 will increase by only around
10 percent for both anthropometric indicators. This calculation ignores between-household inequality due
to natural variation, and overestimates the share of between-group inequality. Accurate evaluation was not
possible because we do not know the share of between-household and within-household components of natural
inequality
23
ponent does not change much. For both anthropometric and consumption measures, the
proportion of between-group inequality within Cambodia is much lower the proportion of
between-country inequality in the world.15
The magnitude of within-group inequality varies quite substantially across the communes.
Figure 7 shows the 95 percent confidence interval of GE(0) ranked from the most equal
communes. As pointed out by Elbers et al. (2003b), a low share of between-group inequality
is consistent with high heterogeneity in within-group inequality. This means that the levels of
malnourishment across the communes may also be heterogeneous, even if the between-group
inequality is small or even zero. Therefore, a low share of between-group GE(0) does not
mean that geographic targeting is ineffective.
This point may be more clearly understood with a simple numerical example for income
distribution. Suppose that there are two villages A and B in a small country and each village
has 100 people. In Village A, everyone earns 10. In Village B, there is one rich person whose
income is 901 and the remaining 99 people earn only 1. Let's suppose that the poverty line is
5. In this case, the between-group inequality measured by the generalized entropy measures
is zero because the average income is 10 for both villages. However, geographic targeting is
obviously very useful because all the poor people live in Village B. This shows that what really
matters for the targeting of poverty alleviation programs is not the inequality of income but
the inequality of poverty. Similarly, what matters for the targeting of child nutrition programs
is the inequality of malnutrition, and not the inequality of height or weight.
To focus on the malnourishment, we propose another way of decomposing health inequal-
ity into between-group and within-group components. Let P be the FGT measure with an
arbitrary parameter, and G be a set of geographic groups such as communes, and {Ig}g G
forms a partition on the set of all the individuals I in the population. We can decompose
the variance V of P into within-group component V
T W and between-group component V B
15Lovell (1998) decomposed GE(0) for consumption. About 70 percent of consumption inequality is ex-
plained by between-country inequality.
24
as follows:
V =
T (Pgi - P¯)2 = (Pgi - P¯g)2 + Ng(P¯g - P¯)2 = VW + V B
gG iIg gG iIg gG
where N #(I), Ng #(Ig), P¯ 1 1
N Pgi, and P¯g Ng Pgi
IgG ig ig
In this formulation, the proportion of the between-group variance to the total variance
V B is constant with respect to an affine transformation of the standardized height or weight.
V T
Hence, the arbitrary choice of reference sex and age group does not matter. Once the "poverty
line" is accepted, the comparison of decomposition analysis for different indicators is easier
with V B. We looked at the between-group share of the variance of FGT measures with
V T
parameter 0, 1 and 2. Table 8 shows the results. As with the generalized entropy mea-
sures, the between group health inequality is lower for standardized height and weight than
consumption.
One should note that VB for FGT measures does not look at the entire distribution.
VT
Whether this is desirable property or not would depend on the purpose of the index. For the
formulation of targeting policies we are more interested in the lower tail of the distribution.
For example, a very tall child getting taller by hypothetically "stealing height" from a little
less taller child would be much less concerning than a very short child getting shorter by
having her height stolen from a less short child.
Another approach we propose to decompose inequality is by using the concentration curve
and concentration index (CI) for an FGT measure P. This approach is attractive as it is
directly related to targeting, a point discussed in more detail later. The concentration curve
is a generalized version of the Lorenz curve, and is drawn according the group an individual
belongs to rather than an individual ranking. Formally, the concentration curve is defined as
follows. Let G {1,2,··· ,G}, ag g Ng g P¯jNj
j=1 N , and bg j=1 . That is, ag is the share
PN
¯
25
of the cumulative population and bg the share of cumulative FGT measure for groups with
index no greater than g. By definition, we have aG = bG = 1. The concentration curve C(q)
is a piecewise linear function of the share of population q, which connects (0,0) and (aj,bj) for
j {1,2,··· ,G}. In general, G may be defined by any individual characteristics, including
SES and income groups. When Pg is not monotonic in g, the concentration curve may cross
the 45-degree line. In this study, we focus on the case where G represents geographic groups.
In addition, we assume that the geographic groups are sorted by the descending order of
P so that Pj Pk for j,k G such that k l. In this case, the concentration curve is
concave and does not cross the 45-degree line. When G represents communes, we shall call
C(q) the commune-level concentration curve, and use a similar terminology for other levels
of geographic aggregation. The individual-level concentration curve (C(q) for G = I) is the
Lorenz curve for P rotated by 180 degrees.
Figure 8 gives an example of a concentration curve for P0. The horizontal axis measures
the cumulative population share q and the vertical axis the cumulative share p of P0 with
OA = OC = 1. At the individual level, P0 can take only zero or one. Hence the individual-
level concentration curve looks like the bold line OJB. Since JB is the proportion of the
well-nourished children to all the children, CJ is the prevalence of malnutrition P0 for the
entire population. The Gini index in Figure 8 is twice the area of the triangle OJB, which is
the area above the 45-degree line and under the individual-level concentration curve. When
the parameter for the FGT measure is zero, the Gini index is 1-P0. The line OJ is straight
for P0, but may not be straight when P has a parameter greater than 0.
Now, consider the commune-level concentration curve. If we have three communes with
different levels of malnutrition, the concentration curve would look like the line OFIB. The
concentration index is twice the area under the 45-degree line and above the concentration
curve, that is CI(= 1 - 2 1C(q)dq). This takes a negative number when the concentration
0
curve lies above the 45-degree line. The absolute value of CI is twice the lightly shaded area
26
OFIB in Figure 8. The Gini index is the CI when the concentration curve is the Lorenz
curve, and provides the upper bound for the maximum absolute value of the CI. Several
decomposition techniques of CI have been proposed. (Clarke et al., 2003; Wagstaff et al.,
2003; Wagstaff and van Doorslaer, 2004) We propose to decompose the Gini index for FGT
measures using an approach very similar to the one used in Wagstaff and van Doorslaer
(2004), First we decompose the Gini index GI into between-group negative concentration
index NCIB, within-group negative concentration index NCIW and the residual GIR so that
GI = NCIB + NCIW + GIR. This decomposition corresponds to the change in negative
CI for a hypothetical re-ordering and redistribution in four steps. First, suppose everyone is
sorted by the descending order of the FGT measure so that the concentration curve C1 is
OJB. Second, suppose that we sort the individuals by the descending order of the commune-
level mean FGT measure each individual belongs to, while keeping the relative ranking
within the commune. The resulting concentration curve C2 looks like OEFHIKB. Third,
we redistribute FGT measure so that everyone gets the commune-level average, in which
case the concentration curve C3 is OFIB. Finally, we redistribute across the communes so
that everyone gets the population-average FGT and the concentration curve C4 becomes the
45-degree line OB.
NCIB is twice the area between C3 and C4, or the lightly shaded area OFIB in Figure
8. NCIW is twice the area between C2 and C3, or the sum of three triangles OEF, FHI
and IKB, which are heavily shaded in Figure 8. Finally, the residual GIR is twice the
area between C1 and C2, or EFHIKJ. GIR is analogous to the transvariation component of
the Gini decomposition. Table 9 shows the results of decomposition of the Gini index for
standardized height. As with GE(0) and the variance of FGT, the proportion of the between-
group component is not large in absolute value. As with other decomposable indicators, the
proportion of the between-group inequality NCIB was similar for standardized weight, and
GI
higher for consumption.
27
The decomposition analysis based on Gini and CI is not as neat as the decomposition of
GE(0) or V because of the existence of GIR. The definition of within-group is somewhat
T
ad hoc because splitting one commune into two communes with the same distribution of the
FGT measure will reduce the within-group component and increase the residual. Yet the CI is
suitable for examining the magnitude of the between-group inequality and has some unique
attractions because of its direct relation to the potential gains from geographic targeting.
While we have seen that the share of between-group inequality is not very large, it has not
been clear whether geographic targeting can be still effective. We now try to answer this
question.
6.3 Concentration curve and geographic targeting
Let us now interpret the concentration curve in the context of geographic targeting. Suppose
that we want to reduce the total FGT measure by the proportion OG in Figure 8. Because
everyone is malnourished on the portion OJ in the individual-level concentration curve, we
need to bring the proportion OD of the total population out of malnourishment. Hence, the
vertical axis can be interpreted as the rate of reduction in FGT, and the horizontal axis can
be interpreted as the proportion of the population targeted.
In this setup, we assume that those who receive assistance are completely brought out of
malnourishment. If the per capita cost of assistance is fixed and normalized to the reciprocal
of the total population, the horizontal axis also represents the cost of FGT reduction. Fixed
per capita cost may be a reasonable approximation when the child nutrition program involves
direct aid in fixed amount in a relatively large scale. Distribution of micronutrients may fall
in this category. We shall relax this assumption in the subsequent discussion.
Suppose now that the FGT parameter is greater than zero so that the concentration curve
looks like in Figure 9(a). In this figure, OE is the proportion of total malnourished children
to the total population (i.e. P0). The dashed line OKB is the commune-level concentration
28
curve.
Let us suppose that the policy-maker wants to eliminate malnutrition by a child nutrition
program. However, the policy maker can reduce the FGT measure only by the proportion
OI because the resources available for the program are limited. Then, noting that OD is the
proportion of malnourished children included in the program to the total population, the
rate of Type I error, or the error of exclusion of malnourished children in the program, is DE.
OE
When the parameter for the FGT measure is zero, it coincides with IC. If perfect individual-
level targeting is possible, the cost of reducing the FGT measure by the proportion OI is OD,
because it is the proportion of the beneficiaries of the program to the total population.
Now suppose instead that we can target the program at the commune level. By this,
we mean we can distinguish children if and only if they are in different communes. We also
assume that the program does not induce children to move, which is a reasonable assumption
because the cost of changing the place of residency is very high for poor people. In general,
not everyone in the least malnourished commune included in the targeting policy receives the
program. We assume that the program in the least malnourished commune is targeted uni-
formly, that is, everyone in that commune receives the program with the same probability.16
With the commune-level targeting, the cost of achieving the same goal in expectation is OF
and the leakage of the program to well-nourished children is DF(= OF-OD). Therefore, the
rate of the Type II error, or the error of inclusion of well-nourished children in the program,
is DF in this case.
OF
While both Type I and Type II errors are closely related to the efficiency of targeting,
they are not very satisfactory measures of efficiency. Type I error tends to go down as the
goal of FGT reduction or the budget available for the program is high, regardless of the level
of geographic areas at which targeting is conducted. Type II error is also slightly difficult
16Recall that per capita cost of the program is fixed. Suppose an assistance worth one dollar goes to a
commune of hundred individuals in the least malnourished commune included in the targeting policy. Instead
of each individual receiving one cent for sure, each individual receives one dollar with probability 0.01.
29
to interpret because a comparison is made against the perfect targeting. We do not exactly
know from the Type II error how much improvement can be made by introducing a particular
targeting scheme.
We use two types of efficiency measures which we shall call budgetary gains and equivalence
gains. The budgetary gains measure how much total expenditure can be reduced to achieve a
given level of malnutrition reduction in comparison with the reference case. The equivalence
gains measure how much more malnutrition reduction one can achieve with a fixed budget
compared with the reference case. As with of Elbers et al. (2004b), we take uniform targeting
at the national level as the reference case. That is, everyone receives the program with an
equal probability in the reference case, and the corresponding national-level concentration
curve is the 45-degree line OB in Figure 9(a).17
Because the cost of achieving the reduction OI in Figure 9(a) by perfect (individual-level),
commune-level and uniform (national-level) targeting are OD, OF and OG, the equivalence
gains are respectively DG FG and 0. Similarly, given the budget OF, the malnutrition
reduction one can achieve from individual-level, commune-level and uniform targeting are
OC(= 1), OI and OH(= OF) respectively. Hence, the equivalence gains from in individual-
level, commune-level and uniform targeting are HC, HI and 0 respectively. Both budgetary
gains and equivalence gains take a value between 0 and 1 for the concentration curves we
consider. They can take negative values if the targeting policy favors well-nourished children
over malnourished children.
Budgetary gains and equivalence gains measure appropriately the performance of a par-
ticular targeting policy. However, we would be also interested in the potential gains from
targeting are captured by a particular targeting policy. In Figure 9(a), commune-level tar-
geting leaves considerable room for improvement and thus the policy maker may want to
17The concentration curve we calculate from the commune-level estimates are subject to the statistical
errors. Since the calculation of FGT reduction is made at the national level, the standard errors are usually
very small.
30
combine geographic targeting with other forms of targeting such as self-targeting.18 How-
ever, if the individual-level concentration curve were OJ'B instead of OJB, there would be
almost no room for improvement. In this case, the policy-maker will not gain much from
devising a more complex targeting scheme.
We propose relative budgetary gains to measure how much a particular targeting policy is
capturing the possible gains from targeting. In Figure 9(a), the relative budgetary gain from
community-level targeting given the goal of malnutrition reduction OI is FG . By definition,
DG
the relative budgetary gain is 1 for perfect targeting and 0 for uniform targeting regardless
of the goal of FGT reduction.
There may not be an obvious choice of the goal OI or the budget OF. It is convenient
to have an overall measure of the efficiency measure of targeting. A natural choice would be
the negative concentration index. For the commune-level targeting, it is twice the heavily
shaded area X in Figure 9(a). Notice that 2 · X = X . This measure is the budgetary
X+Y+Z
gain averaged over all the possible values of FGT reduction goals. Hence, we shall call this
average budgetary gains. An alternative interpretation of the average budgetary gains is
the equivalence gains averaged over the interval between zero and one. Similarly, we shall
call the ratio of negative concentration index for commune-level targeting to that for perfect
targeting average relative budgetary gains, which is X in Figure 9(a). It is also equal to
X+Y
NCIB , or the between-group negative concentration index over the Gini index.
GI
Using the point estimates of the prevalence of stunting and underweight, we drew the
concentration curves for different levels of geographic aggregation as shown in Figure 10(a).
The concentration curves for underweight look similar and are given in Figure 10(b). There
are four points to note here. First, the commune-level targeting is a large improvement over
the stratum-level targeting, which is the best policy-makers can do with the DHS data only.
18An example of a self-targeting program is the food-for-work program, because only poor people without
better outside option are willing to participate in the program to receive food. Food-for-work targeted to a
particular region is an example of the combination of geographic targeting and self-targeting.
31
As shown in Table 9, the average relative budgetary gains NCIB at the commune level is more
GI
than two times larger than that at the provincial level. When compared with ecozone-level
or stratum-level targeting, the improvement is even more dramatic.19
Second, on average, there remains large room for improvement even if targeting is carried
out at the level of very small geographic areas such as the village level. Hence, it is very
important for policy-makers to combine geographic targeting with other forms of targeting
whenever feasible. Third, the equivalence gains vary substantially depending on the propor-
tion of targeted people. This point can be seen more clearly in Figure 11(a), which shows
the equivalence gains for different levels of geographic targeting. We see that the equivalence
gain first goes up and then goes down. By definition, equivalence gains take zero when the
proportion of targeted population is zero or one. The equivalence gains for underweight is
given in 11(b).
Fourth, as with the equivalence gains, budgetary gains change with the goal of FGT
reduction. Relative budgetary gains are suitable for evaluating how well particular targeting
scheme is for a given goal of FGT reduction. Figure 12(a) shows the relative budgetary
gains for stunting. Clearly, commune-level targeting is more efficient if the goal of FGT
reduction is lower, capturing most of the potential gains from targeting. When the goal is
low, commune-level targeting can be as high as five times more efficient than stratum-level
targeting. This is an important point, because realistic values of FGT reduction in the short
run will not be extremely high. For example, a Cambodia Millennium Development Goal
is to reduce the prevalence of stunted children by 35 percent by 2010 and 50 percent by
2015 (MoP, 2003). Hence, the average relative budgetary gains somewhat understate the
efficiency gains of commune-level targeting in the short run. The relative budgetary gains
19To make the graphs readable, we omit stratum-level targeting in the graphs. Stratum-level targeting is
close to provincial-level targeting but slightly less efficient because it is done at a more aggregated level. We
prefer to present provincial-level estimates because they are practically more important. Also, while we report
the results for village-level targeting, we take the commune-level targeting as a benchmark for disaggregated
geographic targeting. This is because commune-level targeting is more realistic than village-level targeting
as communes have some degrees of autonomy whereas villages do very little.
32
for underweight are given in Figure 12(b).
As we have already noted, the efficiency measures we used are based on the assumption
that the per capita cost of the program is fixed. Hence, the concentration curve is useful
when the cost of targeting is approximately in proportion to the share of the population
covered by targeting. However, if the cost of improving the nutrition status differs across the
individuals depending on how severely the individual is malnourished, we need to take into
account the variable costs. This is particularly important when we use higher values of the
parameter in the FGT measures.
To this end, we consider the other extreme case where the per capita cost is variable. We
assume that increasing one unit of a standardized anthropometric indicator of a child costs
the same for all the children. This assumption would be reasonable for direct food (macronu-
trient) aid programs. We also assume in the subsequent discussion that the parameter of
the FGT measure of interest satisfies 1. Otherwise, it is optimal to target assistance to
children whose height or weight is just under the level of negative two Z-score, but such a
targeting policy is unethical and hard to justify.
Now, we shall propose the adjusted concentration curve, which takes into account the
different magnitude of malnourishment in the population. Instead of the share of the pop-
ulation, we have the budget in the horizontal axis, as measured by the total increase in the
standardized height or weight. We shall normalize it by the expected budget that is required
to eliminate malnutrition, which is equal to the point estimate of total malnutrition gap
P1 · N. Given the budget and the level of aggregation at which targeting is carried out, we
calculate the optimal level of transfers to each location and find the expected reduction in
the FGT measure. Plotting the share of the FGT measure reduced in expectation against
various levels of budget, we obtain the adjusted concentration curve. Figure 9(b) provides an
illustration of adjusted concentration curves. It is similar to Figure 9(a) in many respects,
and we can indeed define budgetary gains and equivalence gains in exactly the same manner.
33
However, there are four differences to note. First, the curve is not piecewise linear be-
cause the marginal impact of the child nutrition program diminishes even within the same
geographic location as more and more children get less malnourished. Second, because of the
first point, the adjusted concentration curve for the reference case of uniform targeting is not
the 45-degree line any more. In Figure 9(b), the concentration curve for uniform targeting
is OLB. Third, the scale of the horizontal axis is different. In Figure 9(a), OA = 1, but in
Figure 9(b), we do not have such a simple relationship.
Fourth, the standard errors associated with the point estimates play more important role
for the adjusted concentration curve. For example, when the individual-level concentration
curve is based on data and not estimates, we have OE = 1 in Figure 9(b). If it is based on
estimates, OE 1. This is because eliminating malnutrition with probability one costs more
than the expected cost of elimination of malnutrition.
Also, in the previous setting where the per capita cost was fixed, it was optimal to target
from the locations with highest point estimate of P0. Since the assumption was such that the
proportion of P0 reduced in the location is equal to the share of the population targeted in
that location, we only needed to use the point estimate. However, the adjusted concentration
curve requires more complex calculation because we need to know how the FGT measures
change according to different levels of transfers.
To draw adjusted concentration curves, we need to find the value of minimum expected
FGT measure given the budget and the level of geographic targeting. We use the imputed
anthropometric indicators y~ from previous sections. Formally, given the budget B, the min-
imization problem the policy-maker solves is:
34
1 R z - y~gi, - tg
min (r) · Ind(z > y~gi, + tg)
(r)
{tg}gG NR z
r=1 gG iIg
s.t. tg B and g G,tg 0
gG
where tg is the amount of transfer of the standardized height or weight expressed as a
proportion of the total malnutrition gap. Let the set of targeted locations be T ( {g
G|tg > 0}). It is straightforward to establish that the following condition is necessary and
sufficient for optimality when > 1. For T and h G - T , we have P¯ -1 such
that P -1 = P¯ -1 and Ph-1 P¯ . This means that there is some value P¯
-1 -1 of the FGT
measure with parameter -1, which is common among the targeted locations and no smaller
than that in any other locations.
This is a useful result for calculating the adjusted concentration curve. We employ a
computational algorithm very similar to the one used in Elbers et al. (2004b). First, we can
pick various values of P¯ . We then calculate Pg
-1 -1for various levels of transfer for each
g G, and linearly interpolate to find the transfer amount tg to achieve the given level of
P¯ . If the pre-transfer P
-1 -1 is less than P¯ , we have tg = 0 . Once we find the transfer
-1
for each location, we can calculate the budget and post-transfer P.
Figure 13(a) and Figure 13(b) show the adjusted concentration curves for stunting and
underweight for = 2. The pattern of the adjusted concentration curve is qualitatively some-
what similar to Figure 10(a) and Figure 10(b) in that the individual-level concentration curve
is in the far left of other curves, suggesting that there remains large room for improvement
even if targeting is conducted at the commune level or village level. It also suggests that
commune-level targeting is a significant improvement from provincial-level or stratum-level
targeting as is clear from the graph of relative budgetary gains shown in Figure 14. The ratio
of average relative budgetary gains for commune-level and provincial-level targeting exceeds
35
four for both stunting and underweight.
We have considered two extreme cases, one where the cost per capita is fixed, and the
other where it varies with the individual level of malnutrition. In both cases, we found that
geographic targeting alone leaves large room for improvement. Clearly, geographic targeting
is not a panacea for maximizing the impact of limited resources. However, this does not
undermine the usefulness of geographic targeting because geographic targeting can be easily
combined with other forms of targeting in most cases in order to further improve the efficiency.
In fact, we found that commune-level targeting alone improves efficiency by more than two
times compared with the stratum-level targeting. The improvement is much more dramatic
when the goal is a modest reduction. Given this, the commune-level estimates we produced
can indeed substantially improve the efficiency of targeting.
7 Conclusion
Estimates of the prevalence of child malnutrition were previously available only at the level
of CDHS strata. Stratum-level estimates often mask great disparities in the prevalence of
malnutrition within the stratum. Unless there are strata with an extremely high prevalence
of malnutrition, targeting based on stratum level estimates is unlikely to capture many of
the malnourished children and likely to misallocate resources.
To overcome the problem of limited data, we have developed a methodology to estimate
the prevalence of child malnutrition at the level of small geographic areas. We disaggregated
the estimates of the prevalence of child malnutrition in Cambodia from currently available
17 CDHS strata into 1,594 communes. We have extended the ELL small-area estimation
technique to jointly estimate multiple indicators and allow for a richer structure of error
terms. This is a crucial step to address issues unique to nutrition indicators. While we
applied this methodology to the Cambodian data, it can be easily applied to other countries
36
where census data and survey data with an anthropometric component are available.
Although estimated standard errors in our study are quite high for some communes, the
magnitude of the standard errors for the estimated prevalence of stunting and underweight
at the commune level is, on average, comparable to that for the existing stratum-level esti-
mates derived only from the CDHS data. We argued that high levels of standard errors for
each commune are not necessarily worrisome when a proposed policy intervention delivers
assistance to a relatively large number of communes.
The commune-level estimates we derived in this study can be used for analyzing the
current situation of malnutrition and for shaping targeting policies. We have presented the
commune-level estimates as nutrition maps. These maps allow policy-makers to visually lo-
cate areas of severe malnutrition. We argued that overlaid maps help us identify possible
causes of malnutrition in different locations. This in turn provides policy-makers with valu-
able information on the appropriate design of child nutrition programs. For example, direct
food aid would be helpful if food shortage is the principal cause of malnutrition. However,
local health clinics may prove more helpful where many children suffer from diseases such as
malaria and diarrhea.
We demonstrated three applications of the commune-level estimates. First, we applied
them to the analysis of correlation between consumption poverty, inequality and malnutrition.
We found no simple relationship, but the regression results suggest that non-linear effects of
consumption on the child nutrition status are crucial for understanding the relationship. Our
small-area estimates of consumption and health are very helpful for exploring the relationship
at a disaggregated level between malnutrition and other indicators, including consumption
poverty and inequality.
Second, we conducted decomposition analyses of child health inequality. We first followed
the approach by Pradhan et al. (2003), and then proposed two additional ways of decomposing
inequality by groups. One of them is based on the analysis of variance, and the other uses
37
concentration curves. We consistently found that the between-group component is smaller for
health inequality than consumption inequality. We also found that the proportion of between-
group inequality in the country is small in comparison with the proportion of between-country
inequality in the world. While this application is purely descriptive, it is useful for elucidating
the significance of the geographic information in explaining overall inequality. The magnitude
of the ratio of between-location health inequality to the overall health inequality was not
previously known.
Finally, we evaluated the efficiency gains from geographic targeting. We showed that
concentration curves are closely linked to efficiency measures of targeting. We proposed the
adjusted concentration curve to allow for the variable transfer across the individuals. We
found that commune-level targeting based on the estimates we produced is on average at
least two to three times more efficient than stratum-level targeting. This is the best we can
do with the CDHS estimates. The budgetary gains for commune-level targeting can be five
times as high as those for stratum-level targeting in the short run.
All three of these applications illustrate interesting research questions which can now
be answered with the commune-level estimates we derived. Successful application of our
methodology in other countries is likely to help improve the efficiency of targeting in these
countries. It will also help us to understand the relationship between consumption inequality
and health, and inequality in health outcomes.
References
Alderman, H. (2000) `Anthropometry.' In Designing Household Survey Questionnaires for
Developing Countries: Lessons from Ten Years of LSMS Experience, ed. M. Grosh and
P. Glewwe (Oxford University Press) pp. 251272
Alderman, H., M. Babita, G. Demombynes, N. Makhatha, and B. Ozler (2002) `How small
¨
can you go? combining census and survey data for mapping poverty in South Africa.'
Journal of African Economies 11, 169200
38
Clarke, P.M., U. Gerdtham, and L.B. Connelly (2003) `A note on the decomposition of the
health concentration index.' Health Economics 12, 511516
Curtis, S.L., and M. Hossain (1998) `West Africa spatial analysis prototype explanatory
analysis: The effects of aridity zone on child nutritional status.' Technical Report, Demo-
graphic and Health Survey, Macro International
de Onis, M., E.A. Frongillo, and M. Bl¨ossner (2000) `Is malnutrition declining? an analy-
sis of changes in levels of child malnutrition since 1980.' Bulletin of the World Health
Organization 78, 12221233
Deaton, A. (2003) `Health, inequality, and economic development.' Journal of Economic
Literature XLI, 113156
Demombynes, G., J. Elbers, C.and Lanjouw, J. Lanjouw, J. Mistiaen, and B. Ozler (2002)
¨
`Producing an improved geographic profile of poverty: Methodology and evidence from
three developing countries.' WIDER Discussion Paper 2002/39, United Nations University
Dibley, M.J., J.B. Goldsby, N.W. Staehling, and F.L. Trowbridge (1987a) `Development of
normalized curves for the international growth reference: historical and technical consid-
erations.' American Journal of Clinical Nutrition 46(5), 73648
Dibley, M.J., N.W. Staehling, P. Nieburg, and F.L. Trowbridge (1987b) `Interpretation of Z-
score anthropometric indicators derived from the international growth reference.' American
Journal of Clinical Nutrition 46(5), 749762
Elbers, C., J.O. Lanjouw, and P. Lanjouw (2000) `Welfare in villages and towns: Micro-level
estimation of poverty and inequality.' Timbergen Institute Discussion Paper TI 2000-029/2,
Timbergen Institute
(2002) `Micro-level estimation of welfare.' Policy Research Department Working Paper
2911, The World Bank
(2003a) `Micro-level estimation of poverty and inequality.' Econometrica 71(1), 355364
(2004a) `Imputed welfare estimates in regression analysis.' Journal of Economic Geography
Elbers, C., P. Lanjouw, J. Mistiaen, B. Ozler, and K. Simler (2003b) `Are neighbours equal?
¨
estimating local inequality in three developing countries.' FCND Discussion Paper No. 147,
Food Consumption and Nutrition Division, International Food Policy Research Institute
Elbers, C., T. Fujii, P. Lanjouw, B. Ozler, and W. Yin (2004b) `Poverty alleviation through
¨
geographic targeting.' Policy Research Working Paper 3419, The World Bank
Foster, J.E., J. Greer, and E. Thorbecke (1984) `A class of decomposable poverty indices.'
Econometrica 52, 761766
39
Frongillo, E.A., M. de Onis, and K.M.P. Hanson (1997) `Socioeconomic and demographic
factors are associated with worldwide patterns of stunting and wasting of children.' Journal
of Nutrition 127(12), 23022309
Fujii, T. (2004) `Commune-level estimation of poverty measure and its application in Cam-
bodia.' In Spatial Disparities in Human Development: Perspectives from Asia, ed. Kanbur
R., Venables A.J., and G. Wan (United Nations University Press). Forthcoming
Galler, J.R., and L.R. Barrett (2001) `Children and famine: Long-term impact on develop-
ment.' Ambulatory Child Health 7, 8595
Glewwe, P., H.G. Jacoby, and E.M. King (2001) `Early childhood nutrition and academic
achievement: a longitudinal analysis.' Journal of Public Economics 81, 345368
Haddad, L., and R. Kanbur (1990) `How serious is the neglect of intra-household inequality.'
The Economic Journal 100(402), 86681
Hardy, F., and Health Unlimited Ratanakiri Team (2001) `Health situation analysis
Ratanakiri, Cambodia.' Technical Report, Health Unlimited
Haughton, D., and J. Haughton (1997) `Explaining child nutrition in Vietnam.' Economic
Development and Cultural Change 45(3), 541556
Hentschel, J., J.O. Lanjouw, P. Lanjouw, and J. Poggi (2000) `Combining census and survey
data to study spatial dimensions of poverty: A case study of Ecuador.' The World Bank
Economic Review 14(1), 147166
Kakwani, N. (1977) `Applications of lorenz curves in economic analysis.' Econometrica
45(3), 719728
Kakwani, N., A. Wagstaff, and E. van Doorslaer (1997) `Socioeconomic inequalities in health:
Measurement, computation, and statistical inference.' Journal of Econometrics 77, 87103
Kanbur, R. (1987) `Transfers, targeting and poverty.' Economic Policy 4(1), 112147
Kawachi, I., B.P. Kennedy, K. Lochner, and D. Prothrow-Stith (1997) `Social capital, income
inequality and mortality.' American Journal of Public Health 87(9), 14911498
Khorshed Alam Mozumder, A.B.M., T.T. Kane, A. Levin, and S. Ahmed (2000) `The effect
of birth interval on malnutrition in bangladeshi infants and young children.' Journal of
Biosocial Science 32, 289300
Kunst, A.E., F. Groenhof, J.P. Mackenbach, and EU Working Group on Socioeconomic In-
equalities in Health (1998) `Occupational class and cause specific mortality in middle aged
men in 11 european countries: comparison of population based studies.' British Medical
Journal 316, 16361642
40
Li, Y., G. Guo, A. Shi, Y. Li, T. Anme, and H. Ushijima (1999) `Prevalence and correlates
of malnutrition among children in rural minority areas of China.' Pediatrics International
41, 549556
Lovell, M.C. (1998) `Inequality within and among nations.' Journal of Income Distribution
8(1), 544
Mahalanobis, P.C. (1960) `A method of fractile graphical analysis.' Econometrica 28(2), 325
351
Monteiro, C.A., L. Mondini, A.M. Torres, and I.M. dos Reis (1997) `Patterns of intra-familiar
distribution of undernutrition: Methods and applications for developing societies.' Euro-
pean Journal of Clinical Nutrition 51, 800803
Montgomery, S.M., M.J. Bartley, D.G. Cook, and W.E.J Wadsworth (1996) `Health and
social precursors of unemployment in young men.' Journal of Epidemiology and Community
Health 50, 415422
MoP (2003) `Cambodia millennium development goals report 2003.' Technical Report, Min-
istry of Planning, Royal Government of Cambodia
National Institute of Statistics, Directorate General for Health, and ORC Macro (2001) Cam-
bodia Demographic and Health Survey 2000 (National Institute of Statistics, Directorate
General for Health and ORC Macro)
Nystrom Peck, A.M. (1992) `Childhood environment, intergenerational mobility, and adult
healthevidence from Swedish data.' Journal of Epidemiology and Community Health
46, 7174
Pelletier, D.L., E.A. Frongillo Jr., D.G. Schroeder, and J-P. Habicht (1994) `A methodology
for estimating the contribution of malnutrition to child mortality in developing countries.'
Journal of Nutrition 124, 2106S2122S
Pradhan, M., D.E. Sahn, and S.D. Younger (2003) `Decomposing world health inequality.'
Journal of Health Economics 22(2), 271293
Ravallion, M. (1988) `Expected poverty under risk-induced welfare variability.' The Economic
Journal 98(393), 11711182
Ravallion, M., and K. Chao (1989) `Targeting policies for poverty alleviation under imperfect
information: Algorithms and applications.' Journal of Policy Modeling 11(2), 213224
Sen, A. (2002) `Why health equity?' Health Economics 11, 659666
Shariff, Z.M., J.T. Bond, and N.E. Johnson (2000) `Nutrition and educational achievement
of urban primary schoolchildren in Malaysia.' Asia Pacific Journal of Clinical Nutrition
4(9), 264273
41
Shorrocks, A.F. (1980) `The class of additively decomposable inequality measures.' Econo-
metrica 48(3), 613626
van Doorslaer, E., A. Wagstaff, H. Bleichrodt, S. Calonge, U. Gerdtham, M. Gerfin, J. Geurts,
L. Gross, U. H¨akkinen, R.E. Leu, O. O'Donnell, C. Propper, F. Puffer, M Rodr´iguez,
G. Sundberg, and O. Winkelhake (1997) `Income-related inequalities in health: some in-
ternational comparisons.' Journal of Health Economics 16(1), 93112
Victora, C. (1992) `The association between wasting and stunting: An international perspec-
tive.' Journal of Nutrition 122(5), 11051110
Wagstaff, A., and E. van Doorslaer (2000) `Income inequality and health: What does the
literature tell us?' Annual Review of Public Health 21, 543567
(2004) `Overall versus socioeconomic health inequality: a measurement framework and two
empirical illustrations.' Health Economics 13, 297301
Wagstaff, A., E. van Doorslaer, and N. Watanabe (2003) `On decomposing the causes of
health sector inequalities with an application to malnutrition inequalities in Vietnam.'
Journal of Econometrics 112, 207223
Waterlow, J.C., R. Buzina, W. Keller, J.M. Lane, M.Z. Nichaman, and J.M. Tanner (1977)
`The presentation and use of height and weight data for comparing the nutritional status
of groups of children under the age of 10 years.' Bulletin of the World Health Organization
55(4), 489498
WFP (2001) Identifying Poor Areas in Cambodia: Combining Census and Socio-Economic
Survey Data to Trace the Spatial Dimensions of Poverty (Phnom Penh: World Food Pro-
gramme)
WHO Working Group (1986) `Use and interpretation of anthropometric indicators of nutri-
tional status.' Bulletin of the World Health Organization 64(6), 929941
(1995) `An evaluation of infant growth: the use and interpretation of anthropometry in
infants.' Bulletin of the World Health Organization 73(2), 165174
Wilkinson, R.G. (1996) Unhealthy Societies: The Afflictions of Inequality (Routledge)
World Health Organization (2002) World Health Report 2002: Reducing risks and promoting
healthy life (Geneva: World Health Organization)
Yitzhaki, S., and J. Slemrod (1991) `Welfare dominance: An application to commodity tax-
ation.' American Economic Review 81(3), 480496
Zeini, L.O., and J.B. Casterline (2002) `Clustering of malnutrition among Egyptian children.'
mimeo, Cairo University and Population Council
42
Appendix
A Mathematical Proofs
Proof of Eq (1) First note the following:
E[(u(ch )2] = ( ) + ((,ch)2 +
k) (k) 2 k) 1 (k)
· Ich( )2
E[(u(c ) ] = ( ) +
k) 2 (k) 2 1 k) 1 1 (k)
·· H2c ((,ch)2 + H2c Ich ( )2
hHc hHc
Hence,
wc E (uch )2
Hc ·
cC hHc
1 1 1
= + 2 wcHc 2 2
H2c ,ch + H2c Ich
cC hHc hHc
= + 2 wcHc E (uc )2 - 2
··
cC
=(1 - wcHc)+ 2 wcHcE (uc )2
··
cC cC
Solving for , we have Eq(1).
2
Proof of Eq (2) First note the following:
E[(uch - uc )2] = Hc - 2 2 1
· ·· Hc Ich + 2,ch + H2c Ich+ 2,ch
h Hc
By summing over the households in each cluster, we have
Hc - 1 2
E[ (uch - uc )2] =
· ·· Hc Ich+ 2,ch
h Hc h Hc
Therefore, for all the households in C,
43
2,ch = Hc 1 2
Hc - 2E [(uch - uc )2] -
· ·· (Hc - 1)(Hc - 2)E [ (uch - uc )2] -
· ·· Ich
h Hc
Adding to both sides of the equality and arranging the terms, we get Eq(2).
2
B Tables and Figures
Table 1: GLS regression results for standardized height in Coastal ecozone.
Variable Coef. SE
Intercept 77.48 0.73
(Max years of educ for HH)*(Head has no educ) 1.06 0.16
(Head's years of educ)*(Water from dug well) 0.50 0.11
(# professional women in HH)*(Head has some secondary educ) -16.41 2.85
(# women in HH for less than 5 years)*(# members aged 0) -8.66 1.53
(Head's years of educ)*(Total deaths of children in HH last 12mth) -0.67 0.10
(Child deaths over live births)*(Age of spouse) 0.35 0.07
(Rain water)*(Head completed primary educ) 10.83 1.68
(Sex=Female)*(Head has some secondary educ) 5.95 1.01
(Roof made of rock)*(Age=4) -8.91 0.91
(Rain water)*(Age=3) -6.44 1.21
(Water not from pipe/well/bottle)*(Age=0) 11.95 2.32
(Ratio of female in HH)*(Age=3) -0.16 0.03
(# women in HH worked last 12mth)*(Variance of NDVI in Nov) 12.41 3.15
(Toilet on premise)*(Distance to river) 2.97E-04 6.18E-05
Ratio of head in village with secondary education 21.98 4.45
(Age of head)*(Water from dug well) -0.09 0.02
(# women worked)*(Child death over births) -22.71 4.94
(No women in HH have educ)*(Head has some secondary educ) -5.67 1.91
(Head is male)*(age=0) 3.05 0.67
44
Table 2: GLS regression results for standardized weight in Coastal ecozone.
Variable Coef. SE
Intercept 10.21 0.21
(Max years of educ for HH)*(Head has no educ) 0.20 0.04
(Head's years of educ)*(Water from dug well) 0.11 0.03
(# women in HH for less than 5 years)*(# members aged 0) -2.07 0.38
(Ratio of those ever attended school)*(Max year of educ for females in HH) 1.74E-03 4.32E-04
(Roof made of rock)*(Age=4) -1.34 0.25
(# members aged 0-4)*(Age=0) 0.85 0.10
(Floor material wood)*(Area of rice field in village) 3.99E-04 7.21E-05
(Max female educ in HH is some primary educ)*( ag. land b/w 1993 and 1997) -7.13E-08 1.72E-08
(Flood prone commune)*(Age=4) 1.88 0.34
(# members aged 0-4)*(Water from dug well) -0.43 0.10
(Age of head)*(toilet not on premise) -0.02 3.78E-03
(# younger children)*(Roof made of wood/plastic) 1.15 0.23
(# students)*(Child death over live births) -1.20 0.35
(toilet not on premise)*(head is male) 0.63 0.16
(Roof made of wood/plastic)*(Age=3) -0.95 0.25
(Head has some primary educ)*(Age=4) -0.96 0.23
(Head is male)*(Age=1) -0.73 0.22
(# members 65 or over)*(Age=0) 1.95 0.48
(Max year educ. for females)*(Age=3) -0.21 0.04
Table 3: Comparison of the ecozone-level estimates. Standard error for CDHS Only was
calculated by 100-time two-stage bootstrapping.
CDHS Only This study
Indicator Ecozone Mean SE Mean SE
Urban 37.89 3.30 40.90 1.74
Plain 47.58 2.49 50.62 1.92
Stunting Tonlesap 43.23 2.09 44.69 1.75
Coastal 47.21 5.52 49.65 2.25
Plateau 47.10 2.99 47.26 1.64
Urban 39.58 2.93 39.66 1.93
Plain 47.80 2.44 46.35 1.73
Underweight Tonlesap 45.84 1.95 44.08 2.50
Coastal 38.95 5.28 38.70 2.16
Plateau 46.37 3.87 46.24 1.77
45
Table 4: Commune-level regression of malnutrition indicators on logarithmic mean consump-
tion and inequality. Regressions were run separately. N=1594.
Without Provincial Dummies With Provincial Dummies
Variable Stunting Underweight Stunting Underweight
Coef T-value Coef T-value Coef T-value Coef T-value
Intercept 0.528 30.69 0.505 32.39 0.455 22.47 0.507 27.09
log Y¯ -0.107 -4.50 -0.082 -3.78 -0.002 -0.82 -0.003 -1.41
GE(0) -0.005 -2.01 -0.007 -3.22 -0.054 -2.40 -0.061 -2.90
R2 0.02 0.03 0.21 0.18
Table 5: Commune-level regression of average severity of malnutrition P2 on logarithmic
P0
mean consumption and inequality. Right two columns also includes P0. Regressions were
run separately. N=1594.
Variable Stunting Underweight Stunting Underweight
Coef T-value Coef T-value Coef T-value Coef T-value
Intercept 0.0074 21.31 0.0294 21.87 0.0032 9.46 0.0053 4.30
log Y¯ 0.0001 0.35 -0.0002 -0.16 -4.46E-05 -1.26 -2.77E-05 -0.23
GE(0) -0.0001 -1.50 -0.0002 -1.10 0.0006 1.96 0.0026 2.34
P0 0.0093 25.51 0.0476 35.08
R2 0.19 0.26 0.43 0.59
Table 6: Number of communes by poverty rate (row) and prevalence of underweight (column).
0.00-0.30 0.30-0.45 0.45-0.50 0.50-0.55 0.55-1.00 Total
0.00-0.30 43 169 235 52 50 549
0.30-0.50 19 126 295 62 53 555
0.50-1.00 23 122 208 81 56 490
Total 85 417 738 195 159 1594
46
for t, t
ts.
eighw heigh ations tage.
1424907 onen
(0.00) (0.00) (0.00)
is
corrected andt observ ercenp (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
comp
is of in
y record
heigh
1424907/2130544 standardized erb are
unit Individual/Household 100.00 100.00 100.00 for umn 1424907/2130544 residual
Individual/Household 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
inequalit for figures and
The
(1.13) (1.29) (8.68) record All
standardized ations (0.50) (0.75) (0.81) (0.57) (0.81) (0.71) (1.16) (2.01) (2.82)
tage.
Health Village 13320 cation 0.00 0.00
for thesis. Village 13320 100.00
Unit
observ ercenp 10.87 12.84 64.14 6.28 7.22 6.40 6.48 7.01 5.49 37.14 46.72 45.87 Individual
2.
GE(0). of in paren een-low
yb erb une (1.04) (1.05) and in etb 0.01
individual are (13.16) consumption. 14.73 85.26
1 une (0.45) (0.70) (0.75) (0.47) (0.70) (0.62) (0.88) (1.76) (2.36) Village
is umn 1594 0, are for 1594
Comm
7.69 8.10 Comm
figures 43.19 4.23 4.98 4.31 3.92 4.31 3.20 19.06 23.15 21.53 cation, une 0.04 11.94 88.02
The errors
measured record All 213054
Comm
as
y (0.48) (0.54)
Unit thesis. (15.84) parameter
180 andt (0.31) (0.38) (0.32) (0.27) (0.34) (0.30) (0.71) (1.36) (1.81) within-lo
180
District for Standard District to 0.42 8.20 91.38
paren 2.94 3.65 28.84 eighw 1.92 2.10 1.70 1.85 2.04 1.52 12.00 14.29 12.98 int District
inequalit (2003). in
al. consumption.
are measures heigh vince 3.59 5.62 90.79
et for (0.41) (0.40) andt (0.29) (0.31) (0.24) (0.20) (0.24) (0.21) (0.50) (0.86) (1.00)
(16.32) vince 24 Pro
vince 24
errors Pro GTF consumption. heigh Pro
0.95 0.95 0.73 0.75 0.78 0.59 7.10 8.20 7.20
consumption 213054 1.29 1.49 0.00 0.00
18.69 of for diaob
Pradhan 100.00
and yb
Standard andt (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) standardized Cam
diaob diaob 1
(0.00) (0.00) (0.00) for
1 ariancev
osed
health eighw IW IB R
household standardized Cam 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 C GI C GIGI GI
Cam 0.00 0.00 0.00 the for Gini N N
of prop
as andt of and of tage.
t t 0 1 2 0 1 2 0 1 2
y ations
osition consumption. eigh ations
heigh Heigh W osition 1424907 arameterP osition ercenp
for is Observ
Observ individual in
of
inequalit of
Decomp ist t t
are
Consumption erb Decomp record eigh erb Decomp
7: Standardized 8: Indicator Heigh W
Num 9:
natural household Standardized
standardized Num eighw Standardized Standardized Consumption
unit figures
ableT the and for ableT and for ableT All
47
dia.ob
Cam
in
e
fiv
under
hildrenc
for
ting
stun
of
alence
prev
el
une-lev
Comm
1:
Figure
48
dia.ob
Cam
in
e
fiv
under
hildrenc
fort
eigh
underw
of
alence
prev
el
une-lev
Comm
2:
Figure
49
Figure 3: (a) Prevalence of stunting and underweight in Cambodia (top), and (b) near Phnom
Penh (bottom). H and L respectively mean above and below 45 percent.
50
Figure 4: (a) Prevalence of stunting in comparison with the national average (NA) (top),
and (b) the number of stunted children per square kilometers (bottom).
51
Figure 5: (a) Poverty rate and prevalence of stunting (top), and (b) poverty rate and preva-
lence of underweight in Cambodia.
52
A C
B
Y
X
Figure 6: An illustration of the relationship between consumption and malnutrition. Hori-
zontal axis measures consumption and vertical axis measures probability density. X is the
consumption threshold below which a child is malnourished.
Figure 7: Distribution of commune-level GE(0) in standardized height.
53
C J K B
H I
erahSTGFevitalumuC E
G F
O D A
Cumulative Population Share
Figure 8: An example of concentration curve for P0.
54
t).
(righ
e
B A curv
tration
X G tegduB concen
K L
Y F adjusted
J E of
Z D example
an
C TGF evitaH lumuC
I O
(b)
B A and
J (left)
e
X G
K
Y F
J E erahSnoitalupoPevitalumuC curv
tration
concen
of
Z D
example
C erahS TGF evitaluHmuC
I O An
(a)
9:
Figure
55
tal
horizon
The malnourished
of
t).
(right share
e
eigh
ulativ
cum
underw
fore the
curv
measures
tration axis
concen erticalv
(b)
the
and
and
(left),
ting
stun opulationp
of
fore
curv share
e
tration ulativ
cum
Concen the
(a)
10:
measures
Figure axis hildren.c
56
axis
tal
horizon
The
t).
(right gains.
eigh
alence
underw
equiv
for
gains
measures
alence axis
equiv
(b) erticalv
the
and
and
(left),
ting targeted
stun eb
for to
gains
opulationp
alence of
Equiv share
(a) the
11:
Figure measures
57
The
t).
(right
gains.
eigh
underw budgetary
for e
gains relativ
the
budgetary
e measures
relativ axis
(b)
and erticalv
the
(left), and
ting
stun
reduction
for
GTF
gains of
goal
the
budgetary
e
Relativ measures
(a) axis
12: tal
Figure horizon
58
The
t.
eigh
underw
fore
curv
tration GT.F
in
concen
adjusted reduction
(b) the
and
(left) measures
ting axis
stun
fore erticalv
the
curv
and
tration
budget
concen the
Adjusted measures
(a) axis
13: tal
Figure horizon
59
Figure 14: Relative budgetary gains for adjusted concentration curve in Figure 13. The
horizontal axis measures the goal of reduction in FGT measure P2 . The vertical axis
,(1)
measures relative budgetary gains.
60