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ESTIMATING WEALTH EFFECTS 115
Demography, Volume 38-Number 1, February 2001: 115132 115
ESTIMATING WEALTH EFFECTS WITHOUT EXPENDITURE DATAOR TEARS:
AN APPLICATION TO EDUCATIONAL ENROLLMENTS IN STATES OF
INDIA*
DEON FILMER AND LANT H. PRITCHETT
tures. The econometric evidence suggests that the asset indexas
a proxy of economic status for use in predicting enrollmentsis at
least as reliable as conventionally measured
consumptionexpenditures, and sometimes more so.
This straightforward and pragmatic method of constructing a
proxy for household economic status produces resultsthat are
reassuringly consistent with other approaches (seeMontgomery et al.
2000 and references therein) and poten-tially is broadly
applicable. Demographic and Health Sur-
veys (DHS) have been conducted with nearly identical sur-vey
instruments in more than 40 countries. (In India this sur-vey is
called the National Family Health Survey, or NFHS.)These surveys
include assets and housing conditions but noconsumption
expenditures (except for an experimental con-sumption module
included in Indonesia in 1994, a featurethat we exploit later in
this paper).
Our proposed method for estimating household wealth inthe
DHS/NFHS allows estimates of the association of wealthwith
education across households and permits a comparison owealth gaps
across countries (and in India across states). Inseparate papers we
use the asset index to examine wealth andgender gaps in enrollment
and educational attainment in morethan 35 countries (Filmer 2000;
Filmer and Pritchett 1999a).
We limit ourselves here to demonstrating the validityand
usefulness of an asset index in analyzing education out-comes. The
same method might be equally useful in examining wealth differences
in other socioeconomic outcomes inthe DHS data, such as mortality,
morbidity, utilization ohealth facilities, fertility, and
contraceptive use (BonillaChacin and Hammer 1999; Gwatkin et al.
2000; StecklovBommier, and Boerma 1999). Sahn and Stifel (1999)
havetaken a similar index approach to making comparisons ofrelative
poverty over time and across countries, using DHSdata for nine
countries in Africa.
A proxy for wealth not only is useful in examining ef-fects of
wealth, but also is needed as a control variable inestimating
effects of variables potentially correlated with
household wealth, such as maternal education. The methodproposed
here provides a simple technique for creating awealth proxy in the
absence of either income or expendituredata (an issue discussed
further in Montgomery et al. 2000)
OVERCOMING THE PROBLEM OF RANKINGHOUSEHOLDS IN THE ABSENCE
OFCONSUMPTION OR EXPENDITURE DATA
The DHS and NFHS data present both an opportunity and
achallenge. The opportunity is a rich set of large,
representative
Using data from India, we estimate the relationship
betweenhousehold wealth and childrens school enrollment. We proxy
wealthby constructing a linear index from asset ownership
indicators, us-ing principal-components analysis to derive weights.
In Indian datathis index is robust to the assets included, and
produces internallycoherent results. State-level results correspond
well to independentdata on per capita output and poverty. To
validate the method andto show that the asset index predicts
enrollments as accurately asexpenditures, or more so, we use data
sets from Indonesia, Paki-
stan, and Nepal that contain information on both expenditures
and
assets. The results show large, variable wealth gaps in
childrensenrollment across Indian states. On average a rich child
is 31
percentage points more likely to be enrolled than a poor
child,but this gap varies from only 4.6 percentage points in Kerala
to 38.2in Uttar Pradesh and 42.6 in Bihar.
his paper has both an empirical and a methodological goal.The
empirical goal is to investigate the effect of household eco-nomic
status on childrens educational attainment across thestates of
India. To accomplish this aim, we propose and defenda method for
estimating the effect of household wealth on edu-cational outcomes
even in the absence of survey questions onincome or expenditures.
We use data on asset ownership (e.g.,
owning a bicycle or radio) and housing characteristics
(e.g.,number of rooms, type of toilet facilities), henceforth
calledasset indicators or asset variables, to construct an asset
in-dex. We handle the vexing problem of choosing the appropri-ate
weights by using the statistical procedure of principal com-
ponents. We demonstrate the empirical validity of this
approachfor India by comparing the state-level averages of the
asset in-dex with data on poverty rates and gross state product
percapita. Going further, we use data sets from Indonesia,
Nepal,and Pakistan, which contain both expenditures and asset
vari-ables for the same households, to show a reasonable
correspon-dence between the classification of households based on
the as-set index and a classification based on consumption
expendi-
T
*Deon Filmer, Development Research Group, The World Bank, 1818H
Street NW, Washington, DC 20433; E-mail: [email protected]
H. Pritchett, John F. Kennedy School of Government and The
WorldBank. This research was funded in part through World Bank
research sup-
port grant (RPO 682-11). We would like to thank Harold Alderman,
ZoubidaAllaoua, Gunnar Eskeland, Jeffrey Hammer, Keith Hinchliffe,
ValerieKozel, Alan Krueger, Peter Lanjouw, Marlaine Lockheed, Berk
Ozler, andMartin Ravallion for valuable discussions and comments,
including someon an earlier version of this paper (Filmer and
Pritchett 1998). The findings,interpretations, and conclusions
expressed here are entirely those of the au-thors. They do not
necessarily represent the views of the World Bank, itsexecutive
directors, or the countries they represent.
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116 DEMOGRAPHY, VOLUME 38-NUMBER 1, FEBRUARY 2001
surveys with nearly identical questionnaires covering a
largenumber of countries or Indian states. The challenge is that
theDHS/NFHS surveys contain no data on income or on house-hold
consumption expenditures. The latter is unfortunate be-cause a
large literature establishes the theoretical underpin-
nings of consumption expenditures as a measure of currentand
long-run household (and implicitly individual) welfare.(For
example, see Deaton 1997; Deaton and Muellbauer1980; Deaton and
Zaidi 1999.) As a result, expenditures areroutinely used in
measuring poverty. We overcome the ab-sence of expenditure data by
using the information collectedon assets owned by household members
and on housing char-acteristics. These data are used to generate an
asset index that
proxies for wealth and hence for long-run economic status.Three
clarifications will avoid confusion at the outset.
First, we are not proposing this asset index as a measureeither
of current welfare or of poverty.1 We use the assetindex as a
determinant of current enrollment, which de-
pends on long-run as well as current expenditures: house-
holds will smooth schooling expenditures over time and
areunlikely to respond to temporary shocks by withdrawingchildren
from school.
Second, unlike Montgomery et al. (2000), we are not cre-ating an
asset index as a proxy for current consumption ex-
penditures. We view the asset index and expenditures as aproxy
for something unobserved: a households long-run eco-nomic status.
Therefore, although it is reassuring that thesetwo proxies are
related, discrepancies in the classification ofhouseholds cannot be
assumed to be mistakes of the assetindex. The two, as proxies, have
conceptually and empiricallydistinct limitations; therefore
discrepancies could just as eas-ily indicate limitations of current
consumption expenditures.The major problem with the asset index is
that the weights on
individual indicators are not grounded theoretically. The ma-jor
problem with current expenditures as a proxy for long-runwealth is
the presence of short-term fluctuations.2
Third, we emphasize that the principal-components ap-proach is a
pragmatic response to a data constraint problem.In this paper we
set the modest goal of establishing the valid-ity of this
particular approach in this application; we do notestablish that
our approach is optimal because there may beother methods that
possess superior statistical properties.
Construction of an Asset Index
How does one aggregate various asset ownership indicatorsinto
one variable to proxy for household wealth? Even ifthe question is
simplified by limiting the aggregation to a
linear index, how should the weights be chosen? Equalweights
have the appeal of simplicity and apparent objectiv-ity, but these
qualities only mask the fact that the impositionof numeric equality
is completely arbitrary.
A second option would be to estimate the current valueof
household assets using explicit and implicit prices asweights. If
the data did not include current values, then the
purchase price, the date of purchase, and a suitable
deprecia-tion rate could be used to estimate them. The DHS and
NFHSdata, however, are typical in that they include binary
indica-tors on asset ownership and housing characteristics but
notcurrent value, purchase price, or vintage of assets.
A third possible solution is not to build an index at all
butsimply to enter all of the asset variables separately in a
linear
multivariate regression equation. This procedure
implicitlycreates weights on the variables. Such an approach
handlesthe problem of controlling for wealth in estimating the
im-
pact of other, nonwealth, variables. Yet the linear index of
theassets using regression weights does not estimate the
wealtheffect because many assets exert both a direct and an
indirecteffect on outcomes. For instance, the households use of
elec-tricity for lighting may serve as a proxy for wealth, but
alsomay make study easier and hence may lower the opportunitycosts
of schooling. The availability of piped water not onlymay indicate
greater wealth but also may reduce the timeneeded for water
collection and thus may reduce the opportu-nity costs of schooling.
This argument is even clearer withhealth outcomes because water and
sanitation variables have
strong independent effects on childrens health (Bonilla-Chacin
and Hammer 1999). Therefore, although linear regres-sion
coefficients implicitly produce weights for the linear in-dex of
the asset variables that predicts the dependent variablemost
closely, there is no way to infer from these uncon-strained
coefficients the impact of an increase in wealth.
Using Principal Components
We implement a different approach: we use the
statisticalprocedure of principal components to determine the
weightsfor an index of the asset variables. Principal components is
atechnique for extracting from a set of variables those
feworthogonal linear combinations of the variables that capturethe
common information most successfully. Intuitively the
first principal component of a set of variables is the
linearindex of all the variables that captures the largest amount
ofinformation that is common to all of the variables. (For
read-able and intuitive descriptions of principal components,
seeLindeman, Merenda, and Gold 1980; StataCorp 1999.)
Suppose we have a set ofNvariables, a*1jto a*N j, repre-senting
the ownership ofNassets by each householdj. Prin-cipal components
starts by specifying each variable normal-ized by its mean and
standard deviation: for example, a1j=(a*1j a*1) / (s*1), where a*1
is the mean of a*1j across
1. The limitation in poverty analysis is twofold. First, the
conventionalnotion of poverty is based on the flow of consumption
relative to some pre-determined poverty threshold, whereas we, by
aggregating assets, are estab-lishing only a measure of a stock.
Second, the categorization used is basedon a relative measure (that
is, the households ranking within the distribu-
tion), whereas poverty thresholds typically are based on the
expendituresnecessary for the consumption of a determined bundle of
goods.
2. Current expenditures would be a perfect measure only under
the unre-alistically strong assumptions of perfect foresight and
perfect capital markets.Current expenditures are a popular proxy
for long-run wealth for two mainreasons: the theoretical
justification that expenditures are superior to currentincome as a
proxy for long-run income because of consumption smoothing,and,
perhaps even more important, the pragmatic justification that
expendi-tures are easier to measure than income in most rural
settings. Current expen-ditures, however, are not preferred
unambiguously to asset ownership on ei-ther of these dimensions:
asset ownership also reflects smoothing and is (ifanything) easier
to measure than either income or expenditures.
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ESTIMATING WEALTH EFFECTS 117
holds surveyed in each Indian state varies from 9,963 inUttar
Pradesh to around 1,000 in the small northeasternstates. The survey
includes data on 21 asset indicators thatcan be grouped into three
types: household ownership ofconsumer durables, with eight
questions (clock/watch, bi
cycle, radio, television, bicycle, sewing machine,
refrigera-tor, car); characteristics of the households dwelling,
with12 indicators (three about toilet facilities, three about
thesource of drinking water, two about rooms in the dwellingtwo
about the building materials used, and one each aboutthe main
source of lighting and cooking); and householdlandownership.
Table 1 reports the scoring factors from the principalcomponents
analysis of the 21 variables (see Eq. (3)). Themean value of the
index is 0; the standard deviation is 2.3Because all the asset
variables (except number of rooms)take only the values 0 or 1, the
weights have an easy inter-
pretation: a move from 0 to 1 changes the index by f1i /s*
(reported in column 4). A household that owns a clock has
an asset index higher by 0.54 than one that does not; owning a
car raises a households asset index by 1.21 units; us-ing biomass
as the main cooking fuel lowers the asset index
by 0.67.We sort individuals by the asset index and establish
cut-
off values for percentiles of the population. We then
assignhouseholds to a group on the basis of their value on the
indexFor expository convenience, we refer to the bottom 40% aspoor,
the next 40% as middle, and the top 20% as rich,asking the reader
to remember that this classification doesnot follow any of the
usual definitions of poverty.
The difference in the average index between the pooresand the
middle group is 2.07 units. One example of a combi-nation of assets
that would produce this difference is owning
a radio (0.54), having a kitchen as a separate room (0.37)having
electricity for lighting (0.57), and not having a dwelling of all
low-quality materials (0.55). The average asset index is 3.78 units
higher for the richest than for the middlegroup. This difference is
equivalent to owning a motorscooter (0.91) and a television (0.83),
having a flush toile(0.75) and a house of all high-quality
materials (0.73), andnot using biomass as the main cooking fuel
(0.67).
The Reliability of the Asset Index
For India the asset index performs well on three
dimensionsFirst, it is internally coherent because average asset
owner-ship differs markedly across the poor, middle, and rich
house-holds for each asset; second, it is robust to the assets
included
third, it produces reasonable comparisons with measures
ofstate-level poverty and output. The index has drawbacks, however,
especially possible problems with urban/rural compari-sons.
Internal coherence.The last three columns of Table 1compare the
average ownership of each asset across the
poor, middle, and rich households. We find large
differencesacross groups for almost all assets. Clock ownership is
16%for the poor versus 98% for the rich. Also, the poor cookwith
biomass fuel almost exclusively (96%), whereas only
households and s*1is its standard deviation. These
selectedvariables are expressed as linear combinations of a set of
un-derlying components for each household j:
a1j= v11A1j+ v12A2j+...+ v1NANj... j= 1,...J
aNj= vN1A1j+ vN2A2j+...+ vNNANj, (1)
where the As are the components and the vs are the coeffi-cients
on each component for each variable (and do not varyacross
households). Because only the left-hand side of eachline is
observed, the solution to the problem is indeterminate.
Principal components overcomes this indeterminacy byfinding the
linear combination of the variables with maxi-mum variancethe first
principal componentA1j and thenfinding a second linear combination
of the variables, orthogo-nal to the first, with maximal remaining
variance, and so on.Technically the procedure solves the equations
(R nI)vn=0 for nand vn, where Ris the matrix of correlations
betweenthe scaled variables (the as) and vn is the vector of
coeffi-
cients on the nth component for each variable. Solving
theequation yields the characteristic roots of R, n(also knownas
eigenvalues) and their associated eigenvectors, vn. The fi-nal set
of estimates is produced by scaling the vns so the sumof their
squares sums to the total variance, another restrictionimposed to
achieve determinacy of the problem.
The scoring factors from the model are recovered byinverting the
system implied by Eq. (1), and yield a set ofestimates for each of
theNprincipal components:
A1j=f11a1j+f12a2j+...+f1NaNj... j= 1,...J
ANj=fN1a1j+fN2a2j+...+fNNaNj. (2)
The first principal component, expressed in terms of the
original (unnormalized) variables, is therefore an index foreach
household based on the expression
A1j=f11(a*1j a*1)/(s*1)+...+f1N(a*Nj a*N) / (s*N). (3)
The crucial assumption for our analysis (and it is just
thatanassumption) is that household long-run wealth explains
themaximum variance (and covariance) in the asset variables.There
is no way to test this assumption directly, but in the nexttwo
sections we provide evidence that this method producesreasonable
results. Below we illustrate the method using thestates of India,
and show the internal and external coherence ofthe asset index.
Then we compare this the method with the useof consumption
expenditures in three countries; we find thatthis simple asset
index has reasonable agreement with con-
sumption expenditures and performs as well, or better, in
pre-dicting education outcomes in two of the countries.
CONSTRUCTION AND INTERNAL VALIDITY OFTHE ASSET INDEX IN
INDIA
Construction of the Asset Index Using the NFHSData
The NFHS survey covers about 88,000 households andabout one-half
million individuals. The number of house-
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118 DEMOGRAPHY, VOLUME 38-NUMBER 1, FEBRUARY 2001
tion between poor and rich on housing variables not relatedto
infrastructure, such as all high-quality materials in thedwelling
(less than 1% of the poor versus 82% of the rich)and having a
kitchen as a separate room (31% of the poorversus 85% of the
rich).
22% of the rich do so. One might ask whether the asset in-dex
tends too much to reflect community variables (espe-cially locally
available infrastructure such as electricity forlighting or piped
water) rather than household-specific vari-ables. On this score, we
are reassured by the clear separa-
TABLE 1. SCORING FACTORS AND SUMMARY STATISTICS FOR VARIABLES
ENTERING THE COMPUTATION OF THE
FIRST PRINCIPAL COMPONENT
All India Means_______________________________________________
_________________________________Scoring Scoring Poorest Middle
Richest
Factors Mean SD Factor SD 40% 40% 20%Own Clock/Watch 0.270 0.533
0.499 0.54 0.164 0.739 0.985
Own Bicycle 0.130 0.423 0.494 0.26 0.264 0.510 0.621
Own Radio 0.248 0.396 0.489 0.51 0.101 0.522 0.838
Own Television 0.339 0.209 0.407 0.83 0.000 0.127 0.866
Own Sewing Machine 0.253 0.182 0.385 0.66 0.015 0.179 0.580
Own Motorcycle/Scooter 0.249 0.082 0.274 0.91 0.001 0.031
0.375
Own Refrigerator 0.261 0.068 0.252 1.04 0.000 0.006 0.353
Own Car 0.129 0.012 0.107 1.21 0.000 0.001 0.059
Drinking Water From Pump/Well 0.192 0.609 0.488 0.39 0.800 0.569
0.242
Drinking Water From Open Source 0.041 0.040 0.195 0.21 0.057
0.036 0.005
Drinking Water From Other Source 0.002 0.019 0.138 0.01 0.016
0.027 0.012
Flush Toilet 0.308 0.217 0.412 0.75 0.005 0.175 0.797
Pit Toilet/Latrine 0.040 0.086 0.280 0.14 0.040 0.127 0.111
None/Other Toilet 0.001 0.001 0.029 0.03 0.001 0.001 0.001
Main Source of Lighting Electric 0.284 0.510 0.500 0.57 0.143
0.700 0.989
Number of Rooms in Dwelling 0.159 2.676 1.957 0.08 1.975 2.965
3.739
Kitchen a Separate Room 0.183 0.536 0.499 0.37 0.312 0.643
0.848
Main Cooking Fuel Biomass (Wood/Dung/Coal) 0.281 0.776 0.417
0.67 0.956 0.841 0.224
Dwelling All High-Quality Materials 0.309 0.237 0.425 0.73 0.005
0.218 0.821
Dwelling All Low-Quality Materials 0.273 0.483 0.500 0.55 0.832
0.308 0.017
Own > 6 Acres Land 0.031 0.115 0.319 0.10 0.075 0.155
0.126
Economic Status Index 0.000 2.32 2.00 0.071 3.857
Notes:Each variable beside number of rooms takes the value 1 if
true, 0 otherwise. Scoring factor is the weight assigned to each
variable (normalized by itsmean and standard deviation) in the
linear combination of the variables that constitute the first
principal component. The percentage of the covariance explained
by the first principal component is 26%. The first eigenvalue is
5.37; the second eigenvalue is 1.66.Source:Authors calculation from
NFHS 19921993.
TABLE 2. CLASSIFICATION DIFFERENCES OF THE POOREST 40%: ALL
INDIA
All Variables Except Asset Ownership,Base Case: Drinking Water
and Housing, and Only 8 Asset
All Variables Toilet Facilities Land Ownership Ownership
Variables
Poorest 40% 100.0 95.1 87.7 80.2
Middle 40% 0.0 4.9 12.3 19.7
Richest 20% 0.0 0.0 0.0 0.1
Total 100.0 100.0 100.0 100.0
Spearman RankCorrelation Coefficient,Ranking of Households 1.0
.94 .87 .79
Source:Authors calculation from NFHS 19921993.
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ESTIMATING WEALTH EFFECTS 119
Robustness.The asset index produces very similar
clas-sifications when different subsets of variables are used in
itsconstruction. Table 2 reports the percentage of
householdsclassified in the poorest 40% when all assets are used,
com-
pared with indices based on (1) all the variables except
those
related to drinking water and toilet facilities, (2) ownershipof
consumer durables, housing quality, number of rooms, andland
ownership, and (3) only the ownership of consumerdurables (e.g.,
watch, radio). Almost no households classi-fied in the poorest
group by the index using all variableswould be classified as rich
by any of the more limited mea-sures. The robustness of the
classification is similar for themiddle and the rich groups.
A more general measure of the differences in rankingscan be
derived from the rank correlation coefficient, whichcompares the
degree to which two methods produce the sameranking of households.
Even when the index is constructedwith only consumer durables, the
correlation with the indexthat uses all the variables is .79 (all
correlation coefficients
in Table 2 are significant; p < .001, N = 87,175). Addingmore
variables in constructing the index only increases thesimilarity of
the rankings.
An additional check for robustness is made by using adifferent
methodology for deriving the weights. Althoughthe theoretical
underpinnings and the algorithms used infactor analysis are close
to those for principal components,the two methodologies differ
sufficiently to make factoranalysis a possible alternative
approach. The first factor de-rived from a model analogous to that
described above yieldsa household ranking that has a .988 Spearman
rank correla-tion with a ranking derived from principal
components.Clearly, the results drawn from the asset index approach
arerobust to whether one picks one or the other of these meth-
ods.Comparisons across states.Because the poor, middle,
and rich groups are defined on an all-India basis, statesdiffer
as to the percentage of households in each group.Thus we can
compare state-by-state rankings with moreconventional measures. The
national poverty rate based onconsumption expenditures is 36%,
roughly comparable todefining the asset poor as the poorest 40%
nationally bythe asset index. The rank correlation of the poverty
ratewith the proportion asset poor across states is .794 (p
