Directory UMM :Data Elmu:jurnal:UVW:World Development:Vol28.Issue12.Dec2000:

World Development Vol. 28, No. 12, pp. 2123±2155, 2000
Ó 2000 Published by Elsevier Science Ltd.
Printed in Great Britain
0305-750X/00/$ - see front matter

www.elsevier.com/locate/worlddev

PII: S0305-750X(00)00075-9

Poverty Comparisons Over Time and Across
Countries in Africa
DAVID E. SAHN and DAVID C. STIFEL *
Cornell University, Ithaca, NY, USA
Summary. Ð We use Demographic and Health Surveys (DHS) to compare ``poverty'' at two or
more points in time within and between African countries. Our welfare measure is an index
resulting from a factor analysis of various household characteristics, durables, and household
headsÕ education. An advantage of this measure is that for intertemporal and intraregional
comparisons, we need not rely on suspect price de¯ators and currency conversion factors. The wide
availability and similarity of questionnaires of the DHS facilitate comparisons over both time and
countries. Our results generally show declines in poverty during the previous decade, largely due to
improvements in rural areas. Ó 2000 Published by Elsevier Science Ltd.

Key words Ð Africa, asset index, factor analysis, poverty, stochastic dominance, welfare measures

1. INTRODUCTION
The contentious debate on the e€ectiveness
of economic and social policy in Africa over the
past decade continues largely unresolved. One
reason for the disparate views on the role of
reform in alleviating poverty is that we remain
largely ignorant about the basic question of
what has happened to poverty during the last
10 years. Addressing this issue is a pre-requisite
to improving our understanding of the underlying social and economic processes that have
contributed to changes in economic well-being.
A new generation of nationally representative household income and expenditure surveys
has helped to provide a better understanding of
living standards in Africa. 1 These surveys have
been very useful in our analysis of the level and
characteristics of poverty on the continent.
They have de®ned welfare and the corresponding notion of poverty based on the use of
consumption expenditures (including the

imputed value of home consumption), generally
regarded as the preferred money metric of
utility. 2 Much of the available household
survey data that have been used to measure
poverty are both recent, done within the past 10
years, and in the form of one-time cross-sections. Thus, while we have learned a great deal
about poverty at a particular point in time in
many African countries, the view remains a
snapshot. In the vast majority of African
countries, we remain unable to make inter-

temporal comparisons of poverty due the
unavailability of data. Where survey data are
available at more than one point in time, the
determination of changes has proven problematic. First, survey designs change. It is now
well established that di€erences in recall periods, 3 changes in the survey instrument (e.g.,
the number and choice of item codes listed), 4
and even the nature of interviewer training, can
have large systematic e€ects on the measurement of household expenditures. Compounding
this problem, intertemporal comparisons of

money-metric welfare are only as precise as the
de¯ators used. Consumer price indices are
often suspect in Africa, due to weaknesses in
data collection and related analytical procedures. Thus, relying on ocial CPIs is often
precarious, at best. 5 Alternatives such as
deriving price indexes from unit values, where
quantity and expenditure data are collected,
also have some serious drawbacks. 6
In combination, these factors have limited
what we know about changes in poverty, and
the reliability of the relatively few estimates

* The

authors would like to thank an anonymous
referee, Stephen Younger and George Jakubson for
invaluable comments. They are also indebted to Macro
International Inc., for supplying the data, and in
particular, Bridget James for her assistance and prompt
responses to queries. Final revision accepted: 5 May

2000.

2123

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WORLD DEVELOPMENT

that are available. This motivates our use of the
Demographic and Health Surveys (DHS) as an
alternative instrument for assessing changes in
poverty, relying on an asset index as an alternative metric of welfare.
The DHS have been collected in a large
number of African countries, and in many
cases, at more than one point in time. 7 The
surveys were not designed for econometric (or
even economic) analysis. Instead, the purpose
of the surveys was to assist governments and
private agencies in developing countries to
better evaluate population, health and nutrition

programs. Consequently, there are no data on
income or expenditures, the standard money
metric measures of well-being. Despite this
important drawback, the DHS do contain
information on household assets that can be
employed to represent an alternative to a
money metric utility approach to welfare
measurement. 8 The DHS also have two
distinct advantages: they are available at two or
more points in time for a large number of
countries in Africa, 11 to be precise, and key
survey instruments are standardized for all
countries. Therefore, we can con®dently
compare living standards, across time periods,
within a given country, and also across countries for many of our poverty measures.
In the absence of income or expenditure
measures, we derive a welfare index constructed
from the households' asset information available in the survey. This is the outcome of a
factor analysis of various household characteristics (water source, toilet facilities, and
construction materials) and durables (ownership of radio, television, refrigerator, bicycle,

motorcycle and/or car) as well as education of
the household head. We assume that there is a
common factor, ``welfare,'' behind the ownership of these assets, and allow the factor analysis to de®ne that factor as a weighted sum of
the individual assets. 9 One of the advantages
of this measure is that for intertemporal and
intraregional comparisons, we need not rely on
what are often tenuous and suspect price
de¯ators that are used to compare money
metric measures of welfare. 10
In this paper, we compare ``poverty'' as
measured by our welfare index over time. 11 We
do this by comparing percentages of families
whose welfare falls below a certain level in the
asset index distribution. We also compare the
distributions of our asset welfare measure at the
two (or more) points in time when the DHS
data were collected, using standard tests for

welfare dominance (Ravallion, 1991; Ravallion,
1994; Davidson & Duclos, 1998). That is, we

try to identify distributions that will show less
poverty regardless of the poverty line or
poverty measure used. Our next approach is to
decompose poverty measures regionally (as in
Ravallion & Huppi, 1991). This allows us to see
whether overall changes in poverty are due to
changes in one or more particular regions, or
movements between regions with di€erent
poverty levels. Finally, we use the asset index to
make cross-country comparisons of poverty.
Before presenting our results, we discuss in
some more detail the methods employed, and
the data we use. We conclude with a summary
of our ®ndings.
2. METHODOLOGY
(a) Asset index
To construct an index of the household assets
recorded in the DHS survey requires selecting a
set of weights for each asset. That is, we want
an index of the form

Ai ˆ c^1 ai1 ‡


‡ c^K aiK ;
where Ai is the asset index for household i, the
aik 's are the individual assets, k, recorded in the
survey, and the c's are the weights, which we
must estimate. Because neither the quantity nor
the quality of all assets is collected, nor are
prices available in the data, the natural welfarist choice of prices as weights is not possible.
Rather than imposing arbitrary weights as in
Montgomery, Burk, and Paredes (1997), we let
the data determine them directly. Hammer
(1998) and Filmer and Pritchett (1998) use a
similar method that employs principal component analysis to construct an asset index. The
weights for their indices are the standardized
®rst principal component of the variance-covariance matrix of the observed household
assets. We use factor analysis instead of principal component analysis because the latter
forces all of the components to accurately and
completely explain the correlation structure
between the assets. Factor analysis, on the
other hand, accounts for the covariance of the
assets in terms of a much smaller number of

hypothetical common variates, or factors
(Lawley & Maxwell, 1971). In addition, it
allows for asset-speci®c in¯uences to explain
the variances. In other words, all of the
common factors are not forced to explain the

POVERTY COMPARISONS

entire covariance matrix. In our case, we
assume that the one common factor that
explains the variance in the ownership of the set
of assets is a measure of economic status, or
``welfare.'' Finally, the assumptions necessary
to identify the model using factor analysis are
stated explicitly and provide guidance in
determining which assets should or should not
be included in the index. 12
Unlike with principal component analysis,
we must explicitly impose structure from the
outset. The structural model includes only one

factor:
aik ˆ bk ci ‡ uik
for i ˆ 1; . . . ; N …households†
for k ˆ 1; . . . ; K …household assets†:

…1†

The ownership of each observed asset (k) for
each household (i), represented by the variable
aik , is a linear function of an unobserved
common factor for each household, ci , which
we label ``household welfare.'' 13 Note that the
relationship between the asset and the unobserved common factor, bk , as well as the noise
component (``unique element''), uik , are also
unobserved and must be estimated. 14
To identify the model, we make the following
assumptions:
(A1): Households are distributed iid.
(A2): E…ui jci † ˆ 0 .
Kx1

(A3): V …ui † ˆ Diagfr21 ; . . . ; r2K g.
Structure can now be imposed on the variance-covariance of the observed assets. To see
what these restrictions are, ®rst rewrite the set
of k eqn. (1) in vector form,
…1a†
ai ˆ bci ‡ ui ;
where b ˆ …b1 ; . . . ; bK †. Assumption (A3)
implies that once the common factor accounts
for a portion of the variance in the ownership
of assets, the remainder of the variance, the
disturbance terms (``unique elements''), should
be uncorrelated across assets. Note that these
errors are not constrained to be identically
distributed. This gives us the variance-covariance matrix of the unique disturbances
E…ui u0i † ˆ Diagfr21 ; . . . ; r2K g ˆ W:
Without loss of generality, we assume that the
mean of the common factor (wealth) is zero,
thus the variance of the common factor is
E…ci c0i † ˆ r2c :
Orthogonality of the common factor and the
disturbance (A2) permits us to write the variance of the assets as

2125

E…ai a0i † ˆ E‰…bci ‡ ui †…bci ‡ ui †0 Š;
which gives us
X ˆ bb0 r2c ‡ W:

…2†

Note that identi®cation requires the
normalization of one of the parameters, and
typically it is the variance of the unobserved
factor (r2c  1). Although this normalization
makes it dicult to interpret the coecients on
the common factor …b†, we shall do so anyway
since none of the statistical packages that
provide factor analysis procedures have options
for other normalizations and since interpretation of these parameters is not crucial to the
analysis. 15
If we assume multivariate normality of ci and
ui , we can estimate b and W using maximum
likelihood techniques (Lawley & Maxwell,
1971). Once these parameters have been estimated, the common factor (asset index) can be
estimated for each household, by de®ning the
asset index as the projection of unobserved
household wealth (ci ) on the observed household assets:
E …ci jai † ˆ c1 ai1 ‡


‡ cK aiK ;
ÿ1

c ˆ v…ai † cov…ai ; ci †:

where
…3†

Given the normalization, r2c  1, it is reasonably
straightforward
to
show
that
cov…ai ; ci † ˆ b, and thus c ˆ Xÿ1 b. Finally, the
estimate of the asset index for household i is
de®ned as:
Ai ˆ c^1 ai1 ‡


‡ c^K aiK ;
^r2 :
^ ÿ1 b^
c^ ˆ X
c

where
…3a†

The assets included in the index can be placed
into two categories: household durables and
household characteristics. The household
durables consist of ownership of a radio, TV,
refrigerator, bicycle, and motorized transportation (a motorcycle or a car). The household
characteristics include source of drinking water
(piped or surface water relative to well water),
toilet facilities (¯ush or no facilities relative to
pit or latrine facilities), and ¯oor material (low
quality relative to higher quality). We also
include the years of education of the household
head to account for householdÕs stock of
human capital. 16 Since we want to compare
the assets over the two surveys, the data sets are
pooled and the factor analysis scoring coecients (asset weights) are estimated for the
pooled sample. They are then applied to the

2126

WORLD DEVELOPMENT

separate samples to estimate the wealth indexes
for each of the households. 17
(b) Stochastic tests of welfare dominance
We employ standard tests of welfare dominance to compare distributions of our asset
index over time. The idea is to make ordinal
judgments on how poverty changes for a wide
class of poverty measures over a range of
poverty lines. We explain brie¯y how to estimate the orderings and to perform statistical
inference on them. The discussion follows
Davidson and Duclos (1998) closely.
Consider two distributions of welfare indicators with cumulative distribution functions,
FA and FB , with support in the nonnegative real
numbers. 18 Let
Z x
dFA …y†
D1A …x† ˆ FA …x† ˆ
0

and
DsA …x† ˆ

Z

0

x

Dsÿ1
A …y† dy;

for any integer s P 2. Now distribution A is
said to (strictly) dominate distribution B at
order s if DsA …x† 6 …