1.5~~~~~~~~~~~~~~~~~L~ XI 
Living Standards
Measurement Study                               FILE CO?I
Working Paper No. 83                             .  _0_ 
Growth and Redistribution Components
of Changes in Poverty Measures
A Decomposition with Applications to Brazil and India in the 1980s
Martin Ravallion and Gaurav Datt
FaI   C OP
tlL£  nUtv 



LSMS Working Papers
No. 12     The ECIEL Study of Household Income and Consumption in Urban Latin America: An Analytical
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No.41      Public-Private Sector Wage Differentials in Peru, 1985-86
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(List continues on the inside back cover)



Growth and Redistribution Components
of Changes in Poverty Measures
A Decomposition with Applications to Brazil and India in the 1980s



The Living Standards Measurement Study
The Living Standards Measurement Study (LsMs) was established by the
World Bank in 1980 to explore ways of improving the type and quality of house-
hold data collected by statistical offices in developing countries. Its goal is to foster
increased use of household data as a basis for policy decisionmaking. Specifically,
the LSMS is working to develop new methods to monitor progress in raising levels
of living, to identify the consequences for households of past and proposed gov-
ernment policies, and to improve communications between survey statisticians, an-
alysts, and policymakers.
The LSMS Working Paper series was started to disseminate intermediate prod-
ucts from the LSMS. Publications in the series include critical surveys covering dif-
ferent aspects of the LSMS data collection program and reports on improved
methodologies for using Living Standards Survey (Lss) data. More recent publica-
tions recommend specific survey, questionnaire, and data processing designs, and
demonstrate the breadth of policy analysis that can be carried out using LSS data.



LSMS Working Paper
Number 83
Growth and Redistribution Components
of Changes in Poverty Measures
A Decomposition with Applications to Brazil and India in the 1980s
Martin Ravallion and Gaurav Datt
The World Bank
Washington, D.C.



Copyright X 1991
The International Bank for Reconstruction
and Development/THE WORLD BANK
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First printing September 1991
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ISSN: 02534517
Martin Ravallion is a senior economist in and Gaurav Datt is a consultant to the World Bank's Welfare
and Human Resources Development Division, Population and Human Resources Department.
Library of Congress Cataloging-in-Publication Data
Ravallion, Martin.
Growth and redistribution components of changes in poverty
measures: a decomposition with applications to Brazil and India in
the 1980s / Martin Ravillion and Gaurav Datt.
p. cm. - (LSMS working paper, ISSN 0253-4517; no. 83)
Indudes bibliographical references.
ISBN 0-8213-1940-X
1. Poor-Brazil. 2. Income distirbution-Brazil. 3. Poor-India.
4. Income distribution-India. I. Datt, Gaurav. II. Title.
III. Series.
HC190.P6R38 1991
339.2'2'0954-dc2O                               91-33941
CIP



ABSTRACT
We show how changes in poverty measures can be decomposed into
growth and redistribution components, and we use the methodology to study
poverty in Brazil and India during the 1980s. Redistribution alleviated
poverty in India, though growth was quantitatively more important. Improved
distribution countervailed the adverse effect of monsoon failure in the late
1980s on rural poverty. However, worsening distribution in Brazil, associated
with the macroeconomic shocks of the 1980s, mitigated poverty alleviation
through the limited growth that occurred. India's higher poverty level than
Brazil is accountable to India's lower mean consumption; Brazil's worse
distribution mitigates the cross-country difference in poverty.
v



ACKNOWLEDGEMENTS
This paper is a product of the World Bank Research Project 675-04,
and the authors are grateful to the World Bank's Research Committee for their
support. The authors are grateful to journal referees for their comments on
an earlier draft. They have also benefited from the comments of Louise Fox,
Raghav Gaiha, Nanak Kakwani, Samuel Morley, George Psacharopoulos, and
Dominique van de Walle.
vi



TABLE OF CONTENTS
1.         Introduction  .1.......  ...  ...  ...  ...   . .
2.         A Decomposition for any Change in Poverty . . . . . . . . 3
3.         Implementation Using Parameterized Lorenz Curves and
Poverty Measures.                                      7
4.         Poverty in India, 1977-1988 . . . . . . . . . . . . . . . 10
5.         Poverty in Brazil, 1981-1988  . . . . . . . . . . . . . . 18
6.         A Comparison of Poverty in Brazil and India . . . . . . . 21
7.   Conclusions. . . ........  25
Notes    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .  29
References  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  31
LIST OF TABLES
Table 1    Poverty Measures for Alternative Parameterizations of
the Lorenz Curve.                                      8
Table 2    Poverty in India and Brazil Since the late 1970s  . . . . 12
Table 3    Decompositions for Rural India (Including Consumer
Durables)   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  13
Table 4    Decompositions for Rural India (Excluding Consumer
Durables)   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  14
Table 5    Decompositions for Urban India (Including Consumer
Durables)   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  17
Table 6    Decompositions for Urban India (Excluding Consumer
Durables)   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  17
Table 7    Decompositions for Brazil .....  .  .  .  .  .  ..  .  .  .   . 22
Table 8    Poverty Measures for Brazil and India, 1983 . . . . . . . 22
Table 9    Decomposition of the Difference in Poverty Between
Brazil and India in 1983  . . . . . . . . . . . . . . . 23
vii



1.    INTRODUCTION
There is often an interest in quantifying the relative contribution of
growth versus redistribution to changes in poverty measures. For example,
one might want to know whether shifts in income distribution helped or hurt
the poor during a period of overall economic contraction. Unfortunately, the
numerous existing inequality measures are not particularly useful here. One
certainly cannot conclude that a reduction in inequality (by any measure
satisfying the usual Pigou-Dalton criterion) will reduce poverty. And even
when a specific reduction (increase) in inequality does imply a reduction
(increase) in poverty, the change in the inequality measure can be a poor
guide to the quantitative impact on poverty. A time series of an inequality
measure can be quite uninformative about how changes in distribution have
affected the poor.
This paper shows how changes in poverty measures can be rigorously
decomposed into growth and distributional effects, and it illustrates the
methodology with recent data for India and Brazil.1
The recent history of poverty in these two countries is of
interest from a number of points of view. In Brazil, the 1980s witnessed much
lower income growth rates than the 1970s. The effect on poverty of this
aggregate stagnation is of particular concern in the light of the widely held
belief that inequality in Brazil has also worsened in the 1980s. The effects
on the poor of the macroeconomic shocks and adjustments of the 1980s in Brazil
are of concern. By contrast, reasonable growth rates were sustained in India
during the 1980s, and (unlike many developing countries) India survived the
period without significant macroeconomic disturbances. However, the mid to
late 1980s saw lower GDP growth rates overall, due to the low or negative
growth rates in agriculture. Monsoon failures were accompanied by concerted
efforts to protect the poor, though we know of no empirical evidence as to
whether or not those efforts were successful in avoiding an increase in
poverty in the late 1980s, and, if so, what contribution distributional
changes made.
1



The decomposition methodology proposed here is a descriptive tool
which can help answer these questions. The following section discusses the
decomposition in theory, while section 3 discusses how the theory can be
implemented using parameterized poverty measures and Lorenz curves. Section 4
then gives an application to recent data on consumption distributions for
rural and urban India. In addition to the substantive issues of interest
about poverty in that country, we use these data to investigate a number of
more methodological issues of interest about the decomposition. Section 5
gives analogous results for Brazil over a similar period, while section 6 uses
the methodology to compare poverty levels between the two countries at one
point in time. Some concluding comments are offered in Section 7.
2



2.   A DECOMPOSITION FOR ANY CHANGE IN POVERTY
We confine attention to poverty measures which can be fully
characterized in terms of the poverty line, the mean income of the
distribution, and the Lorenz curve representing the structure of relative
income inequalities. The poverty measure Pt at date (or region/country2) t is
written as
Pt= P(Z/,tLt)                                (1)
where z is the poverty line, Mt is the mean income and Lt is a vector of
parameters fully describing the Lorenz curve at date t. (Homogeneity in z and
p is a common property of poverty measures.) The level of poverty may change
due to a change in the mean income pt relative to the poverty line, or due to
a change in relative inequalities Lt. For now we can delay discussion of the
poverty measure's precise functional form, or of the Lorenz curve's
parameterization.
The growth component of a change in the poverty measure is defined as
the change in poverty due to a change in the mean while holding the Lorenz
curve constant at some reference level Lr. The redistribution component is
the change in poverty due to a change in the Lorenz curve while keeping the
mean income constant at the reference level Mr. A change in poverty over
dates t and t+n (say) can then be decomposed as follows:
Pt+n - Pt = G(t,t+n;r) + D(t,t+n;r) + R(t,t+n;r)    (2)
growth   redistribution  residual
component   component
in which the growth and redistribution components are given by
G(t,t+n;r) - P(Z/Pt+n,Lr) - P(Z/pt'Lr)
D(t,t+n;r) E P(Z/lJr,Lt+n) - P(Z/MrILt)
3



while R( ) in (2) denotes the residual. In each case, the first two arguments
in the parentheses refer to the initial and terminal dates of the
decomposition period, and the last argument makes explicit the reference date
r with respect to which the observed change in poverty is decomposed.
The residual in (2) exists whenever the poverty measure is not
additively separable between p and L, i.e., whenever the marginal effects on
the poverty index of changes in the mean (Lorenz curve) depend on the precise
Lorenz curve (mean). In general, the residual does not vanish. Nor can it be
apportioned between the growth and redistribution components, as some recent
attempts at poverty decomposition have sought to do. For example, Kakwani and
Subbarao (1990) present results of a decomposition of poverty measures over
time for India into "growth" and "inequality" components in which the latter
is determined as the difference between the actual change in poverty and the
growth component. The residual is thus allocated to the redistribution
component. This is entirely arbitrary, and also gives the false impression
that the decomposition is exact. Similarly, Jain and Tendulkar (1990) make
the residual appear to vanish by not using consistent reference dates for
evaluating the "growth" and "distribution" components. In effect, this also
amounts to arbitrarily allocating the residual to either the redistribution or
the growth component, though which one depends on the reference dates chosen.
Of course, the main issue here is not that the residual must always be
separately calculated, but that the growth and redistribution components must
be evaluated consistently.
However, the residual itself does have an interpretation. To see
this, it is instructive to note that, for r=t, the residual in (2) can be
written
R(t,t+n;t) = G(t,t+n;t+n) - G(t,t+n;t)
= D(t,t+n;t+n) - D(t,t+n;t)               (3)
4



The residual can thus be interpreted as the difference between the growth
(redistribution) components evaluated at the terminal and initial Lorenz
curves (mean incomes) respectively. If the mean income or the Lorenz curve
remains unchanged over the decomposition period, then the residual vanishes.3
Separability of the poverty measure between the mean and Lorenz
parameters is also required for the decomposition to be independent of the
choice of the reference (PrLr). That choice is arbitrary; the reference
point need not even be historically observed. The initial date of the
decomposition period is a natural choice of a reference, and this is what we
use in the empirical work.
Since it is arbitrary, we shall also investigate the sensitivity
of the decomposition to the choice of reference. For that purpose, the result
in (3) is useful. It tells us that the residual using date t as the reference
also gives the change in both the growth component and the redistribution
component which would result from switching the reference to date t+n. The
decomposition using the initial year as the reference contains all the
information necessary to calculate the decomposition using the final year as
the reference, and vice versa.
The decomposition can also be applied to multiple periods (more
than two dates), though a word of caution is needed. A desirable property for
such a decomposition scheme is that the growth, redistribution and residual
components for the sub-periods add up to those for the period as a whole.
However, this property will not hold in general if we use the initial date of
each sub-period as the reference. The problem is easily rectified on noting
that the violation occurs because the reference (p, L) keeps changing over the
sub-periods. The remedy is to maintain a fixed reference date for all
decomposition periods, and again the initial date of the first decomposition
period is a natural choice. Sub-period additivity is then satisfied. Suppose
we have another sub-period from date t+n to t+n+k, say, in addition to the one
from t to t+n considered above. Then:
5



G(t,t+n;r) + G(t+n,t+n+k;r) = G(t,t+n+k;r)
D(t,t+n;r) + D(t+n,t+n+k;r) = D(t,t+n+k;r)
R(t,t+n;r) + R(t+n,t+n+k;r) = R(t,t+n+k;r)
as required for sub-period additivity.4
The interpretation of the residual in the multi-period context is
similar to that for a single decomposition period. For a sequence of dates
(0,1,..t,..T), let Rt denote the residual R(t-l,t;O). The analogue to (3) can
then be written in terms of cumulative components
T
E Rt = R(0,T;0) = G(0,T;T) - G(0,T;0)
t=l
= D(O,T;T) - D(O,T;O)                        (4)
Thus, the cumulative residual measures the change in both the cumulative
growth and redistribution components that would result from switching the
reference from date 0 to date T.
6



3.    IMPLEMENTATION USING PARAMETERIZED LORENZ CURVES AND POVERTY MEASURES
The decomposition can be readily implemented using standard data
on income or consumption distributions for two or more dates. Explicit
functional forms for P(z/pt,Lt) are derivable for a wide range of existing
poverty measures and parameterized Lorenz curves.   We shall use three common
poverty measures, the headcount index H given by the proportion of the
population who are poor, the poverty gap index PG given by the aggregate
income short-fall of the poor as a proportion of the poverty line and
normalized by population size, and the Foster-Greer-Thorbecke (FGT) P2
measure, similar to PG but based on the sum of squared proportionate poverty
deficits. In fact each of these measures is a member of the FGT class of
measures P. defined by
pa = E [ (z-yi)/z]l/n
Yi<z
where yi is the income or consumption of the i'th household or individual, z
is the poverty line, n is the population size, and a is a non-negative
parameter. H is obtained when a=O; PG is obtained when a=1; P2 is obtained
when a=2.
From any valid parameterized Lorenz curve L(p), H is calculatable
using the aforementioned fact that pL'(H)=z. (Noting that L'(p) is
invertible - either explicitly or numerically - for any valid Lorenz curve.)
The poverty gap index is then calculated as PG = (1 - pP/z)H, where pP =
pL(H)/H denotes the mean income or consumption of the poor. P2 is obtained as
the integral of [1-(p/z)L'(p)]2 over the interval (0,H).
We have derived formulae for the FGT poverty measures for each of
two parametric specifications of the Lorenz curve, namely the Kakwani (1980)
model and the elliptical model of Villasenor and Arnold (1989). Table 1 gives
the functional forms of these Lorenz curves, and the implied poverty measures.
The derivations of P2 use standard methods of integration. The elliptical
7



Table 1: Poverty Measures for Alternative Parameterizations of the Lorenz Curve
Kakwani Lorenz Curve                           Elliptical Lorenz Curve
Equation of the    L(p) = p-ep7(1-p)6                              L(1-L) = a(p2-L) + bL(p-l) + c(p-L)
Lorenz curve                                                       or,
(L(p))                                                            L(p) = - [bp + e + (mp2+np+e2)l/2]/2
Headcount index    0H7(1-H)6[7    6                                                              2     2H -[n + r(b+2z/){(b+2z/)2_m-/2]/(2m)
(H)
Poverty gap         PG = H - (#/z)L(H)                             PG = H - (#/z)L(H)
index (PG)
Go
Foster-Greer-       P2 = (1-#/z)[2PG - (1-#/z)H]                   P2 = 2PG - H - (/42/z2)[aH + bL(H)
Thorbecke (P2)            + 02(#2/z2)[72B(H,27-1, 26+1)                 - (r/16)ln{(l-H/sl)/(l-H/s2)}]
- 275B(H,27,26) + 62B(H,2'y+1,26-1)]
k
Note:               B(k,r,s) = Jpr-l(l-p)s-ldp                       e  = -(a+b+c+l);
m  = b2 - 4a;
n  = 2be - 4c;
r  = (n2 - 4me2)1/2
s1 = (r - n)/(2m)
S2 = -(r+n)/(2m)



model gives somewhat easier computational formulae (generating explicit forms
for all poverty measures; the Kakwani specification requires numerical methods
for inverting L'(H) and tabulations of incomplete Beta functions). Subject to
consistency with the theoretical conditions for a valid Lorenz curve, the
choice of Lorenz curve specification was made according to goodness of fit.5
The estimated Lorenz curves for both India and Brazil used in the following
sections tracked the data extremely well; R-squares ranged between 0.995 and
1.000 for the two functional forms. (Such values of R-square are not uncommon
for these functional forms of the Lorenz curves.) Imprecision associated with
the Lorenz curve estimation seems unlikely to be of serious concern.6
9



4.    POVERTY IN INDIA, 1977-1988
We have estimated poverty measures and their decompositions for
rural and urban India from the National Sample Surveys (NSS) of 1977-78, 1983,
1986-87, and 1988. There are a number of problems of comparability across
these surveys. The following points should be particularly noted:
i) Doubts have been raised about the 1977-78 survey estimates of
expenditures on consumer durables, which greatly exceeded estimates for other
years, particularly in rural areas.7 The problem is most serious at high
consumption levels, and so may not have much effect on poverty measures.
However, the associated distortions in the fitted Lorenz curve could still
have a significant effect on the decomposition.
ii) The 1988 distribution is based on a sample which only covered
the last six months of that year, while the rest are for a full year. (The
survey was also done in the first half of 1990, but the results are not yet
available.)
iii) The 1986-87 and 1988 samples were much smaller than those for
the other years. 25,800 households were sampled in 1986-87 and 12,000 in 1988
(half year) versus 157,900 and 117,900 in 1977-78 and 1983 respectively.8
But they still appear to be large enough to give adequate precision.9
We are able to take corrective action only with regard to i).
Results for all years are reported here for both total consumption
expenditure, and consumption net of durables.10 Our calculations have used
the Planning Commission (Sixth Plan) poverty line up-dated by Minhas et al.
(1987) to a per capita monthly expenditure of Rs 89 at 1983 all-India rural
prices. The Consumer Price Index for Agricultural Laborers (CPIAL) and The
Consumer Price Index for Industrial Workers (CPIIW) are used as deflators over
the entire period for rural and urban areas respectively.11 12 An estimate
of the all-India urban-rural price differential for 1973-74 is derived from
Bhattacharya et al (1980), which is updated for the period 1977-78 to 1988
using CPIAL and CPIIW. The Kakwani Lorenz curve performed well on these data,
and passed all necessary conditions for a locally valid Lorenz curve. The
10



initial year was used as the reference, fixed over all dates to ensure sub-
period additivity, as discussed above.
Table 2 gives our estimated poverty measures for India (as well as
those for Brazil, to be discussed later). Results are reported for the
distributions of consumption net of durables - those for total consumption
were very similar, and are available from the authors. However, as we will
see, the treatment of durables makes far more difference to the decomposition
results.
All poverty measures fell over the period, though not all
continuously, with an increase in the headcount index in rural areas between
1986-87 and 1988. However, the increase is small, and (given the lower sample
sizes in the latter two surveys) it is probably not significant statistically
at a reasonable level. 13 Both the poverty gap index and the theoretically
preferred P2 declined over all sub-periods in rural areas. The pattern is
similar for urban areas. There was a particularly sharp fall in rural poverty
between 1983 and 1986-87.
The comparison of poverty measures across sectors is also of
interest. Historically, poverty lines adjusted for cost of living differences
have shown higher poverty measures in rural areas than in urban areas, and
this is common in developing countries (World Bank, 1990, chapter 2). This is
confirmed for the two earlier years of our study period. However, the results
for the latter two years suggest a reversal in the poverty ranking of the two
sectors, with generally higher measures in urban areas. (The exception being
the headcount index for 1988 which returns to being higher in rural areas,
though the difference is small; see Table 2.) The contribution of the urban
sector to total poverty has increased quite dramatically over the period. For
example, using the Foster-Greer-Thorbecke P2 index, the proportion of total
poverty accountable to the urban sector increased from 20.1% in 1977-78 to
29.8% in 1988, with the sharpest increase occurring between 1983 and 1986-87,
largely reflecting the aforementioned fall in rural poverty.
11



Table 2: Poverty in India and Brazil Since the late 1970s
Poverty/
inequality
measure           1977-78    1981       1983     1985    1986-87   1987    1988
Rural India
H                 52.68      -       45.13      -        36.84      -      38.66
PG                16.03      -       12.74      -         9.44      -       9.40
P2                 6.67      -        4.97      -         3.48      -       3.25
Gini index         0.299    -         0.289    -          0.283    -        0.283
Urban India
H                 46.80      -       39.69      -        38.32      -      37.12
PG                14.20      -       10.91      -        10.46      -      10.49
P2                 5.93      -        4.17       -        3.98      -       3.91
Gini index         0.318    -         0.323      -        0.339    -        0.328
Brazil
H                  -        26.46    32.14    26.23       -        24.23   26.47
PG                 -        10.07    13.09      9.90      -         9.46   10.71
P2                 _         4.96     6.81      4.82      -         4.79    5.58
Gini index         -         0.580    0.591    0.593    -           0.597   0.615
Note:    Poverty measures in percent; those for India are based on
consumption excluding expenditure on durables (see text).
Tables 3 and 4 give our estimates of the decomposition of changes in
rural poverty, for total consumption and consumption net of durables
respectively. Tables 5 and 6 give the corresponding results for urban India.
The Tables give the increments in percentage points, both in the aggregate and
by components and sub-periods. For example, the rural headcount index
(including consumer durables) is estimated to have started at 53.92% in 1977-
78, falling by 15.86 points to 38.06% in the latter half of 1988. By sub-
periods, this was made up of a fall in the index of 8.97 points over 1977-78
to 1983, 8.08 points between 1983 and 1986-87, and it rose by 1.46 points
between 1986-87 and 1988. By components, distributionally neutral growth
12



accounted for 9.74 points, distributional shifts accounted for 6.05 points,
with the residual making up the balance of 0.07 points.
Table 3: Decompositions for Rural India (Including Consumer Durables)
Period          Growth           Redistribution         Residual      Total change
component           component                          in poverty
(Percentage points)
Headcount index (H)
1977-8 to 83    -2.58               -6.51               0.12              -8.97
1983 to 86-7    -8.61                0.19               0.34              -8.08
1986-7 to 88      1.46               0.27              -0.54               1.19
1977-8 to 88    -9.74               -6.05              -0.07             -15.86
Poverty gap index (PG)
1977-8 to 83    -1.18               -2.09               0.14              -3.13
1983 to 86-7    -3.52               -0.18               0.42              -3.28
1986-7 to 88      0.55              -0.54              -0.14              -0.13
1977-8 to 88    -4.14               -2.81               0.41              -6.54
Foster-Greer-Thorbecke index (P2)
1977-8 to 83    -0.57               -0.90               0.08              -1.39
1983 to 86-7    -1.61               -0.11               0.23              -1.49
1986-7 to 88      0.24              -0.46              -0.04              -0.26
1977-8 to 88    -1.94               -1.47               0.30              -3.11
A number of points are noteworthy from the results of Tables 3 and
4:
i) The adjustment for durables makes considerable difference to the
decompositions, particularly for the period 1977-78 to 1983. When durables
are included, the redistribution component dominates the growth component for
all poverty measures. However, the ranking is fully reversed when durables
are excluded (Table 4). The growth component now dominates for all measures.
As doubts can be raised about the 1977-78 durables expenditures in the NSS, we
suspect the results of Table 4 to be closer to the truth, and we will confine
our attention to those results in the following discussion.
13



Table 4: Decompositions for Rural India (Excluding Consumer Durables)
Period          Growth           Redistribution         Residual      Total change
component           component                           in poverty
(Percentage points)
Headcount index (H)
1977-8 to 83    -6.45               -1.18               0.09              -7.54
1983 to 86-7    -7.33               -0.72              -0.24              -8.29
1986-7 to 88      1.04               1.44              -0.66               1.82
1977-8 to 88   -12.74               -0.46              -0.82             -14.02
Poverty gap index (PG)
1977-8 to 83    -2.82               -0.53               0.06              -3.29
1983 to 86-7    -2.87               -0.54               0.11              -3.30
1986-7 to 88      0.39              -0.19              -0.24              -0.04
1977-8 to 88    -5.31               -1.26              -0.06              -6.63
Foster-Greer-Thorbecke index (P2)
1977-8 to 83    -1.40               -0.34               0.04              -1.70
1983 to 86-7    -1.34               -0.28               0.13              -1.49
1986-7 to 88      0.17              -0.37              -0.03              -0.23
1977-8 to 88    -2.56               -0.99               0.13              -3.42
ii) While the growth component dominates the redistribution
component in all sub-periods, the relative importance of the two can vary
greatly according to which measure of poverty is used. This is most striking
for the last period, 1986-87 to 1988. For the headcount index we find that
both the growth and redistribution components contributed to the increase in
poverty. However, for the other two measures, changes in distribution
mitigated the adverse effect of the decrease in the mean. Roughly speaking,
people with consumption around the poverty line became worse off over this
sub-period, while the poorest became better off. However, the problems of
comparability between these NSS rounds should be recalled, though we do not
know what direction of bias, if any, may be attributed to those problems.
14



iii) The residuals in the decomposition vary a good deal in size.
Our results suggest it would be hazardous to assume the residual is zero, or
simply lump it into the redistribution component. For example, for the
headcount index (excluding durables) over the whole period, 1977-78 to 1988,
the residual exceeds the redistribution component (in absolute value), and by
a wide margin. However, in all other cases the residual is small relative to
both growth and redistribution components. Thus the decomposition is
generally quite insensitive to a change of reference from the initial to final
year. (Using the results of Section 2, the changes involved in making such a
switch for the whole period can be obtained easily from Tables 3 and 4 by
simply adding the residual to the growth and redistribution component. The
residual using the final year as the reference is simply the additive inverse
of the reported residual for the initial year.)
iv) Our results also illustrate that a conventional inequality
index can be a poor guide to the way distributional shifts can affect poverty
measures. For example, the Gini index is unchanged to three decimal places
between 1986-87 and 1988 (excluding durables; the index value is .283).
However, distributional shifts over that sub-period did have a sizable impact
on both the headcount index and the Foster-Greer-Thorbecke P2 measure, albeit
in opposite directions (Table 4).
v) The rather sharp fall in rural poverty over the whole period,
particularly between 1983 and 1986-87, warrants further comment. 1986-87 was
not a good agricultural year; indeed, it was a bad one in much of Western
India, with below normal rainfall and a decline in output. It is arguable
that the CPIAL may have under-estimated the rate of inflation; the CPIAL
increased by 13 percent over this period while wholesale prices increased by
19 percent. Similar concerns about the use of CPIAL as a deflator for the
period 1973-74 to 1983 have been expressed by Minhas et al. (1987). The
poverty measures are quite sensitive to changes/measurement errors in the
deflator. For instance, an under-estimation of inflation over the period 1983
to 1986-87 by 1 percent would result in underestimating the headcount, the
15



poverty gap, and the Foster-Greer-Thorbecke P2 indices of poverty for 1986-87
by 2.1, 2.9 and 3.4 percent respectively. However, only the growth component
of the decomposition is affected; since the initial year's mean consumption is
used as the reference, the redistribution component is independent of real
mean consumption on subsequent dates.
Some of the above points are also borne out in our results for urban
India in Tables 5 and 6. The growth component is again dominant over the
period as a whole, though shifts in distribution were important in certain
sub-periods. However, by most measures, shifts in urban distribution
mitigated poverty alleviation within that sector. This was largely due to a
worsening in distribution between 1983 and 1986-87. For the headcount index,
this was substantially offset by favorable distributional effects between
1986-87 and 1988 (a fall in inequality is also indicated by the Gini index;
see Table 2). However, the other poverty measures suggest a continued
worsening in distribution from the point of view of the urban poor. In all
cases, distributionally neutral growth would have enhanced the rate of poverty
alleviation over the period as a whole. The urban results seem more robust to
the treatment of durables.
16



Table 5: Decompositions for Urban India (Including Consumer Durables)
Period          Growth           Redistribution          Residual      Total change
component           component                           in poverty
(Percentage points)
Headcount index (H)
1977-8 to 83    -3.15               -1.30               -0.04              -4.49
1983 to 86-7    -4.41                3.02                0.03              -1.36
1986-7 to 88    -0.36               -1.91                1.01              -1.26
1977-8 to 88    -7.92               -0.18                0.98              -7.12
Poverty gap index (PG)
1977-8 to 83    -1.33               -0.96                0.02              -2.27
1983 to 86-7    -1.75                1.48               -0.16              -0.43
1986-7 to 88    -0.14               -0.05                0.15              -0.04
1977-8 to 88    -3.22                0.46                0.02              -2.74
Foster-Greer-Thorbecke index (P2)
1977-8 to 83    -0.65               -0.65                0.03              -1.27
1983 to 86-7    -0.83                0.76               -0.11              -0.18
1986-7 to 88    -0.06               -0.02               -0.02              -0.10
1977-8 to 88    -1.55                0.09               -0.09              -1.55
Table 6:  Decompositions for Urban India (Excluding Consumer Durables)
Period          Growth           Redistribution          Residual      Total change
component           component                            in poverty
(Percentage points)
Headcount index (H)
1977-8 to 83    -8.35                1.26               -0.03              -7.12
1983 to 86-7    -3.26                1.79                0.10              -1.37
1986-7 to 88    -0.79               -1.95                1.54              -1.20
1977-8 to 88   -12.41                1.11                1.62              -9.68
Poverty gap index (PG)
1977-8 to 83    -3.47                0.30               -0.12              -3.29
1983 to 86-7    -1.24                0.99              -0.20               -0.45
1986-7 to 88    -0.29                0.10                0.22               0.03
1977-8 to 88    -5.00                1.39              -0.10               -3.71
Foster-Greer-Thorbecke index (P2)
1977-8 to 83    -1.69               -0.01               -0.06              -1.76
1983 to 86-7    -0.57                0.55               -0.17              -0.19
1986-7 to 88    -0.13                0.13               -0.07              -0.07
1977-8 to 88    -2.40                0.67               -0.29              -2.02
17



5.    POVERTY IN BRAZIL, 1981-1988
The period 1981-1983 was one of recession and macroeconomic
adjustment in Brazil, achieved through a combination of tighter monetary
policies, exchange rate policies, and some fiscal restraint, with the burden
of adjustment falling heavily on the private sector (Fox and Morley, 1991).
An attempt was made to buffer the poor from the burden of adjustment by
improving distribution using wage policies; in particular full indexation of
wage rates (and, indeed, more than full indexation at low wage rates) was
allowed in the early 1980s (Fox and Morley, 1991). The mid-1980s saw signs of
a return to the higher growth rates of the 1970s, though progress in the late
1980s was quite uneven, with some large year-to-year fluctuations.
We have estimated the poverty measures and the decomposition using
new data on five household income surveys for Brazil during the 1980s, the
data being made available to us in an unusually detailed partition of income
groups; the data are for tabulations of income shares for 40 income groups.14
An urban-rural split is not available. The distributions for Brazil in the
1980s are for household income per capita (rather than consumption expenditure
as for India15). Labor incomes are thought to be measured well by these
surveys, but not other sources, such as (probably most importantly in this
context) the value of income from own farm production (Fox, 1990). For the
poverty line we have used a household income per capita of one quarter of the
minimum wage rate and have adjusted for inflation using the INPC index for a
low-income consumption bundle; in both respects we follow the practice of Fox
and Morley (1991) and Fox (1990) who discusses these points further. Poverty
estimates for Brazil in this period are undoubtedly sensitive to likely
measurement errors in estimating rates of inflation, though the index we have
used appears to be the most reliable one available (Fox, 1990). The
elliptical model of the Lorenz curve was preferred for our Brazil data.16
Table 2 also gives our estimates of the three poverty measures for
Brazil. The measures show no sign of either a trend increase or decrease in
poverty over the period. There is considerable variation across sub-periods,
18



with a sharp increase from 1981 to 1983 by all measures, followed by a similar
decline to 1987, with an increase indicated from 1987 to 1988. The pattern
broadly follows the ebb and tide of the macroeconomic aggregates over this
period (Fox and Morley, 1991); it is clear that the fortunes of Brazil's poor
are tied to changes in national income.
Table 5 gives the sub-period decompositions for Brazil, again using
the initial year as the fixed reference. Over the full period we find that,
underlying the negligible change in the poverty measures, both the growth and
redistribution components were strong, with roughly opposite effects. Changes
in distribution tended to increase poverty, but there was sufficient growth in
the mean income per person to counteract their effect. The main mechanism for
the observed adverse redistributional component of poverty change during the
1980s seems to have been the relatively slow growth of employment in the
formal sector (particularly the private formal sector) and the consequent
overcrowding in the informal sector, where average incomes were only about
half of those in the formal sector even during the closing years of the 1980s
(Fox and Morley, 1991). The bulk of the adverse distributional effect was in
the two sub-periods when poverty increased, namely 1981 to 1983 and 1987 to
1988. Both a decline in mean income and adverse distributional shifts
contributed to the increase in poverty during the recession period 1981-83,
though the former factor was quantitatively more important. Attempts to
improve distribution during the recession did not prove successful. The
recovery of 1983-85 saw poverty measures fall by about the same amount they
had increased over the previous sub-period. This was due almost entirely to
distributionally neutral growth.
A few points of interest emerge from the comparison of India and
Brazil. Unlike India, Brazil did not experience a trend decline in poverty
during the 1980s.   And the two countries differ dramatically in terms of the
relative contributions of growth versus redistribution. For Brazil,
distributional effects were adverse in their poverty alleviation impact over
the 1980s; the poor did not participate fully in the growth that occurred.
19



The headcount index of poverty would have fallen by a 4.5 percentage points
over the period if only growth had been distributionally neutral. By
contrast, distributional effects contributed to the alleviation of poverty in
India between 1977 and 1988, though growth accounted for the bulk of the
improvement, including that for the Foster-Greer-Thorbecke P2 measure.
20



6.    A COMPARISON OF POVERTY IN BRAZIL AND INDIA
In the preceding two sections, we have used local poverty lines for
each country. These will not generally imply the same standard of living;
local assessments of what constitutes "poverty" will naturally vary. For
example, local poverty lines tend to be positively correlated with the average
incomes of countries (Ravallion et al., 1991). In comparing poverty measures
across countries (or, indeed, across regions of the same country) one would
like to control for this variation, by imposing the same real poverty line.
We also need to control for the fact that while the Brazilian
poverty line refers to per capita income, the Indian one refers to per capita
consumption. A related adjustment is required for the survey means. For the
purpose of this comparison we have used the Summers and Heston (1988) estimate
of purchasing power parity (PPP) adjusted consumption per capita for Brazil
relative to India, rather than the mean income from the survey. An equivalent
consumption poverty line for Brazil is then derived such that when used with
the PPP adjusted consumption per capita it results in the same level of
poverty as is obtained using income data with the income poverty line.
Table 8 gives poverty estimates for Brazil and India in 1983, using
each country's poverty line alternately.17 At either poverty line, and for
either measure, poverty is significantly higher in India than Brazil.18
Applying the methodology outlined above, we now ask how much of this
difference in poverty is due to the difference in means across the two
countries (the "growth" component) and how much is due to differences in
distribution (the "redistribution" component). There are some potentially
important caveats. Recall that the Brazil survey is for household income
while India's is for consumption. While we have attempted to address the non-
comparability of the survey means above, we have no choice but to use the
survey Lorenz curves, though one should note that Brazil's income Lorenz curve
would probably show greater inequality than one would find in a consumption
distribution, if such were available. This would no doubt lead to an over-
21



estimation of the difference in poverty attributable to the difference in
distribution between the two countries.
Table 7: Decompositions for Brazil
Period       Growth    Redistribution        Residual           Total change
component       component                             in poverty
(Percentage points)
Headcount index (H)
1981 to 83    3.96             1.65             0.07                  5.68
1983 to 85   -5.84             0.02            -0.10                -5.91
1985 to 87   -2.61             0.46             0.15                -2.00
1987 to 88   -0.01             2.33            -0.08                  2.24
1981 to 88   -4.49             4.46             0.04                  0.01
Poverty gap index (PG)
1981 to 83    2.18             0.72             0.11                  3.02
1983 to 85   -3.18             0.15            -0.16                -3.19
1985 to 87   -1.34             0.92            -0.01                -0.44
1987 to 88    0.00             1.39            -0.15                  1.24
1981 to 88   -2.34             3.19            -0.21                  0.64
Foster-Greer-Thorbecke index (P2)
1981 to 83    1.39             0.37             0.09                  1.85
1983 to 85   -2.00             0.15            -0.14                -1.99
1985 to 87   -0.81             0.87            -0.09                -0.03
1987 to 88    0.00             0.93            -0.14                  0.79
1981 to 88   -1.42             2.31            -0.27                  0.62
Table 8: Poverty Measures for Brazil and India, 1983
Poverty line:
India                         Brazil
Poverty
measure               India        Brazil           India         Brazil
H                   43.87         14.00           86.01          32.14
PG                  12.29          3.79           39.00          13.09
P2                   4.77          1.35           21.20           6.81
22



Table 9: Decomposition of the Difference in Poverty Between Braxil and India
in 1983
Poverty   Reference    Growth       Redistribution       Residual       Difference
line                   component      component                         in poverty
(Percentage points)
Headcount index (H)
India      India         43.77          -22.09             8.19            29.87
Brazil       51.96          -13.90            -8.19             29.87
Brazil     India         84.81            2.68           -33.62            53.87
Brazil       51.19          -30.94            33.62             53.87
Poverty gap index (PG)
India      India         12.25          -24.98            21.23             8.50
Brazil       33.48           -3.75           -21.23              8.50
Brazil     India         38.77          -16.54             3.68            25.91
Brazil       42.45          -12.86            -3.68             25.91
Foster-Greer-Thorbecke index (P2)
India      India          4.74          -20.38            19.06             3.42
Brazil       23.80           -1.32           -19.06              3.42
Brazil     India         21.11          -20.63            13.91            14.39
Brazil       35.02           -6.72           -13.91             14.39
Table 9 gives the decomposition estimates, for each poverty
line/measure and each country as the reference.  The results should now be
self-explanatory, though particular attention should be drawn to two points:
i) The redistribution component is generally negative (and the one
exception is small). Thus, the difference between the two countries' Lorenz
curves is such that, holding either mean constant, poverty would be hiaher in
Brazil than India. Alternatively, the actual difference in poverty between
the two countries is less than the difference expected on the basis of their
mean consumption levels alone; the latter is mitigated by the relatively more
"adverse" distribution in Brazil.
ii) In a number of cases, the residual turns out to be large.
Clearly, ignoring the residual could give quite misleading results. For
23



example, with the headcount index, using Brazil for both the poverty line and
the reference, virtually all of the difference in poverty may seem
attributable to the difference in means. However, that does not imply that
the redistribution component is negligible; indeed, it is large enough to
cancel out roughly 60 percent of the "growth" component.
24



7.    CONCLUSIONS
In the voluminous literature on the relationship between growth,
distribution and poverty, the following empirical question has remained
begging: how much of any observed change in poverty can be attributed to
changes in the distribution of income, as distinct from growth in average
incomes? Standard inequality measures can be misleading in this context. The
decomposition proposed here offers a tool for rigorously quantifying the
contribution of distributional changes to poverty alleviation, controlling for
growth effects, and the contribution of growth, controlling for relevant
distributional changes. Our approach differs from some recent attempts at
poverty decomposition by not confounding the residual component with either
the growth or the redistributional component. However, like any descriptive
tool, the proposed decomposition has its limitations. For example, the
decomposition cannot tell us if an alternative growth process with better
distributional implications would have been more effective in reducing
poverty. That would require an appropriate model of growth and distributionl
change.
We have illustrated the decomposition with a comparative analysis of
the recent evolution of poverty measures for Brazil and India, using newly
available data, largely for the 1980s. India's performance in poverty
alleviation was better than Brazil's over this difficult period. For example,
toward the end of the 1980s, the two countries had an almost identical poverty
gap index (though Brazil's being for a local poverty line with higher
purchasing power), while India's index of 10 years earlier had been about 50%
higher than Brazil's had been at the beginning of the 1980s. India's progress
over the 1980s has been uneven across sectors, with the urban sector
contributing a rising share of aggregate poverty.
In comparing these countries, our results indicate quite different
impacts on the poor of distributional changes over the 1980s, though the
differences are more marked in some sub-periods than others. Over the longest
periods considered here, distributional shifts have aided poverty alleviation
25



in India at a given mean consumption, while they have hindered it in Brazil.
Without any change in the mean, India's poverty gap would still have fallen
quite noticeably (from 16% of the poverty line to 11% in rural areas) while
Brazil's would have increased equally sharply (from 10% to 13%). With
Brazil's worsening distribution (from the point of view of the poor), far
higher growth rates than those of the 1980s would have been needed to achieve
the same impact on poverty as India attained over this period.
Growth and distributional effects on poverty were quite uneven over
time in both countries, and the effects of instances of negative growth were
notably different between the two. Contraction in the mean due to the poor
agricultural years of 1986 and 1987 was associated with a (modest) improvement
in distribution in India, such that poverty continued to fall (at least by the
distributionally sensitive P2 measure). Contraction in Brazil due to the
macroeconomic shocks of the 1980s was associated with a marked worsening in
distribution, exacerbating the adverse effect on poverty.
India's higher poverty level than Brazil's (at poverty lines with
constant purchasing power) is largely attributable to the former country's
lower mean. Indeed, at a given mean, Brazil would be the country with higher
poverty by most measures. We find sizable differences in both means and
distributions between the two countries. For example, with India's Lorenz
curve of the mid-1980s, virtually all of the 44% of the population who did not
attain the poverty line we have used would have escaped poverty at Brazil's
mean. But nearly twice as many would be poor in India if it had Brazil's
Lorenz curve. On the other hand, while 32% of Brazil's population fell below
that country'B poverty line in 1983, the proportion would have been negligible
(about 1%) at the same mean with India's Lorenz curve, while it would have
risen to over 80% at India's mean with Brazil's Lorenz curve.
Plainly, such calculations cannot also tell us whether a shift in
distribution (or mean) is politically or economically attainable at a given
mean (distribution). For example, it might be argued that a shift to India's
Lorenz curve by Brazil would entail a significant loss of mean income, with
26



ambiguous net effects on poverty, or that rapid growth to Brazil's mean by
India might entail a significant worsening in distribution. But the
decompositions do at least allow us to quantify the relative importance to the
poor of the existing differences in means and inequalities.
27






NOTES
1.    The first application of the method proposed here is Ravallion and Huppi
(1989), drawing on results of this paper. A simplified version of our method is
used in the latest World Development Report (World Bank, 1990).  Alternative
decomposition techniques have been used by Kakwani and Subbarao (1990) and Jain
and Tendulkar (1990) on data for India. However, there are potentially important
theoretical differences between these methods and that proposed here, which we
will discuss below.
2.    Throughout this exposition we shall only refer to differences in poverty
measures over time.   However, the decomposition can also be used to better
understand differences in poverty measures between countries or regions.   We
shall illustrate this type of application later.
3.   Note that R(t,t+n; t) = - R(t,t+n; t+n).  Thus it is also possible to make
the residual vanish by simply averaging the components obtained using the initial
and final years as the reference. But this is arbitrary.
4.   The poverty decompositions proposed by Kakwani and Subbarao (1990) and Jain
and Tendulkar (1990) do not satisfy sub-period additivity.
5.    We also tried a non-linear maximum likelihood estimator of the elliptical
model on the India data for 1983, but found that this gave almost identical
results to OLS on the linear-in-parameters specification in Table 1. (Estimates
of the poverty measures were within 0.1% of each other.)
6.   On the suggestion of a referee, we looked into the possibility of obtaining
the standard errors of the decompositions, but this seemed intractable. The
problem is two-fold. First, one cannot dismiss the possibility that disturbance
terms associated with Lorenz functions may be distributed non-spherically. This
does not pose a problem for the estimation of the poverty measures (and hence the
decompositions) as the OLS estimates of the Lorenz parameters are still unbiased,
but it does create a problem for the estimation of the standard errors of the
poverty measures. Second, while the poverty measures are a function of the Lorenz
parameters as well as the mean income, the estimates of the Lorenz parameters are
constructed differently to that for mean income. The former are estimated
econometrically while a sample estimate of the latter is taken directly from
published reports. In this context, it is not obvious how the sampling
distribution of the poverty measure can be defined.
7.    For further discussion see Jain and Tendulkar (1989).
8.    Smaller samples are now being collected on an annual basis, together with
the larger samples at five yearly intervals.  Results for the full sample of
1987-88 were not available at the time of writing.
9.     For a random sample, the standard error of the headcount index can be
readily calculated using well-known results on the sampling distribution of
proportions; the standard error of the headcount index H is V[H(l-H)/N] where N
is the sample size. The standard error for the smallest rural (urban) sample
(1988) is 1.5% (1.9%) of our estimated headcount index; for 1986-87 the
corresponding figure is 1.0% (1.3%), while for both of the earlier years it is
less that .5% (.6%).
10.    Jain and Tendulkar (1989) attempt to deal with this problem by revising
the NSS data.  We have not done so here for two reasons: i) the best way of
making such revisions is quite unclear, and ii) in any case it could reasonably
be argued that consumption net of durables is a better indicator of living
standards for poverty measurement.
29



11.    These are perhaps not ideal price indices for poverty analysis, as for
instance argued by Minhas et al., (1987, 1988) who also develop alternative
indices. But as their indices end in 1983 and their data are unavailable we have
used the CPIAL and CPIIW as deflators over the whole period of our analysis. (We
note some reservations on these price indices below.)
12.   We ignore spatial price differentials.  Elsewhere we have made allowance
for inter-state price differentials in poverty assessments for India in 1983,
building the all-India estimates up from the state level estimates (Datt and
Ravallion, 1990).  The aggregate results for rural India are very similar to
those estimated here, so the simplification does not appear to be worrying.
13.   Using the usual formula for the standard error of the difference between
two population proportions,
se(Hl-H2) = V{[Hj(1-Hj)/Nj] + [H2(1-H2)/N2]}
one finds that [H1-H2]/se(H1-H2) = 1.8 between the 1986-87 and 1988 surveys using
total consumption. The difference is more significant when consumer durables are
excluded (2.7), though the durables estimates for these latter years are not in
doubt.
14.    We are grateful to Louise Fox for providing us with the distributional
data for Brazil.
15.   There has not been a national expenditure survey for Brazil since 1974-75.
16.    For these data, the Kakwani specification violated the aforementioned
theoretical conditions for a locally valid Lorenz curve.
17.    A further technical problem in making this comparison is that we have
separate consumption distributions for rural and urban India, but do not have an
all-India distribution. This does not matter if we are only interested in
comparing  poverty  levels,  since  the  FGT  poverty  measures  are  sub-group
decomposable.  However, if we want to simulate poverty for alternative means or
Lorenz curves, as we will be doing below, then we would require country-specific
Lorenz curves. The all-India Lorenz curve is estimated from the rural and urban
Lorenz curves and means as follows. Given rural and urban Lorenz curves, LR(PR)
and LU(pU), for any PR in the interval (0,1), the corresponding Pu is obtained
as the solution of LU(pU) = PRLR(PR)/MU. For any pair (PR,PU) thus obtained, the
cumulative population proportion for the country as a whole is of course their
population-weighted average, viz., Pc = wRpR + wUpu. The cumulative proportion
of income or expenditure corresponding to Pc is obtained as
LC = [WRPRLR(PR) + wUpULU(pU)]/yC
where pC is the mean income or expenditure for the country as a whole. We thus
generate a set of points on the countrywide Lorenz curve which can be
parameterized as before.
18.    Note that the simulated all-India Lorenz curve performs quite well in
estimating poverty. The poverty measures in Table 8 approximate those obtained
as population-weighted sums of rural and urban measures of table 2 to the third
significant digit.  The rural and urban population weights, .76 and .24, are
derived using the assumption that the growth in rural and urban populations
during the 1981-83 has been at the same rate as during the inter-censal period
1971-81.
30



REFERENCES
Bhattacharya, N., P.D.Joshi and A.B. Roychoudhury, 1980, Regional Price
Indices Based on NSS 28th Round Consumer Expenditure Survey Data,
Sarvekshana 3, 107-121.
Datt, G., and M. Ravallion, 1990, Regional Disparities, Targeting, and Poverty
in India, Policy, Planning and External Affairs Working Paper 375, The
World Bank, Washington D.C.
Foster, J., J. Greer, and E. Thorbecke, 1984, A Class of Decomposable Poverty
Measures, Econometrica 52, 761-765.
Fox, M.L., 1990, Poverty Alleviation in Brazil, 1970-1987, Brazil Country
Department, The World Bank, Washington, D.C., (processed).
Fox, M.L., and S.A. Morley, 1991, Who Paid the Bill? Adjustment and Poverty
in Brazil, 1980-1995, Background Paper for the World Development Report
1990, PRE Working Paper 648, The World Bank, Washington, D.C.
Jain, L.R., and S.D. Tendulkar, 1989, Inter-Temporal and Inter-Fractile-Group
Movements in Real Levels of Living for Rural and Urban Population of
India: 1970-71 to 1983, Journal of Indian School of Political Economy
1, 313-334.
Jain, L.R., and S.D. Tendulkar, 1990, Role of Growth and Distribution in the
Observed Change of Headcount Ratio-Measure of Poverty: A Decomposition
Exercise for India, Technical Report No. 9004, Indian Statistical
Institute, Delhi.
Kakwani, N., 1980, On a Class of Poverty Measures, Econometrica 48, 437-446.
Kakwani, N., 1990, Testing the Significance of Poverty Differences with
Applications to Cote d'Ivoire, LSMS Working Paper 62, The World Bank,
Washington, D.C.
Kakwani, N., and K. Subbarao, 1990, Rural Poverty and its Alleviation in
India, Economic and Political Weekly 25: A2-A16.
Minhas, B.S., L.R. Jain, S.M. Kansal, and M.R. Saluja, 1987, On the Choice
of Appropriate Consumer Price Indices and Data Sets for Estimating
the Incidence of Poverty in India, Indian Economic Review 22: 19-49.
Minhas, B.S., L.R. Jain, S.M. Kansal, and M.R. Saluja, 1988, Measurement of
General Cost of Living for Urban India, Sarvekshana 12, 1-23.
Ravallion, M., G. Datt, and D. van de Walle, 1991, Quantifying the Absolute
Poverty in the Developing World, Review of Income and Wealth,
(forthcoming).
Ravallion, M., and M. Huppi, 1989, Poverty and Undernutrition in Indonesia
During the 1980s, Policy, Planning and Research Working Paper 286, World
Bank, Washington DC.
Villasenor, J., and B. C. Arnold, 1989, Elliptical Lorenz Curves, Journal of
Econometrics 40, 327-338.
World Bank, 1990, World Development Report 1990: Poverty, Oxford University
Press for The World Bank, Washington DC.
31



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LSMS Working Papers (continued)
No.48      Confronting Poverty in Developing Countries: Definitions, Information, and Policies
No. 49     Sample Designs for the Living Standards Surveys in Ghana and Mauritania/Plans de sondage
pour les enquetes sur le niveau de vie au Ghana et en Mauritanie
No.50      Food Subsidies: A Case Study of Price Reform in Morocco (also in French, 50F)
No. 51     Child Anthropometry in C6te d'lvoire: Estimates from Two Surveys, 1985 and 1986
No. 52     Public-Private Sector Wage Comparisons and Moonlighting in Developing Countries: Evidence
from C6te d'Ivoire and Peru
No. 53     Socioeconomic Determinants of Fertility in C6te d'Ivoire
No.54      The Willingness to Pay for Education in Developing Countries: Evidence from Rural Peru
No. 55     Rigidite des salaires: Donnees microeconomiques et macroeconomiques sur l'ajustement du marche
du travail dans le secteur moderne (in French only)
No. 56     The Poor in Latin America during Adjustment: A Case Study of Peru
No. 57     The Substitutability of Public and Private Health Care for the Treatment of Children in Pakistan
No. 58    Identifying the Poor: Is "Headship" a Useful Concept?
No. 59     Labor Market Performance as a Determinant of Migration
No. 60     The Relative Effectiveness of Private and Public Schools: Evidence from Two Developing Countries
No. 61     Large Sample Distribution of Several Inequality Measures: With Application to COte d'Ivoire
No. 62     Testingfor Significance of Poverty Differences: With Application to C6te d'Ivoire
No. 63     Poverty and Economic Growth: With Application to C6te d'Ivoire
No. 64     Education and Earnings in Peru's Informal Nonfarm Family Enterprises
No. 65     Formal and Informal Sector Wage Determination in Urban Low-Income Neighborhoods in Pakistan
No. 66     Testingfor Labor Market Duality: The Private Wage Sector in C6te d'Ivoire
No.67      Does Education Pay in the Labor Market? The Labor Force Participation, Occupation, and Earnings
of Peruvian Women
No. 68     The Composition and Distribution of Income in C6te d'lvoire
No. 69     Price Elasticities from Survey Data: Extensions and Indonesian Results
No. 70     Efficient Allocation of Transfers to the Poor: The Problem of Unobserved Household Income
No. 71    Investigating the Determinants of Household Welfare in C6te d'Ivoire
No. 72     The Selectivity of Fertility and the Determinants of Human Capital Investments: Parametric
and Semiparametric Estimates
No. 73     Shadow Wages and Peasant Family Labor Supply: An Econometric Application to the Peruvian Sierra
No. 74     The Action of Human Resources and Poverty on One Another: What We Have Yet to Learn
No. 75     The Distribution of Welfare in Ghana, 1987-88
No. 76     Schooling, Skills, and the Returns to Government Investment in Education: An Exploration Using
Data from Ghana
No. 77     Workers' Benefits from Bolivia's Emergency Social Fund
No. 78     Dual Selection Criteria with Multiple Alternatives: Migration, Work Status, and Wages
No. 79     Gender Differences in Household Resource Allocations
No. 80     The Household Survey as a Tool for Policy Change: Lessons from the Jamaican Survey of Living
Conditions
No. 81     Patterns of Aging in Thailand and C6te d'Ivoire
No. 82     Does Undernutrition Respond to Incomes and Prices? Dominance Tests for Indonesia



Ravallion/Datt               Growth and Redistribution Components of Changes in Poverty Measures  The World Bank (t
x
O0 .
40-4
0
71  AZ    M3