POLICY RESEARCH WORKING PAPER 28 83
Assessing the Distributional Impact
of Public Policy
B. Essama-Nssab
The World Bank
Poverty Reduction and Economic Management Netwvork
Poverty Reduction Group
September 2002
P POLICY RESFARCH WOIOKING, PAPEK 2883
Abstract
Economic developmenit necessarily chaniges the welfare the maximii priniciple. This principle offers a ullifying
of socioCcololilic groups to various degrees, dependinig framework for analyzing the socioeconiomic impact of
on differenctes in their social arrangements. The public policy by using a wvide variety of evaluationi
challenge for policvyrakers is to select the changes that functions, inequality indicators (like the extended Gini
will be most socially desirable. Essama-Nssaih coefficient), and poverry indices (such as Sen's index and
demonistrates the usefulness of distributional analysis for the meilimbrs of the Foster-Greer-Thorbecke family).
social evaluation and, more specifically, for welfare The author also examines, within the context of
evaluatioll, uislig data from the 1994 Integrated commodity taxation, oiow to identify socially desirable
Houseihold Survey in Guinea. Because the inttrinationial policy options usinlg both the dominance criterion and
commiiiunity has declared poverty eradication a abbreviated social welfare fulictions. He includes
fundamental objective of developmeit, the autIlor uses a computer roLitinies for calculating various welfare indices
poverty-focused approach to social evaluationi based on and for plotting the relevant concenltrationi curves.
This paper-a product of the Poverty Reductio n Group, Poverty Reduction and Economilic Management Net-work-is part
of a larger effort in the network to ulinlerstand the povertx and social impa;ct of public policy. Copies of the paper are
available free from the World Bank, 181 8 H Street NW, Washington, DC 204.3.3. Please contact Oykiao Kootzeniew, room
XIC4-554, telephone 202-473-5075, fax 202-522-3283X , email address okootzemew\(@wvorldbanik.org. Policy Research
Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at
bessamilanissah@(- w\vorldbank.org. September 2002. (50 pages)
The lPolic Research Workinzg Paper Series disseminates the findinigs of wuork in pro)gress to) enicou rage the excanige of ideas abouit
developmient issues-An obiective oo the series is to get the findinis soit quickl), vien if tbe presentations are less than fullid polished. The
papers carry the names of the aothors a1nd shooild be cited according/v. The findings, interpretations, and conclusions expressed in this
ps/Pcr are entirely those o/ the authors. IThey do nzot necessar)il represent the viewv of the World Bank, its Execitive l)irectors, or the
coitiitr-ics they represenit.
P'roducedi by the Research Advisorv Staff
ASSESSING THE DISTRIBUTIONAL IMPA CT OF PUBLIC POLICY
B. Essaina-Nssah
Poverty Reduction Group
The World Bank
Washington, D.C.
Table of Contents
1. Introduction ........................................................1
2. Maximin Approach to Poverty-Focused Evaluation ..................................................3
The Logic of Social Evaluation .................3......................................3
Distribution of Social Weights ........................................................4
Decomposition by Factor Components ....................................................... 12
3. Truncation by a Poverty Line ....................................................... 16
Distribution of Social Weights by Poverty Status ................................................ 17
Decomposability of the Gini Family of Indices by Population Subgroups .......... 17
The Use of Poverty Gaps ....................................................... 21
How Desirable is Truncation? ................. ...................................... 27
4. Impact Analysis ....................................................... 29
Social Desirability of Feasible Policy Options ..................................................... 29
Unambiguous Welfare Comparisons ....................................................... 32
Use of Abbreviated Social Welfare Functions ...................................................... 38
Changes in the Abbreviated Social Welfare Function .............................. 39
Poverty Impact ....................................................... 40
5. Conclusion ....................................................... 43
References ....................................................... 45
1. Introduction
The purpose of this paper is to fit distributional impact analysis within the logic of
social evaluation and to illustrate its implementation using data from the 1994 Integrated
Household Survey in Guinea'. The perspective of development as empowerment,
advocated by Sen(1999) and outlined in the World Development Report (WDR)
2000/2001, entails essentially the expansion and the distribution of socioeconomic
opportunities with implications for individual and collective well-being. Distributional
analysis, a key input in policy formulation and evaluation, involves a comparison of
alternative distributions of some indicator of the living standard.
There is an intimate relationship between evaluation and development to the
extent that the very definition of development involves an evaluative judgment. The
domain of development hinges on the notion of the things that are worth promoting (Sen
1989). The concept of living standard therefore plays a fundamental role both in the
formulation of development objectives and in the assessment of development
effectiveness. However, this multidimensional concept is not easy to implement
empirically. The identification of the valuable dimensions of the living standard depends
essentially on the underlying view about personal characteristics and social arrangements
that are deemed important in the realization of any life plan.
The Millennium Development Goals (MDGs) set by the United Nations with
respect to development and poverty eradication are consistent with the empowerment
approach to development. They identify income, health, education, shelter and
governance as critical components of the living standard. In general these goals are set
for the year 2015 relative to 1990 and are meant to provide guidance to both national and
international policies and programs. For our current purposes, we select consumption per
capita as an indicator of opportunities for well-being at the household level. It will be
obvious that the methodology discussed in this paper can easily be extended to other
dimensions of living that may be represented by a quantitative variable distributed over a
population.
Fundamentally, evaluation involves the examination and weighing of a
phenomenon according to some explicit or implicit yardstick (Weiss2 1998). We can
leam a great deal about an evaluative approach by distinguishing the information
required for passing judgments from that which has no direct evaluative role (Sen 1999).
The information pertains to the valuable aspects of the object of evaluation, and to the
rule for combining these valuable elements into an aggregative judgment. For instance,
the utilitarian approach to social evaluation is based on the utility sum total in the social
states under consideration. In this framework, attention is focused on individual well-
' Enquete Integrale avec Module Budget-Consommation (EIBC). The survey was carried out by the
National Statistical Office within the Ministry of Plan and Cooperation.
2 More explicitly, this author defines evaluation as "a systematic assessment of the operation and/or the
outcomes of a program or policy, compared to a set of explicit or implicit standards, as a means of
contributing to the improvement of the program or policy".
1
being as represented by the concept of utility, and the goodness of a social state depends
on the sum total of utilities associated with that state [regardless of how these utilities are
distributed among individuals (Sen 1999)].
Widespread poverty in the developing world remains a serious challenge for the
development community and may have prompted the inclusion of poverty eradication
among the MDGs. The World Bank has declared poverty reduction its overarching
objective and a benchmark measure of its performance as a development institution. In
view of these considerations, we emphasize poverty-focused evaluation in this paper. If
development is about empowering people to take charge of their destinies (Wolfensohn
1998), then poverty must be seen as the deprivation of basic capabilities to lead the kind
of life one has reason to value (Sen 1999). In this perspective, the identification of
poverty must go beyond lowness of income. This invitation however does not deny the
fact that inadequate income can lead to capability deprivation. The notion of relative
deprivation plays an important role in shaping the evaluative framework discussed here.
In the context of applied policy analysis, it is not enough to have an analytical or
evaluative framework, available data must be processed according to that framework in
order to draw relevant conclusions. Invariably, one needs a computing platform to do the
job. We propose to show that the syntax of EViews can easily be exploited to do the job at
hand. EViews stands for Econometric Views, a Windows version of a software designed by
Quantitative Micro Software (QMS) for the processing of time series data and the conduct
of econometric analysis. We find that many people who are already using EViews for other
purposes and interested in distributional issues may not necessarily be familiar with the
fundamental concepts and techniques of distributional analysis. In addition, depending on
their level of mastery of the software, they may not even think of EViews as appropriate for
handling household survey data. Yet the current version of the software (Version 4.1) can
handle 4 million observations per series (variable) and the total number of observations (i.e.
number of variables times the number of observations per variable) is limited only by the
available Random Access Memory (RAM). In addition the syntax is sufficiently strait-
forward to allow the user to plot common curves such as cumulative distributions,
concentration or Lorenz curves. It is also easy to compute indices of social welfare,
inequality and poverty.
The outline of the paper is as follows. Section 2 presents a poverty-focused
evaluation framework based on the maximin principle. The concept of relative
deprivation underpins the distribution of social weights in the formulation of aggregative
judgments. Section 3 focuses on the implications of the traditional approach to poverty
analysis based on the use of a poverty line. In particular, it is shown that when the
distribution of welfare is truncated on the basis of a poverty line, the Gini coefficient can
be additively decomposed into two components, one measuring the within group
inequality and the other the inter-group inequality. Impact analysis is reviewed in
Section 4. In that Section, we show how the ranking of socioeconomic situations can
vary with the specification of social weights. The basic EViews routines used to produce
illustrations are provided in boxes. Concluding remarks are presented in the last Section
of the paper.
2
2. Maximin Approach to Poverty-Focused Evaluation
A poverty assessment is a key ingredient in the formulation of a poverty reduction
strategy. It is a determination of the nature, extent and determinants of poverty at both
the individual and societal level. Ultimately, such an assessment is an exercise in social
evaluation to the extent that it offers a criterion for comparing alternative social
arrangements. Before considering the implied distribution of social weights, we first
review the logic of evaluation.
The Logic of Social Evaluation
The notion of evaluation is usually contrasted with that of valuation. The former
relates to the assessment of the relative merits of actions while the latter applies to the
comparison of things (Dasgupta 2000). Thus, evaluation applies to strategies and
policies3. Essentially, evaluation entails four basic aspects: (1) the identification of the
object of evaluation along with its valuable dimensions; (2) the valuation of the various
components of the object; (3) the formulation of an overall judgment; and (4) the ranking
of alternatives.
We can learn a great deal about an evaluative approach by distinguishing the
information required for passing judgments from that which has no direct evaluative role
(Sen 1999). The information pertains to the valuable aspects of the object of evaluation,
and to the rule for combining these valuable elements into an aggregative judgment.
When seen as an assessment of individual advantage and social progress, the object of
social evaluation is the determination of the extent to which the prevailing social
arrangements maintain and improve the living standard of the participants. The
distribution of the living standard within the population is thus the yardstick by which we
judge the performance of a socioeconomic system. The identification of the valuable
dimensions of the living standard corresponds to the specification of what Sen (2000)
calls the focal space of evaluation.
To arrive at an overall judgment, one needs to aggregate individual conditions
into an indicator of a social state. In Sen's terminology, this aggregation rule represents
the focal combination. One standard approach is to define an additively separable social
welfare function as follows.
(2.1) W = jhxh
h=1
where ph is the social weight attached to the level of the welfare of individual (or
household) h, as indicated by xh. We may invoke the concept of Equally Distributed
3A strategy is a conditional action that depends on the state of the world or on actions taken by other
decision makers. A policy is a definite course of action chosen from a feasible set to govern current and
future actions. A policy statement identifies objectives and associated means.
3
Equivalent (EDE) welfare to abbreviate the above function as follows: W(VP)=W(x). VP
is -he level of welfare such that, if enjoyed equally by each member of society, collective
well-being would be equivalent to the one associated with the observed distribution4.
The definition of the covariance between two variables allows us to express the EDE
welfare as:
(2.2) V6n h=- xh = ,pufX +cov(x,f)
where both f and x are n-dimensional vectors. No generality is lost if we normalized
social weights such that p=l. In that case, average social welfare could be written as:
(2.3) V = x + cov(x,, )
The covariance term would be equal to zero if either , or x were constant. A constant x
means that everybody has the same level of living, and therefore there is no inequality to
worry about. However, a constant 1 means everybody receives equal consideration in
social evaluation regardless of her/his standard of living. In this case, social evaluation is
not concerned with inequality. Thus, expressions (2.2) and (2.3) may be viewed as a
decomposition of the social welfare function into the size and distribution components.
The former is represented by the mean of the distribution of the living standard indicator,
while the second is measured by the covariance between the social weights and the levels
of the living standard.
The focal space and the focal combination define the informational basis of social
evaluation. This may be viewed as a set of value judgments underlying the specification
of the objects of value both from the individual and social perspective. Once the relevant
indicator of the living standard has been selected, the specification of a social welfare
function boils down to the distribution of social weights through the specification of ph
for each individual or class of individuals. How can one go about this? One possibility is
to invoke a theory of social justice to guide the distribution of social weights. We use the
maximin principle in building up a poverty-focused evaluative framework.
Distribution of Social Weights
A focus on poverty in social evaluation requires that extra consideration be given
to the worse-off relative to the better-off both analytically and politically. Sen (1997: 33)
explains the ethical underpinning of the ordinary Gini coefficient in terms of the pairwise
maximin principle. According to this criterion the welfare level of any pair of individuals
must be equated to the welfare of the worse off of the two. This is consistent with the
Dalton principle of transfers according to which rich to poor transfers improve social
welfare. This value judgment may be built in the social welfare function by first ranking
4 The concept is used by Atkinson (1970) in a normative approach to the measurement of income
inequality.
4
individuals according to some criterion of social desert, then assigning social weights in
such a way that of any two individuals the more deserving receives a higher weight.
More specifically, suppose that we rank individuals according to their level of
consumption xh, then we assign social weights on the basis of ranks in such a way that if
h*1, commodity j is considered a
luxury. If the elasticity is between 0 and 1, the corresponding commodity is considered a
necessity. When this elasticity is negative, the commodity is an inferior good (Gamer
1993: 135).
Table 2.4. Gini Elasticities for Selected Expenditure Components in Guinea (1994)
Aversion Total Expenditure Cereals Beverages Food Electricity Energy Non-Food
1.50 1.00 0.43 1.51 1.02 1.83 0.85 1.29
2.00 1.00 0.50 1.43 1.05 1.76 0.92 1.24
2.50 1.00 0.55 1.39 1.07 1.70 0.95 1.21
3.00 1.00 0.58 1.36 1.07 1.65 0.97 1.18
3.50 1.00 0.61 1.34 1.08 1.61 0.98 1.17
4.00 1.00 0.63 1.33 1.08 1.58 0.99 1.15
4.50 1.00 0.65 1.32 1.08 1.55 0.99 1.14
5.00 1.00 0.66 1.31 1.08 1.53 1.00 1.13
5.50 1.00 0.68 1.30 1.08 1.51 1.00 1.12
6.00 1.00 0.69 1.30 1.08 1.49 1.00 1.12
Source: Computed
Table 2.4 presents Gini Engel elasticities for selected expenditure components in
Guinea. This information reveals that food expenditure is distributed very much like total
expenditure. The distribution of expenditure on energy is also very close to that of total
expenditure. Beverages and electricity are clearly luxury goods while cereals are a
necessity. In general, it appears that inequality in the distribution of household
expenditure in Guinea is due to non-food expenditure.
The area between a concentration curve and the 45 degree line is known as the
area of concentration. It is equal to - cov[xj, (1 - p)]/ pj = cov(xj, p)I ,uj. Therefore,
r%J(2) is equal to the area of concentration for xj divided by the area between the 45
degree line and the Lorenz curve of x (Yitzhaki and Lewis 1996:549). This geometric
interpretation provides a necessary condition for characterizing the position of a
concentration curve relative to the 45 degree line and the Lorenz curve. Thus when the
Gini Engel elasticity is negative, the concentration curve is concave and lies above the 45
degree line. When the elasticity is equal to zero, the curve coincides with the 45 degree
line. When the elasticity is between zero and 1, the concentration curve lies between the
45 degree line and the Lorenz curve. Finally, when the elasticity is greater than one the
concentration curve lies below the Lorenz curve.
Finally, let qj stand for the cumulative distribution obtained by ranking
individuals by increasing order of component j. Let GJ(v) be the extended Gini
coefficient of component j. Expression (2.19) also implies that the overall Gini is equal to
9 Yitzhaki (1994a) calls it Gini income elasticity. Furthermore, (2.19) shows that Engel-aggregation holds
for these elasticities to the extent that their weighted sum is equal to one. The weights are the shares of the
total budget spent on each commodity.
14
the weighted average of the concentration indices of the components, G(v) = AjCj(v).
j=1
If we multiply each concentration index in this expression by a neutral element
[Gj(v)/Gj(v)], we obtain the following alternative decomposition of the extended Gini
coefficient:
(2.22) G(v) = EA( G1(v ,j (V) = jG( (v) = 2jR j (v)Gj (v)
j=1 ~ Gj (v) j=1 cov[Xj qj j=I
Box 2.4: Plotting Concentration Curves in EViews
INCLUDELYCDF
LOAD %O
SMPL @ALL
CALL LYCDF({%1}(1), {%1}(2), {%1}(3))
SERIES P=F_HAT
SERIES L45=P
GROUP LCC P L45
!M={%2}.@COUNT
FOR !K=1 TO !M
%sv={%2).@SERIESNAME(!K)
SERIES x{!K}={%1}(3)*{%2}(!K)
SERIES SHARES{!K}=X{!K}I@SUM(X{!K})
SMPL @FIRST @FIRST
SERIES LP{%sv} =SHARES{!K}
SMPL @FIRST+1 @LAST
LP{%Sv}=LP{%Sv}(-1) + SHARES{!K}
LCC.ADD LP{%Sv}
SMPL @ALL
NEXT
FREEZE(LCCS) LCC.XY
LCCS.SCALE RANGE(O, 1)
'End of Program
The coefficient Rj(v) is known as the "Gini correlation" between component j
and overall x. This expression thus reveals that the contribution of a component to
overall inequality is determined by three factors: (1) the proportion of the component in
the total value of x, (2) the correlation between the component and the total, and (3) the
extent of inequality in the distribution of the component.
Figure 2.2 shows the configuration of concentration curves of two items from the
1994 Integrated Household Survey in Guinea. The concentration curve of cereals lies
between the Lorenz curve of total expenditure and the 45 degree line. We therefore
expect its Gini elasticity to be positive but less than one. Expenditure on beverages is
more unequally distributed than total expenditure. The corresponding concentration
curve lies below the Lorenz curve. Thus we expect the Gini elasticity of beverages to be
grater than one. The values of Gini elasticities implied by this configuration are
presented in table 2.4. This table also reveals that the distribution of food expenditure is
15
very close to that of total expenditure. Expenditures on electricity and nonfood items are
more concentrated in high income households.
Figure 2.2. Guinea 1994: Concentration Curves of Cereals and Beverages with respect to
Total Expenditure
1.0 -
0.9 -
0.8-
0.7-
0.6-
0.5-
0.4 Tta
0.3 - Cereals
Beverages
0.2-
0.1
0.0 -
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
3. Truncation by a Poverty Line
The standard approach to poverty analysis is to partition the population
exhaustively into two mutually exclusive groups on the basis of a poverty line, and to
assign a weight equal to zero to the wellbeing of anybody whose living standard is above
the poverty line. Such a partition raises at least two interesting issues. The first one
relates to the decomposability of the Gini family of indices, and the second to the
interpretation of some well known poverty indices within the framework defined by (2.1).
Before considering these issues, we first examine some implications for the aggregate
distribution of the social weights defined by (2.4).
16
Distribution of Social Weights by Poverty Status
We focus here on how the relative social weight attached to each of these groups
varies with the aversion parameter. Table 3.1 contains the results of such an experiment
using household survey data from Guinea. We find that the poor account for 16 percent
of the mean rank, and the non-poor for 84 percent. This stems from the fact that the
overall mean rank (i.e. the mean of the cumulative distribution) is equal to 0.5. The mean
rank of the poor is about 0.20 while that of the non-poor is 0.70. The weighted average
of the two numbers is equal to 0.5. The weights used here are the respective population
shares. When the aversion parameter is equal to one, each group receives, on average, a
weight equal to its population share. As the aversion parameter increases above 1, most
of the social weight is shifted to the poor.
Table 3.1. Distribution of Average Social Weight in Guinea by Poverty Status in 1994 and by
Level of Aversion
ShareofMeanRank v=l v=2 v=3 v=4 v=5 v=6
Poor 0.16 0.40 0.64 0.79 0.87 0.92 0.95
Nonpoor 0.84 0.60 0.36 0.21 0.13 0.08 0.05
Total 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Source: Computed
Decomposability of the Gini Family of Indices by Population Subgroups
Truncation by a poverty line implies that the ordinary Gini coefficient can be
written as:
(3.1) G = (s,p,G, + s2p2G2) + Gb
where the term between parentheses represents within group inequality, while the term
outside stands for between group inequality. The term si measures the proportion of total
welfare enjoyed by grout i, and pi is the population share of that group.
Anand(1983:320) shows that, in this case, between group inequality is equal to:
(3.2) G = n2n2 I P 1= ns2 L1 [ P2 -2min(p, I P2)]
Assuming that the first group is the poor group, then the above expression reduces to:
(3.3) Gb = (P, -s.)
17
Inequality between the two groups, as measured by the ordinary Gini coefficient, is equal
to the proportion ofpoor in the population minus their income share. This is a particular
case of a general case we encountered in Section 2 when testing the covariance and the
linear segment approaches to Gini calculation. In general, when the subgroup
distributions do not overlap, Gb can be computed as the Gini for the distribution where
everybody has her/his group average welfare.
Furthermore, in the context of the extended Gini, between group inequality is
computed as follows (Yitzhaki 2002: 77):
(3.4) Gb (v) = Pi S [I - (1 - p.)V]
Table 3.2 shows the results of a decomposition of the extended Gini coefficients
associated with the distribution of household expenditures in Guinea in 1994. The
decomposition is based on (3.1) and (3.4). The first column of the table contains levels
of the aversion parameter. The second column indicates within group inequality, while
the third and fourth columns represent between group inequality respectively in terms of
Gb(v) and its share in overall inequality (presented in the last colunn). These results
indicate that, given the poverty line, most of the observed inequality in the distribution of
household expenditure in Guinea is accounted for by the between components. When the
aversion parameter ranges from 1 to 6, the share of between group inequality increases
from 0 to 84 percent. This suggests that poverty-focused evaluation must also pay
attention to inequality between the poor and the rest of the population.
The use of a poverty line to divide the population into two groups means that the
corresponding distributions of welfare do not overlap. It is useful to note the
decomposition of the Gini coefficient when the sub-group distributions may overlap. The
resulting expression suggests an indicator of social exclusion. Yitzhaki(1994b) proposes
an index of the degree of overlapping between distributions which allows a more general
and transparent decomposition of the Gini coefficient. In this general case, the Gini
coefficient can be decomposed into three distinct components: the first component is linked
to intra-group inequality, the second is an indicator of between-group inequality, and the
third is an indicator of the overlapping of the distributions. The overlapping index can also
be interpreted as a measure of segmentation and stratification. Such an indicator may reveal
the extent of social exclusion of some socioeconomic groups.
18
Table 3.2. Inequality between Poor and Nonpoor in Guinea in 1994
Aversion Within Between Share of Overall
between
1.00 0.00 0.00 0.00 0.00
1.50 0.15 0.13 0.46 0.28
2.00 0.17 0.23 0.58 0.40
2.50 0.16 0.31 0.66 0.47
3.00 0.15 0.37 0.71 0.52
3.50 0.13 0.42 0.76 0.55
4.00 0.12 0.46 0.79 0.58
4.50 0.11 0.48 0.80 0.60
5.00 0.11 0.51 0.84 0.61
5.50 0.10 0.52 0.83 0.63
6.00 0.10 0.54 0.84 0.64
Data Source: 1994 Integrated Household Survey
Suppose that a population has been divided into m subgroups indexed by k.
Consider any two groups j and k. The overlapping of group k by group j reflects the fact
that some individuals from group k have a standard of living that falls within the range of
the distribution of the living standard within group j. The extent of this overlapping can
be measured by the covariance between the level of the living standard in group k and the
relative rank the members of k would receive, had they been considered as members of
group j. In this context, relative ranks are measured by the relevant cumulative
distributions.
To see more clearly what is involved, let F(x) and Fk(x) stand respectively for the
overall CDF and the CDF within group k. Also let Fj(x) be the relative rank that
members of k would get had they been considered as belonging to j. By definition of the
CDF, if all observations in k have a value that is less than or equal to the minimum in the
range of group j, Fk,(x) would be equal to zero. If all values in group k are greater or
equal to the maximnum in j, F,(x)=1. In either one of these extreme cases, covk[x,
F,j(x)]=O. This is the covariance between the values of x in group k and their relative
rank in j. The covariance is calculated using the distribution k (Yitzhaki 1994b: 149). A
non-zero value of this covariance reflects some overlapping of group k by group j. A
normalized overlapping index is given by the following expression.
(3.5) 04 = ~~~covk Ex, Fir (x)]
covk[x,Fk(x)]
The index has the following properties: (1) It is greater or equal to zero and less than or
equal to 2; (2) It is equal to one if the distribution of group j is identical to the distribution
of group k; (3) for a given segment of distribution j that falls within the range of
distribution k, the closer the observations of j are to the mean of k, the higher Oki.
19
The overlapping of group k with the overall population (including group k itself) is
defined as:
(3.6) O= covk[x, F (x)]
Covk [x, Fk (x)]
It can be shown that (Milanovic and Yitzhaki 2002: 160):
m
(3.7) Ok = Pk +pjOV
jok
where Pk iS the population share of group k. Letting Sk stand for the share of group k in
total welfare (as represented by income or expenditure), the ordinary Gini coefficient
may be written as:
(3.8) G = ,sk OkGk + Gb
k=1
where Gb = 2COVlUk'Fk] is an indicator of between group inequality. It is equal to
b
twice the covariance between the mean welfare of each group and the group's mean rank
in the overall distribution, divided by the overall mean of the welfare indicator. Using
(3.7), we have:
m m m
(3.9) G= ESPkGk + Gb +ESkGk ELpjO.I
k=1 k=1 j*k
The first term on the right hand side of (3.9) measures within group inequality as a
weighted average of the subgroup Ginis where the weights are equal to the subgroup
population share times the share of welfare (as measured by the indicator x). The share
of group k in x is equal to: Sk = Pklk . The second term stands for between-group
A
inequality. The last term, is an indicator of the extent of "cross-overlapping" [to
distinguish it from global overlapping measured by (3.6)]. This term is equal to zero
when subgroup distributions do not overlap.
An application of the above decomposition to the distribution of per capita
household expenditure in Guinea in 1994 produced the following results.
20
Table 3.3 Gini Decomposition of Inequality in the Distribution of Household Expenditure in
Guinea by Area of Residence
Population Expenditure Mean Mean Gini Global Cross-
Share Share Expenditure Rank Overlap Overlap
Conakry 0.17 0.31 849843.00 0.13 0.38 0.58 0.41
Other 0.16 0.20 598799.30 0.10 0.38 0.85 0.69
Urban
Rural 0.67 0.49 342785.10 0.27 0.33 0.96 0.29
Guinea 1.00 1.00 469461.30 0.5 0.40 1.00 0.00
Data Source: 1994 Integrated Household Survey.
The overall Gini index is estimated at 0.40. The decomposition presented in table
3.3 above implies that the within-group inequality is equal to 0.14, the between-group
component is equal to 0.11 while the overlapping component is 0.15. Thus about 28
percent of the observed inequality in Guinea in 1994 is accounted for by the between
group component (when the population is classified by area of residence). Looking at the
overlapping components, it can be seen that no area stands out as a perfect stratum.
However, in relative terms, the rural area has the least amount of overlapping with the
rest of the distribution compared to the urban areas. This fact is also supported by the
pattern of mean expenditures.
The Use of Poverty Gaps
At the individual level, poverty measurement involves two basic steps: (1) the
selection of a poverty line indicating a threshold below which the person is declared poor,
and (2) the computation of poverty gaps measuring the relative distance between an
individual level of welfare and the chosen poverty line. Kakwani(1999:605) defines a
class of additively separable poverty measures starting from the notion of deprivation.
Let z be the poverty line, and xh the level of welfare enjoyed by individual h in a society
comprising n individuals. Let xV(z,xb) stand for an indicator of deprivation at the
individual level. The following restrictions are imposed on the indicator: (i) it is equal to
zero when the welfare level of the individual is greater or equal to that specified by the
poverty line; (ii) the indicator is a decreasing convex function of welfare, given the
poverty line.
Poverty measures of this class reflect the average deprivation suffered by the
whole society and may be written, as:
I n
(3.10) P(z,x) = - 1 /t(Z x )-
n h=1
The class of poverty measured defined by (3.10) is called additively separable
because the deprivation felt by an individual depends only on a fixed poverty line and
her/his level of welfare and not on the welfare of other individuals in society.
21
Furthermore, if the entire population is divided exhaustively into mutually exclusive
socioeconomic groups, this class of measures allows one to compute the overall poverty
as a weighted average of poverty in each group. The weights here are equal to population
shares. Thus, such indices are also additively decomposable.
We wish to interpret expression (3. 10) in the context of the general social welfare
function defined by (2.1). We focus our attention on one prominent subgroup of the class
of poverty indices due to Foster, Greer and Thorbecke (1984). The associated
deprivation function may be written as follows (Jenkins and Lambert 1997:318).
(3.11) YIFGT (z, xh, a) = max {(1-x / z) ,O}.
If we define the relative poverty gap of individual h as gh=max{(z_xh)/z, 0}, it
becomes clear that in the context of poverty-focused evaluation defined by the Foster-
Greer-Thorbecke (FGT) class of indices, the individual poverty gap plays a dual role in
defining both individual welfare and the social weights assigned to the individual in
social evaluation. To see this point more clearly, we rewrite (3.11) as:
(3.12) yfFGT(z,x ,a) = max{I,8(1-xh /Z),0}.
The social weight attached to the condition of individual h is now equal to:
h= (I- Xh / Z)a-1 . The parameter a is an indicator of aversion for inequality among the
poor. When a=0, the social weight assigned to individual h is equal to: 1h= ( J- h
This coefficient balances individual deprivation in such a way that on the basis of (3.12),
each poor person counts for one in social evaluation and each non-poor counts for zero.
Using expression (3.10), we find that aggregate poverty is equal to:
(3.13) Po 1 qFGT (Z, Xh,0)
n h=1n
where q is now the total number of poor people in the population. Po is a measure of
poverty incidence in the population. This measure does not take into consideration
inequality among the poor.
When the aversion parameter is equal to one, the relevant social weights are all
equal to one, regardless of individual deprivation. Aggregate level poverty is given by
the poverty gap ratio defined as follows:
(3.14) PI =-EiVfT(ZnX -Emax(I _ X 0 I- )
n h=1 nl~ h=Z
where 1tp is the average welfare of the poor. This index is also known as a measure of
poverty intensity. One possible interpretation of this indicator is based on the following
22
considerations. Think of x as income, and consider a situation where x is observable and
it is possible to give everybody a transfer of (z-x). Afterwards, there would be no more
poverty as every individual would have at least an income equal to z. Let q stand for the
number of poor. The total income transferred to the poor by this operation is q(z-pp).
Normalizing by the size of the population, we get Po(z-p.p)=zP1. Thus in an ideal world
of incentive-preserving transfers and perfect targeting, zPI is viewed as the minimum
amount of resources that must be transferred, on average, from the non-poor to the poor
in order to eradicate income poverty. The poverty gap ratio does not account for
inequality among the poor. To do so we must set the aversion parameter to values higher
than one. Thus setting a=2 produces the following estimator for aggregate poverty.
(3.15) P2 =imax[(x1xhPz)2,O]=(1-p/z)P+ PO
n h=
where tp and cyp stand respectively for average welfare of the poor and the standard
deviation of the welfare indicator among the poor. If everybody had a level of living
equal to the poverty line, the average welfare of the poor would be equal to z. The term
cp/z represents the coefficient of variation in these circumstances. The second expression
of P2 on the right hand side of (3.15) thus reveals clearly how this estimator takes into
consideration inequality among the poor.
The structure of the FGT family of poverty indicators reveals that a poverty
indicator translates the type of concerns policy makers have about aggregate poverty.
Typically, three dimensions are of interest: (i) incidence, (ii) intensity and (iii) inequality
among the poor. Incidence is the proportion of the total population living below the
minimum standard, while intensity (or depth) is the extent to which the well-being of the
poor falls below the minimum. Most poverty indicators are designed to capture at least one
of these three dimensions. Interestingly, there is a device known as the TIP curvel° which
provides a graphical summary of incidence, intensity and inequality dimensions of
aggregate poverty based on the distribution of poverty gaps (absolute or relative, Jenkins
and Lambert 1997:317). This curve is constructed in three steps: (1) rank individuals
from poorest to richest; (2) form the cumulative sum of the poverty gaps divided by
population size; and (3) plot the resulting cumulative sum of poverty gaps as a function
of the cumulative population share. Assuming that the n individuals in the population are
ranked from poorest to richest, then for all integers k¸n the TIP curve may be defined as
(Jenkins and Lamnbert 1997: 319):
(3.16) JL(p) = g; p=-; JL(O) = o
n'h=l n
It is clear from the above expression that the computation of the TIP curve is
analogous to that of the Lorenz curve. Figure 3.1 below shows a TIP curve for the
distribution of per capita expenditure in Guinea using the official poverty line set at
0 TIP stands for " three 'i's of poverty", that is incidence, intensity and inequality.
23
Guinean francs (GNF) 293,714 for 1994. This curve is based on normalized poverty gaps
obtained by dividing absolute gaps by the poverty line. The curve is an increasing
concave curve such that, at any given percentile, the slope is equal to the poverty gap for
that percentile. In the general framework defined by (2.1) and (3.12), the social weight
attached to a percentile is a monotonic transformation of the poverty gap. Thus the
curvature of the TIP curve reveals the underlying scheme of social weights. In this
normalized case, all weights vary from a maximum of 1 for lower ranking individuals to
a minimum of 0 for people above that poverty line. The closer the standard of living is to
zero the closer the social weight gets to one. The closer the standard of living is to the
poverty line, the closer the social weight is to zero.
Figure 3.1. A TIP Representation of Poverty in Guinea in 1994
.14
.12 -
.10-
.08 -
.06 -
.04 -
.02-
.00- I I I I I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
The curve represents simultaneously the three basic dimensions of aggregate
poverty as follows: (1) the length of the non-horizontal section of the curve reveals
poverty incidence (in figure 3.1, incidence equal about 40 percent); (2) the intensity
aspect of poverty is represented by the height of the curve; and (3) the degree of
concavity of the non-horizontal section of the curve translates the degree of inequality
among the poor. The use of relative poverty gaps allows us to read off the horizontal and
vertical axes, values of members of the FGT family. For Guinea, intensity is estimated at
13 percent about. This corresponds to the vertical intercept at p=1 in figure 3.1.
24
Box 3.1 Computing and Plotting a TIP Curve in EViews
INCLUDE LYCDF
LOAD %0
SMPL @ALL
CALL LYCDF({%1}(1), {%1)(2), {%1}(3))
SERIES GAP={%2}-YH
SERIES NGAP=GAP/{%2}
SERIES DUMGP=O
SMPL IF NGAP>O
DUMGP=1
SMPL @ALL
SCALAR POP=@SUM(POPH)
SERIES PH=F_HAT
SERIES WNGAP=(POPH*NGAP)/POP
SERIES TGAPW=DUMGP*(WNGAP)
SMPL @FIRST @FIRST
SERIES JPW= TGAPW
SMPL @FIRST+1 @LAST
JPW=JPW(-1) +TGAPW
SMPL @ALL
GROUPJC PH JPW
FREEZE(TIPC) JC.XY
'END OF PROGRAM
Jenkins and Lambert(1997) explain that if all absolute poverty gaps were equal
among the poor, the concave segment of the TIP curve would become a straight line with
slope equal z, the poverty line. In addition, there are maximum and minimum poverty
situations that set boundaries to the TIP curve in a manner analogous to a Lorenz curve.
The TIP curve would coincide with the horizontal axis if there were no poor in the
population under consideration. If all incomes (or expenditures) are equal to zero so that
the relative poverty gaps are all equal to one, the TIP curve would be a straight line from
the origin with a vertical intercept equal to 1 at p=l.
Table 3.4: Poverty in Guinea by Area of Residence
Poverty Conakry Other Urban Rural Guinea
Measure
Po 0.07 0.24 0.53 0.40
PI 0.01 0.07 0.18 0.13
P2 0.00 0.03 0.08 0.06
Source: Computed
The program in Box 3.1 was used to produce figure 3.1. It requires the user to fill in
the values of three arguments. The WORKFILE containing the relevant data, a GROUP
containing three series (total expenditure, the household size and the household weight), and
a SCALAR equal to the poverty line. The program can be easily edited to include formulae
25
for the three members of the FGT family discussed above. In the case of Guinea, we
obtained the following results by area of residence.
The results presented in table 3.4 reveal that, poverty in Guinea (as measured by
the FGT class of indices) is essentially a rural phenomenon. About 53 percent of the
rural population lived in poverty in 1994. The next poorest area consists of the urban
centers outside of the capital city, where poverty incidence is estimated at 24 percent.
Income poverty is lowest in the capital city of Conakry where incidence stood at 7
percent.
Sen 's Measure of Poverty
The FGT family of poverty indices relies on the coefficient of variation in order to
account for inequality among the poor. This dimension of poverty may be implemented
by combining truncation with the weighing scheme expressed by (2.4). If Gp represents
the Gini coefficient of the distribution of the living standard among the poor, according to
Sen (1997:173), the following expression is an indicator of welfare among the poor:
(3.17) w, =,u,(l-Gp)
It represents the level of per capita level of living, which, if enjoyed equally by every
poor person, would provide the same level of social well-being among the poor as the
current distribution.
Table 3.5. Guinea 1994: Inequality by Poverty Status
Aversion Sen Gini for Poor Gini for Non-Poor Overall Gini
1.00 0.13 0.00 0.00 0.00
1.50 0.16 0.10 0.23 0.28
2.00 0.18 0.16 0.32 0.40
2.50 0.19 0.21 0.37 0.47
3.00 0.20 0.25 0.40 0.52
3.50 0.21 0.27 0.42 0.55
4.00 0.21 0.30 0.44 0.58
4.50 0.22 0.32 0.45 0.60
5.00 0.22 0.34 0.46 0.61
5.50 0.23 0.35 0.47 0.63
6.00 0.23 0.36 0.48 0.64
Source: Computed
Sen (1997:173) proposes a poverty index that is analogous to the poverty gap
indicator of the FGT family. The only difference between the two is that Sen uses wp in
lieu of [tp. Hence the expression:
(3.18) 5 =P Pt12 wp 6
26
It is useful to recall the axioms underpinning Sen's poverty index: (l) focus; (2)
monotonicity; (3) weak transfer; (4) symmetry, (5) scale invariance. Focus requires that
the poverty measure depend only on the situation of the poor. The living conditions of
the non-poor are irrelevant. Monotonicity requires an increase in the poverty measure
whenever the well-being of the poor decreases. The weak transfer axiom makes the
measure sensitive to changes in the distribution of living conditions among the very poor.
Thus, if resources are transferred from one poor person to a relatively poorer one, the
weak transfer axiom implies that the poverty measure should decrease.
The extended Gini coefficient may be used in expression (3.18) to obtain an
extended version of Sen's poverty indicator written as follows.
(3.19) S(v) =PO [ - u,[I -GP(v)]]
Note that the generalized Sen index of poverty is analogous to the poverty gap ratio defined
by (3.14). In fact both indices are equivalent when the aversion parameter v=1. The results
presented in tables 3.4 and 3.5 confirm this fact for the case of the distribution of household
expenditures in Guinea in 1994. We note that S(1)=P=0.13. This observation suggests
another way of extending the Sen index of poverty. Instead of using the extended Gini to
measure inequality among the poor, one could use another index such as the Atkinson index
of inequality
Table 3.5 shows values of extended Sen index along with estimates for the extended
Gini coefficient for values of the aversion parameter ranging from 1 to 6. All indices
increase monotonically with v. The results also reveal that inequality is higher among the
non-poor than among the poor.
How Desirable is Truncation?
To be sure, both the FGT and Sen approaches to poverty analysis are consistent with
the maximin approach discussed in Section 2. Within that framework, social weights are
assigned to individuals on the basis of some notion of social desert. The more deserving the
individual the higher the social weight assigned to her/his situation. The Gini family of
indices implements this idea as follows. First, individuals are ranked in decreasing order of
social desert. Second, social weights are assigned according to (2.4) which describes each
weight as a function of the relative rank of the individual and the degree of inequality
aversion. As revealed by figure 2.1, the level of aversion for inequality implies a cut-off
rank such that people before it receive higher social weights than people after the cut-off
" The Atkinson index of inequality is also based on the concept of equally distributed equivalent (EDE)
welfare applied to a specific social welfare function. In this framework, the difference between average
welfare and the EDE welfare is considered as the per capita social cost of inequality. The Atkinson index
is equal to the per capita social cost divided by average welfare (See Larnbert 1993b:131-138) for
analytical details.
27
point. Our interpretation of expression (3.12) indicates that the FGT method does
something very similar subject to the following adjustments. First, the social weights are
now a function of the relative poverty gap. Second, the cut-offpoint is no longer tied to the
choice of the aversion parameter, it is imposed exogenously by the poverty line. Third,
everybody after the cut-off point now receives a weight of zero, regardless of her/his welfare
level. Similar considerations apply to Sen's index of poverty. We argue that the problem
here is not so much with the use of the poverty line as it is with ignoring every person
beyond the cut-off point.
It is evident that truncation implements Sen's interpretation of the focus
assumption. As mentioned above, this interpretation renders the living standard of the
non-poor irrelevant for the purpose of social evaluation. As argued in the beginning of
Section 2 of this paper, social evaluation is a critical input into public policy formulation
and implementation. Indeed any policy recommendation is constrained by such an
evaluative input, the reliability of which is determined by the organizing framework
(view of the world) and the quality of the data set to which the framework applies.
There are two basic approaches to policymaking that shape the informational
needs of the exercise. The normative approach seeks to maximize a social welfare
function subject to the economy's resource, technology and institutional constraints. In
the classical version, the resulting optimal program is supposed to be implemented by a
set of competitive and complete markets given the prevailing ownership of resources
(Dixit 1996: 4-5). In the context of the positive approach, policymaking is viewed as
involving strategic interactions among various socioeconomic agents subject to potential
conflict and cooperation. In this context, Aristotle is reported to have stated that "It is
when equal have or are assigned unequal shares, or people who are not equal, equal
shares, that quarrels and complaints break out." (Young 1994:64).
In the positive perspective, a policy may be viewed as a social contract among
participants which is enforceable within a given governance structure. Governance
structure involves three basic elements:(1) abstract and universal rules of the social game;
(2) enforcement institutions; and (3) mechanisms for the resolution of conflicts over both
the rules and their enforcement (Fristchtak 1994) 2. Any policy choice entails a
distribution of burdens and advantages that creates winners and losers. Governance
capacity is therefore the ability to coordinate the aggregation of these diverging private
interests into an outcome that can credibly be taken to represent public interest. This is a
key consideration in the investigation of political feasibility'3 of public policy. Such an
investigation pertains to the way gainers and losers form coalitions and use the political
system to their advantage. As Kanbur (1994:8) explains it, the outcome hinges crucially on
the threshold at which a gain or a loss becomes so significant that an individual or a group
12 This author further explains that governance capacity in a modem state may be assessed in
terms of the mere existence of such rules, institutions and mechanisms, and the degree to which they are
universal and predictable. Govemance capacity is also determined by the extent to which the state is
autonomous vis-a-vis private interests in society.
'3 Thus Kanbur (1994:4) explains that desirability is determined by welfare economics while feasibility
stems from political economy.
28
feels compelled to organize and fight. At this point it may be worth distributing real or
symbolic pay-offs to the losers in order to buy social peace.
The above political economy considerations suggest that truncation may be too
drastic an approach to poverty-focused evaluation. Such considerations imply that we
must not ignore the non-poor totally in our social calculus. The Dalton principle and its
implementation by the Gini family of indices offer a way out of drastic truncation. This
framework is consistent with a milder interpretation of the focus assumption which now
requires only that we assign higher weights to the welfare interest of the poor relative to
that of the non-poor. The particular range of social weights selection in the evaluation is
an outcome of the governing political process.
4. Impact Analysis
We view distributional impact as a comparison of social states based on the
associated distributions of pay-offs from socioeconomic interaction. In this Section, we
focus on the welfare impact of public policy. One particular state, known as the
counterfactual, plays a crucial role in the assessment of the impact of policy. By
definition, the counterfactual describes the state of the world that would have prevailed
had the policy in question not been implemented. Thus impact assessment involves the
comparison of two states of affairs: one with and the other without the policy. This
comparison will be based on the welfare criterion defined by (2.1). The discussion is
organized around three points:(l) social desirability of feasible policy reforms; (2)
unambiguous welfare comparisons; and (3) the use of abbreviated social welfare
functions.
Social Desirability of Feasible Policy Options
Policy design and evaluation involve a determination of desirable actions within a
feasible set. Considering the public budget as the policy instrument par excellence, the
set of feasible collective actions must be viewed as determined by the budgetary process
in the broadest sense of the term in order to capture the political economy dimension of
feasibility. To be concrete, we focus on commodity taxation and assume revenue
neutrality. Yitzhaki and Lewis(1996:543) argue that this assumption allows one to
ignore the issue of the optimal size of government activity. Social desirability of a
feasible action depends on the chosen social evaluation criterion or social welfare
function.
In general, the impact of a policy change on the welfare of individual h, may be
analyzed within the standard model of consumer behavior. The consumer is assumed to
choose the best bundle of commodity that she can afford. At the optimum, this behavior
can be characterized by the indirect utility function defined as follows:
(4.1) vh(q,yh )=max{uh(xh) st. q.xh =yh}
29
where q is a vector of consumer prices and yh is the income of consumer h. One can
invoke Roy's identity (Varian 1992: 106) to compute the impact of the policy on the
welfare of individual h as:
m
(4.2) dv" =-Oh( xhdqj)+dyh
j=1
Expression (4.2) above implies that the marginal impact, in terms of income, of a
unit increase in the tax on commodity j (assumed to be a private good) is given by the
following expression:
(4.3) mv j= - h _Xi
In the case of a tax increase, expression (4.3) measures the loss imposed on consumer h
as the consumption rate of commodity j. The total impact of a change in all commodity
taxes may now be expressed as:
m
(4.4) dvh =mvhdt =-xhdq
j=I j=1
The social impact of such a reform may be written as:
n n ~~~m
(4.5) dW= 33"dv" = hVh 3h xhdqj
h=l h.4 j=1
where ph is now the marginal social weight of the income of individual h. This
coefficient is defined as 8h _(aW) )
The change in social welfare induced by the tax reform may be transformed as
follows. First, we change the order of summation in (4.5), then we multiply by the
n
neutral element (xj/xj) where xj = Exi is the aggregate base of the tax on commodity j.
h=l
This transformation leads to the following expression:
m , phXh
(4.6) dW=-ExjE -w dqj
i h=1 Xi
To further apprehend the structure of the change in social welfare, we need to
consider the impact of the tax reform on the public budget. Government revenue is equal
to:
30
m
(4.7) B = Ztjxj(q,y)
j=I
where xj(q,y) is the demand for commodity j (the tax base) as a function of prices and
incomes. A small change in all taxes leads to the following change in government
revenue.
(4.8) dB tj rjdtj
Where r; is the marginal revenue associated with a change in the jlh tax. The marginal
tax reform may be characterized by a vector of tax changes dt, or by a vector of tax
revenues 6.
Revenue-neutrality implies that dB=O. Given that q is the vector of consumer
prices, we have dt=dq. According to (4.8), we may write dqj = Lj . This implies the
r.
following expression for the change in social welfare:
(4.9) dW = -E d
Three important parameters are embedded in the above expression. The first one reveals
the distributional characteristic of commodity j. The parameter is defined as (Mayshar
and Yitzhaki 1995:795):
e
flhxh
(4.10) DCj h=l 2 0
The second parameter is the marginal efficiency cost of funds collected through taxation
of commodity j. It is defined as:
(4.11) MECFj = X1 1 l 1
ri 1+- tk
xj k=1 8t1
Slemrod and Yitzhaki (2001:6) explain that this parameter is an indicator of the extent of
leakage from the tax base (hence efficiency cost) associated with adjustment in behavior
by the taxpayer in response to the change in tax burden. This may be thought of as an
31
incentive effect of the tax on j. The marginal efficiency cost is equal to the ratio of the
cost of funds to the taxpayers to the value of the funds going to the public treasury.
The third parameter is the marginal social cost of funds defined as follows:
fi a h hE x hx
(4.12) MSCFj = __ __ h- __ = Xj (
The above expression reveals that the marginal social cost of funds is equal to the
distributional factor times the marginal efficiency cost of raising funds through a tax on
commodity j.
It is instructive to note that the distributive component may also be written as
follows:
n n
XI6hx llnX/J6hXh
(4.13) DCj = _h __ h=1 ]6___j _6
When social weights are chosen according to (2.4), then we know that .1p=l and the
second term within the brackets is equal to minus the extended concentration coefficient
of commodity j. Therefore, the marginal social cost of funds for this commodity is equal
to:
(4.14) MSCFj = MECFj [1- Cj (v)] = MECFj [1- i7j (v)Gx (v)]
The impact of the tax change on social welfare is thus equal to:
m
(4.15) dW = -EMSCF, 5j
j=1
m
The policy option is feasible if dB = E,j > 0 has a nontrivial solution. It is socially
j=1
desirable if dW2O. The final determination rests on the specification of the social
weights ph. If we impose only minimal restrictions on social weights, then a wide class
of social welfare functions would agree on the characterization of the policy option. This
situation corresponds to dominance ranking. However, the selection of a unique set of
weights allows one to assess all policy options on the basis of the implied criterion.
Unambiguous Welfare Comparisons
As noted above, social desirability depends on the value judgments underpinning
the social welfare function. Such judgments can take the form of restrictions placed on
32
the social weights ph. Suppose that we adopt an individualistic welfare function of the
type defined by (2.1) subject to the restriction that Pbh 2 0 for each h. A Pareto-improving
tax reform would have to improve the welfare of at least one individual without hurting
any. This could be characterized in terms of (4.4) using the implication of (4.8) that
dqj =- . A Pareto-improving marginal tax reform must satisfy the following (n+l)
linear restrictions:
m m
(4.16) dB =Xj 2 0; dvh = Xh(x /xj)MECFjj ˇ 0 Vh
j=I j,=
The above expression reveals that the marginal impact of the reform on consumer h is
equal to minus the weighted sum of modified consumption shares. The weights are the
marginal tax receipts i, while the modified consumption share of each commodity are
obtained by multiplying each share by the corresponding marginal efficiency cost of
funds.
As noted in Section 2, the Dalton principle may be built in the social welfare
function by first ranking individuals according to some criterion of social desert, then
assigning social weights in such a way that of any two individuals the more deserving
receives a higher weight. To see clearly what is involved, consider a society of three
individuals ranked from the poorest to the richest. Under the Dalton principle, the pattern
of social weights is :PI1ˇ2i3P3. Given that social weights are now chosen such that each
is nonnegative and adjacent ones satisfy (p-I-Phb)>O it is desirable to express the welfare
improving condition in a way that is consistent with this restriction. Mayshar and
Yitzhaki (1995:797) show that a Dalton-improving policy may be characterized in tenns
of cumulative marginal impact.
The cumulative marginal impact is defined as:
(4.17) cmv =ZdvL; i = 1, 2, 3.
i=1
By definition, dvh = cmvh - cmvh'. The change in social welfare due to a marginal tax
reform is thus equal to:
3
(4.18) dW =/hdvh =(/, -32)cmv' +(,/32 _/ )cmv2 +/63cmv3
h=1
Expression (4.18) is a sum of cross products. The first term of each product is known to
be nonnegative. It is therefore clear that if the second term is also nonnegative the whole
sum will be nonnegative as well. The reform will be welfare improving (i.e. dW20) if
each cmvh >0. The condition for Dalton-improvement may thus be stated generally as:
33
m
(4.19) dB = E 5j 2 0; cmvh 2 0 Vh
j=1
The condition for Pareto-improvement implies that for a Dalton-improvement, but not the
other way around. Mayshar and Yitzhaki(1995:798) emphasize that, within this
framework, the social ranking is exogenous and need not be based on income. They
further note that when the ranking is based on income, the Dalton criterion is equivalent
to the second degree dominance criterion based on the generalized Lorenz curve.
To further expose the structure of the Dalton criterion, on the basis of (4.9) we
write the cumulative marginal impact as follows.
h m h
(4.20) cmv' =h dv' = - Si E(x';Ixj)MECFj
1=1 jI=1 1=1
In the above expression, the term (x; / xj )MECFj represents a point on the
i=l
concentration curve of commodity j scaled by that commodity marginal efficiency cost of
funds. Thus (4.20) shows that the design of a Dalton-improving indirect tax reform is
equivalent to searching for a vector 8 such that Yj8j2O and the 8-weighted sum of scaled
concentration curves for the commodities is everywhere non-positive' .
Let's now focus on the simple two-commodity case where commodity k is taxed
in order to subsidize the consumption of commodity s while keeping the public budget
balanced. The revenue neutrality constraint implies that (oS+8o=0. The condition for
Dalton-improvement may thus be written as:
h h
(4.21) _(x5 /Ix, Xk ), MECFk 5 0 Vh
Since o, is negative by assumption, the reform will be Dalton-improving if the modified
concentration curve for commodity s lies nowhere below that for commodity k. We may
say that commodity s Dalton dominates commodity k. If the two commodities happen to
have identical positive MECFs15, then we need only compare the ordinary concentration
curves. It is in fact the relative magnitudes of the MECFs that determine whether to use
14 Mayshar and Yitzhaki(1995: 800) propose the following algorithm in the case of strict revenue-
n ~~~~~~~~~2
neutrality. min [maxk- cmv' (3), 0)] st. , j = 0; 3, 0. A solution is achieved when the
J h=1 ~~~~~~~~j=1
objective function is equal to zero for nontrivial values of the vector 6. In fact the constraint that 8170 is
meant to avoid trivial solutions. The authors further explain that one must compute two sets of solutions
for positive and negative values of 6,. Since the scale of the reform can be set arbitrarily, this implies
checking solutions for 51=1 and for 51=-l. Finding a solution for these two values means that there exists a
Dalton-improving tax reform that does not involve a change in the tax rate of commodity 1.
15 Estimates of MECFs are known to be sensitive to changes in the structure of preferences (Mayshar and
Yitzhaki 1995:803).
34
the ordinary concentration curves or the modified ones. It is instructive to note that, if the
concentration curve of commodity s lies nowhere below the Lorenz curve of total
expenditure (or income), then a subsidy on this commodity financed by a proportional
income tax would increase welfare (Yitzhaki and Slemrod 1991: 486). In the same spirit,
Yitzhaki and Thirsk 1990:14) explain that a tax on wages may be interpreted as a tax on
all expenditures made by workers.
Finally, to focus only on efficiency considerations, we look at cmvn. In the case
of a revenue neutral reform involving two commodities, expression (4.20) implies that:
n
(4.22) cmv" = Xdvh = -(MECF, -MECFk)35 20
This expression reveals that the neutral tax reform involving a subsidy for commodity s
will reduce deadweight loss if MECFs>MECFk.
There is a necessary condition for Dalton improvement based on Gini elasticities
of the two commodities involved. Recall that if commodity s dominates commodity in
terms of expression (4.21), then it must be true that the area of concentration of s
multiplied by the marginal efficiency cost of s must be less than the area of concentration
of commodity k times its marginal efficiency cost. This condition may be stated in terms
of concentration indices as follows.
(4.23) - [C3 (v)MECF, - Ck(v)MECFk ] O 0
Based on definition (4.11), we write the ratio of the marginal efficiency coefficients as
_MECFk
aSk = . Using the definition of the Gini Engel elasticity, the necessary condition
-MECF,
for Dalton improvement can be expressed as:
(4.24) - [q, (v) - ask m7k(v)]GX (v) 2 0
This condition can be used to narrow down the set of commodities on which to perform
pairwise comparisons of modified concentration curves (Yitzhaki and Thirsk 1990:9).
When both commodities have identical MECFs, then the necessary condition for Dalton
improvement presented in (4.22) reduces to the following inequality: M (V) < 7k (V) .
Condition (4.21) can be verified graphically by plotting on the horizontal axis the
cumulative proportions of individuals in the income distribution, and on the vertical axis
the difference between the concentration curve of commodity s and the concentration
curve of commodity k, multiplied by ask. Yitzhaki and Slemrod(1991) call this the
DCC(p) curve (the "difference in concentration curves" curve). This curve starts at (0,0)
and ends at (1, 1- ao). If it lies everywhere above the horizontal axis, commodity s
dominates commodity k; if it is located entirely below the horizontal axis, then
commodity k dominates s. If the curve crosses the horizontal line, there is no dominance
to speak of.
35
The DCC(p) curve allows a combined presentation of both the efficiency gain
from the reform and its distribution among income groups. If the curve is increasing at p,
then individuals located at that percentile gain from the policy. If the curve is decreasing
then they are losing from the reform. DCC(1)=(1- ak) provides an indication of whether
the cumulative gain for the whole society is positive, zero or negative. The outcome
hinges on how ask compares to 1. When this ratio is equal to one, the policy reform is
neutral with respect to efficiency (no efficiency gain, nor loss). However, if the DCC(p)
curve lies above the horizontal axis for all other values of p, we conclude that the policy
is welfare improving (in the sense of Dalton) on account of distribution. When DCC(1)<
0 (implying that ask>l) condition (4.21) cannot hold for all h, since it fails to hold for
h=n.
It is useful to note that the same methodology can help analyze the case where a
subsidy is financed by a proportional income tax. In this case, we have to compare the
concentration curve for commodity s to the Lorenz curve of the income distribution.
Figure 4.1. Difference in Concentration Curves for Cereals and Beverages in Guinea 1994
.30-
.2 5-
.20-
.1 5 -
.00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
To illustrate the point, we compare the distributional characteristics of two
commodities, cereals and beverages, using data from the 1994 integrated household
survey from Guinea. Figure 2.2 shows the concentration curves of the two commodities
along with the Lorenz distribution of total household expenditure. It is evident from that
figure that the consumption of cereals in Guinea is more equally distributed than total
consumption and the consumption of beverages. Not having estimates for relative
efficiency costs, we proceed as if ask were equal to one (the case of neutrality vis-a-vis
efficiency). Under this assumption, we would expect welfare dominance to the extent
that the concentration curve for cereals lies totally above the concentration curve for
36
beverages over the entire range of the cumulative distribution of per capita expenditure.
Figure 4.1 confirms this view. It plots the difference between the concentration of the
consumption of cereals and that of beverages. The DCC curve lies entirely above the
horizontal axis, thus it would be socially desirable to implement a commodity tax reform
that would shift the tax burden away from cereals and towards beverages while keeping
the public budget balanced. In addition, figure 4.1 reveals that at least 85 percent of the
population would benefit from such a move.
It is useful to note the concept of TIP dominance in the context of truncated
analysis. Given a poverty line z, if a TIP curve a lies entirely over another TIP curve b,
we say that a TIP-dominates b. In other words, there is more poverty in situation a than
in situation b, regardless of the dimension we choose to focus on: incidence, intensity or
inequality among the poor, and for all poverty lines less than or equal to z.
Figure 4.2. A TIP Comparison of Poverty in Guinea by Area of Residence
(Data Source: 1994 Integrated Household Survey)
.20
Rural
.16 -
.1 2-
.08-
Other U rban
.04-
Conakry
.00- I , , I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Figure 4.2 illustrates the point with three TIP curves for three population sub-
groups in Guinea based on the area of residence of the household in 1994: (1) Conakry,
the capital city; (2) other urban centers and (3) the rural area. The dominance relation
among these curves reveals that, regardless of the dimension considered, poverty in
Guinea (as measured by the FGT class of indices) is essentially a rural phenomenon.
About 53 percent of the rural population lived in poverty in 1994. The next poorest area
consists of the urban centers outside of the capital city, where poverty incidence is
estimated at 24 percent. Income poverty is lowest in the capital city of Conakry where
incidence stood at 7 percent.
37
Our discussion of TIP curves focuses on the FGT class of poverty indices.
However it is worth noting that Jenkins and Lambert's (1997) results are more general.
Consider the class of Generalized Poverty Gap (GPG) poverty indices. The members of
this class are increasing Schur-convex' functions of absolute poverty gaps given the
poverty line. In addition, these indices are replication invariant. A sub-class of these
indices, GNPG, is defined on normalized poverty gaps (e.g. FGT). As it turns out, TIP
dominance based on absolute poverty gaps is equivalent to a unanimous poverty ordering
by all members of the GPG class, and for all poverty lines that are at most equal to the
chosen one17.
Use of Abbreviated Social Welfare Functions
Dominance criteria provide a general framework for identifying unambiguous
rankings of social states in terms of the distribution of the living standard. However, the
relation of dominance is a partial ordering in the sense that it could fail to rank two
situations. For instance when two concentration (or Lorenz) curves intersect, we loose the
ability to draw unambiguous conclusions about the inequality or welfare content of the
distributions under comparison.
Sen (1989: 18) explains that the dorminance approach to social evaluation provides a
minimal partial order on the focal space. The Pareto improvement test discussed above
(based on the social welfare function defined by 2.1) is an example of such a minimal
ordering to the extent that it requires only non-negative social weights. Sen (1989) also
explains that it is possible to go beyond the scope of this minimal order by further restricting
social weights to lie within a particular range. The Dalton criterion, for instance further
restricts the admissible range associated with the Pareto criterion. The narrower the range,
the more extensive the overall ranking will be in comparison to minimal dominance. A
social evaluation function based on a unique set of weights (e.g. 2.5) would induce a
complete ordering of socioeconomic states. The weights in question are a reflection of
the underlying value judgments. These value judgments determine the structure of index
numbers used to assess the inequality and social welfare effects of a policy based on induced
distributional changes. In the end, the selection of evaluative weights boils down to
priority setting among the different dimensions of the quality of life (e.g. components of
consumption) and among diverse individuals or groups (within resource and institutional
constraints). In this subsection we focus on index numbers based on the maximin principle,
and on normalized poverty gaps.
16 By analogy to Schur-concavity in the case of inequality and welfare which ensures that inequality falls
and welfare increased when the distribution of resources is "smoothed" by equalizing transfers, Schur-
convexity require that poverty fall when poverty gaps are smoothed (Jenkins and Lambert 1997).
17 Jenkins and Lambert(1997) also reveal a close link between the poverty orderings based on TIP
dominance and those associated with generalized Lorenz dominance. They show that distribution a
dominates distribution b on the basis of the generalized Lorenz curve if and only if the TIP curve for b lies
nowhere below that of a, for all common poverty lines z. The generalized Lorenz curve is equal to the
ordinary Lorenz curve times the mean of the corresponding distribution.
38
Changes in the Abbreviated Social Welfare Function
When an economy undergoes a shock (exogenous or policy), its structure and the
implied distribution of welfare may change significantly. In the particular case of policy
reform, the desirability and feasibility of a policy proposal depend essentially on the
implications of the proposal for efficiency and equity. We may used the abbreviated
social welfare function defined by (2.5) to track the effects of a policy. To simplify
matters, we focus the analysis at the margin. Consider therefore the enactment of a
policy that leads to marginal changes (dxn) in the living standard of the population
involved. The logic behind expression (2.5) leads us to the following assessment of the
induced welfare impact.
l n
(4.25) dV(v) =-, w' (v)dx4 = Hla + v cov[a,(l -p)]
n h=1
where a stands for the distribution of marginal benefits induced by the reform.
The above expression is equivalent to the following'8:
(4.26) dV(v) = Iia [1- Ca (v)] = Ia [1- 7a (v)G. (v)]
where 17a (v) = G ( ) is the ratio of the concentration of marginal benefits to the overall
Gx (v)
Gini index of inequality in the distribution of the living standard prior to the reform.
Expression (4.26) shows that a first-order assessment of the welfare impact of a
policy reform within the maximin framework can be based on three parameters: (1) the
average marginal benefit of the reform (ta), (2) the overall Gini index of inequality Gl(v)
and (3) the Gini Engel elasticity of the marginal benefit of the reform la(v). A Gini
Engel elasticity greater than one means that the distribution of marginal benefits is more
unequal than the initial distribution of the living standard. Therefore the reform is
inducing more inequality. This distributional effect will lower welfare. The overall
impact depends on the sign and size of the average benefit.
When the living standard is composed of different components, we may be
interested in welfare changes due to a change in one component. Kakwani(1995:5)
provides a way of computing the elasticity of V(v) with respect to the mean of the jlh
component.
(4.27) SK ,j [l - G(v)] + j [G(v) - Cj (v)] X G(v) - Cj (v) 1 - [1 pK (v]
J ~~~~u[l - G(v)] + 1-G(v)
According to Kakwani(1995:5) this elasticity, which measures the effect of a change in the
jlh income component on total welfare and may be interpreted as the sum of the "income"
and the inequality effect. The income effect is equal to the share of the component in total
expenditure (or income) Xj, while the inequality effect is equal to this share times a
18 The expression is obtained by factoring out pa and multiplying the resulting concentration coefficient by
the neutral element [GX(v)/Gx(v)]. Also note the analogy between this expression and that of the marginal
social cost of funds (4.14).
39
progressivity index denoted by PK (v). A positive value of this index means that the
change in the jth component is progressive in the sense that it favors the poor more than the
rich. A negative value implies regressivity. If the change in the jlh income component is
distributed in proportion to total income, its concentration index will be equal to the Gini
index and the progressivity index will be zero. In this case neither the rich nor the poor are
favored. This progressivity index may guide the design of an optimum tax (or expenditure)
policy. The methodology described here may also be used to evaluate the effect of price
changes on total welfare
Poverty Impact
One may be interested in analyzing the poverty impact of policies and shocks
based on poverty indices such as those of the FGT family. As a general rule, the poverty
impact of a policy depends on the degree of targeting. Options range from perfect
targeting to no targeting at all. In the extreme case of no targeting, any effect of policy
on the poor is linked to the "trickle down mechanism". However, policy makers may
resort to a coarser approach to targeting based on a broad definition of population
subgroups (Kanbur 1987a:72). Such policies will affect both the poor and the non-poor
within the targeted socioeconomic group. For instance, price support for a particular crop
will affect both poor and non-poor farmers engaged in the cultivation of the crop. A
subsidy on a particular food item will affect all those who are consuming it. At the
margin, such an analysis relies on the derivatives of the poverty indices used with respect
to changes in the welfare indicator. For the FGT family of indices, the first derivative of
the poverty gap with respect to the welfare indicator is equal to:
(4.28) 8xFGT - mi a (1- Xh /Z-l o
aXh 1z)'1
and the second derivative is:
(4.29) a2 VFGT max{ _(a ) Xh- /-Z)al a >1
For positive values of the aversion parameter, these derivatives indicate that members of
the FGT family of indicators are non-decreasing convex functions of the welfare
indicator.
Kanbur(1987a:73) notes that a policy may have either an additive or a
multiplicative effect on the level of individual welfare. Consider first the additive case.
Policy implementation changes all levels of welfare to (xh+t), so that individual poverty
19 See Kakwani (1995:5-7) for details
40
gaps are now equal to: yIFGT (Z, X, a) = max {(1 - (xh + t) / z)a,0} . This implies the
derivative of the poverty gap with respect to t is equal to:
dFGT - min.{--(1 - (XI + t) / z)a ,0}
dt +t/z 'O}
This suggests that the derivative of the average poverty gap with respect to t is equal to:
dP, a aI~ a
(4.30) dt = _x ( _- max[(1 -(xh +t)/z),O]) = --P
Kanbur interprets this expression as the shadow price of budgetary expenditure when one
is seeking to minimize Pa subject to a budgetary constraint. When a=1, the amount by
which poverty intensity changes when the welfare indicator increases marginally is
proportional to the head count ratio, i.e. Po.
If policy implementation has a multiplicative effect such that post policy welfare
is equal to (1+t)xh, then it can be shown that the derivative of the average poverty gap is
equal to:
(4.31) ~dP. a (Jp _Pa<
(4.31) dt 1+t al_ ).
Pa ~~~~ZPa
On the basis of expressions (4.35) and (4.36) the total impact of growth and redistribution
on income poverty may be written as:
(4.37) dP d,u + dG
(4.37) ~~P =1p I
Ravallion (1994b) argues that the above decomposition may lead to large errors in
the case of big discrete changes. A different approach is therefore required. Instead of
summarizing inequality by the Gini index, one may use a parameterized Lorenz curve
along with the mean income to decompose changes in poverty into growth and inequality
components, and a residual".
20 Ravallion and Datt (1992) note that the existence of this residual depends on whether or not the poverty
index is additively separable between the mean and the Lorenz curve. The residual would vanish if the
mean income or the Lorenz curve remained constant over the decomposition period.
42
The growth-inequality relationship thus seems fundamental in analyzing the
dynamics of poverty. If growth is distributionally neutral, poverty is expected to be
reduced on such a path21. If one drops the neutrality assumption, then the outcome
becomes ambiguous. In this case the distributional impact and the poverty implications
depend essentially on the initial structure of the economy and the. profile of the
adjustment process.
5. Conclusion
This paper sought to demonstrate how one might perform distributional impact
analysis within a poverty-focused evaluative framework. The approach is illustrated with
household level data from Guinea, using EViews as a computing platform. The focus on
poverty is important for at least two reasons. Widespread poverty in the developing
world remains a serious challenge for the development community. Furthermore, the
ethics of empowerment which underpins current development thought entails the
expansion and the distribution of socioeconomic opportunities with implications for
individual and collective well-being. These considerations have prompted the
development community to make poverty reduction a fundamental objective of
socioeconomic development, and a benchmark measure of the performance of various
social arrangements. In this context, poverty is seen as the deprivation of basic
capabilities to lead the type of life one has legitimate reasons to value.
Any evaluation is characterized by the underlying criterion. The object of social
evaluation is the determination of the extent to which prevailing social arrangements
promote individual and collective well-being. This requires identification of the objects
of value, and an aggregation rule for the comparison of social states. The need for
aggregation raises the fundamental issue of weights to attach to each constituent of the
aggregate. The choice of social weights is based on value judgments. If one believes that
an incentive-preserving transfer of resources from rich to poor would increase collective
well-being, then the maximin principle provides an adequate foundation to a poverty-
focused evaluation. When implemented in the context of additively separable social
welfare functions, the principle leads to social evaluation functions that are decomposable
into two components revealing both the average living standard and its distribution
among the population. The distribution component is equal to the covariance between
the living standard and the social weights. Thus, the maximin approach to social
evaluation offers a way of combining both efficiency and equity considerations in social
evaluation. In addition, the linearity of the covariance operator allows a factor
decomposition of the inequality components on the basis of the constituents of the living
standard.
Further specification of social weights is needed to determine the extent of
poverty focus of the evaluation. The Gini family of indices provides a weighing scheme
based on relative ranks of individuals (according to some criterion of social desert), and
on a focal parameter indicating the degree of aversion to inequality. This aversion
21 The time frame is important in this context as we should distinguish between short and long-run impacts
associated respectively with fluctuations in output, and steady-state growth in capacity output.
43
parameter also determines a cut-off rank such that people below the cut-off point receives
higher weights than people above it. In that sense, the standard approach to poverty
analysis based on the truncation of the distribution of the living standard by a poverty line
is quite consistent with the maximin approach. However, this truncation appears
undesirable on political economy grounds.
The criterion presented in this paper can guide the identification of desirable
policy options. This entails a ranking of social states on the basis of the values assumed
by the criterion in each state. The scope of the ranking depends on the acceptable range
assigned to social weights. This range is a reflection of the extent of the restrictions
placed on the social weights. The milder the restrictions, the more robust the. implied
comparisons. This is the essence of the dominance approach to evaluation based on the
comparison of distribution functions. When dominance fails, one can resort to
abbreviated social welfare functions. Such functions usually translate the concept of
equally distributed equivalent (EDE) welfare. Gini-based evaluation functions
incorporate a focal parameter that summarizes the underlying value judgments. This
parameter can be used in sensitivity analysis.
In the end, the selection of evaluative weights boils down to priority setting
among the different dimensions of the quality of life and among diverse individuals or
groups (within resource and institutional constraints). The maximin approach illustrates
the link between social weights and the underlying value judgments. It is important to
note that in the selection of evaluative weights, one has a choice between a technocratic
and a democratic approach (Sen 1999). The ethics of empowerment imply a
determination of explicit evaluative weights from a participatory approach based on open
public debate involving all concerned. This seems to be one of the sure ways to detect
the value system that commands respect among the participants in the relevant social
arrangement.
44
References
Anand, S. 1983. Inequality and Poverty in Malaysia: Measurement and Decomposition.
Oxford: Oxford University Press.
, and Ravallion. 1993. Human Development in Poor Countries: On the Role
of Private Incomes and Public Services. Journal of Economic Perspectives. Vol.
7, No.l: 133-150.
Atkinson, A. B. 1970. On the Measurement of Inequality. Journal of Economic Theory,
2, 244-263.
, and Bourguignon, F. 1987. Income Distribution and Differences in
Needs. In G. R. Feiwel (ed.) Arrow and the Foundations of the Theory of
Economic Policy. London: Macmillan.
Becker, Gary, S. 1995. Human Capital and Poverty Alleviation. Human Resources
Development and Operations Policy Working Paper No. 52. Washington, D.C:
The World Bank.
Blackwood, D. L. and Lynch, R.G. 1994. The Measurement of Inequality and Poverty: A
Policy Maker's Guide to the Literature. World Development, Vol. 22, No. 4, 657-
578.
Callan, T. and Nolan, B. 1991. "Concepts of Poverty and the Poverty Line." Journal of
Economic Surveys, Vol. 5, No.3, 243-261.
Chotikapanich Duangkamon and Griffiths William. 2001. On Calculation of the
Extended Gini Coefficient. Review of Income and Wealth. Series 47, Number 4:
541-547.
Cowell, Frank, A. 1995. Measuring Inequality. London: Prentice Hall.
Coulter, F.A., Cowell, F. A. and Jenkins, S.P. 1992. Differences in Needs and the
Assessment of Income Distributions. Bulletin of Economic Research, 44: 77-124.
Dahlby, Bev. 1998. Progressive Taxation and the Social Marginal Cost of Public Funds.
Journal of Public Economics, 67: 105-122.
Dardadoni, V. and Lambert, P.J. 1988. Welfare Rankings of Income Distributions: A
Role for the Variance and Some Insights for Tax Reform. Social Choice and
Welfare., 5,1-17.
Dasgupta Partha. 2000. Valuation and Evaluation. In Osvaldo Feinstein and Robert
Piccio-tto (eds), "Evaluation and Poverty Reduction: Proceedings from a World
Bank Conference". Washington, D.C.: The World Bank.
45
Datt, G. 1998. Computational Tools for Poverty Measurement and Analysis. Food
Consumption and Nutrition Division (FCND) Discussion Paper No. 50.
Washington: International Food Policy Research Institute.
Deaton, A. 1997. The Analysis of Household Surveys: A Microeconometric Approach
to Development Policy. Baltimore: The John Hopkins University Press.
Dixit, A. K. 1996. The Making of Economic Policy: A Transaction-Cost Politics
Perspective. Cambridge (Massachussets): MIT Press.
Duclos, Jean-Yves. 2000. Gini Indices and the Redistribution of Income. International
Tax and Public Finance, 7: 141-162.
Ebert, Udo. 1997. Social Welfare when Needs Differ: An Axiomatic Approach.
Economica 64, 233-244.
Essama-Nssah, B. 2000. Inegalite, pauvrete et bien-etre social: Fondements analytiques
et normatifs. Brussels: De Boeck Universit6.
1999. Designing a Socioeconomic Policy for Poverty Reduction.
Lecture prepared for presentation at the Department of Sociology, the College of
Arts and Sciences, American University, Washington, DC. (March)
Fields, G. S. 2001. Distribution and Development: A New Look at the Developing
World. New York: Russell Sage Foundation.
_ 1980. Poverty, Inequality and Development. Cambridge: Cambridge
University Press.
Foster J., Greer, J. and Thorbecke, E. 1984. A Class of Decomposable Poverty
Measures. Econometrica, Vol. 52, No.3, 761-766. (May).
Frischtak, Leila L. 1994. Governance Capacity and Economic Reform in Developing
Countries. World Bank Technical Paper, no. 254. Washington, D.C.: The World
Bank.
Garner, Thesia I. 1993. Consumer Expenditures and Inequality: An Analysis Based on
Decomposition of the Gini Coefficient. The Review of Economics and Statistics
75: 134-138.
Huang, Chi-fu, and Litzenberger. Robert H. 1988. Foundations for Financial
Economics. Englewood (New Jersey): Prentice Hall.
Jenkins, S. 1991. The Measurement of Income Inequality. In Lars Osberg (Ed.)
Economic Inequality and Poverty: International Perspectives. Armonk (New
York): Sharpe.
46
, and Lambert, Peter J. 1997. Three 'I's of Poverty Curves, with Analysis of
UK Poverty Trends. Oxford Economic Papers, 49: 317-327.
Kakwani, Nanak. 1999. Inequality, Welfare and Poverty: Three Interrelated Phenomena.
In Jacques Silber (ed.) "Handbook of Income Inequality Measurement'. Boston:
Kluwer Academic Publishers.
. 1995. Income Inequality, Welfare and Poverty: An Illustration Using
Ukrainian Data. Washington: Banque mondiale. Document de travail de
Recherche sur les politiques, no 1411.
. 1990. Poverty and Economic Growth with Application to C6te d'Ivoire, Living
Standards Measurement Study Working Paper No. 63, Washington: Banque
mondiale.
Kanbur, S. M. R. 1994. Welfare Economics, Political Economy, and Policy Reform in
Ghana. Policy Research Working Paper No. 1381. Washington, D.C.: The World
Bank.
_ 1987a. Measurement and Alleviation of Poverty with an Application
to the Effects of Macroeconomic Adjustment. IMF Staff Papers.
1987b. Structural Adjustment, Macroeconomic Adjustment and
Poverty: A Methodology for Analysis. World Development, Vol. 15, No. 12:
1515-1526.
Lambert, Peter J. 1999. Redistributional Effects of Progressive Income Taxes. In
Jacques Silber (ed.) "Handbook of Income Inequality Measurement". Boston:
Kluwer Academic Publishers.
_ 1993a. Evaluating Impact Effect of Tax Reforms. Journal of Economic
Surveys, vol. 7, No. 3, 205-242.
1993b. The Distribution and Redistribution of Income: A Mathematical
Analysis. Manchester: Manchester University Press.
and Aronson, J. R. 1993. Inequality Decomposition Analysis and the Gini
Coefficient Revisited. The Economic Journal, 103, 1221-1227. The Royal
Economic Society.
Leibbrandt, M. V., Woolard, C. D. and Woolard, I. D. 1996. The Contribution of
Income Components to Income Inequality in South Africa: A Decomposable Gini
Analysis. Living Standards Measurement Study. Working Paper No. 125.
Washington: Banque mondiale.
Lerman, R. I. anid Yitzhaki, S. 1994. Effect of Marginal Changes in Income Sources on
U.S. Income Inequality. Public Finance Quarterly, Vol. 22, No. 4, 403-417.
47
_ 1989. Improving the Accuracy of Estimates of Gini Coefficients. Journal
of Econometrics, 42, 43-47.
. 1985. Income Inequality Effects by Income Source: A New Approach
and Applications to the United States. Review of Economics and Statistics, 67,
No. 1, 151-156 (February).
_ 1984. A Note on the Calculation and Interpretation of the Gini Index.
Economics Letters 15, 363-368.
Mayshar, Joram and Yitzhaki, Shlomo. 1996. Dalton-Improving Tax Reform: When
Households Differ in Ability and Needs. Journal of Public Economics, 62: 399-
412.
. 1995. Dalton-Improving Indirect Tax Reform.
The American Economic Review, Vol. 85, No. 4: 793-807.
Milanovic Branko and Yitzhaki Shlomo. 2002. Decomposing World Income
Distribution: Does the World Have a Middle Class? Review of Income and
Wealth, Series 48, No. 2 (June): 155-178.
Podder, N. 1993. The Disaggregation of the Gini Coefficient by Factor Components and
its Applications to Australia. The Review of Income and Wealth, Series 39, No. 1,
51-61, (March).
Quantitative Micro Software (QMS). 2000a. EViews : User's Guide. Irvine CA: QMS.
. 2000b. EViews: Command and Programming
Reference. Irvine CA: QMS.
Ravallion, Martin. 1994a. Poverty Comparisons. Chur (Suisse): Harwood Academic.
_ 1994b. Decomposing Changes in Poverty Measures: A Comment on
Kakwani. Washington: World Bank (mimeo).
. and Datt, G. 1992. Growth and Redistribution Components of Changes in
Poverty Measures: A Decomposition with Applications to Brazil and India in the
1980s. Journal of Development Economics 38, 275-295.
, and Huppi Monika. 1991. Measuring Changes in Poverty: A
Methodological Case Study of Indonesia during an Adjustment Period. The
World Bank Economic Review, Vol. 5, No.5: 57-82.
Roemer, John E. 1998. Equality of Opportunity. Cambridge, Massachusetts: Harvard
University Press.
Sah, Raaj K, and Stiglitz, Joseph E. 2002. Peasants Versus City-Dwellers: Taxation and
the Burden of Economic Development. Oxford: Oxford University Press.
48
Sen, A. 2000. Social Justice and the Distribution of Income. In Anthony B. Atkinson
and Francois Bourguignon (eds.) "Handbook of Income Distribution, Volumel.
Amsterdam: Elsevier.
_ ._ 1999. Development as Freedom. New York: Alfred A. Knopf
1997. On Economic Inequality (Expanded edition with a substantial annexe
by James E. Foster and Amartya Sen). Oxford: Clarendon Press.
1995. Inequality Reexamined. Cambridge, Massachusetts: Harvard
University Press.
_ 1989. The Concept of Development. In Hollis Chenery and T.N.
Srinivasan (eds), Handbook of Development Economics, Vol. 1. Amsterdam:
Elsevier.
. et al. 1987. The Standard of Living. Cambridge: Cambridge University Press.
Shorrocks, A. F. 1983. Ranking Income Distributions. Economica 50, 1-17.
, and Foster, J. 1987. Transfer Sensitive Inequality Measures. Review of
Economic Studies, 54, 485-497.
Slemrod Joel and Yitzhaki Shlomo. 2001. Integrating Expenditure and Tax Decisions:
The Marginal Cost of Funds and Marginal Benefits of Projects. Working Paper
8196. National Bureau of Economic Research (NBER).
_ 1996. The Costs of Taxation and the Marginal
Efficiency Cost of Funds. IMF Staff Papers. Vol. 43, No.1: 172-198.
Stark, Oded, Taylor, J.E. and Yitzhaki, S. 1988. Migration, Remittances and Inequality:
A Sensitivity Analysis Using the Extended Gini Index. Journal of Development
Economics 28, 309-322.
Stem, Nicholas and Stiglitz, Joseph E. 2000. A Framework for a Development Startegy
in a Market Economy. In Edmond Malinvaud, Jean-Claude Milleron, Mustapha
K. Nabli, Amartya K. Sen, Ariun Sengupta, Nicholas Stem, Joseph E. Stiglitz,
and Kotaro Suzumura (eds.), "Development Strategy and Management of the
Market Economy". Volume 1. Oxford: Oxford University Press.
Varian, Hal R. 1992. Microeconomic Analysis. New York: Norton & Company.
Wodon, Quentin T. 1999. Between Group Inequality and Targeted Transfers. Review
of Income and Wealth, Series 45, No.1 (March): 21-39.
Wolfensohn, James D. 1999. A Proposal for a Comprehensive Development Framework
(A Discussion Draft). Washington, D.C.: The World Bank.
49
1998. The Other Crisis. Address to the Board of Governors
(October 6). Washington D.C.: The World Bank.
World Bank. 2000. World Development Report 2000/2001: Attacking Poverty. Oxford:
Oxford University Press.
_ 1997. Guinea: A Socioeconomic Assessment of Well-Being and Poverty.
Institutional and Social Policy Unit and Country Department 16, Report
No. 16465-GUI.
Yitzhaki, Shlomo. 2002. Do We Need a Separate Poverty Measurement? European
Journal of Political Economy. Vol. 18: 61-85.
_. 2001. A Public Finance Approach to Assessing Poverty Alleviation.
National Bureau of Economic Research, Working Paper 8062.
_ 1994a. "On the Progressivity of Commodity Taxation", in Wolfgang
Eichhorn (Eds) Models and Measurement of Welfare and Inequality, Heidelberg:
Springer-Verlag.
1994b. Economic Distance and Overlapping of Distributions. Journal of
Econometrics, 61: 147-159.
. 1990. On the Effect of Subsidies to Basic Food Commodities in Egypt.
Oxford Economic Papers, 42: 772-792.
_ 1983. On an Extension of the Gini Index of Inequality. International
Economic Review, Vol. 24, No.3, 617-628.
1982. Relative Deprivation and Economic Welfare. European
Economic Review, 17, 99-113.
, and Lewis, Jeffrey, D. 1996. Guidelines on Searching for Dalton-
Improving Tax Reform: An Illustration with Data from Indonesia. The World
Bank Economic Review, Vol. 10, No. 3, 541-62.
, and Slemrod, Joel. 1991. Welfare Dominance: An Application to
Commodity Taxation. The American Economic Review, Vol. 81, No. 3: 480-
496.
, and Lerman, Robert I. 1991. Income Stratification and Income
Inequality. Review of Income and Wealth, Series 37, No. 3 (September): 313-
329.
, and Thirsk, W. 1990. Welfare Dominance and the Design of Excise
Taxation in the C6te d'Ivoire. Journal of Development Economics, 33,1-18.
Young, H. Peyton. 1994. Equity: In Theory and Practice. Princeton: Princeton
University Press.
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