Integrating Inter-Personal Inequality in Counting Poverty
Indices: The Correlation Sensitive Poverty Index Nicole Rippin 24
June 2014
Slide 2
Deutsches Institut fr Entwicklungspolitik (DIE)2 Outline
I.Introduction II.The identification of the poor III.The
aggregation of the individual characteristics of the poor in the
ordinal framework III.I The Multidimensional Poverty Index (MPI)
III.II The Correlation Sensitive Poverty Index (CSPI) IV.Empirical
application V.Conclusion I. Introduction II. The Identification
Step III. The Aggregation Step IV. Empirical Application V.
Conclusion
Slide 3
Deutsches Institut fr Entwicklungspolitik (DIE)3 Insufficient
income has for a long time been considered to be a good proxy for
poverty in all its various facets. The income approach, however,
relies on critical assumptions: Over time, serious concerns have
been raised regarding the appropriateness of these simplifying
assumptions (e.g. Rawls, 1971; Sen 1985, 1992; Drze and Sen, 1989;
UNDP, 1997). Economic Resources Assumption: equal individual
conversion factors Ignoring in particular: -Personal
heterogeneities -Variations in physical environment -Differences in
social climate UtilityGoods Assumption: perfect and complete
markets Ignoring in particular: -The role of public goods -Limited
access -Asymmetric information ChoiceConversion Introduction I.
Introduction II. The Identification Step III. The Aggregation Step
IV. Empirical Application V. Conclusion
Slide 4
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion It was Amartya Sen, who developed a new
approach to measure poverty and welfare: the capability approach
(1979, 1985, 1992, 1999, 2009). Thus, the capability approach
implies a multidimensional approach to poverty measurement.
Economic Resources Assumption: equal individual conversion factors
Ignoring in particular: -Personal heterogeneities -Variations in
physical environment -Differences in social climate Utility Goods
Assumption: perfect and complete markets Ignoring in particular:
-The role of public goods -Limited access -Asymmetric information
ChoiceConversion Capability Set Functioning Bundle Choice
Introduction 4
Slide 5
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion Empirical evidence demonstrates that
considerable population shares might be multidimensional poor but
not income poor, and vice versa (e.g. Klasen, 2000). Already a
strong trend in the last decade, multidimensional poverty
measurement has been given a further boost through the introduction
of the first internationally comparable Multidimensional Poverty
Index MPI (Alkire and Santos, 2010). However, in the
multidimensional framework inequality does not only exist within,
but also across dimensions; consequently there exists a tension
between the two concepts of distributive justice and efficiency
that does not exist in the one-dimensional framework: [A]n attempt
to achieve equality of capabilities without taking note of
aggregative considerations can lead to severe curtailment of the
capabilities that people can altogether have (Sen, 1992).
Introduction 5
Slide 6
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion In the ordinal context, inequality across
dimensions is usually considered as the spread of simultaneous
deprivations across the population, thus only accounting for
distributive justice. This work suggests to define inequality
across dimensions as the correlation-sensitive spread of
simultaneous deprivations across the population. This rigour
definition accounts for the tension between the two concepts of
distributive justice and efficiency that Sen mentioned and has
strong implications on the identification of the poor and the
aggregation of individual poverty characteristics. Introduction
6
Slide 7
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 7 Theoretical Background represents a set
of n persons represents a set of k poverty attributes K represents
the respective vector of threshold levels + K represents a vector
of weights such that K represents the achievement vector of person
i Person i is deprived with respect to attribute j if represents
the deprivation vector of person i such that if and if For any ,
the deprivation matrix is denoted by + NK A poverty index is
defined by Society A has higher poverty than society B if and only
if P ( X A ) P ( X B ) is the weighted sum of deprivations of
person i
Slide 8
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 8 Let be an identification function so
that person i is poor if and not poor if Three specifications for
have been suggested so far: According to the union method,
deprivation in one attribute is deprivation in all attributes
(perfect complements): According to the intersection method,
poverty only occurs when there is deprivation in all attributes
(perfect substitutes): Union and Intersection Method
Slide 9
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 9 Intermediate Method (Dual Cut-Off) In
response to the limited practicability of union and intersection
method, the idea of an intermediate approach was brought up by Mack
and Lindsay (1985) and formally introduced by Foster (2007) and
Alkire and Foster (2007, 2011). According to the intermediate
method, individual i is poor if the weighted sum of deprivations is
higher than a predetermined minimum level: The intermediate method
provides a practicable solution, the theoretical justification is,
however, questionable: up to the cut- off, attributes are
considered to be perfect substitutes, from the cut-off onwards,
however, the very same attributes are considered to be perfect
complements. There is another way to identify the poor that can be
derived directly from the aggregation step by fully accounting for
the two concepts of distributive justice and efficiency.
Slide 10
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 10 The Equality-Promoting Change 10 For
any and X, is obtained from X by an equality-promoting change, if
for some individuals g and h, and A distributional change is said
to be equality-promoting whenever the difference in the number of
simultaneously suffered deprivations between two individuals is
reduced Based on Chakravarty and DAmbrosio (2006), Jayaraj and
Subramanian (2010) introduced the equality-promoting change in
order to capture inequality across dimensions: Jayaraj and
Subramanian (2010) then formulated the axiom Nonincreasingness
under Equality-Promoting Change: For any and X, if is obtained from
X by an equality-promoting change, then The axiom captures
distributive justice, yet it neglects efficiency by disregarding
possible correlations between attributes.
Slide 11
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 11 The Inequality Increasing Switch
Depending on the nature as well as the strength of the correlations
between attributes, poverty might very well increase under an
equality-promoting change. Thus, I introduce the concept of an
inequality increasing switch: Define Then, for two individuals g
and h such that, matrix X is said to be obtained from matrix by an
inequality increasing switch of attribute l if and An inequality
increasing switch is a switch of attributes that increases
(reduces) the number of deprivations suffered by the person with
higher (lower) initial deprivation Duclos, Sahn and Younger (2006)
for instance argue that complementarities exist between the two
poverty dimensions education and nutrition as better nourished
children learn better. If the degree of complementarity is strong
enough, poverty decreases with increasing inequality.
Slide 12
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 12 A New Axiom Based on this concept I
formulate the axiom Sensitivity to Inequality Increasing Switches:
For any and X, if is obtained from X by an inequality increasing
switch of non-complementary attributes, then Further, if is
obtained from X by an inequality increasing switch of complement
attributes, then Example: i = 2, j = 5, z = (1 1 1 1 1)
Slide 13
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 13 A New Class of Ordinal Poverty Indices
The new axiom directly implies a new multiple step identification
function that is nondecreasing in the number of deprivations and
has a nondecreasing (nonincreasing) marginal in case attributes are
considered to be substitutes (complements). The former accounts for
distributive justice, the latter for efficiency. Property 1 A
multidimensional poverty measure P satisfies AN, NM, MN, SF, PP,
FD, SD and SIIS if and only if for all and X : with non-decreasing
in and a nondecreasing (nonincreasing) marginal in case attributes
are considered to be substitutes (complements).
Slide 14
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 14 A New Identification Function Consider
the following multiple step identification function: 1 1 0 min IM 1
min IS 1 1 1 max min U The relationship between distributive
justice and efficiency is determined by an indicator for inequality
aversion: alpha In case, approximates a concave shape: as already
the loss in one attribute can barely be compensated, there is no
need for a strong focus on inequality In case, approximates a
convex shape: the loss in one attribute can easily be compensated,
there is a need for a strong focus on inequality
Slide 15
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 15 The Correlation Sensitive Poverty
Index (CSPI) For the empirical application, I introduce the
Correlation Sensitive Poverty Index (CSPI), a simple form of the
new class of correlation sensitive poverty measures: Different from
any other additive/counting index, the CSPI can be decomposed into
a product of poverty incidence, intensity and inequality: The
headcount ratio measuring poverty incidence; the aggregate
deprivation count ratio measuring poverty intensity; and the
Generalized Entropy inequality index of deprivation counts
measuring inequality.
Slide 16
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 16 The Multidimensional Poverty Index
(MPI) The MPI extracts information on simultaneous deprivations but
only to verify whether a household is poor or not, afterwards this
information is disregarded. In the following I will compare the
CSPI with the Multidimensional Poverty Index (MPI): with if and
otherwise In other words, the MPI completely neglects inequality
across dimensions: it assumes that poverty attributes are not
correlated at all (thereby neglecting efficiency) and considers all
individuals above the dual cut-off line equally poor, regardless of
the number of dimensions in which they are deprived (thereby
neglecting distributive justice).
Slide 17
Deutsches Institut fr Entwicklungspolitik (DIE) Consequently,
the MPI can only be decomposed in the product of (censored) poverty
incidence and intensity: The censored headcount ratio measuring
poverty incidence and the censored aggregate deprivation count
ratio measuring poverty intensity. I. Introduction II. The
Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 17 The Multidimensional Poverty Index
(MPI)
Slide 18
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 18 The Structure of MPI and CSPI The
structure of the MPI which is also used for the CSPI: DimensionMain
CapabilityIndicatorThreshold (Household Level) HealthBodily Health
Nutrition At least one of the following: 1. At least one woman age
15-49 with BMI < 18.5 2. At least one child with weight-for-age
z-score < -2.0 Child Mortality RateAt least one child under the
age of 18 died Education Senses, Imagination and Thought
SchoolingNo member with at least five years of schooling
EnrolmentAt least one child in school age not enrolled Living
Standards Bodily Health Control over Environment Cooking Fuel
Harmful material is used for cooking (straw, dung, coal etc.)
Sanitation Toilet either unhygienic (no facility, open lid, etc.)
or shared Water Water source is unprotected or more than 30 minutes
away ElectricityNo access to electricity FloorFloor material is
earth, sand or dung AssetsNot more than one small asset and no
car/truck
Slide 19
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 19 An Example from India The following
example is taken from the Indian DHS 2005: Household 3 is deprived
in five indicators (electricity, water, sanitation, floor and
cooking fuel) yet it is not included in the calculation of the MPI.
0.0280.000 no yesno5 0.0490.000 no yesno yesno4 0.0770.000 no yes
no 3 0.1510.389 noyes noyes no yes2 0.5220.722 yesnoyesnoyes noyes
1
AssetsCookingFlooringSanitationWaterElectricityNutritionMortalityAttendanceYears
CSPIMPILiving StandardHealthEducationHH A Comparison of Five Indian
Households (DHS 2005) 0.0280.000 no yesno5 0.0490.000 no yesno
yesno4 0.0770.000 no yes no 3 0.1510.389 noyes noyes no yes2
0.5220.722 yesnoyesnoyes noyes 1
AssetsCookingFlooringSanitationWaterElectricityNutritionMortalityAttendanceYears
CSPIMPILiving StandardHealthEducationHH A Comparison of Five Indian
Households (DHS 2005) A transfer from household 1 to household 2
does not change the value of the MPI which is still 0.222; it
changes, however, the value of the CSPI, from 0.135 to 0.143.
Slide 20
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 20 Indian Poverty Maps according to
MPI
Slide 21
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 21 Indian Poverty Maps according to
CSPI
Slide 22
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 22 Conclusion In a multidimensional
framework, two types of inequality exist: inequality within and
inequality across dimensions. This axiomatic modification implies a
new method for the identification of the poor that accounts for
both the distribution of attributes as well as the correlations
between them. However, in the ordinal framework, inequality across
dimensions is usually equated with the spread of simultaneous
deprivations across the population (distributive justice). This
work suggests an extended definition of inequality between
dimensions as the correlation-sensitive spread of simultaneous
deprivations across the population. In order to operationalise this
more holistic definition of inequality between dimensions, a new
axiom, Sensitivity to Inequality Increasing Switches, is
introduced.
Slide 23
Deutsches Institut fr Entwicklungspolitik (DIE) I. Introduction
II. The Identification Step III. The Aggregation Step IV. Empirical
Application V. Conclusion 23 Conclusion It also leads to a whole
new class of ordinal poverty indices that are the first additive
indices able to capture correlation- sensitivity and inequality
while at the same time being fully decomposable (according to
dimensions and population subgroups). The new way to measure
poverty has interesting implications for policy making: It accounts
for efficiency, i.e. scarce resources are applied in a way that
their impact is strongest; It accounts for distributive justice,
i.e. ensures that the neediest are not left behind; Due to its
decomposability according to population sub- groups and poverty
dimensions as well as the three Is of poverty (incidence, intensity
and inequality), it provides a detailed picture of the poverty
structure in a given country.
Slide 24
Deutsches Institut fr Entwicklungspolitik (DIE)24 Thank you for
your attention! German Development Institute/ Deutsches Institut fr
Entwicklungspolitik (DIE) Tulpenfeld 6 D-53113 Bonn Telefon: +49
(0)228-949 27-0 E-Mail: [email protected] www.die-gdi.de
www.facebook.com/DIE.Bonn www.youtube.com/DIEnewsflash