Integrating Inter-Personal Inequality in Counting Poverty
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Integrating Inter-Personal Inequality in Counting Poverty Indices: The Correlation Sensitive Poverty Index . Nicole Rippin 24 June 2014. Outline. Introduction The identification of the poor The aggregation of the individual characteristics of the poor in the ordinal framework

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Integrating Inter-Personal Inequality in Counting Poverty Indices:The Correlation Sensitive Poverty Index

Nicole Rippin

24 June 2014


Outline
Outline

  • Introduction

  • The identification of the poor

  • 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)

  • Empirical application

  • Conclusion

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion


Introduction

  • Insufficient income has for a long time been considered to be a good proxy for poverty in all its various facets.

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • The income approach, however, relies on critical assumptions:

Economic Resources

Choice

Goods

Conversion

Utility

  • Assumption: perfect and complete markets

  • Ignoring in particular:

  • The role of public goods

  • Limited access

  • Asymmetric information

  • Assumption: equal individual conversion factors

  • Ignoring in particular:

  • Personal heterogeneities

  • Variations in physical environment

  • Differences in social climate

  • Over time, serious concerns have been raised regarding the appropriateness of these simplifying assumptions (e.g. Rawls, 1971; Sen 1985, 1992; Drèze and Sen, 1989; UNDP, 1997).


Introduction

  • It was Amartya Sen, who developed a new approach to measure poverty and welfare: the capability approach (1979, 1985, 1992, 1999, 2009).

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

Capability Set

Choice

Functioning Bundle

Choice

Utility

Economic Resources

Choice

Goods

Conversion

  • Assumption: perfect and complete markets

  • Ignoring in particular:

  • The role of public goods

  • Limited access

  • Asymmetric information

  • Assumption: equal individual conversion factors

  • Ignoring in particular:

  • Personal heterogeneities

  • Variations in physical environment

  • Differences in social climate

  • Thus, the capability approach implies a multidimensional approach to poverty measurement.


Introduction

  • Empirical evidence demonstrates that considerable population shares might be multidimensional poor but not income poor, and vice versa (e.g. Klasen, 2000).

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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

  • 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.

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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.


Theoretical Background

  • Person i is deprived with respect to attribute j if

  • ℕrepresents a set of k poverty attributes

  • ℝ+K represents a vector of weights such that

  • ℝK represents the achievement vector of person i

  • ℕrepresents a set of n persons

  • ℝKrepresents the respective vector of threshold levels

  • A poverty index is defined by ℝ

  • represents the deprivation vector of person isuch

    that if and if

I. Introduction

II. The IdentificationStep

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • For any ℕ, the deprivation matrix is denoted by ℝ+NK

  • Society A has higher poverty than society B if and only if

    P(XA) ≥ P(XB)

  • is the weighted sum of deprivations of person i


Union and Intersection Method

  • Let ℝ ℝ be an identification function so that

    person i is poor if and not poor if

I. Introduction

II. The IdentificationStep

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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):


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).

I. Introduction

II. The IdentificationStep

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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.


The Equality-Promoting Change

  • Based on Chakravarty and D’Ambrosio (2006), Jayaraj and Subramanian (2010) introduced the equality-promoting change in order to capture inequality across dimensions:

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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

  • Jayaraj and Subramanian (2010) then formulated the axiom Nonincreasingness under Equality-Promoting Change:

10

For any and X, ifis obtained from X by an

equality-promoting change, then

  • The axiom captures distributive justice, yet it neglects efficiency by disregarding possible correlations between attributes.


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.

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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.

  • 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


A New Axiom

  • Based on this concept I formulate the axiom Sensitivity to Inequality Increasing Switches:

    For any and X, ifis obtained from X byan

    inequality increasing switch of non-complementary attributes,

    then

    Further, if is obtained from Xby an inequality increasing

    switch of complement attributes, then

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • Example: i = 2, j = 5, z = (1 1 1 1 1)


A New Class of Ordinal Poverty Indices

Property 1

A multidimensional poverty measure P satisfies AN, NM, MN, SF, PP, FD, SD and SIISif and only if for all and X :

with ℝ ℝ non-decreasing in and a nondecreasing (nonincreasing) marginal in case attributes are considered to be substitutes (complements).

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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.


=

max

ρ

1

1

a

<

ˆ

a

>

=

1

ρ

δ

1

a

>

ˆ

a

<

=

1

ρ

δ

ˆ

min

min

=

δ

min

δ

δ

δ

=

1

IM

U

IS

A New Identification Function

  • Consider the following multiple step identification function:

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • The relationship between distributive justice and efficiency is determined by an indicator for inequality aversion: alpha

ρ

  • 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

0

δ


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:

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • Different from any other additive/counting index, the CSPI can be decomposed into a product of poverty incidence, intensity and inequality:

    The headcountratiomeasuringpovertyincidence;

    the aggregate deprivation count ratio measuring

    poverty intensity; and

    the Generalized Entropy inequality index of deprivation counts

    measuringinequality.


The Multidimensional Poverty Index (MPI)

  • In the following I will compare the CSPI with the Multidimensional Poverty Index (MPI):

    with if and otherwise

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • The MPI extracts information on simultaneous deprivations but only to verify whether a household is poor or not, afterwards this information is disregarded.

  • 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).


The Multidimensional Poverty Index (MPI)

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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.


The Structure of MPI and CSPI

  • The structure of the MPI which is also used for the CSPI:

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion


A Comparison of Five Indian Households (DHS 2005)

A Comparison of Five Indian Households (DHS 2005)

HH

HH

Education

Education

Health

Health

Living Standard

Living Standard

MPI

MPI

CSPI

CSPI

Years

Years

Attendance

Attendance

Mortality

Mortality

Nutrition

Nutrition

Electricity

Electricity

Water

Water

Sanitation

Sanitation

Flooring

Flooring

Cooking

Cooking

Assets

Assets

0.722

0.722

0.522

0.522

1

1

yes

yes

yes

yes

yes

yes

no

no

yes

yes

yes

yes

no

no

yes

yes

no

no

yes

yes

0.389

0.389

0.151

0.151

2

2

yes

yes

no

no

no

no

no

no

yes

yes

yes

yes

no

no

yes

yes

yes

yes

no

no

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

0.000

0.000

0.077

0.077

3

3

no

no

no

no

no

no

no

no

no

no

0.000

0.000

0.049

0.049

4

4

no

no

yes

yes

no

no

no

no

no

no

no

no

yes

yes

no

no

no

no

no

no

0.000

0.000

0.028

0.028

5

5

no

no

yes

yes

no

no

no

no

no

no

no

no

no

no

no

no

no

no

no

no

An Example from India

  • The following example is taken from the Indian DHS 2005:

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • Household 3is deprived in five indicators (electricity, water, sanitation, floor and cooking fuel) yet it is not included in the calculation of the MPI.

  • 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.


Indian Poverty Maps according to MPI

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion


Indian Poverty Maps according to CSPI

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion


Conclusion

  • In a multidimensional framework, two types of inequality exist: inequality within and inequality across dimensions.

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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.

  • 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.


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).

I. Introduction

II. The Identification Step

III. The Aggregation Step

IV. Empirical Application

V. Conclusion

  • 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 I’s of poverty (incidence, intensity and inequality), it provides a detailed picture of the poverty structure in a given country.


Thank you for your attention!

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Deutsches Institut für Entwicklungspolitik (DIE)

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