Multidimensional poverty measurement - PowerPoint Presentation

Slide1

Multidimensional poverty measurement

Elisabetta Aurino

Partnership for Child Development

Imperial College London

& University of OxfordSlide2

Recalling unidimensional approach?

Limits – spell outSlide3

Problems with unidimensional approach

Appropriateness of

utility as the measure for welfareInterpersonal heterogeneityAssumptions of perfect markets, no increasing returns, and no externalities Targeting and means testing: information distortion; incentive distortion; disutility and social stigma; administrative costs and corruption; political sustainability

Join

t-distribution

of deprivationsSlide4

How about another approach?

Alternatively approaches propose

to measure well-being directly by observing outcomesSen: poverty as the inability of individuals to achieve a minimum level in a set of outcomes (such as the inability to be healthy, well-fed, clothed, sheltered...).Hence,

Sen’s

approach to poverty is inherently

multidimensional.

NOTE

: not all the multidimensional measures are theoretically linked to

Sen’s

approach!Slide5

Advantages of the CA for measuring poverty

Focuses directly on achievements

:Personal heterogeneities in their ability to convert resources in well-being levels;Can capture the impact of public goods on welfare Aggregation and equivalence scales: by observing capabilities directly, it does not need to make assumptions about adult equivalence and household specific economies of scale.

Revealing

joint deprivations

for the same person at the same time.

Direct targeting and means testing

.Slide6

Which are the key issues related to this approach?

Choose the space:

Capabilities of functionings?Which dimensions are important?Which indicator(s) best measure that dimension?Set the “poverty line” for each dimension/indicatorWhich weights to assign to each of these dimensions?What about dimensions for which no data are available?Slide7

Note 1: Plural methods

essential

The CA is incomplete. It does not provide a definitive list of capabilities which should be relevant for all the people and in all contexts.Theoretically, there are many degrees of freedom in how to implement the CA (standard of living (resources), functionings, capabilities...) However, in practice, there are far fewer realistic options, due to theoretical and empirical difficulties.Slide8

Note 2:

Measure reflects context

“What we focus on cannot be independent of what we are doing and why” (Sen 2004, p. 79)Particular objectives of the exercise: a. The purpose of the evaluation b. The region, or sector, or years of interest

c. The methodologies

2.

Unchangeable constraints

(

might

include)

a. Data

b. Political powers

c. Time and costs (e.g. of participation)Slide9

Note 3.

functionings or capabilities?

Capability = functionings + freedomCapability is the freedom to enjoy valuable functionings.Functionings are valuable activities and states that make up people’s well-beingMost frequently focus on functionings or resources data rather than capabilities.

This might seem disappointing, given the importance given to freedom in the CA!

A key dilemma for the capabilities approach has been

how to measure what people could do (their opportunity freedom), as opposed to what they actually do (their achieved functionings

).Slide10

Minimal capabilities

Sen

recognises that in contexts where extreme poverty is prevalent,

it

is

sufficient

to

measure

deprivation

in

“

minimal capabilities

” (Sen 1997

)

F

unctionings

(and the corresponding basic capabilities) of

crucial importance

for the life of an individual, (e.g. the ability to be well-nourished and well-sheltered, the capability of escaping avoidable morbidity and premature mortality, and so forth

)Slide11

Functionings

and Indicators

Which are direct indicators of functionings? A. Asset index

B. Subjective well-being/Happiness

C. Body mass index

D. Literacy

E. Years of schooling

F. Self-reported health

G. Income of 10000 Euro per month.

H. To be safe from violence.Slide12

From Concept to Implementation:

The introduction of a multidimensional framework leads to additional theoretical and empirical difficulties in the measurement of poverty.

Every choice in the context of multidimensional poverty analysis implies a specific value judgement, which have to be clearly specified.Moreover, those choices should be based on PUBLIC DISCUSSION about the nature, the relative merits and the importance of various capabilities, together with a debate on more technical issues, such as the weighting scheme. Slide13

Steps for constructing MD

Poverty Measures

Choice of Unit of Analysis Choice of the DimensionsChoice of the Variables/Indicators

Choice of

Normalisation

Choice of

Poverty

Cutoffs

for each indicator/dimension

If relevant,

Aggregation within dimensions.

Choice of

Weights

within and across dimensions.

Identification

(Who is poor)

Aggregation

(How much poverty does a society have)Slide14

1. Choice of the Unit of Analysis

IndividualsHouseholds

Choice depends upon purpose and data. Slide15

2. Choice of Dimensions (theory)

It’s a value judgement!

Sen (2004), 2 criteria:Value and priority (for relevant group(s)): basic importance.ii) Appropriateness for institutional response:

social influenciability.Slide16

2. Choice of dimensions

(in practice)

Existing data or convention.Theory: implicit assumptions on what people do value or should value (e.g. Nussbaum’s list).Public ‘consensus’: a list that has achieved a degree of legitimacy due to public consensus (e.g. universal human rights; MDGs).Ongoing deliberative participatory process

: a process that periodically elicit the values and perspectives of stakeholders

Empirical evidence regarding people’s values

: empirical data on values, or on consumer’s preferences and behaviour.Slide17

2. Choice of dimensions (in practice) (2)

REMEMBER:

Try always to justify why and the methodology according to which you chose a particular set of dimensions, in order to favour open discussion and debate. Mention the other dimensions that you wanted to include, but you couldn’t for lack of data.Slide18

Can you think about some possible dimensions?Slide19

Often Observed Dimensions

An interesting result is that lists of dimensions developed by researchers of different backgrounds are surprisingly similar.

Life, Health, Reproduction.Security.Work and Leisure.Education, Knowledge, Skills.Relationships.Self-direction, Empowerment, Agency.Political life, Governance.Inner Peace and Self Expression.

Culture and Spirituality.Slide20

3. Choice of Variables/Indicators

Normative Justification

Kind of indicator (functioning/resource/utility) (input/output/outcome; stock/flow)Data AvailabilityInstitutional/Historical Considerations

Literature on that indicator/database

Interrelations with other indicators

Accuracy of individual level data for

hh

or

hh

level data for individual Slide21

4.

NormalisationTransformation

of the original variables into commensurable units in order to avoid to sum up “apples and oranges”.Normalisation is required prior to any data aggregation as the indicators in a data set often have different measurement units. Slide22

5. Choice

of Poverty Cutoffs

For each indicator there is the need to choose a poverty threshold, in order to assess deprivation in that specific indicator.The idea is: “Beneath a certain level of capability, in each area, a person has not been enabled to live in a true human way” (Nussbaum 2000, p. 74). Slide23

Example

of Deprivation cutoffs

Examples: Not deprived (in bold) in dimension x if:Schooling: how many years of school have you completed?6 or more (NOT DEPRIVED)1-5 years

b. Drinking water:

What is the main source for drinking?

Piped water

Well/Pump (electric hand)

Rain water

River water

Water collection basinSlide24

7. Setting weights

Rationale

1. NormativeImportance: absolute importance of a dimension for poverty Priority: urgency of making progress in a dimension at a given time (e.g. 3-year plan)

2.

Statistical

Data driven

: (i) frequency-based; (ii) quality of data; (iii) most favourable weights.

Descriptive statistics

: (i)principal components analysis; (ii) cluster analysis (latent variable models).

Regression-basedSlide25

Weights, where?

Within

dimensions (e.g. Asset index in the MPI; education index in HDI).Between dimensions (e.g. across 3 dimensions of HDI/HPI/MPI).Among people in the distribution, i.e. to give greater priority to the most disadvantaged (e.g. think at the role of α in FGT).Slide26

Normative weights:

Equal weights

Most common approach (e.g. HDI, HPI).Underlying hypothesis: dimensions of well-being are perfect substitutes.‘Agnostic viewpoint’: all the indicators are presumed to be equally important. This, at a first sight, might seem a ‘neutral’ choice of the researcher. However, as we saw, weights reflect an important aspect of the trade-offs between the dimensions, which, in turn, imply value judgement.

With equal weighting, trade-offs and value judgements are hidden. Slide27

Weights and Choice of Dimensions

In the capability approach, because capabilities are of intrinsic value, the relative weights on different capabilities or dimensions that are used in society-wide measures are value judgments. Weights can

represent (Alkire & Santos 2010):1) the enduring

importance of a capability relative to other capabilities or

2) the

priority of expanding one capability relative to others in the next phase.

Need for public debate!Slide28

8. Aggregation

Aggregation is concerned with summarising

all the available information in order to get a synthetic index.There are many ways to aggregate:- means,-statistical-based models,-and poverty indices, such as the Alkire & Foster.Slide29

Review: Unidimensional Poverty

Variable – income

Identification – poverty lineAggregation – Foster, Greer & Thorbecke (1984)E.g. x=(7,3,4,8), poverty line z=5Deprivation vector g

0

=(0,1,1,0)

Headcount Ratio: P0=

μ

(g

0

)=2/4

Normalised

gap

vector

g

1

=(0, 2/5, 1/5, 0)

Poverty

Gap: P1=

μ

(g

1

)=3/20

Squared

gap

vector

g

2

=(0, 4/25, 1/25, 0)

FGT

measure

: P2=

μ

(g

2

)=5/100Slide30

Multidimensional data

Achievement of person

i

for dimension

j

INDIVIDUALS i=1,

…n

DOMAINS j

=1,

…d

CUTOFFS VECTORSlide31

Multidimensional data

: example

Matrix of well-being scores for n persons in d domains.

CUTOFFS

DOMAINS j

Income Health

Edu

NutriSlide32

The

Alkire

& Foster (2010) Multidimensional Poverty MeasureSlide33

Some preliminary tools…

In order to understand how the AF works, we need to understand some basic building blocks of the methodology, that will be useful to calculate our poverty measures.Slide34

1. From the original matrix to the

deprivation matrix

Replace entries: 1 if deprived, 0 if not deprived.

These entries fall below

cutoffs

.Slide35

Identification

in

multidimensional settingsUnidimensional poverty: y <= z

MD poverty:

Set z

for

each

dimensions, AND

D

ecide

the

number of dimensions needed

in order to identify somebody as poor.

If a person meets a given identification criterion, then the person is considered to be ‘poor’.

Def.:

Deprivation

:

we use this term to indicate that a person’s achievement in a given dimension falls below the poverty line for that specific dimension (=

cutoff

).Slide36

Identification –

Counting Deprivations

PERSONS

DOMAINS

c

Question: who is poor?

It depends on how

we set the identification criterion

, i.e. on

how many dimensions

we require a person

is deprived at the same time

in order to be considered poor. Slide37

3 approaches to Identification

Union approach

: the person must be deprived in AT LEAST ONE DIMENSION (e.g. Tsui 2002; Bourguignon & Chakravarty 2003).Intersection approach: in order to be considered poor, the person must be deprived in

ALL DIMENSIONS

.

Counting Approach

(

Alkire & Foster 2007)

DUAL CUTOFF

: gives priority to those people who are deprived in several (but not necessarily all!) dimensions. It sets a number of deprivations (or, if the dimensions are not equally weighted, the weighted sum of the dimensions) for which a person is considered being poor. Slide38

Identification

–Union approach

Q/ Who is poor?

A1/ poor if deprived in any

dimension|

c

i

≥ 1

Union approach often predicts high numbers.

q=3

DOMAINS

c

iSlide39

Identification –

Intersection

approach

Q/ Who is poor?

A2/ poor if deprived in all

dimensions|

c

i

=d

Demanding requirement (especially if d is large).

Often identifies a very narrow slice of population.

q=1

DOMAINS

c

iSlide40

Identification –

Counting approach

Q/ Who is poor?

A3/ Fix cutoff

k

 d

; then identify as poor if

c

i

≥k

(E.g. k=2)

NOTE

: Includes both union (k=1) and intersection (k=d) approaches.

Developed by Alkire & Foster (2007).

q=2

DOMAINS

c

iSlide41

Identification – The problem empirically (

Alkire & Seth 2008)

k=1 Union

H

91.2%

2

3

75.5

%

54.4 %

4

5

33.3 %

16.5 %

6

7

6.3 %

1.5 %

8

9

0.2 %

0.0 %

10 Intersection

0.0

%

Poverty in India for 10 dimensions:

91 % of population would be targeted using union,

0% using intersection.

Need something in the middle!

Note: as k rises, the focus shifts to the poorest of the poor (acute deprivation).Slide42

The role of k

k

is a policy variable that governs the range of simultaneous deprivations each poor household necessarily must have in order to be considered poor.As k goes up,the number of households who will be considered poor goes down,but the intensity or breadth of deprivations in any poor household goes up.The problem is how to set

k.Slide43

9. Aggregation

In the past years, boom of the literature on aggregation methods for MD measures of poverty.

Why? Recognition of the multidimensionality of well-being and poverty + increase availability of data.Different approaches:Axiomatic: Chakravarty et al. (1998);

Tsui

(2002); Bourguignon &

Chakravarty

(2003);

Alkire

& Foster (2007; 2009).

Non Axiomatic: Information Theory; fuzzy set; counting, etc...Slide44

9. Aggregation (ctd.)

We will examine more deeply Alkire & Foster (2007, 2009).

Theoretical approach: Capability Approach;Extension to the multidimensional case of the FGT family of poverty measures;Easy to understand;The method was used to construct UNDP’s Multidimensional Poverty Index (Alkire & Santos 2010), that we will analyse later.Slide45

Aggregation: Alkire & Foster 2007

DOMAINS

c(k)

PERSONS

Once you set k, the first thing to do is to censor data of nonpoor (e.g.

k=2

).

Similarly per g

1

(k) etc...

This is an implication of the

FOCUS axiom

: we are not interested to what happens to the non-poor.Slide46

a. Headcount Ratio

DOMAINS

c(k)

PERSONS

H = q/n

Two poor persons out of four:

H=1/2

[k=2]Slide47

Critique to the Headcount Ratio

DOMAINS

c(k)

PERSONS

Suppose the number of deprivation rises for person 2:

The number of the poor remains the same:

H=1/2

.

It does not take into account the

depth of poverty

in that dimension

(violates dimensional monotonicity).Slide48

Average deprivation share among poor

As we know, the Headcount Ratio is a very crude measure of poverty. It is insensitive to both monotonicity and transfer.

We need to broaden our informational basis, by including more information on the share of deprivation among the poor. A =c(k)/qdA includes additional information on the

breadth of deprivations

experienced by the poor.

This partial index conveys relevant information about MD poverty, namely, the fraction of possible dimensions

d

experienced by a poor person

i

. Slide49

Aggregation – Including the share of deprivations among poor

PERSONS

DOMAINS

c(k)

c(k)/d

Deprivation shares among poor

A = average deprivation share among poor:

A=

(2

/4 + 4/

4)/2

= 3/4Slide50

b. Adjusted Headcount Ratio (1)

DOMAINS

c(k)

c(k)/d

Adjusted Headcount Ratio: M

0

=HA=

μ

(g

0

(k))

M

0

=HA= (2/4)*(3/4) = 6/16 = 0. 375Slide51

b. Adjusted Headcount Ratio (2)

Adjusted Headcount Ratio = M

0=HA=μ(g0(k))

M

0

is a MD poverty measure which combines information on:

The prevalence of poverty (H)

The average

breadth

of deprivations poor people suffer (A).

The equivalent definition

M

0

=

μ

(g

0

(k))

interprets

M

0

as the total number of deprivations experienced by the poor, c(k)=|

g

0

(k)|, divided by the maximum number of deprivations that could possibly experienced by all people,

nd.Slide52

b. Adjusted Headcount Ratio (3)

As a simple product of the two partial indices H and A, M

0 is sensitive to the frequency (H) and the breadth (A) of MD poverty. It is similar to the FGT measure for the poverty gap P

1

=HI; here M

0

=HA.

Easy to calculate and to interpret.

UNDP’s MPI is a form of M

0

.

In particular, M

0

satisfies

dimensional monotonicity,

as we will see from the following example.Slide53

M0 is sensitive to the breadth of deprivation

Suppose the number of deprivation rises for person 2:

DOMAINS

c(k)

c(k)/d

M

0

=HA= (2/4)*(7/8) = 7/16 = 0. 4375

M

0

is increased for the additional deprivation of person 2. It hence satisfies dimensional monotonicity.Slide54

b. Adjusted Headcount Ratio (4)

However, it does not provide any information regarding

the depth of deprivation in one dimension. In other words, M0 doesn’t satisfy the traditional monotonicity requirement, according to which poverty should increase as a poor person becomes more deprived in any given dimension. Consequently we will need another measure, that we can develop for

cardinal data

only.Slide55

To Sum Up...

Matrix of information:

n people and d dimensions. Who is MD poor?a. Identification:

z

vector (

d

x

1

) of

poverty

cutoffs

 dimension

d

identification criterion

(union, intersection, dual cutoff approach) Define

k

of interest.

identify the set of poor people.Slide56

b. Aggregation

– Alkire & Foster (2007, 2009)

Summarise all the available information in only one number.How? 1. Censor data of non poor  g0

(k)

2.

Headcount Ratio

H=q/n

problem: no breadth and depth of poverty.

Define

A=

c(k)/qd,

average deprivations share across the poor.Slide57

3. Adjusted Headcount Ratio

M0=HA=μ(g0

(k))

Satisfies

dimensional

monotonicity

(

breadth

of

poverty

).

Problem: no info on the depth of poverty (monotonicity within dimensions).

Define

G= |g

1

|/| g

0

|

, average poverty gap across all instances in which poor persons are deprived.Slide58

4.

Adjusted Poverty Gap

M1=HAG=μ(g1(k))

Combines information on the prevalence of poverty, the average range of deprivation and the average depth across deprived dimensions.

Problem: it does not take into account whether the increase in deprivation occurs for a person who is slightly or acutely deprived.

Define:

S=|g

2

(k)|/|g

0

(k)|

Average severity of deprivationsSlide59

5.

Adjusted FGT Measure M

2 = HAS = μ(g2(k))Sensitive to inequalities in the distribution of deprivations among the poor.

We can generalise these results to a class of MD poverty measures:

6.

Adjusted FGT class

M

α

=

μ

(g

α

(k))

for

α

≥ 0. Slide60

UNDP’s Multidimensional Poverty IndexSlide61

The MPI and the HPI

In November 2010, UNDP has launched the new ‘Multidimensional Poverty Index (MPI)’, that has substituted the Human Poverty Index in the global estimates of multidimensional poverty.

The MPI was developed by Alkire & Santos (2010), by adopting the Alkire&Foster methodology to measure multidimensional poverty.Slide62

The MPI (Alkire & Santos 2010)

Developed by following

Alkire & Foster (2007,2009).Captures the number of households which experience multiple deprivations at the same time (acute poverty)  Micro analysis now!Portrays the composition of poverty for those households, i.e. in which dimensions or indicators they are deprived.It is also decomposable by geographic location (in order to show variation in poverty within countries) and subgroups of population.Slide63

Our steps and the MPI

Choice of

Unit of AnalysisChoice of the DimensionsChoice of the Variables/Indicators

Choice of

Normalisation

Choice of Poverty

Cutoffs

for each indicator/dimension

If relevant,

Aggregation within dimensions.

Choice of

Weights

within and across dimensions.

Identification

(Who is poor)

Aggregation

(How much poverty does a society have)Slide64

Weights Indicators

1.67

1.67

1.67

1.67

0.55

0.55

0.55

0.55

0.55

0.55

Weights Dimensions

1/3

1/3

1/3Slide65

Source: Alkire & Santos (2010)Slide66

Choice of weights and poverty cutoff

k

There are 10 indicators. Equal weights between and within indicators.Alkire & Santos (2010) computed the MPI for two values of k: k=2, k=3.Here we will consider k=3, that means that a household is to be considered poor if the weighted sum of its deprivations exceeds 3.Let’s do an example in order to understand how the index works in practice.Slide67

Example of Identification: Tabitha

Source: Alkire & Santos (2010)Slide68

Why is it important to decompose?

Alkire & Santos (2010)Slide69

Problems with the MPI?

From the CA perspective, problems with some of the indicators chosen. Are the means confused with the ends?Loss of information due to composite indicators.

Data comparability and update issues.Slide70

Further references

Alkire

, S. & Seth, K. (2008). Measuring Multidimensional Poverty in India. A New Proposal. OPHI WP 15.Alkire, S. and Santos, M.E. 2010. Acute Multidimensional Poverty: A New Index for Developing Countries. OPHI Working Paper 38.Bourguignon, F., & Chakravarty, S. R. (2003). The Measurement of Multidimensional Poverty. Journal of Economic Inequality.

1(1), pp. 25-49.

Deutsch, J., &

Silber

, J. (2005). Measuring Multidimensional Poverty. An Empirical Comparison of Various Approaches. The

Review of Income and Wealth

51, pp. 145-174.Slide71

References

Ravallion

, M. (1992). Poverty Comparisons. A Guide to Concepts and Methods. Living Standards Measurement Study Working Paper No. 98.Rawls, J. (1971). A Theory of Justice. Cambridge, Massachusetts: Belknap Press of Harvard University Press. Ruggeri Laderchi, C. (2008). Do Concepts Matter? An Empirical Investigation of the Differences Between a Capability and a Monetary Assessment of Poverty. In Comim,F., Qizilbash,M

., &

Alkire,S

. (

eds

). The Capability Approach. Concepts, Measures and Applications. Cambridge: Cambridge University Press.

Sen, A. (

1999)

. Development as Freedom. Oxford: Oxford University Press.

Sen, A.K. (1987). The Standard of Living: Lecture II, Lives and Capabilities. In G. Hawthorn (ed.). The Standard of Living: The Tanner lectures on Human Values. Cambridge: Cambridge University Press

Sen, A. K. (1976). Poverty: An Ordinal Approach to Measurement.

Econometrica

, 44(2), pp. 219-31.

World Bank. (1990), World Development Report: Poverty, Oxford University Press for the World Bank.

Rowntree

, S. (1901).

Poverty

. A

Study

of Town Life. MacMillan.Slide72

Thanks!

E.aurino@imperial.ac.uk