Value Judgements in Multidimensional Poverty Measurement ... · methodology M ka =(ρ k,Ma)...

Value Judgements in Multidimensional

Poverty Measurement Design

Sabina Alkire, Jose Manuel Roche and Maria Emma Santos

OPHI Workshop, Oxford, 28 June 2012

Two parts:

• Measurement methodology

• Value Judgements

– Constraints

– Complementary Analyses

– Uncertainty/Incompleteness

– Authority

Measurement methodology

• Why focus on a particular method? – Focused discussion

– Actual examples

– Practical Benefits

– Clarity

And note:

– Relevance to other methods during field-building

Multidimensional Poverty- our challenge:

• A government would like to create an official

multidimensional poverty indicator

• Desiderata

– It must understandable and easy to describe

– It must conform to “common sense” notions of poverty

– It must be able to target the poor, track changes, and guide

policy.

– It must be technically solid

– It must be operationally viable

– It must be easily replicable

• What would you advise?

Methodology

• Identification – Dual cutoffs

• Aggregation – Adjusted FGT

• All value judgements are assumed given for now:

– Purpose, Dimensions, Indicators, Cutoffs, Weights/Values etc

• Today we focus on one measure M0, which can be used with ordinal, categorical, binary, or cardinal data. It has been used extensively, for practical reasons.

Review: Unidimensional Poverty

Variable – income

Identification – poverty line

Aggregation – Foster-Greer-Thorbecke ’84

Example Incomes = (7,3,4,8) poverty line z = 5

Deprivation vector g0 = (0,1,1,0)

Headcount ratio P0 = m(g0) = 2/4

Normalized gap vector g1 = (0, 2/5, 1/5, 0)

Poverty gap = P1 = m(g1) = 3/20

Squared gap vector g2 = (0, 4/25, 1/25, 0)

FGT Measure = P2 = m(g2) = 5/100

Multidimensional Data

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

Domains

Persons

13.1 14 4 1

15.2 7 5 0

12.5 10 1 0

20 11 3 1

Multidimensional Data

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

Domains

Persons

z ( 13 12 3 1) Cutoffs

13.1 14 4 1

15.2 7 5 0

12.5 10 1 0

20 11 3 1

Deprivation Matrix

Replace entries: 1 if deprived, 0 if not deprived

Domains

Persons

13.1 14 4 1

15.2 7 5 0

12.5 10 1 0

20 11 3 1

Deprivation Matrix

Replace entries: 1 if deprived, 0 if not deprived

Domains

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Normalized Gap Matrix

Normalized gap = (zj - yji)/zj if deprived, 0 if not deprived

Domains

Persons

z ( 13 12 3 1) Cutoffs

These entries fall below cutoffs

13.1 14 4 1

15.2 7 5 0

12.5 10 1 0

20 11 3 1

Normalized Gap Matrix

Normalized gap = (zj - yji)/zj if deprived, 0 if not deprived

Domains

Persons

0 0 0 0

0 0.42 0 1

0.04 0.17 0.67 1

0 0.08 0 0

Squared Gap Matrix

Squared gap = [(zj - yji)/zj]2 if deprived, 0 if not deprived

Domains

Persons

0 0 0 0

0 0.42 0 1

0.04 0.17 0.67 1

0 0.08 0 0

Squared Gap Matrix

Squared gap = [(zj - yji)/zj]2 if deprived, 0 if not deprived

Domains

Persons

0 0 0 0

0 0.176 0 1

0.002 0.029 0.449 1

0 0.006 0 0

Identification

Domains

Persons

Matrix of deprivations

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Identification – Counting Deprivations

Domains c

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Identification – Counting Deprivations

Q/ Who is poor?

Domains c

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Identification – Dual Cutoff Approach

Q/ Who is poor?

A/ Fix cutoff k, identify as poor if ci > k

Domains c

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Q/ Who is poor?

A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2)

Domains c

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Q/ Who is poor?

A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2)

Domains c

Persons

Note Includes both union (k = 1) and intersection (k = d)

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Identification – The problem empirically

Union 1 91.2%

2 75.5%

3 54.4%

4 33.3%

5 16.5%

6 6.3%

7 1.5%

8 0.2%

9 0.0%

Inters. 10 0.0%

Poverty in India for

10 dimensions:

91% of population

would be targeted

using union,

0% using intersection

Need something in

the middle. (Alkire and Seth 2009)

Aggregation

Censor data of nonpoor

Domains c

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 1 0 0

Aggregation

Censor data of nonpoor

Domains c(k)

Persons

Similarly for g1(k), etc

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Aggregation – Headcount Ratio

Domains c(k)

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Aggregation – Headcount Ratio

Domains c(k)

Persons

Two poor persons out of four: H = 1/2

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Critique

Suppose the number of deprivations rises for person 2

Domains c(k)

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Critique

Domains c(k)

Persons

Critique

Domains c(k)

Persons

No change!

Violates ‘dimensional monotonicity’

Aggregation

Return to the original matrix

Domains c(k)

Persons

Aggregation

Return to the original matrix

Domains c(k)

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Aggregation

Need to augment information deprivation shares among poor

Domains c(k) c(k)/d

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Aggregation

Need to augment information deprivation shares among poor

Domains c(k) c(k)/d

Persons

A = average deprivation share among poor = 3/4

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Aggregation – Adjusted Headcount Ratio

Adjusted Headcount Ratio = M0 = HA

Domains c(k) c(k)/d

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Adjusted Headcount Ratio = M0 = HA = m(g0(k))

Domains c(k) c(k)/d

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Adjusted Headcount Ratio = M0 = HA = m(g0(k)) = 6/16 = .375

Domains c(k) c(k)/d

Persons

0 0 0 0

0 1 0 1

1 1 1 1

0 0 0 0

Aggregation: Adjusted Poverty Gap

Adjusted Poverty Gap = M1 = M0G = HAG

Domains

Persons

Average gap across all deprived dimensions of the poor:

g1 (k)

0 0 0 0

0 0.42 0 1

0.04 0.17 0.67 1

0 0 0 0

Aggregation: Adjusted Poverty Gap

Adjusted Poverty Gap = M1 = M0G = HAG = m(g1(k))

Domains

Persons

Obviously, if in a deprived dimension, a poor person becomes

even more deprived, then M1 will rise.

Satisfies monotonicity

g1 (k)

0 0 0 0

0 0.42 0 1

0.04 0.17 0.67 1

0 0 0 0

Aggregation: Adjusted FGT

Consider the matrix of squared gaps

Domains

Persons

0 0 0 0

0 0.422 0 12

0.042 0.172 0.672 12

0 0 0 0

Aggregation: Adjusted FGT

Adjusted FGT is M = m(g(k))

Domains

Persons

Satisfies transfer axiom

0 0 0 0

0 0.422 0 12

0.042 0.172 0.672 12

0 0 0 0

Aggregation: Adjusted FGT Family

Adjusted FGT is Ma = m(ga(t)) for a > 0

Domains

Persons

Theorem 1 For any given weighting vector and cutoffs, the

methodology Mka =(ρk,Ma) satisfies: decomposability,

replication invariance, symmetry, poverty and deprivation

focus, weak and dimensional monotonicity, nontriviality,

normalisation, and weak rearrangement for a>0;

monotonicity for a>0; and weak transfer

for a>1.

ga (k)

0 0 0 0

0 0.42a 0 1a

0.04a 0.17a 0.67a 1a

0 0 0 0

International MPI

National Poverty

Mexico, Colombia

Well-being

Bhutan’s GNH

Adaptations

Empowerment

Energy

Governance

Some Applications

Examples

UNDP’s

2010 Human Development Report first published the MPI

(updated annually for countries with new data)

The MPI (UNDP 2010) • The MPI 2011 is an international index of acute

multidimensional poverty developed at OPHI

• In 2011 it covers 109 developing countries.

• It was launched in 2010 in the Human Development

Report, and updated in 2011, 2012

• It complements the $1.25/day poverty by bringing

more dimensions into view

• It is the first measure to reflect joint distribution of

disadvantages.

Data: Surveys Demographic & Health Surveys (DHS - 54)

Multiple Indicator Cluster Surveys (MICS - 32)

World Health Survey (WHS – 17)

Additionally we used 6 special surveys covering urban

Argentina (ENNyS), Brazil (PNDS), Mexico (ENSANUT),

Morocco (ENNVM), Occupied Palestinian Territory

(PAPFAM), and South Africa (NIDS)

Constraints: Data are 2000-2010, and not all have all 10

indicators.

MPI Dimensions Weights & Indicators

Measurement: Indicators & Cutoffs

• Health – Child Mortality: If any child has died in the family

– Malnutrition: If any interviewed adult in the family has

low Body Mass Index; if any child is more than 2 standard

deviations below the reference normal weight for age,

WHO standards) [WHS has male & female data but no

child data; MICS has child data but no adult data; DHS

has women 15-49 & child]

• Education

– Years of Schooling: if no person in the household

has completed 5 years of schooling

– Child Enrolment: if any school-aged child is out

of school, where school-aged is an eight year

period from the national starting age.

• Standard of Living

– Electricity (no electricity is deprived)

– Drinking water (MDG definitions)

– Sanitation (MDG definitions + not being shared)

– Flooring (dirt/sand/dung are deprived)

– Cooking Fuel (wood/charcoal/dung are deprived)

– Assets (deprived if do not own a car/truck and do

not own more than one of these: radio, tv,

telephone, bike, motorbike, or refrigerator)

Identification: Who is poor?

A person is multidimensionally poor if they are

deprived in 33% of the dimensions at the

same time.

How do you calculate the MPI?

• The MPI uses the Alkire Foster method:

• H is the percent of people who are identified as poor,

it shows the incidence of multidimensional poverty.

• A is the average proportion of weighted deprivations

people suffer at the same time. It shows the intensity

of people’s poverty – the joint distribution of their

deprivations. The MPI is appropriate for ordinal data, and satisfies properties like subgroup consistency,

dimensional monotonicity, poverty & deprivation focus. MPI is

like the poverty gap measure – but looks at breadth instead –

what batters a person at the same time.

Formula: MPI = M0 = H × A

What is new? Intensity.

The MPI starts with each person, and constructs a

deprivation profile for each person.

Some people are identified as poor based on their joint

deprivations. The others are identified as non-poor.

• Most multidimensional poverty measures look at

deprivations one by one, not at the household level.

• Counting measures do look at coupled deprivations but only

provide a headcount, giving no incentive to target those

who are deprived in most things at the same time or to

reduce intensity.

Deprived in 67% of dimensions.

It doesn’t tell the full story

But it gives some idea.

MPI – Key Results

Global Results:

These results are for 109 developing countries, selected

because they have DHS, MICS or WHS data since 2000.

Special surveys were used for Argentina, Brazil, Mexico,

Morocco, Occupied Palestinian Territory, and South Africa

They cover 5.3 billion people - 78.6% of the world’s population

Of these 5.3 billion people, 31% of people are poor.

That is 1.65 billion people. (2008 population figures taken from Population Prospects 2011; 2010 Revision).

Half of the world’s MPI

poor people live in

South Asia, and 29% in

Sub-Saharan Africa

MPI poor people by region

Total Population in 109 MPI countries

The MPI Headcount Ratios and the $1.25/day Poverty

103 of our 109 Countries have

income; only 71 have income

poverty data within 3 years of MPI.

Income data ranges from 1992-2008;

MPI from 2000-2010.

Intensity is highest in the poorest countries.

But there is variety…H in High-income countries 1-7%

H in High- and Upper Middle-income countries 1-40%

H in Middle- and High-income Countries 1-77%

H in Low-income Countries ranges from 5-92%

Ghana, Nigeria, and Ethiopia

Ethiopia’s Regional Disparities

Ethiopia

Ethiopia’s Regional Disparities

Addis Ababa

Somali

Harari

Nigeria’s Regional Disparities

Nigeria

Nigeria’s Regional Disparities

South West

North East

Nigeria

Ghana’s Regional Disparities

Greater

Northern Ghana

CHANGES OVER TIME

Ghana, Nigeria, and Ethiopia

Let us Take a Step Back in Time

Nigeria

Ethiopia

Ethiopia: 2000-2005 (Reduced A more than H)

Nigeria

Ethiopia

Nigeria

Ethiopia

Nigeria 2003-2008 (Reduced H more than A)

Nigeria

Ethiopia

Nigeria

Ethiopia

Ghana 2003-2008 (Reduced A and H Uniformly)

Nigeria

Ethiopia

Nigeria

Ethiopia

Pathways to Poverty Reduction

Ghana Nigeria Ethiopia

Assets

Cooking Fuel

Flooring

Safe DrinkingWater

ImprovedSanitation

Electricity

Nutrition

Child Mortality

SchoolAttendance

Years ofSchooling

Nigeria: Indicator Standard Errors

Ethiopia’s Regional Changes Over Time

Addis Ababa

Harari

Nigeria’s Regional Changes Over Time

South South

North Central

Inside the Regions of Nigeria

NorthCentral

NorthEast

NorthWest

SouthEast

SouthSouth

SouthWest

ved in

... Assets

Cooking Fuel

Flooring

Safe DrinkingWaterImprovedSanitationElectricity

Nutrition

Child Mortality

Years ofSchoolingSchoolAttendance

Robustness checks

to ‘value judgements’

(choice of parameters)

Robustness to poverty cutoff

k= 20% to 40%

• 90% of the possible pairs of countries have a

dominance relation for k 2 to 4. That is, we

can say that one country is unambiguously

poorer than another regardless of whether we

require to be poor in 20, 30 or 40% of the

weighted indicators.

Robustness to Weights MPI Weights 1 MPI Weights 2 MPI Weights 3

Equal weights:

33% each

(Selected

Measure)

50% Education

25% Health

25% LS

50% Health

25% Education

25% LS

Pearson 0.992

Spearman 0.979

Kendall (Taub) 0.893

Pearson 0.995 0.984

Spearman 0.987 0.954

Kendall (Taub) 0.918 0.829

Pearson 0.987 0.965 0.975

Spearman 0.985 0.973 0.968

Kendall (Taub) 0.904 0.863 0.854

Number of countries: 109

Weights 2

50% Education

25% Health

25% LS

Weights 3

50% Health

25% Education

25% LS

Weights 4

50% LS

25% Education

25% Health

Robustness to Weights

Summary:

•High Correlations: 0.97 and above

•High Rank Concordance: 0.90 and

•85% of all possible pairwise

comparisons are robust

Complements monetary poverty measures

Gives a ‘high resolution’ lens on poor people’s lives

An overview and a ‘dashboard’

Changes over time – can change relatively quickly

Provides incentives to reduce intensity and incidence.

Can be used to identify the poorest

Adaptable for National Poverty Measures (or M&E)

Research and Policy: large agenda is ongoing

Uses of an MPI

Value Judgement 1: Selection of Data

- existing data

- internationally comparable

- legitimacy: MDGs

- malnutrition rather than income

- updated infrequently

Value Judgement 2: Selection of

Dimensions

Dimensions are ‘notional’ –

affect wts, communication

Follows precedent: HDI,

Possible because of data

Value Judgement 3: Selection of Indicators

Data constrained

Reflect MDGs (consensus)

Relatively Comparable

*note: technicalities in

construction are hardly

normatively justified but

matter a lot – e.g. hh

Value Judgement 4: Selection of Weights

Weights are ‘nested’ –

equal then equal.

This is easy to

understand, and often

Robust to a range of

plausible weights

Most controversial.

1/6 on Health and

Education

Indicators

1/18 on standard

of living indicators.

Identification: Who is poor?

A person is multidimensionally poor if they are

deprived in 33% of the dimensions at the

same time.

Colombia’s National MPI:

5 Dimensions, 15 Variables, Nested Weights

Educational

Conditions Childhood & Youth

Work Health Housing & Public

Services

Schooling

Illiteracy

School

Attendance

At the right

Access to

infant

services

No Child

Labour

Absence of

long-term

unemploy-

Coverage

Access to health

care given a

necessity

Improved Water

Flooring

Overcrowding

Sanitation

Exterior

Formal work 0.1

0.2 0.2 0.2 0.2 0.2

0.1 0.1

0.04 Poverty cutoff =

Territorial

Mexico’s National Measure: 6 social deprivations (1/12) + income (1/2)

Social Rights Deprivations

Population

Current income per capita

Six Social Rights: • Education

• Health

• Social Security

• Housing

• Basic Services

• Food

0 3 2 1 4 5 6

Social Rights

Deprivations

Mexico’s Identification:

poverty = (income + 1); extreme = (lower income + 3)

With Deprivations

EXTREME Multidimensional

Poverty

Moderate Multidimensional

Poverty

Vulnerable by social deprivations

Vulnerable by income

5 2 4 1 6

Ideal Situation

Without

Deprivations

MULTIDIMENSIONALLY POOR Basic Needs £

Food £

Income

Day 1:

Purpose of poverty measure

Dimensions to communicate measure

Particular Indicators used to measure poverty

Deprivation Cutoffs how much of each indicator?

Poverty Cutoff who is poor?

Values/Wts what are the relative weights of indicators?

Day 2:

Procedure: Who decides normative issues? What is the

appropriate role of poor people, governments, and

statistical or technical experts?

Plural Criteria: How should statistical, political, and

participatory input be coordinated in measurement design?

Thank you

www.ophi.org.uk

Purpose

Aim of each session - discuss how to: • make the value judgements inherent in this decision (options)

• balance normative, technical, & political issues (priority)

• update over time

Chair to summarize:

1. How would we suggest to those charged with designing the multidimensional

poverty measure that they undertake the three steps above?

2. What pressing research questions have been noted?

3. (does the question need to be reformulated or changed?)

Participants to contribute:

• Literature – please jot or email annotated biblio, stating why you propose each

and what you see it adding (ophi@qeh.ox.ac.uk)

• People / Projects with expertise or research (as above)

• Ideas that you feel like sharing in writing

For today, we presume that the value judgements pertain to the

design of a long-term official measure of multidimensional poverty.

The poverty measure will inform policy design, and reflect positive

change that can be influenced by public policy.

This is to be updated periodically (say every 2 years) using time series

data that are nationally representative and can be decomposed by

region and relevant social groups.

The survey design will take place after the measure is designed.

The purpose of the evaluative exercise shapes all choices, e.g.

National Poverty Measure – to span decades

Youth Poverty Measure – once, to profile youth issues

Targeting exercise – to benefit poorest of the poor

Monitoring measure – to track progress to given goals

International Comparisons – across nations

Community Development – show changes transparently

To some extent, the purpose, having been determined, shapes the

value judgements. Should these be taken ‘as given’?

E.g. a measure designed to monitor progress towards a national development plan

might systematically exclude public debate.

Should omission of public debate require justification? Space of resources?

E.g. a measure designed to document a given set of human rights from the

universal declaration might ignore cultural values.

How justify the ‘need’ for contextual vs comparable measures ?

E.g. a very rigorous measure designed to evaluate a small poverty intervention may

cost more than the intervention itself.

E.g. a measure run in a famine-prone area may be framed to exclude malnutrition

E.g. a measure may be designed to target 20% of people when 50% are destitute

Value Judgements in Multidimensional Poverty Measurement ... · methodology M ka =(ρ k,Ma)...

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