Multidimensional Poverty Measurement and Analysissticerd.lse.ac.uk/seminarpapers/ses17062015.pdf · Multidimensional Poverty Measurement and Analysis. Sabina Alkire, James Foster,

Multidimensional Poverty Measurement and Analysis

Sabina Alkire, James Foster, Suman Seth, Maria Emma Santos,

José Manuel Roche and Paola Ballon

17 June 2015LSE

Multidimensional Measurement Methods:

multidimensionalpoverty.org

ContentsChapter 1 – IntroductionChapter 2 – The frameworkChapter 3 – Overview of Methods for Multidimensional Poverty AssessmentChapter 4 – Counting Approaches: Definitions, Origins and ImplementationsChapter 5 – The Alkire-Foster Counting MethodologyChapter 6 – Normative Choices in Measurement DesignChapter 7 – Data and AnalysisChapter 8 – Robustness Analysis and Statistical InferenceChapter 9 – Distribution and DynamicsChapter 10 – Some Regression models for AF measures

ContentsChapter 1 – IntroductionChapter 2 – The FrameworkChapter 3 – Overview of Methods for Multidimensional Poverty AssessmentChapter 4 – Counting Approaches: Definitions, Origins and ImplementationsChapter 5 – The Alkire-Foster Counting MethodologyChapter 6 – Normative Choices in Measurement DesignChapter 7 – Data and AnalysisChapter 8 – Robustness Analysis and Statistical InferenceChapter 9 – Distribution and DynamicsChapter 10 – Some Regression models for AF measures

How can we measure poverty multidimensionally?

• Chapter 3

Dashboards, Composite Indices, Venn Diagrams, Dominance, Statistical, Fuzzy, Axiomatic and Counting

(Suman will present in a moment)

Where has a counting approach been used?

• Chapter 4

History of counting approaches, including Europe’s counting based measures (up to and including EU-2020), and Latin America’s Unmet Basic Needs.

What is this M0 anyway?

• Chapter 5 (I will discuss in a moment)

How to choose dimensions, indicators in M0?

• Chapter 6

Purpose, feasibility, technical and statistical strength, ease of communication, legitimacy.

(Sabina will discuss in a moment)

What are the different techniques to check the robustness of M0?

• Chapter 8

Dominance tests, statistical tests.

(Sabina will discuss in a moment)

How to conduct dynamic analyses using M0?

• Chapter 9

Absolute and relative changes, significance, dimensionalchanges, demographics – for cross-section & panel data. (Sabina will discuss in a moment)

What kind of post-estimation econometric analysis can be done?

• Chapter 10

• Micro and macro linear regression analysis, determinantsof poverty at the household level, and at the country level.

• (Paola will discuss in a moment)

The Alkire-Foster Methodology

Multidimensional DataMatrix of well-being scores for n persons in d dimensions

Persons

z = ( 13 12 3 1) Cutoffs

13.1 14 4 115.2 7 5 012.5 10 1 020 11 3 1

Dimensions

Replace entries: 1 if deprived, 0 if not deprived

Persons

z = ( 13 12 3 1) Cutoffs

These entries fall below cutoffs

13112001105.120572.1514141.13

Multidimensional Data

Dimensions

Deprivation MatrixReplace entries: 1 if deprived, 0 if not deprived

Persons

0010111110100000

Dimensions

Identification – WeightsDeprivation Matrix Weighted Deprivation Matrix

000000

wwwwwww

[ ]4321 wwwww =

0010111110100000

Dimensions Dimensions

Identification – Counting DeprivationsAssuming equal weights and

Persons

0010111110100000

Dimensions

IdentificationQ/ Who is poor?

Persons

0010111110100000

Dimensions

Identification – Union ApproachQ/ Who is poor?A1/ Poor if deprived in any dimension ci ≥ 1

Persons

0010111110100000

Dimensions

Identification – Union ApproachQ/ Who is poor?A1/ Poor if deprived in any dimension ci ≥ 1

Persons

Observations

Union approach often predicts very high numbers.Charavarty et al ’98, Tsui ‘02, Bourguignon & Chakravarty

2003 etc use the union approach

0010111110100000

Dimensions

Identification – Intersection Approach Q/ Who is poor?A2/ Poor if deprived in all dimensions ci = d

Persons

0010111110100000

Dimensions

Identification – Intersection Approach Q/ Who is poor?A2/ Poor if deprived in all dimensions ci = d

Persons

ObservationsDemanding requirement (especially if d large)Often identifies a very narrow slice of population

Atkinson 2003 first to apply these terms.

0010111110100000

Dimensions

Identification – Dual Cutoff Approach Q/ Who is poor?A/ Fix cutoff k, identify as poor if ci > k

Persons

0010111110100000

Dimensions

Identification – Dual Cutoff Approach Q/ Who is poor?A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2)

Persons

0010111110100000

Dimensions

Identification – Empirical Example

Poverty in India for 10 dimensions

91% of population would be targeted using union

0% using intersection

We need something in the middle (Alkire and Seth 2009)

Aggregation k = 2 Censor data of non-poor

Persons

0010111110100000

Dimensions

Aggregation k = 2 Censored weighted deprivation matrix and censored

deprivation scorec(k)

Persons( )

0000111110100000

Dimensions

k = 2 Censored weighted deprivation matrix

Persons

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

Aggregation – Headcount Ratio

0000111110100000

Dimensions

Suppose the number of deprivations rises for person 2

Dimensions c(2)

Critique

0000111110110000

Suppose the number of deprivations rises for person 2

Dimensions c(2)

Two poor persons out of four: H = ½No change!

Violates ‘dimensional monotonicity’

Critique

0000111110110000

Aggregation Return to the original censored weighted deprivation matrix

Dimensions c(2)

Persons( )

0000111110100000

Aggregation - Intensity Need to augment information

Dimensions c(k) c(k)/d

0000111110100000

4/44/2

Deprivation shares among poor

Aggregation - Intensity Need to augment information

A = average deprivation share among poor = 3/4

0000111110100000

4/44/2

Deprivation shares among poor

Aggregation: Adjusted Headcount Ratio Adjusted Headcount Ratio = M0 = HA

Persons

M0 = HA = (1/2)*(3/4) = 0.375

0000111110100000

4/44/2

Aggregation: Adjusted Headcount Ratio Adjusted Headcount Ratio = M0 = HA = μ( 0(k))

Persons

M0 = HA = (1/2)*(3/4) = 0.375M0 = μ( 0(k)) = 6/16 = 0.375

0000111110100000

4/44/2

Aggregation: Adjusted Headcount Ratio Suppose the number of deprivations rises for person 2

Persons( )

0000111110110000

4/44/3

Aggregation: Adjusted Headcount Ratio Suppose the number of deprivations rises for person 2

Persons

A = average deprivation share among poor = 7/8M0 changes! M0 = 7/16 = 0.4375

Satisfies dimensional monotonicity

0000111110110000

4/44/3

Interpretation: conveys information on deprivations

Applicability: valid for ordinal data

Simplicity: easy to compute

Useful properties– Subgroup decomposition– Dimensional breakdown

Expandable: If variables are all cardinal can go further

Methodology: Adjusted Headcount Ratio

METHODOLOGIES FORMULTIDIMENSIONAL POVERTYCOMPARISONS

(Ch 3)

Methodologies− Dashboard Approach− Composite Indices

− Venn Diagrams− Dominance Approach− Statistical Approaches− Fuzzy Sets Approach− Axiomatic Approach

Marginal methods using aggregate dataand ignoring joint distribution of deprivations (even when feasible)

Methodologies reflecting joint distribution of deprivations

Ignoring Joint Distribution

Income Education Shelter Water

1. D ND ND ND

2. ND D ND ND

3. ND ND D ND

4. ND ND ND D

Income Education Shelter Water

1. ND ND ND ND

2. ND ND ND ND

3. ND ND ND ND

4. D D D D

Joint Distribution I Joint Distribution II

ND: Not DeprivedD: Deprived

Venn Diagrams

Multiple indicators from the Europe 2020 target

At-risk of poverty Severe

material deprivation

Joblessness

Diagrammatic representation of all possible logical relations between a finite number of dimensions with binary options (Introduced by John Venn in 1880)− Used by Atkinson et al. (2010), Ferreira and Lugo (2013), Naga and

Bolzani (2006), Roelen et al. (2009), Alkire and Seth (2013), Decancq, Fleurbaey, and Maniquet (2014), Decanq and Neumann (2014)

Venn Diagrams: Pros and Cons

Advantages− A visual tool to explore overlapping binary deprivations− Considers the joint distribution of deprivations− Intuitive for 2-4 dimensions

Disadvantages− May not identify who is multidimensionally poor− No summary measure (thus, no complete ordering)− Every dimension converted into binary options− Difficult to read for 5 or more dimensions

Dominance Approach

Ascertains whether poverty is unambiguously lower or higher regardless of parameters and poverty measures− Unidimensional: Atkinson (1987), Foster and Shorrocks (1988)− Multidimensional: Bourguignon and Chakravarty (2002), Duclos,

Sahn & Younger (2006)

Such a claim certainly has strong political power!– Avoids the possibility of contradictory rankings

Key tool: Cumulative distribution function

Dominance Approach

Unidimensional DominanceBi-dimensional DominanceDuclos, Sahn and Younger (2006)

b ' b '' b

yF xF( )yF b"

( )xF b"( )yF b'

( )xF b'

Dominance Approach: Pros and Cons

Advantages− Offers tool for strong empirical assertions about poverty comparisons− Considers the joint distribution of achievements/deprivations− Avoids ‘controversial’ decisions on parameter values

Disadvantages− No summary measure, No complete ordering− Allows pair-wise dominance, but not cardinally meaningful difference− Dominance conditions depend on relationship between dimensions− For 2+ dimensions, limited applicability for smaller datasets− Stringent less intuitive conditions for dominance beyond first order

Statistical Approaches

The main aim is to reduce dimensionality− May be used for poverty identification, poverty aggregation, or both− Are used during measurement design for

− Exploring relationships across variables− Setting weights

Statistical Approaches: Pros and Cons

Advantages− Considers joint distribution− Some (e.g. MCA) can be used with ordinal data− Helps clarify relations among indicators: strengthen indicator design

Disadvantages− Poverty identification and measurement are often not transparent

− Not straightforward for communicating− Identification is mostly relative (based on percentiles of the score)− Comparisons across time may be difficult

Fuzzy Sets Approach

In poverty measurement, thresholds/cutoffs dichotomizepeople into sets of the deprived and non-deprived or poor and non-poor

Yet there may be uncertainty about where to set cutoffs− “… it is undoubtedly more important to be vaguely right than

to be precisely wrong.” (Sen 1992: 48-9)

This approach explore how to be vaguely right− Zadeh (1965), Cerioli & Zani (1990), Cheli & Lemmi (1995),

Chiapero-Martineti (1994, 1996, 2000)

Fuzzy Sets – IdentificationExtend Venn diagrams: allow varying degrees of membership to

the extent of poverty/deprivation

The selection of the membership function is key

Poor Non-PoorTraditional

Fuzzy unboundedMembership

Fuzzy boundedMembershipCertainly

PoorCertainlyNon-Poor

Fuzzy Sets Approach: Pros and Cons

Advantages− Offers summary measure− Offers hierarchy among dimensions; explicit tradeoffs− Considers joint distribution of deprivations

Disadvantages− Justification of membership function is not straightforward− Robustness tests are not mostly provided− Some membership functions may misuse ordinal data− Fuzzy sets results may conflict with Dominance results

Axiomatic Approach

Develops poverty measures that comply with a number of desirable properties

Unidimensional: Sen (1976), Watts (1969), Foster, Greer and Thorbecke(1984), Chakravarty (1983), Clark, Hemming and Ulph (1981), Atkinson (1987), among others.

Multidimensional: Chakravarty, Mukherjee and Ranade (1998), Tsui (2002), Bourguignon and Chakravarty (2003), Chakravarty and D’Ambrosio(2006), Alkire and Foster (2007, 2011), Bossert, Chakravarty and D’Ambrosio (2009), Maasoumi & Lugo (2008), Decancq, Fleurbaey, and Maniquet (2014) among others

[Most extends FGT (1984), then Watts (1969) or Chakravarty (1983)

Advantages− Allows looking at joint distribution of deprivations − Offers summary measure of poverty − Provides clearer understanding on how measures behave due to

different transformations (biggest advantage!)

Disadvantages− Relies on normative judgments (May require various robustness tests) − No single measure can satisfy all desirable properties (properties

themselves often need strong justifications)− Final poverty measures are difficult to interpret intuitively when they

are made to satisfy many properties simultaneously

Axiomatic Approaches: Pros and Cons

Comparison of Methodologies

MEASUREMENT DESIGN

(Ch 2,3,5,6,7)

Why Measure? Action ‘with vigour’Coordination ~ Policy Design ~ Monitoring ~ Targeting ~ Allocation

“Positive changes have often occurred and yielded some liberation when the remedying of ailments has been sought actively and pursued with vigour”

Jean Dreze and Amartya Sen India: An Uncertain Glory 2013

How measure? Select Indicators, Cutoffs, Values

Example: Global MPI

Example: Colombia’s MPI

Example: EU-SILC MPI

Here we vary the weights and poverty cutoff and weights on a set of 12 indicators from EU-SILC data over time.

Lived Environment

Health

Education

Living Standards(EU-2020)

How choose parameters? Select Indicators, Cutoffs, Values

Normative: (Ch 6)Public Debate (participation, lit, survey)Explicit Scrutiny (communicate)Standards, Plans, Laws, Priorities (so is used)

Technical: (Ch 7)Unit of Identification ; Applicable populationRedundancy/associationData issues: eg accuracy at individual/hh level

Robustness tests (Ch 8)

Build a deprivation score for each person

Select Indicators, Cutoffs, Values

k = 33%

1. Select Indicators, Cutoffs, Values

. Build a deprivation score for each person

3. Identify who is poor

k = 33%

Build a deprivation score for each person

Identify who is poor

Select Indicators, Cutoffs, Values

Compute MPI (=M0 from James): MPI = H×A

MPI Censored Deprivation Matrix g0(k)MPI = H*A = .442k=33.33% or 3.333

Indicators c(k) c(k)/d

H = headcount ratio = ¾ = 75%A = intensity = (0.776+0.553+0.442)/3=0.59 = 59%

MPI = HA = .442

0 0 0 0 0 0 0 0 0 01.67 1.67 1.67 1.67 .55 0 0 0 0 .55

0 1.67 0 1.67 .55 0 .55 .55 .55 00 0 0 1.67 .55 .55 .55 0 .55 .

07.765.534.42

0.776.553.442

Robustness of 2010 Global MPI

No indicator duplicates the information of others

GLOSSARY

Censored headcount ratio (hj): The proportion of people who are multidimensionally poor and deprived in each of the indicators.Censoring: The process of removing from consideration deprivations belonging to people who do not reach the poverty cutoff and focusing in on those who are multidimensionally poor.

Deprivation cutoffs (𝒛𝒛𝒋𝒋): The achievement levels for a given dimension below which a person is considered to be

deprived in a dimension.

Deprived: A person is deprived if their achievement is strictly less than the deprivation cutoff in any dimension.Incidence (𝑯𝑯): The proportion of people (within a given population) who experience multidimensional poverty. This is also called the ‘multidimensional headcount ratio’ or simply the ‘headcount ratio’. Sometimes it is called the ‘rate’ or ‘incidence’ of poverty. It is the number of poor people 𝑞𝑞 over the total population 𝑛𝑛.

Intensity (𝑨𝑨): The average proportion of deprivations experienced by poor people (within a given population) or the average deprivation score among the poor. The intensity is the sum of the deprivation scores, divided by the number of poor people.

Percentage contribution of each indicator: The extent to which each weighted indicator contributes to poverty.Poor : A person is identified as poor if their deprivation score (sum of weighted deprivations) is at least as high as the poverty cutoff: ci>𝒌𝒌

Poverty cutoff (𝒌𝒌): This is the cutoff or cross-dimensional threshold used to identify the multidimensionallypoor. It reflects the proportion of weighted dimensions a person must be deprived in to be considered poor. Because more deprivations (a higher deprivation score) signifies worse poverty, the deprivation score of all poor people meets or exceeds the poverty cutoff.

Uncensored or raw headcount ratios: The deprivation rates in each indicator, which includes all people who are d d dl f h h h l d ll

UNFOLDING M0 (CH 5) DECOMPOSITIONS

PARTIAL INDICES: ⌂ - Headcount ratio H ⌂ - Intensity A

SUB-INDICES: ⌂ - censored headcount ratio ⌂ - dimensional contributions

Afghanistan

Indonesia

Cameroon

M0 or MPI: Headline results

Disaggregated DataFull profiles online for 803 subnational regions plus rural-urban for 108 countries

Afghanistan

Indonesia

Cameroon

H and A: intuitive + new

Namibia

Brazil

Argentina

Indonesia

Guatemala

Nigeria

Tajikistan

ZimbabweCambodia

Bangladesh

Gambia

Tanzania MalawiRwanda

AfghanistanMozambique

Congo DR

Burundi

Guinea-Bissau

Liberia

SomaliaEthiopia Niger

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Percentage of People Considered Poor (H)

Poorest Countries, Highest MPI

The size of the bubbles is a proportional representation of the total number of MPI poor in each country

India: (H, A)

Decomposing India: H: 12.4% to 79.3%A: 40.2% to 60.3%

Censored Headcount RatioPercentage of the population who arePoor and Deprived in each indicator.

What is the censored headcount ratio of each dimension?

Income: 1/4 Education: 2/4Sanitation: 1/4 Electricity: 1/4

Contribution Percentage that each weighted deprivation contributes to overall poverty (or absolute)

MULTIDIMENSIONALPOVERTY DYNAMICS:

(Ch 9)

Paper, Datasets and Indicators

Alkire, S. & Seth, S. (2015) Multidimensional poverty reduction in India between 1999 and 2006: Where and how? World Development 72, 93-108

Two rounds of Demographic Health Surveys (DHS)• DHS 1998-99 (NFHS II)• DHS 2005-06 (NFHS III)

Minor adjustments were made for four indicators for strict comparability• School Attendance, Child Mortality, Nutrition, Floor

India’s Change in MPII

1999 2006 ChangeMPII 0.300 0.251 -0.049*

Incidence (H) 56.8% 48.5% -8.1%*

Intensity (A) 52.9% 51.7% -1.2%*

• MPII (Indian MPI) fell significantlyDetails in Alkire and Seth (2015)

• Per annum reduction in incidence (H) was larger than the reduction in consumption expenditure headcount ratio between 1993/94 and 2004/05

(Tendulkar Committee Report 2009)88

Dominance in Headcount Ratios for Different Poverty Cutoffs

-15%-5%5%

15%25%35%45%55%65%75%85%95%0.0

Poverty Cutoff1999 2006 Change

Absolute Reduction in MPI by Large States

We combined Bihar and Jharkhand, Madhya Pradesh and Chhattishgarh, and Uttar Pradesh and Uttarakhand

-0.110 -0.090 -0.070 -0.050 -0.030 -0.010

Andhra Pradesh (*) [0.299]Kerala (*) [0.136]Tamil Nadu (*) [0.195]Karnataka (*) [0.255]Jammu (*) [0.226]Gujarat (*) [0.248]Orissa (*) [0.381]Maharashtra (*) [0.226]West Bengal (*) [0.339]Himachal Pradesh (*) [0.154]Eastern States (*) [0.315]Madhya Pradesh (*) [0.368]Haryana () [0.19]Uttar Pradesh (*) [0.348]Rajasthan () [0.341]Punjab (*) [0.117]Bihar () [0.442]

Absolute Change (99-06) in MPI-I

Significant reduction in all states except Bihar, Haryana & Rajasthan.

Comparison with Change in Income Poverty Headcount Ratio (p.a.)

-3.50%-3.00%-2.50%-2.00%-1.50%-1.00%-0.50%0.00%0.50%

Change in MD Poverty (k = 1/3) Change in PCE Poverty

Andhra Pradesh

Arunachal Pradesh

Gujarat

HaryanaHimachal Pradesh

Jammu & Kashmir Karnataka

Kerala

Madhya Pradesh

Maharashtra

Manipur

Meghalaya

Mizoram

Nagaland

OrissaPunjab

RajasthanSikkim

Tamil Nadu

Tripura

Uttar Pradesh

West Bengal

∆MHR = 0.354 ‒ 0.029×MHR R² = 0.241

10 20 30 40 50 60 70 80

Monetary Poverty Headcount Ratio (MHR) in 1993/94 (in Percentage Points)

Andhra Pradesh

Arunachal Pradesh

Goa Gujarat

Haryana

Himachal Pradesh

Jammu & KashmirKarnataka

Kerala

Madhya Pradesh

Maharashtra

ManipurMeghalaya

Mizoram

Nagaland

Orissa

Punjab

RajasthanSikkim

Tamil Nadu

Tripura

Uttar Pradesh

West Bengal

∆H= 0.014×H ‒ 2.111R² = 0.072

10 20 30 40 50 60 70 80

Multidimensional Headcount Ratio (H) in 1999 (in Percentages)

Absolute reduction in monetary poverty rates across states

Absolute reduction in MPI poverty rates across states

Absolute Reduction in MPII by Social groups

-0.110 -0.090 -0.070 -0.050 -0.030 -0.010

Urban (*) [0.116]

Rural (*) [0.368]

General (*) [0.229]

OBC (*) [0.301]

SC (*) [0.378]

ST (*) [0.458]

Sikh (*) [0.115]

Christian () [0.196]

Hindu (*) [0.306]

Muslim () [0.32]

Absolute Change (99-06) in MPI-I

Religion

Slower progress for STs and Muslims

Improvement in Poverty: H or A?

Andhra Pradesh

Arunachal Pradesh

Assam Bihar

GoaGujarat

HaryanaHimachal Pradesh

Jammu & Kashmir

Karnataka

Kerala

Madhya Pradesh

Maharashtra Manipur

Meghalaya

Mizoram

Nagaland

Orissa

Punjab

Rajasthan

Tamil Nadu

TripuraUttar Pradesh

West Bengal

-3.4% -2.9% -2.4% -1.9% -1.4% -0.9% -0.4% 0.1% 0.6%

Annual Absolute Variation in % Headcount Ratio (H)

Reduction in Intensity of Poverty (A)

Bad/Good

Bad/BadReduction in Incidence of Poverty (H)

Good /Good

Good/ Bad

Performance consistently strongest in Kerala, TN, & AP.

1999 2006H 56.8% 48.5%A 52.9% 51.7%

Change in Censored Headcount Ratios

-12.0%

-10.0%

Indicator (Statistical Significance) [1999 CH Ratio]

Changes in Censored Headcount Ratios

We have annual trial measures over time for 31 European countries 2006-2012 (Alkire Apablaza & Jung 2014)

These can be gender disaggregated

Women are often significantly poorer, and always have higher deprivations in education and health

1. Intuitive – easy to understand2. Birds-eye view - can be unpacked

a. by region, ethnicity, rural/urban, etcb. by indicator, to show compositionc. by ‘intensity’ to show inequality among poor

3. Adds Value: a. focuses on people with multiple deprivationsb. shows people’s simultaneous deprivations.

4. Incentives to reach the poorest of the poor5. Flexible: you choose indicators/cutoffs/values6. Robust to wide range of weights and cutoffs7. Academically Rigorous

Policy Interest – Why?

National MPI: Chile, launched Feb 2015

Led by Mexico, Bhutan, Colombia, many countries are developing national MPIs for policy.

In the SDGs, Poverty is Multidimensional

Open Working Group Goal 1 Target 1.2: by 2030, reduce at least by half the proportion of men,

women and children of all ages living in poverty in all its dimensions according to national definitions.

Sixty-Ninth Session of the UN General Assembly Dec 2014.

(A/RES/69/238) 5. Underlines the need to better

reflect the multidimensional nature of development and poverty...

UNSG Synthesis Report Dec 2014:2.1 Shared Ambitions: ... Member States

will need to fill key sustainable development gaps left by the Goals, such

as the multidimensional aspects of poverty

5.1 Measuring the new dynamics ... Poverty measures should reflect the multi-dimensional nature of poverty.

SOME REGRESSION MODELSFOR AF METHOD:

(Ch 10)

What are we missing?Indonesia (1993) provides the following characterisation (descriptive) of multidimensional poverty (M0=0.133) (Ballon & Apablaza, 2013)

MD poor households characteristics of the household head

Average Proportion

Years of Age Household Male Muslimeducation size head

2.1 25.5 5.1 80% 91%

we still miss the « effect » (size)of each of these characteristics on overall poverty in a multivariate framework.

Why is this important?

From a policy perspective, in addition to measuringpoverty we must perform some vital analysesregarding the transmission mechanisms betweenpolicies and poverty measures.

This is to assess how poverty is explained by non-M0 related variables

How can we account for this?

Through regression analysis we can account forthe “effect/size” of micro and macro determinantsof multidimensional poverty.

We can differentiate between:

• ‘micro’ regressions: unit of analysis is the householdor the person

•‘macro’ regressions: unit analysis is some “spatial”aggregate, such as a province, a district or a country.

This chapter

This chapter provides the reader with a generalmodelling framework for analysing thedeterminants of Alkire–Foster poverty measures, atboth micro and macro levels of analyses.

This modelling framework is studied within the classof Generalised Linear Models (GLM’s).

GLM’s are preferred as the data analytic technique.They account for the bounded and discrete natureof the AF-type dependent variables.

Micro and Macro RegressionsWhat are some vital regression analysis we may wish to study with AF measures?

Micro regressions:

a) explore the determinants of poverty at the household level

b) create poverty profiles;

Macro regressions

a) explore the elasticity of poverty to economic growth,

b) understand how macro variables such as average income,public expenditure, decentralization, infrastructure density,information technology relate to multidimensional poverty levelsor changes across groups or regions—and across time.

Dependent variable AF measure: 𝑌𝑌

Range of 𝑌𝑌

Regression Model Level Conditional Distribution 𝑝𝑝𝑌𝑌(𝑦𝑦)

Binary (𝑐𝑐𝑖𝑖 ≥ 𝑘𝑘) 0,1 Probability Micro Bernoulli

𝑀𝑀0,𝐻𝐻 [0,1] Proportion Macro Binomial

Which are some ‘focal’ variables to regress?

Generalised Linear Modelling

The GLM family of models involves predicting a function(g) of the conditional mean of a dependent variable as alinear combination of a set of explanatory variables (thelinear predictor). This function is referred to as the linkfunction .

A GLM takes the form:

Classic linear regression is a specific case of a GLM inwhich the conditional expectation of the dependent variableis modelled by the identity function.

( ) ∑+==j

ijjiY iig xx ββηµ 0|

Generalized Linear Regression Models with AF Measures

Dependent variable AF measure: 𝑌𝑌

Range of 𝑌𝑌

Regression Model

Level Conditional Distribution

𝑝𝑝𝑌𝑌(𝑦𝑦)

Link 𝑔𝑔(𝜇𝜇𝒊𝒊) = 𝜂𝜂𝒊𝒊

Mean function 𝜇𝜇𝒊𝒊 = 𝐺𝐺(𝜂𝜂𝑖𝑖)

Binary (𝑐𝑐𝑖𝑖 ≥ 𝑘𝑘) 0,1 Probability Micro Bernoulli Logit loge𝜇𝜇𝑖𝑖

1 − 𝜇𝜇𝑖𝑖 Λ(𝜂𝜂𝑖𝑖)

𝑀𝑀0,𝐻𝐻 [0,1] Proportion Macro Binomial Probit Φ−1(𝜇𝜇𝑖𝑖) Φ(𝜂𝜂𝑖𝑖) Note: Φ(∙) and Λ(∙) are the cumulative distribution functions of the standard-normal and logistic distributions, respectively. For the binary model, the conditional mean 𝜇𝜇𝑖𝑖 is the conditional probability 𝜋𝜋𝑖𝑖 .

A binary model in the GLM framework

The outcomes of this binary variable occur with probability πiwhich is a conditional probability given the explanatory variables:

For a binary model the conditional distribution of thedependent variable, or random component in a GLM, isgiven by a Bernoulli distribution.

1 if and only if 0 otherwise

( )iiYiii Y xx ||Pr µπ =≡

A binary model in the GLM framework

To ensure that the πi stays between 0 and 1, a GLM commonlyconsiders two alternative link functions (g): probit link -quantile function of the standard normal distribution function,and the logit link – quantile of the logistic distributionfunction.

The logit model (log of the odds) of π gives the relativechances of being multidimensionally poor.

0 1 1log ...1e i k kix xπ β β β

π= + + +

Example

Poverty profile for West Java, Indonesia in 1993(Ballon & Apablaza, 2013)

We regresses the log of the odds of beingmultidimensionally poor (with k=33%) ondemographics, and socio-economic characteristics ofthe household head.

These have been selected on the grounds of‘restraining’ any ‘possible’ endogeneity issue thatmay arise in the construction of this poverty profile.

Logistic regression results – West Java, 1993

Variable

Parameter Robust t ratio Significance

Estimate Std. Err. level

Years of education of household head

-0.68 0.03 -19.65 ***

Female household head

0.24 0.09 2.71 ***

Household size

0.09 0.01 7.02 ***

Living in urban areas

-0.85 0.07 -11.40 ***

Being Muslim

-0.02 0.32 -0.07 n.s.

0.98 *** denotes significance at 5% level; n.s. denotes non-significance

Estimated parameters exhibiting a negative sign denote a decreasein the odds, this is obtained as (1-odds ratio)*100.

For the effect of education (1-0.51)*100 ↓49%,For the effect of gender (1.28-1)*100% ↑ 28%.

abilit

2 4 6 8 10Years of education of household head

Urban Rural

Logistic regression

Macro Regression Models for M0 and H

H and M0 are indices, bounded between zero and one

Thus an econometric model for these endogenousvariables must account for the shape of theirdistribution, which has a restricted range of variationthat lies in the unit interval.

H and M0 are therefore fractional (proportion) variablesbounded between zero and one with the possibility ofobserving values at the boundaries.

Papke and Wooldridge (1996) Approach

To model H or M0 we follow the modeling approachproposed by Papke and Wooldridge (1996).

Papke and Wooldridge propose a particular quasi-likelihood method to estimate a proportion.

The method follows Gourieroux, Monfort andTrognon(1984) and McCullagh and Nelder (1989) andis based on the Bernoulli log-likelihood function

The way forward..

EUSILC: Correlations (Cramers’ V) across uncensored deprivation headcount ratios

q-jobless s mat dep education noise pollution crime housing health chr. illness morbidity u.m. needs

AROP 0.44 0.45 0.23 0.24 0.16 0.18 0.25 0.23 0.36 0.21 0.23q-jobless 1.00 0.30 0.19 0.26 0.18 0.20 0.23 0.20 0.45 0.20 0.15s mat dep 1.00 0.22 0.30 0.22 0.22 0.40 0.23 0.41 0.15 0.20education 1.00 0.20 0.15 0.13 0.21 0.34 0.48 0.28 0.16

noise 1.00 0.61 0.46 0.32 0.25 0.36 0.25 0.30pollution 1.00 0.38 0.24 0.19 0.37 0.19 0.23

crime 1.00 0.24 0.17 0.37 0.18 0.20housing 1.00 0.24 0.37 0.21 0.28health 1.00 0.91 0.65 0.22

chr illness 1.00 0.93 0.50morbidity 1.00 0.16um needs 1.00

EUSILC: Redundancy values across uncensored deprivation headcount ratios

q-jobless sev. mat dep education noise pollution crime housing health chr.

illness morbidity u.m. needs

AROP 0.27 0.22 0.09 0.03 0.01 0.03 0.1 0.07 0.03 0.05 0.06q-jobless 1 0.18 0.06 0.04 0.02 0.05 0.07 0.11 0.09 0.1 0.05

sev. mat dep 1 0.07 0.06 0.05 0.06 0.18 0.12 0.05 0.07 0.14education 1 -0.01 -0.01 -0.01 0.06 0.19 0.14 0.12 0.02

noise 1 0.41 0.25 0.12 0.03 0.04 0.03 0.05pollution 1 0.25 0.1 0.03 0.05 0.03 0.05

crime 1 0.09 0.03 0.05 0.03 0.05housing 1 0.07 0.04 0.04 0.08health 1 0.42 0.55 0.11

chr. illness 1 0.39 0.1morbidity 1 0.08u.m. needs 1

Redundancy: ratio of percentage deprived in both indicators to lower of the two total deprivation headcount ratios

Figure 5: Dimensional Decomposition Measure 1 k=26% by country (2009) ranked from poorest

EUSILC: Bubble graph of changes Measure 1 by H and A 2006-2009-2012

Figure 9: Changes in the adjusted headcount ratio M0by region over time

Measure 1 k=26% Measure 2 k=21% Measure 3 k=34%M0 M0 M0

Multidimensional Poverty Measurement and Analysissticerd.lse.ac.uk/seminarpapers/ses17062015.pdf · Multidimensional Poverty Measurement and Analysis. Sabina Alkire, James Foster,

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