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
Multidimensional Measurement Methods:
multidimensionalpoverty.org
Multidimensional Measurement Methods:
multidimensionalpoverty.org
Multidimensional Measurement Methods:
multidimensionalpoverty.org
Multidimensional Measurement Methods:
multidimensionalpoverty.org
Multidimensional Measurement Methods:
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
Multidimensional Measurement Methods:
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
Multidimensional Measurement Methods:
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
Multidimensional Measurement Methods:
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
Multidimensional Measurement Methods:
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
Multidimensional Measurement Methods:
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
Multidimensional Measurement Methods:
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
Multidimensional Measurement Methods:
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)
Multidimensional Measurement Methods:
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.
Multidimensional Measurement Methods:
What is this M0 anyway?
• Chapter 5 (I will discuss in a moment)
Multidimensional Measurement Methods:
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)
Multidimensional Measurement Methods:
What are the different techniques to check the robustness of M0?
• Chapter 8
Dominance tests, statistical tests.
(Sabina will discuss in a moment)
Multidimensional Measurement Methods:
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)
Multidimensional Measurement Methods:
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
X
=
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
X
Multidimensional Data
Dimensions
Deprivation MatrixReplace entries: 1 if deprived, 0 if not deprived
Persons
=
0010111110100000
0g
Dimensions
Identification – WeightsDeprivation Matrix Weighted Deprivation Matrix
=
000
000000
2
4321
420
wwwwwww
g
[ ]4321 wwwww =
=
0010111110100000
0g
Dimensions Dimensions
Identification – Counting DeprivationsAssuming equal weights and
c
Persons
=
0010111110100000
0g
1420
1
djj
w d=
=∑
Dimensions
IdentificationQ/ Who is poor?
c
Persons
1420
=
0010111110100000
0g
Dimensions
Identification – Union ApproachQ/ Who is poor?A1/ Poor if deprived in any dimension ci ≥ 1
c
Persons
1420
=
0010111110100000
0g
Dimensions
Identification – Union ApproachQ/ Who is poor?A1/ Poor if deprived in any dimension ci ≥ 1
c
Persons
Observations
Union approach often predicts very high numbers.Charavarty et al ’98, Tsui ‘02, Bourguignon & Chakravarty
2003 etc use the union approach
1420
=
0010111110100000
0g
Dimensions
Identification – Intersection Approach Q/ Who is poor?A2/ Poor if deprived in all dimensions ci = d
c
Persons
1420
=
0010111110100000
0g
Dimensions
Identification – Intersection Approach Q/ Who is poor?A2/ Poor if deprived in all dimensions ci = d
c
Persons
ObservationsDemanding requirement (especially if d large)Often identifies a very narrow slice of population
Atkinson 2003 first to apply these terms.
1420
=
0010111110100000
0g
Dimensions
Identification – Dual Cutoff Approach Q/ Who is poor?A/ Fix cutoff k, identify as poor if ci > k
c
Persons
=
0010111110100000
0g
1420
Dimensions
Identification – Dual Cutoff Approach Q/ Who is poor?A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2)
c
Persons
=
0010111110100000
0g
1420
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
c
Persons
=
0010111110100000
0g
1420
Dimensions
Aggregation k = 2 Censored weighted deprivation matrix and censored
deprivation scorec(k)
Persons( )
=
0000111110100000
0 kg
0420
Dimensions
k = 2 Censored weighted deprivation matrix
c(2)
Persons
Two poor persons out of four: H = 1/2
Aggregation – Headcount Ratio
( )
=
0000111110100000
20g
0420
Dimensions
Suppose the number of deprivations rises for person 2
Dimensions c(2)
Critique
( )
=
0000111110110000
20g
0430
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
20g
0430
Aggregation Return to the original censored weighted deprivation matrix
Dimensions c(2)
Persons( )
=
0000111110100000
20g
0420
Aggregation - Intensity Need to augment information
Dimensions c(k) c(k)/d
( )
=
0000111110100000
20g
0420
4/44/2
Deprivation shares among poor
Aggregation - Intensity Need to augment information
Dimensions c(k) c(k)/d
A = average deprivation share among poor = 3/4
( )
=
0000111110100000
20g
0420
4/44/2
Deprivation shares among poor
Aggregation: Adjusted Headcount Ratio Adjusted Headcount Ratio = M0 = HA
Dimensions c(k) c(k)/d
Persons
M0 = HA = (1/2)*(3/4) = 0.375
( )
=
0000111110100000
20g
0420
4/44/2
Aggregation: Adjusted Headcount Ratio Adjusted Headcount Ratio = M0 = HA = μ( 0(k))
Dimensions c(k) c(k)/d
Persons
M0 = HA = (1/2)*(3/4) = 0.375M0 = μ( 0(k)) = 6/16 = 0.375
( )
=
0000111110100000
20g
0420
4/44/2
g
g
Aggregation: Adjusted Headcount Ratio Suppose the number of deprivations rises for person 2
Dimensions c(k) c(k)/d
Persons( )
=
0000111110110000
20g
0430
4/44/3
Aggregation: Adjusted Headcount Ratio Suppose the number of deprivations rises for person 2
Dimensions c(k) c(k)/d
Persons
A = average deprivation share among poor = 7/8M0 changes! M0 = 7/16 = 0.4375
Satisfies dimensional monotonicity
( )
=
0000111110110000
20g
0430
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
Cum
ulat
ive
Dis
trib
utio
n Fu
nctio
n
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
How measure? Select Indicators, Cutoffs, Values
Example: Colombia’s MPI
Example: EU-SILC MPI
How measure? Select Indicators, Cutoffs, Values
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 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 .
)
5
(
5
g k
=
07.765.534.42
0.776.553.442
Robustness of 2010 Global MPI
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
79
Disaggregated DataFull profiles online for 803 subnational regions plus rural-urban for 108 countries
Afghanistan
Indonesia
Cameroon
80
H and A: intuitive + new
Namibia
Brazil
Argentina
Indonesia
Guatemala
Ghana
Lao
Nigeria
Tajikistan
ZimbabweCambodia
Nepal
Bangladesh
Gambia
Tanzania MalawiRwanda
AfghanistanMozambique
Congo DR
Benin
Burundi
Guinea-Bissau
Liberia
SomaliaEthiopia Niger
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Aver
age
Inte
nsity
of
Pove
rty
(A)
Percentage of People Considered Poor (H)
Poorest Countries, Highest MPI
China
India
The size of the bubbles is a proportional representation of the total number of MPI poor in each country
India: (H, A)
82
Decomposing India: H: 12.4% to 79.3%A: 40.2% to 60.3%
83
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
84
Contribution Percentage that each weighted deprivation contributes to overall poverty (or absolute)
85
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
87
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
56
0.111
0.167
0.222
0.278
0.333
0.389
0.444
0.500
0.556
0.611
0.667
0.722
0.778
0.833
0.889
0.944
1.000
Perc
enta
gre o
f Pop
ulat
ion P
oor S
ubjec
t to
MPI
Pove
rty C
utof
fs
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
Stat
es (S
igni
fican
ce) [
MPI
-I in
1999
]
Significant reduction in all states except Bihar, Haryana & Rajasthan.
90
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
91
Andhra Pradesh
Arunachal Pradesh
Assam
Bihar
Goa
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
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
10 20 30 40 50 60 70 80
Abs
olut
e C
hang
e in
Mon
etar
y H
eadc
ount
Rat
io p
.a. b
etw
een
19
93/9
4 an
d 20
04/0
5 (i
n Pe
rcen
tage
Poi
nts)
Monetary Poverty Headcount Ratio (MHR) in 1993/94 (in Percentage Points)
Andhra Pradesh
Arunachal Pradesh
Assam
Bihar
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
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
10 20 30 40 50 60 70 80
Abs
olut
e Cha
nge
in M
ultid
imen
sion
al H
eadc
ount
Rat
io
p.a.
bet
wee
n 19
99 a
nd 2
006
(in P
erce
ntag
e Po
ints
)
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
Stat
es (
Sign
ifica
nce)
[M
PI-I
in 1
999]
Religion
Caste
Slower progress for STs and Muslims
93
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
-1.0%
-0.8%
-0.6%
-0.4%
-0.2%
0.0%
0.2%
0.4%
-3.4% -2.9% -2.4% -1.9% -1.4% -0.9% -0.4% 0.1% 0.6%
Ann
ual A
bsol
ute
Varia
tion
in %
Int
ensi
ty (A
)
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%
94
Change in Censored Headcount Ratios
-12.0%
-10.0%
-8.0%
-6.0%
-4.0%
-2.0%
0.0%
Abs
olut
e C
hang
e in
CH
Rat
io
Indicator (Statistical Significance) [1999 CH Ratio]
95
Changes in Censored Headcount Ratios
96
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
97
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|
iη
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
ii
c kY
≥=
( )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
Odds
Estimate Std. Err. level
ratio
Years of education of household head
-0.68 0.03 -19.65 ***
0.51
Female household head
0.24 0.09 2.71 ***
1.28
Household size
0.09 0.01 7.02 ***
1.10
Living in urban areas
-0.85 0.07 -11.40 ***
0.43
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%.
0.1
.2.3
.4Pr
edic
ted
prob
abilit
y
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
119
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
120
Figure 5: Dimensional Decomposition Measure 1 k=26% by country (2009) ranked from poorest
121
EUSILC: Bubble graph of changes Measure 1 by H and A 2006-2009-2012
122
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
k k k
123