Multidimensional Poverty
Comparisons:
The Issue of Inequality
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
1
Outline
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
1.
Introduction
2.
The Identification of the Poor
3.
The Aggregation of the characteristics of the poor
3.1 Core Axioms
3.1
The Core Axioms
3.2
A new Inequality Axiom
3.3
Two Unique Index Classes
3.4
A Numerical Example
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
4.
Summary
5.
© 2011 d·i·e
Empirical Application
4.1
Poverty Rates and Country Rankings
4.2
Decomposition
Summary
Nicole Rippin: Multidimensional Poverty Comparisons
2
Introduction: How should poverty be measured?
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
Multidimensional poverty measures are needed, not necessarily to replace but
to amend traditional income poverty measures (e.g. Rawls 1971, Sen 1985 &
1992, Drèze and Sen 1989, UNDP 1997)
Different approaches exist to derive multidimensional poverty indices (e.g.
fuzzy set approach, distance function approach, information theory approach,
axiomatic approach)
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Four main papers dealt with the extension of the one-dimensional axiomatic
approach to a multidimensional framework (Chakravarty, Mukherjee & Ranade
1998, Tsui 2002, Bourguignon & Chakravarty 2003, Chakravarty & Silber
2008)
Nicole Rippin: Multidimensional Poverty Comparisons
3
The framework
0.
Outline
i = 1,…,n individuals
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
j = 1,…,k attributes
z  Z ; Z  Rk threshold levels
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
xi  Rk
k-row vector of attributes of individual i
Individual i is deprived with respect to attribute j if xij  z j
4.2 Decomposition
5.
Summary
© 2011 d·i·e
S j ( X ) is the set of individuals deprived with respect to attribute j
Nicole Rippin: Multidimensional Poverty Comparisons
4
The Identification of the Poor
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
The identification of the poor: Common Methods:

Union Method: i is poor if j  1,2,..., k  : xij  z j

Intersection Method: i is poor if xij  z j j
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
However, for additive poverty measures both methods are practically
inapplicable, leading to either exaggerated or minimised poverty rates
Summary
In response, Alkire and Foster (2009) introduced a new identification method:

Dual Cut-off Method: i is poor if x ij  z j for j  1,2,..., k
and # j  d
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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Weaknesses of the Dual Cut-off Method
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
The dual cut-off method implies several weaknesses:

Arbitrariness: The choice of the cut-off lacks theoretical foundation
but affects country rankings

Discontinuity: The cut-off leads to a hardly justifiable discontinuity in
the identification of the poor: households suffering deprivations just
below the cut-off receive a weight of zero whereas households just
above the cut-off enter the index with full weight

Laborious: The dual cut-off method renders calculations cumbersome
since poverty measures have to be calculated k times
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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The Core Axioms
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
Anonymity (AN): For any ( X ; z )  K  Z : P ( X ; z )  P( X ; z ) where  is
any permutation matrix of appropriate order
Any personal characteristics apart from endowments are irrelevant for poverty
measurement
Continuity (CN): For any z  Z , P is continuous on K
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
Monotonicity (MN): For any ( X ; z ); (Y ; z )  K  Z if:
i) for any h, xhl  yhl   , where yhl  zl ,   0,
ii) xil  yil i  h, xij  yij j  l , i,
then P (Y ; z )  P ( X ; z ).
The poverty index does not increase if, ceteris paribus, a poor individual
experiences an endowment increase in a dimension in which it is deprived
m
Principle of Population (PP): For any ( X ; z )  K  Z ; m  N : P( X ; z )  P( X ; z )
where X m is the m-fold replication of X
The poverty index does not depend on the size of the population
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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The Core Axioms
0.
Outline
Focus (FC): For any ( X ; z );(Y ; z )  K  Z : if
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
i) for any h such that xhl  zl , yhl  xhl   ,   0,
ii) yil  xil i  h yij  xij j  l , i,
then P ( X ; z )  P (Y ; z ).
The poverty index does not change if an individual receives more of a
dimension in which it is not deprived
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Non-Decreasingness in Subsistence Levels (NS): For any X  K , z  Z ,
( X ; z ) is non-decreasing in z j j.
The poverty index does not decrease if, ceteris paribus, the threshold levels
increase
Summary
Non-Poverty Growth (NG): For any
(Y ; z )  K  Z , if X is obtained from Y
by adding a rich person to the population, then P ( X ; z )  P (Y ; z ).
The poverty index does not increase with the population size of the non-poor
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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The Core Axioms
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
Subgroup Decomposability (SD): For any X 1 ,..., X m  K and
m
P( X 1 , X 2 ,..., X m ; z )  i 1 ni nP( X i ; z )
with
z Z :
ni being the population size of subgroup X i , i  1,..., m and

m
n  n.
i 1 i
Factor Decomposability (FD): For any ( X ; z )  K  Z :
P( X ; z )   j 1 a j P( x j ; z j )
with a j  0 being the weight attached to attribute j and
k

k
j 1
a j  1.
Normalization (NM): For any ( X ; z )  K  Z : P ( X ; z )  1 if xij  0i, j
and P ( X ; z )  0 if xij  z j i, j.
Unit Consistency: For any ( X ; z );(Y ; z )  K  Z : if P ( X ; z )  P (Y ; z )
then P ( X; z )  P (Y; z ) with  being the diagonal matrix
diag (1 ,...,  k ),  j  0j.
Poverty orderings are not affected by a change of the unit of measurement
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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The Core Axioms
0.
Outline
Uniform Majorization (UM): For any z  Z and X, Y of the same dimension,
1.
Introduction
if X P  BY Pand B is not a permutation matrix, then P ( X ; z )  P (Y ; z ), where
2.
The Identification Step
3.
The Aggregation Step
X P Y P is the attribute matrix of the poor corresponding to X(Y) and B  bij 
is some bistochastic matrix of appropriate order.
An equalising operation does not increase poverty
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
But in the multidimensional case, inequality does not only exist within
dimensions, but also between dimensions
Consider the following situation:
i  2, j  3, z  3 3 3 3 3
0.5 0 0 0 0
 1 0 0 0 0
X

Y 
;
 1 5 10 7 6



0.5 5 10 7 6
Nicole Rippin: Multidimensional Poverty Comparisons
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The Core Axioms
0.
Outline
1.
Introduction
matrix Y by a weak inequality increasing switch of attribute l from one poor
2.
The Identification Step
individual to another if for some individuals g, h:
3.
The Aggregation Step
3.1 Core Axioms
3.2 New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
Weak Inequality Increasing Switch: Matrix X is said to be obtained from
i)
y hl  y gl  z l ; y gm  z m  y hm
ii) x gl  y hl , x hl  y gl ; x gm  y gm , x hm  y hm
iii) xil  y il , xim  y im i  g , h; xij  y ij j  l , m, i
Through a switch of endowments, the individual that is already deprived in
fewer dimensions receives a higher amount of an attribute with regard to
which both individuals are deprived.
Non-Decreasingness under Weak Inequality Increasing Switch (NDW):
For any
5.
Summary
(Y ; z )  K  Z , if X  K is obtained from Y by a weak inequality
increasing switch between two poor individuals, then P ( X ; z )  P (Y ; z ).
Like UM, NDW can only be satisfied by cardinal poverty indices
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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The Core Axioms
0.
Outline
1.
Introduction
i  2, j  3, z  3 3 3 3 3
2.
The Identification Step
3.
The Aggregation Step
5 0 0 0 0
Y 
;
1
2
10
7
6


3.1 Core Axioms
Consider the following situation:
1 0 0 0 0
X 

5 2 10 7 6
3.2 New Inequality Axiom
Strong Inequality Increasing Switch: Matrix X is said to be obtained from
3.3 Unique Index Classes
matrix Y by a weak inequality increasing switch of attribute l from one poor
3.4 A Numerical Example
individual to another if for some individuals g, h:
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
i) y hl  z l  y gl ; y gm  z m  y hm ;y gk  z k ; y hk  z k
ii) x gl  y hl , x hl  y gl ; x gm  y gm , x hm  y hm ;x gk  y gk , x hk  y hk
iii) xil  y il , xim  y im , xik  y ik i  g , h; x ij  y ij j  l , m, k , i
Through a switch, the number of deprivations of the individual that is already
deprived in less dimensions is reduced.
Non-Decreasingness under Strong Inequality Increasing Switch (NDS):
For any (Y ; z )  K  Z , if X  K is obtained from Y by a strong inequality
increasing switch between two poor individuals, then P ( X ; z )  P (Y ; z ).
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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Two unique classes of indices
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
Proposition 1:
The only family of poverty indices satisfying CN, FC, SD, FD, SI, MN, UM, NM
and NDW is of the form
P( X ; z )  1 n i 1  j 1 a j f i xij z j 
n

k

with f i : 0,   R1 continuous, non-increasing in (.), increasing in
di  # xij  z j , with f(0) = 1 and f (t )  0t  1. Also a j  0are constants
k
with  j 1 a j  1.
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
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Two unique classes of indices
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 New Inequality Axiom
Proposition 2:
The only family of poverty indices satisfying CN, FC, SD, FD, SI, MN, NM and
NDS is of the form
P ( X ; z )  1 n iS
j

k
j 1
a j  ij
3.3 Unique Index Classes
3.4 A Numerical Example
with
4.
 i  (0,1] increasing in d i # xij  z j
 ij  
0
Empirical Application
4.1 Rates and Rankings

4.2 Decomposition
5.
Summary
© 2011 d·i·e
Also a j  0 are constants with
if
if
xij  z j
xij  z j
 j 1 a j  1.
k
Nicole Rippin: Multidimensional Poverty Comparisons
14
Empirical application: the poverty indices
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
I utilize four different poverty indices for the poverty comparisons which all
satisfy an increasing number of sensitivity axioms:
MPI  1 n iS
j

POR  1 n iS

k
j 1
a j  ij
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
j
k
j 1
a j i  ij
NDS
PFGT ( X ; z )  1 n  j 1 iS a j 1  xij z j 
2
k
UM
j
4.2 Decomposition
5.
Summary
PCR ( X ; z )  1 n  j 1 iS a j i 1  xij z j 
2
k
UM & NDW
j
i 
© 2011 d·i·e

k
j 1
a j  ij

1 if
and  ij  
0 if
xij  z j
xij  z j
Nicole Rippin: Multidimensional Poverty Comparisons
15
Empirical application: dimensions, weights and
thresholds
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
The MPI comprises three equally weighted poverty dimensions: education,
health and living standards themselves captured by an overall of ten indicators
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
16
Five Indian Households…
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
HH
1
2
3
4
5
Education
Years
xmi = 0 zj = 5
15
10
9
5
0
Health/Nutrition Health/Nutrition Living Standards
Assets
BMI
w/a z-scores Sleeping Rooms Weighted Sum
xmin=14 zj=18.5 xmin=-4.5 zj = -2 xmin = 0 zj = 0.3 xmin = 0 zj = 0.27
30.29
-0.21
0.25
1.00
19.32
2.73
0.32
0.15
17.19
-1.46
0.29
0.25
18.47
-2.02
0.25
0.26
19.17
-5.58
0.06
0.00
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
As an illustration, consider the following numerical example which is drawn
from the Indian household DHS (2005)
Summary
© 2011 d·i·e
HH
1
2
3
4
5
All
MPI
POR
FGT
PCR
0.000 Rank 1
0.000 Rank 1
0.600 Rank 3
0.800 Rank 4
0.800 Rank 4
0.320
0.040 Rank 1
0.040 Rank 1
0.360 Rank 3
0.640 Rank 4
0.640 Rank 4
0.256
0.006 Rank 2
0.040 Rank 4
0.018 Rank 3
0.005 Rank 1
0.725 Rank 5
0.146
0.007 Rank 1
0.018 Rank 2
0.047 Rank 4
0.033 Rank 3
0.607 Rank 5
0.128
Nicole Rippin: Multidimensional Poverty Comparisons
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Empirical application: changes in poverty rates and
rankings
0.
Outline
A Sample of 28 Countries
Country
MPI 6
Value
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Rank
Por
Value
Rank
Change
0.004
Rank 1
0.008
Rank 1
Armenia
0.009
Rank
2
0.012
Rank
2
Moldova
0.021
Rank
3
0.021
Rank
3
Azerbaijan
0.085
Rank
4
0.054
Rank
4
Peru
0.139
Rank 5
0.086
Rank 5
Morocco
0.139
Rank 6
0.090
Rank 6
Ghana
0.174
Rank 7
0.104
Rank 7
Zimbabwe
0.175
Rank 8
0.106
Rank 8
Bolivia
0.184
Rank 9
0.107
Rank 9
Swaziland
0.187
Rank 10
0.113
Rank 10
Namibia
0.263
Rank 11
0.156
Rank 11
Cambodia
0.271
Rank 12
0.159
Rank 12
Congo, Rep.
0.285
Rank 13
0.178
Rank 14
-1
India
0.291
Rank 14
01.87
Rank 16
-2
Cameroon
0.292
Rank
15
0.174
Rank
13
+2
Bangladesh
0.302
Rank 16
0.183
Rank 15
+1
Kenya
0.306
Rank
17
0.193
Rank
17
Haiti
0.326
Rank 18
0.194
Rank 18
Zambia
0.350
Rank 19
0.218
Rank 19
Nepal
0.368
Rank 20
0.248
Rank 22
-2
Nigeria
0.385
Rank 21
0.236
Rank 20
+1
Malawi
0.393
Rank 22
0.240
Rank 21
+1
DR Congo
0.412
Rank 23
0.269
Rank 23
Benin
0.481
Rank 24
0.321
Rank 25
-1
Mozambique
0.484
Rank 25
0.308
Rank 24
+1
Liberia
0.557
Rank 26
0.390
Rank 26
Mali
0.569
Rank 27
0.391
Rank 27
Ethiopia
0.642
Rank
28
0.475
Rank
28
Niger
Methodology: Countries sorted in descending order by the MPI
The MPI’s neglect of inequality leads to
an artificial distortion of poverty rates
which are understated in less poor
countries and exaggerated in poorer
countries
Nicole Rippin: Multidimensional Poverty Comparisons
18
Empirical application: changes in poverty rates and
rankings
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Table 4:
Country
Implications for vulnerable population groups
 (MPI – Por)
Rural
7-10
Religion of Minority
Areas
members Christianity
Islam
0.215
0.048
Armenia
0.062
0.037
Moldova
0.092
0.076
0.017
Azerbaijan
0.057
0.003
Peru
0.023
-0.003
Morocco
0.044
0.005
-0.001
Ghana
0.027
0.005
0.004
Zimbabwe
0.042
0.006
Bolivia
0.014
0.009
-0.008
Swaziland
0.013
0.005
Namibia
0.007
-0.003
0.000
Cambodia
0.009
0.004
-0.002
Congo, Rep.
0.003
-0.007
-0.008
India
0.009
-0.008
-0.014
Cameroon
0.004
-0.004
Bangladesh
0.007
-0.013
-0.013
Kenya
0.002
-0.012
Haiti
-0.002
-0.012
-0.009
Zambia
0.003
-0.008
Nepal
-0.008
-0.005
-0.043
Nigeria
0.003
-0.008
-0.005
Malawi
-0.001
-0.010
DR Congo
0.001
-0.010
-0.019
Benin
-0.012
-0.012
-0.009
Mozambique
-0.027
-0.007
Liberia
-0.015
-0.014
-0.015
Mali
-0.003
-0.019
-0.010
Ethiopia
-0.015
-0.014
-0.015
Niger
Methodology: Countries sorted in descending order by the MPI.
The MPI’s neglect of inequality leads to
an artificial distortion of the contribution
of vulnerable population subgroups:
their contribution is overstated in less
poor countries and understated in
poorer countries
Nicole Rippin: Multidimensional Poverty Comparisons
19
Empirical application: changes in poverty rates and
rankings
Country Comparisons in 28 Countries
0.
Outline
Country
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
Moldova
Armenia
Azerbaijan
Peru
Swaziland
Bolivia
Zimbabwe
Ghana
Namibia
Congo, Rep.
Morocco
Cameroon
Zambia
Kenya
DR Congo
Nigeria
Liberia
Malawi
Haiti
Bangladesh
Benin
Cambodia
India
Nepal
Mozambique
Mali
Niger
Ethiopia
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Value
H
0.008
0.006
0.011
0.045
0.040
0.056
0.051
0.061
0.043
0.059
0.056
0.085
0.076
0.089
0.085
0.104
0.124
0.107
0.117
0.088
0.120
0.106
0.104
0.105
0.130
0.195
0.254
0.259
0.228
0.246
0.360
0.584
0.641
0.663
0.799
0.711
0.633
0.825
0.578
0.785
0.839
0.888
0.916
0.836
0.905
0.951
0.883
0.829
0.841
0.927
0.846
0.903
0.938
0.909
0.971
0.982
FGT
I
0.033
0.025
0.030
0.078
0.063
0.085
0.064
0.086
0.068
0.071
0.097
0.108
0.091
0.100
0.093
0.124
0.138
0.113
0.133
0.107
0.143
0.114
0.123
0.116
0.138
0.215
0.261
0.264
Pcr
Rank

Value
H
I
Rank

Rank 2
Rank 1
Rank 3
Rank 6
Rank 4
Rank 9
Rank 7
Rank 11
Rank 5
Rank 10
Rank 8
Rank 13
Rank 12
Rank 16
Rank 14
Rank 17
Rank 24
Rank 21
Rank 22
Rank 15
Rank 23
Rank 20
Rank 18
Rank 19
Rank 25
Rank 26
Rank 27
Rank 28
-1
+1
-2
+1
-3
-3
+4
+3
-1
+1
-2
+1
-1
-7
-3
-3
+5
-2
+2
+5
+5
-
0.004
0.004
0.008
0.028
0.027
0.038
0.031
0.043
0.033
0.042
0.045
0.062
0.062
0.069
0.069
0.087
0.093
0.089
0.099
0.085
0.100
0.094
0.96
0.104
0.119
0.162
0.226
0.237
0.228
0.246
0.360
0.584
0.641
0.663
0.799
0.711
0.633
0.825
0.578
0.785
0.839
0.888
0.916
0.836
0.905
0.951
0.883
0.829
0.841
0.927
0.846
0.903
0.938
0.909
0.971
0.982
0.016
0.015
0.022
0.048
0.042
0.058
0.039
0.060
0.052
0.051
0.077
0.079
0.073
0.077
0.075
0.104
0.103
0.094
0.112
0.103
0.119
0.101
0.114
0.115
0.127
0.178
0.233
0.241
Rank 2
Rank 1
Rank 3
Rank 5
Rank 4
Rank 8
Rank 6
Rank 10
Rank 7
Rank 9
Rank 11
Rank 13
Rank 12
Rank 14
Rank 15
Rank 17
Rank 19
Rank 18
Rank 22
Rank 16
Rank 23
Rank 20
Rank 21
Rank 24
Rank 25
Rank 26
Rank 27
Rank 28
-1
+1
-1
+1
-2
+1
-2
+2
+1
-1
+1
-1
-2
-3
+4
-2
+2
+2
-
Nicole Rippin: Multidimensional Poverty Comparisons
20
Empirical application: changes in poverty rates and
rankings
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
© 2011 d·i·e
Country Rankings in 29 Indian States
State
FGT
Value
H
I
Kerala
0.021
0.557
0.038
Delhi
0.042
0.590
0.072
Sikkim
0.055
0.703
0.078
Goa
0.039
0.626
0.062
Manipur
0.047
0.727
0.064
Himachal Pradesh
0.048
0.729
0.065
Mizoram
0.062
0.754
0.082
Punjab
0.052
0.653
0.079
Tamil Nadu
0.068
0.799
0.085
Jammu & Kashmir
0.063
0.772
0.081
Nagaland
0.091
0.839
0.108
Uttaranchal
0.071
0.769
0.092
Haryana
0.071
0.778
0.091
Arunachal Pradesh
0.101
0.814
0.124
Maharashtra
0.078
0.847
0.092
Karnataka
0.091
0.837
0.109
Andhra Pradesh
0.099
0.848
0.116
Tripura
0.080
0.824
0.097
Gujarat
0.090
0.819
0.110
0.083
Assam
0.837
0.099
Meghalaya
0.126
0.852
0.148
Orissa
0.114
0.858
0.133
Rajasthan
0.131
0.892
0.147
West Bengal
0.105
0.843
0.124
Chhattisgarh
0.099
0.891
0.111
Uttar Pradesh
0.123
0.899
0.136
Madhya Pradesh
0.135
0.905
0.150
Jharkhand
0.130
0.898
0.145
Bihar
0.167
0.925
0.180
Pcr
Rank

Value
H
I
Rank

1
3
7
2
4
5
8
6
10
9
17
11
12
21
13
18
19
14
16
15
25
23
27
22
20
24
28
26
29
-1
-4
+2
+1
+1
-1
+2
-1
+1
-6
+1
+1
-7
+2
-2
-2
+4
+3
+5
-4
-1
-4
+2
+5
+2
-1
+2
-
0.014
0.033
0.041
0.031
0.037
0.036
0.047
0.045
0.050
0.052
0.069
0.058
0.063
0.083
0.067
0.077
0.083
0.076
0.082
0.083
0.105
0.109
0.117
0.107
0.100
0.113
0.129
0.134
0.170
0.557
0.590
0.703
0.626
0.727
0.729
0.754
0.653
0.799
0.772
0.839
0.769
0.778
0.814
0.847
0.837
0.848
0.824
0.819
0.837
0.852
0.858
0.892
0.843
0.891
0.899
0.905
0.898
0.925
0.026
0.056
0.059
0.050
0.051
0.050
0.062
0.069
0.063
0.068
0.083
0.076
0.081
0.102
0.079
0.092
0.098
0.092
0.100
0.100
0.123
0.127
0.131
0.127
0.112
0.126
0.142
0.149
0.183
1
3
6
2
5
4
8
7
9
10
14
11
12
18
13
16
19
15
17
20
22
24
26
23
21
25
27
28
29
-1
-3
+2
+2
-1
+1
-3
+1
-1
-4
+2
-2
+3
+2
-1
-2
-3
+1
+4
+1
-
Nicole Rippin: Multidimensional Poverty Comparisons
21
Empirical application: Indian poverty maps
0.
Outline
Chattisgarh
MPI
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
[0,.05]
(.05,.1]
(.1,.15]
(.15,.2]
(.2,.25]
(.25,.3]
(.3,.35]
(.35,.4]
(.4,.5]
No data
Empirical Application
4.1 Rates and Rankings
FGT
Por
[0,.05]
(.05,.1]
(.1,.15]
(.15,.2]
(.2,.25]
(.25,.3]
(.3,.35]
No data
Pcr
4.2 Decomposition
5.
Summary
[0,.02]
(.02,.04]
(.04,.06]
(.06,.08]
(.08,.1]
(.1,.12]
(.12,.14]
(.14,.16]
(.16,.18]
No data
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
[0,.02]
(.02,.04]
(.04,.06]
(.06,.08]
(.08,.1]
(.1,.12]
(.12,.14]
(.14,.16]
(.16,.18]
No data
22
Summary
0.
Outline
1.
Introduction
2.
The Identification Step
3.
The Aggregation Step
3.1 Core Axioms
3.2 A New Inequality Axiom
3.3 Unique Index Classes
3.4 A Numerical Example
4.
Empirical Application
4.1 Rates and Rankings
4.2 Decomposition
5.
Summary
I introduced a new axiom that removes an anomaly in the way poverty indices
account for multidimensional inequality
The new axiom solves the exaggeration problem for additive poverty indices
by implying a change in the identification of the poor: any household that is
deprived is considered poor to a certain degree, i.e. receives an individual
weight that depends on the number of dimensions in which it is deprived
In the ordinal case, it removes some weaknesses of the MPI as induced by the
dual cut-off method: arbitrariness, discontinuity and distortion while at the
same time introducing sensitivity with regard to inequality among the poor. At
the same time it is much easier to calculate than the MPI as it is only
calculated once
Due to its specific two-step method, it is the first composite index that allows
for a degree of association-sensitivity between dimensions while it is still
additive and therefore decomposable
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
23
Thank you!
© 2011 d·i·e
Nicole Rippin: Multidimensional Poverty Comparisons
24