Transcript Slide 1

Strategies of multidimensional
measurement
Andrea Brandolini
Banca d’Italia, Department for Structural Economic Analysis
2012 ISFOL Conference
“Recognizing the Multiple Dimensions of Poverty:
How Research Can Support Local Policies”
Rome, 22 -23 May 2012
Background
World Bank, World Development Report 2000/2001:
Attacking Poverty
“This report accepts the now traditional view of
poverty … as encompassing not only material
deprivation (measured by an appropriate concept of
income or consumption), but also low achievements
in education and health. … This report also broadens
the notion of poverty to include vulnerability and
exposure to risk – and voicelessness and
powerlessness” (italics added)
Multidimensionality in poverty research
Absolute number
700
600
As a % ratio to "income poverty"
24
Multidimensional poverty
20
500
16
400
12
300
8
Multidimensional
deprivation
200
4
100
0
0
95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
Source: author’s search of "exact phrase" in Google Scholar, 21 May 2012.
Background
Alkire & Foster “Counting and multidimensional poverty
measurement”, Journal of Public Economics, 2011
“Multidimensional poverty has captured the attention
of researchers and policymakers alike due, in part, to
the compelling conceptual writings of Amartya Sen
and the unprecedented availability of relevant data.”
Background
Europe 2020 strategy
Five headline targets for member states’ policies:
“Reduction of poverty by aiming to lift at least 20
million people out of the risk of poverty or social
exclusion”
Risk of poverty or social exclusion → multidimensional
Poor population comprises people …
… either living in households with very low work intensity
(where adults work less than 20% of total work potential)
… or at-risk-of-poverty after social transfers
(equivalised income below 60 % of national median)
… or severely materially deprived
(at least 4 out of 9 deprivations owing to lack of resources)
Outline
• Multidimensionality in practice
• Empirical strategies
– Do we want a single number?
– Weighting
– Functional form
• Health and income deprivation in France,
Germany and Italy, 2000
• Conclusions
Multidimensionality in practice
• Multidimensionality has intuitive appeal
• Problems arise in transforming intuition into hard data
• Not every indicator needs to be appropriate
E.g. “proportion of persons meeting friends or
relatives less than once a month or never”
(Eurostat 2000; Townsend 1979)
Infrequent meetings with friends may signal
… weak social ties
but also
… preference for quietness
… or passion for internet
Multidimensionality in practice
 Multidimensional measurement without theory
may be misleading
• What is needed?
– Identification of relevant dimensions
– Construction of corresponding indicators
– Understanding of indicator metrics
– Empirical strategies, i.e. tools to deal with
multidimensionality
Empirical Strategies for Multiple Dimensions
Item-by-item
analysis
Supplementation
strategy
Vector
dominance
Non-aggregative
strategies
Sequential
dominance
Multivariate
techniques
Multidimensional
poverty indices
Comprehensive
analysis
Aggregative
strategies
Well-being
indicator
Equivalence
scales
Source: author’s elaboration based on Brandolini e D’Alessio 1998.
Social welfare
approach
Counting
approach
Empirical strategies
• Alternative strategies differ for extent of manipulation
of raw data
 the heavier the structure imposed on data, the
closer to complete cardinal measure
• Focus on aggregate measures, i.e. multidimensional
index or well-being indicator (both single number
but …)
 Do we want a single number?
 Weighting
 Functional form
Do we want a single number?
• Pros: communicational advantage
 single complete ranking more likely to capture
newspaper headlines and people’s
imagination than multidimensional scorecards
(‘Eye-catching property’, Streeten on HDI)
• Cons:
1. different metrics
2. informational loss
3. imposed trade-offs (complements/substitutes)
Weighting
• Different weighting structures reflect different views
Sen  ‘ranges’ of weights rather than single set
• Alternatives:
– Equal weighting. Lack of information about
‘consensus’ view. But no discrimination.
– Data-based weighting. Frequency-based or
multivariate techniques. Caution in entrusting a
mathematical algorithm with a normative task
– Market prices. Existing for some attributes only,
inappropriate for well-being comparisons
Functional form
(Old) HDI measured average achievement in human
developments in a country as
1  Li  L  1  2  Ai  A  1  Gi  G   1  ln Yi  ln Y
   
   
  
HDIi  
3  L  L  3  3  A  A  3  G  G   3  ln Y  ln Y
where: Y = GDP per capita
L = life expectancy at birth
A = adult literacy
G = gross school enrolment
Upper/lower bars = max/min
Replace prefixed minima and maxima and simplify
HDIi  0.0056Li  0.0022Ai  0.0011Gi  0.0556 lnYi  0.3951



Iso-HDI Contours
85
Japan
Life expectancy at birth (years)
80
Argentina
75
1 year
= $2,658 in Japan
= $166 in Kyrgyzstan
Hungary
70
Kyrgyzstan
65
Russia
60
Higher
HDI
55
50
45
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
GDP per capita (PPP US$)
Source: author’s elaboration on data drawn from UNDP (2005). All countries shown in the figure
have similar values of the education index, comprised between 0.93 and 0.96.
Functional form
Union vs. intersection
x2
Non
poor
z2
10
Union poor
H1+H2–H1,2
Intersection
poor
H1,2
0
0
z1
10
x1
Atkinson’s counting index: A = 2-κ(H1+H2) + (1–21-κ)H1,2
κ = 0 union
κ↑
more weight on multiple deprivations
κ → ∞ intersection
Iso-poverty contours for
Bourguignon-Chakravarty measure
If θ → ∞ substitutability
tends to 0, contours =
rectangular curves
x2
10
z2
If θ=α=1 attributes are
perfect substitutes and
convex part becomes
straight line
The higher  relative to ,
the more the two attributes
are substitutes
0
z1
10
0


 
 



x i 1 
x i 2   
1
P2  i w 1 max 1 
,0    w 2 max 1 
,0   
n
z
z
1
2



  
 

x1
Health and income deprivation in
France, Germany and Italy, 2000
• European Community Household Panel (ECHP)
• All persons aged 16 or more
• Two indicators:
– Health status: measured on a scale from 5 (very
good) to 1 (very bad) and based on respondent’s
self-perception
Health-poor = bad or very bad health
– Household equivalent income
Income-poor = equivalent income < median
Health and income deprivation
(percentage values)
Healthpoor
Incomepoor
Healthpoor
and
incomepoor
France
8.0
15.2
2.0
21.2
Germany
19.0
11.2
3.1
27.1
Italy
11.5
19.5
2.7
28.3
Source: author’ elaboration on ECHP data, Wave 8.
Healthpoor
or
incomepoor
Health and income deprivation in
France, Germany and Italy, 2000
Bourguignon-Chakravarty index - Different parameter values
Germany
=0.5, w=0.5 0.100
0.160
=1, w=0.5 0.012
=5, w=0.5
Italy
0.120
0.075
0.009
0.080
0.050
0.006
0.040
0.025
0.003
France
0.000
0.000
1
10

100
1000
0.000
1
10

100
1000
1
10

100
Source: author’ elaboration on ECHP data, Wave 8. Logarithmic scale for horizontal axes.
1000
Health and income deprivation in
France, Germany and Italy, 2000
Bourguignon-Chakravarty index - Different weighting
Germany
0.160
=0.5, =2 0.080
=1, =2 0.012
0.120
0.060
0.080
0.040
0.006
0.040
0.020
0.003
Italy
=5, =2
0.009
France
0.000
0.00
0.25
0.50
0.75
0.000
1.00
0.00
0.25
0.50
0.75
0.000
1.00
0.00
from health only to income only
Source: author’ elaboration on ECHP data, Wave 8.
0.25
0.50
0.75
1.00
Bourguignon-Chakravarty index
• Health-poor: score=1,2
• Consistent with cutoff at any value between 2 and 3
– cutoff = 3 (used above)
possible values=1/3,2/3
– cutoff = 2+
possible values=0,1/2
Contribution of health lower with 2+
– Germany
0.0110 instead of 0.0232
– France
0.0134 instead of 0.0195
• Agreement on identification of poor health status does not
lead to unambiguous definition of poverty cutoff and then
consistent with different values of index
 Serious shortcoming, as general problem for any
indicator in discrete space
Health and income deprivation in
France, Germany and Italy, 2000
Atkinson’s counting index
30
25
A = 2-κ(H1+H2) + (1–21-κ)H1,2
Italy
κ=0
κ↑
union
more weight on
multiple deprivations
κ → ∞ intersection
20
15
10
5
Germany
France
0
0
1
2
3
4
5
k
6
7
8
9
Source: author’s elaboration on ECHP data, Wave 8.
10
Conclusion
• Measurement of poverty and inequality in a
multidimensional space poses new problems relative
to measurement in unidimensional spaces
• Understanding sensitivity of results to underlying
hypotheses is crucial part of analysis
• But there is value added!
Thank you for your attention!