Transcript S.A.M.P.L.E. Small Area Methods for Poverty and Living

S.A.M.P.L.E.
Small Area Methods for
Poverty and Living condition Estimates
Siena – 5 November 2013
New indicators and models for inequality
and poverty with attention to social
exclusion, vulnerability and deprivation
Gianni Betti
University of Siena
EU – FP7 - SSH-2007-1
Grant Agreement no 217565
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Table of contents
List of Tasks of WP1:
1. Task 1.1. The indicators of poverty
2. Task 1.2. EU-SILC over sampling
3. Task 1.3. Pooled estimates of indicators
4. Task 1.4. Indicators for Local Government
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Task 1.1. The indicators of poverty - 1
Thematic literature review:
Traditional poverty measures.
Review of several Multidimensional.
Fuzzy measures.
Background of the Laeken Indicators.
 Proposal for new multidimensional and fuzzy measures of poverty and
inequality:
Fuzzy monetary and Fuzzy non-monetary indicators following the
ntegrated Fuzzy and Relative Approach (CRIDIRE).
Fuzzy monetary Depth and Fuzzy Supplementary Depth indicators
(WSE).
 Development of re-sampling methods for variance estimation for
multidimensional measures of poverty:
Jack Knife Repeated Replication method (CRIDIRE).
Bootstrap Method (WSE).
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Task 1.1. The indicators of poverty - 2
Poverty is a Fuzzy State
It is not a discrete attribute characterised in terms of presence or absence
It is rather a vague predicate that manifests itself with different shades and degrees
Poor
0
Non-poor
Z
Y
Nevertheless, traditional methods of analysis treat poverty as dichotomous variable, a
simplification that wipes out all the nuances that exist between the two extremes
SEVERE
MATERIAL
HARDSHIP
HIGH
WELFARE
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Task 1.1. The indicators of poverty - 3
Membership functions
Reconsider the definition of the membership function
based on monetary variables

Cheli and Lemmi (1995)
n

w
i 

i

i 1F  l
n
 w
i 
 l1 

Betti and Verma (1999)


w

ly
l



i

i

1


FM
1

L


i
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(
M
),
i
w
y

l l

1
l

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Task 1.1. The indicators of poverty - 4
Corresponding to the following projections:
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Task 1.1. The indicators of poverty - 5
Definition of the membership function
Betti, Cheli Lemmi and Verma (2005, 2006)


1




w
|
y

y
w
y
|
y

y




i



i






1



.






FM

1

F
1

L
F

.




i
i
w
|
y

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w
y
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

 1

 1










The definition of the membership function is based on the monetary
variable, where the alpha parameter is chosen such that the mean is
equal to the Head Count Ratio.
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Task 1.1. The indicators of poverty - 6
Poverty and inequality
The Fuzzy Monetary (FM) measure, as defined in the previous slide, is
expressible in terms of the generalised Gini measures. This family of
measures (often referred to as "s-Gini") is a generalisation of the
standard Gini coefficient, the latter corresponding to G with  =1.
In the continuous case it is defined as:

1




.




G


.


1
.
1

F
F

L
F
.
dF





1

0
Betti, Cheli Lemmi and Verma (2006) define it as:
“Integrated Fuzzy and Relative” (IFR)
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Task 1.1. The indicators of poverty - 7
Proposal for new multidimensional and fuzzy
Fuzzy Supplementary Indicator
To quantify and put together diverse indicators several steps are necessary:
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Identification of items;
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Transformation of the items into the [0, 1] interval;
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Exploratory and confirmatory factor analysis;
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Calculation of weights within each dimension (each group);
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Calculation of scores for each dimension;
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Calculation of an overall score and the parameter;
•
Construction of the fuzzy deprivation measure in each dimension (and
overall).
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Task 1.1. The indicators of poverty - 8
7 dimensions are identified:
1. Basic life-style – these concern the lack of ability to afford most basic requirements:
Keeping the home (household’s principal accommodation) adequately warm; Paying
for a week’s annual holiday away from home; Eating meat chicken or fish every
second day, if the household wanted to; Ability to make ends meet.
2. Financial situation – these concern the lack of ability to pay in time due to financial
difficulties: Inability to cope with unexpected expenses; Arrears on mortgage or rent
payments; Arrears on utility bills; Arrears on hire purchase instalments.
3. Housing amenities – these concern the absence of basic housing facilities (so basic
that one can presume all households would wish to have them): A bath or shower; An
indoor flushing toilet; Leaking roof and lamp; Rooms to dark.
4. Environmental problems – these concern problems with the neighbourhood and the
environment: Pollution; Crime, violence, vandalism; Noise.
5. Consumer durables - these concern enforced lack of widely desired possessions
("enforced" means that the lack of possession is because of lack of resources): A car
or van; A colour TV; A pc; A washing machine; A telephone.
6. Health related – these concern problems with personal health: General health;
Chronic illness; Mobility restriction.
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Task 1.1. The indicators of poverty - 9
Development of SAS programs for poverty
measures and variance estimation
Methods proposed in theory:
Jack-knife repeated replications (JRR - CRIDIRE)
Taylor linearisation (CRIDIRE)
Bootstrap (WSE)
Implementation with SAS and R routines for JRR and Bootstrap
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Task 1.1. Some empirical results - 1
Figure 1. EU: Net equivalent income – NUTS1 regions
3.4
8.8
9.2
9.3
9.4
n.a
-
8.8
9.2
9.3
9.4
10
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Task 1.1. Some empirical results - 2
Figure 2. Head Count Ratio NUTS2 regions (country poverty lines)
2.4 - 10 .9
10.9 - 1 2.9
12.9 - 1 5.9
15.9 - 2 0.0
20.0 - 4 9.0
n.a.
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Task 1.1. Some empirical results - 3
Figure 3. Overall Non-monetary deprivation rates, NUTS1 regions
8.3 11.4
14.8
17.6
19.9
n.a
11 .4
- 1 4.8
- 1 7.6
- 1 9.9
- 3 4.3
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Task 1.1. Some empirical results - 4
Figure 4. Environmental Problems, NUTS1 regions
8.2 - 13 .4
13.4 - 1 7.4
17.4 - 2 0.1
20.1 - 2 5.6
25.6 - 3 2.6
n.a
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Task 1.1. Some empirical results - 5
Figure 5. Environmental Problems, NUTS2 regions
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