Small area Estimation of Italian poverty and social exclusion indicators

1
Small area Estimation of Italian poverty and
social exclusion indicators

• Stefano Falorsi
• Michele DAlò
• Loredana Di Consiglio
• Fabrizio Solari
• Matteo Mazziotta
• Claudia Rinaldelli
• ISTAT
• solari_at_istat.it

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
2
Outline

• Indicators and composite indexes
• Reliability of indexes
• Small area estimators
• Experimental study
• Results
• Conclusions

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
3
Indicators and composite indexes

• The socio-economic analysis of the geographical
  areas should include different indicators, for
  measuring different dimensions of the phenomena.
• A synthetic description of the multi-dimensional
  phenomena can be then provided assembling the
  individual indicators into a single index, on the
  basis of an underlying model of the
  multi-dimensional concept that is intended to be
  measured.
• Composite measures are used when individual
  indicators cannot adequately capture such
  multi-dimensional concepts.

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
4
Composite indexes
i) Standardization Let Xxij denote the
original data matrix of indicators, we denote
with and the mean and the
standard deviation of the j-th indicator,
where The standardized of indicators
matrix Zzij is computed as follows
if the j-th indicator is concordant with the
phenomenon to be measured, if the j-th
indicator is disconcordant with the phenomenon
to be measured.
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
5
Composite indexes
ii) Aggregation a) Simple Mean of the
Indicators The simple mean of the indicators is
given by b) MPI The index proposed by
Mazziotta and Pareto (2007) is defined
as where
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
6
Indicators and composite indexes

• The indicators are usually obtained on the basis
  of sample survey observations and they are
  subjected to sample variability.
• This aspect should be considered also when
  analyzing the composite index obtained starting
  from the single indicators.
• Caution should be taken when drawing conclusions,
  when indexes are unreliable.
• In this study we considered how the improvement
  in the estimation of each indicator positively
  affects the composite indexes.

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
7
Experimental study

• We have considered the Italian provinces (NUTS3)
  and the following indicators
• Unemployment rate
• Poverty rate (threshold 0.6 median of
  equivalised income)
• Rate of individuals with at least ISCED 2
• 500 samples were drawn using bootstrap technique
  from EU-SILC and LFS 2005 samples.

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
8
Experimental study

• Indicators of unemployment rate and poverty rate
  are evaluated by means of direct estimators are
  affected by a large variability, therefore small
  area estimators may achieve improvement in the
  evaluation of the phenomenon.
• We have considered EBLUP on unit level and area
  level models, where the following covariates
  where used
• poverty rate
• Age (6 classes)
• unemployment and educational level rates
• Sex by Age (5 classes)
• Model group separate models for geographical
  macro-areas defined as North-Center and South of
  Italy

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
9
Small area estimators
Unit level EBLUP (Battese et al., 1988)

• The EBLUP of the mean value assumes a
  linear mixed model with unit-specific auxiliary
  variables, random area-specific effects and
  errors independently normally distributed
• and it is given by
• where

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
10
Small area estimators
Area level EBLUP (Fay and Herriot, 1979)

• The area level EBLUP assumes a linear mixed model
  using area-specific auxiliary variables
• The expression of the EBLUP is
• where again

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
11
Preserving ranks
Euclidean distance (D) Spearman correlation
coefficient (r )
Composite index Composite index Composite index Composite index
Estimator Mean Mean MPI MPI
D r D r

Direct 9.17 0.95 9.25 0.95
Unit Level EBLUP 8.20 0.96 8.14 0.96
Area Level EBLUP 8.10 0.96 8.07 0.96
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
12
Bias Direct Estimators
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
13
Bias Unit Level EBLUP
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
14
Bias Area Level EBLUP
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
15
MSE Direct Estimators
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
16
MSE Unit Level EBLUP
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
17
MSE Area Level EBLUP
International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010
18
Final remarks

• The experimental study showed that the
  performances of composite indexes improve (both
  in terms of MSE and of preserving rankings) if
  using SAE methods to compute indicators when
  direct estimators are not reliable.
• Further improvement may be achieved by means of
  enhanced small area estimators, introducing more
  complex models
• Use of triple goals estimators (Shen Louis,
  1998) targeting the compromise between mean value
  and ranking estimation, seems to be the most
  appropriate in this context.

International Conference on Indicators and Survey
Methodology 2010, Wien 25-26 February 2010