Small area Estimation of Italian poverty and social exclusion indicators

Stefano FalorsiMichele D’Alò

Loredana Di ConsiglioFabrizio Solari

Matteo MazziottaClaudia Rinaldelli

ISTAT

solari@istat.it

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

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

Outline

Indicators and composite indexesReliability of indexesSmall area estimatorsExperimental studyResultsConclusions

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.

Indicators and composite indexes

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

i) Standardization

Let X={xij }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 Z={zij } 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.

jxM

jxS

n

xn

iij

x j

1M

n

)x(n

ixij

x

j

j

1

2MS

10S

M100

j

j

x

xij

ij

)x(z

10S

M100

j

j

x

xij

ij

)x(z

Composite indexes

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

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

izi MM

iz

iz

iz

iz

iV

k

)z(

k

zk

jij

z

k

jij

z M

SC

M

SM 1

2

1

iii zzzi CVSMMPI

Composite indexes

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

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.

Indicators and composite indexes

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

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

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

Experimental study

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

iddTidid euxy

),(Niid~e,(Niid~u eidud22 0 ),0

ˆX)()ˆ)xX(y~(y

~dd

Tddddd 1

Small area estimators

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

dy

deuud nˆˆˆ 222

The area level EBLUP assumes a linear mixed model using area-specific auxiliary variables

The expression of the EBLUP is

where again

ddTddd euXyy

ˆX)(ˆ~~ T

ddddd 1yy

Small area estimatorsArea level EBLUP (Fay and

Herriot, 1979)

),(Niid~e,(Niid~u eidud22 0 ),0

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

deuud nˆˆˆ 222

Composite index

Estimator Mean 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

Preserving ranks Euclidean distance (D) Spearman correlation coefficient (r )

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

Bias Direct Estimators

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

Bias Unit Level EBLUP

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

Bias Area Level EBLUP

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

MSE Direct Estimators

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

MSE Unit Level EBLUP

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

MSE Area Level EBLUP

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

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.

Final remarks

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