Small area Estimation of Italian poverty and social exclusion indicators

1. Small area Estimation of Italian poverty and social exclusion indicators Stefano Falorsi Michele D’Alò Loredana Di Consiglio Fabrizio Solari Matteo Mazziotta Claudia Rinaldelli ISTAT solari@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 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. 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 Unitlevel 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 Arealevel 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 ) 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