Matteo Mazziotta and Adriano Pareto Istat - Methodological Office Valentina Talucci

1. Composite Indices to Measure Poverty and Social Inequality in Europe Matteo Mazziotta and Adriano Pareto Istat - Methodological Office Valentina Talucci University of Rome “La Sapienza” Wien, february 24-26 2010

2. Conference on Indicators and Survey Methodology 2010 Introduction Aim of the work Individuating individual indicators that represent the phenomena Comparing different composite indices in order to find a robust solution “Designing” social inequality in Europe Wien, february 24-26 2010

3. Conference on Indicators and Survey Methodology 2010 Definitions Social inequality “...refers to the ways in which socially-defined categories of persons are differentially positioned with regard to access to a variety of social “goods”, such as the labour market and other sources of income, the education and healthcare system, and form of political representation and participation.” Poverty (UN Statement, June 1998) “…is a denial of choices and opportunities, a violation of human dignity. It means lack of basic capacity to participate effectively in society. It means not having enough to feed and cloth a family, not having a school or clinic to go to, not having the land on which to grow one’s food or a job to earn one’s living, not having access to credit. It means insecurity, powerlessness and exclusion of individuals, household and communities. It means susceptibility to violence, and it often implies living on marginal or fragile environments, without to clean water or sanitation” Wien, february 24-26 2010

4. Conference on Indicators and Survey Methodology 2010 Multidimensional phenomena • Social inequality and poverty are complex multidimensional • They cannot be reduced to the income dimension • Multidimensionality has theoretical advantages but statistical difficulties • Which is the better approach to measurement and evaluation? Wien, february 24-26 2010

5. Conference on Indicators and Survey Methodology 2010 Measuring social inequality and poverty - 1 • From one to many dimensions • A growing consensus about going beyond income and per capita product • UNRISD, ILO, basic needs, PQLI • Capability approach and Human Development • An increasing number of composite indices of development, well-being, QoL, …(OECD Global Project “Measuring Progress of Societies”) • …but not of social inequality and poverty Wien, february 24-26 2010

6. Conference on Indicators and Survey Methodology 2010 Measuring social inequality and poverty - 2 • Working with many dimensions:Theoretical and methodological problems • Choice of dimensions or of the “informational basis” (Sen, 1999) concept of justice or ethics • Choice of indicators • Use of the included information • Standardization/normalization • Space/time comparisons • Using “profiles”: pro and cons • Using composite indices: pro and cons Wien, february 24-26 2010

7. Conference on Indicators and Survey Methodology 2010 Composite index: general aspects • Main steps • selecting a group of elementary indicators, usually expressed in different unit of measurement • normalizing elementary indicators to make them comparable • aggregating the normalized indicators by composite indices (mathematical functions) • Problems • finding data • losing information • researcher arbitrariness for: • selection of indicators • normalization of data • choice of the aggregation function • Advantages • unidimensional measurement of the phenomenon • immediate availability • simplification of the geographical data analysis Wien, february 24-26 2010

8. Conference on Indicators and Survey Methodology 2010 Methods for composite index building An alternative methodology: MPI The method proposed by the authors wants to supply a synthetic measure of a set of “non-substitutable” indicators. The alternative composite index, called MPI (Mazziotta-Pareto Index), starts from a linear aggregation and introduces penalties for the geographical areas with “unbalanced” values of the indicators. • The steps to compute MPI are the following: • normalization of the individual indicators by “standardization”; • aggregation of the standardized indicators by arithmetic mean with penalty function based on “horizontal variability” (standardized values variability for each unit). The penalty is based on the coefficient of variation. Wien, february 24-26 2010

9. Conference on Indicators and Survey Methodology 2010 Methods for composite index building An alternative methodology: MPI The standardization Transforming each indicators in a standardized variables with mean equal to 100 and standard deviation equal to 10: the obtained values are usually included in the range 70-130. This standardization allows to solve the problem of the “ideal country”, because the corresponding vector is composed by the mean values. In this way, it is easy to individuate the geographical areas that are over the mean value (values greater than 100) and the geographical areas that are under the mean value (values smaller than 100). Wien, february 24-26 2010

10. Conference on Indicators and Survey Methodology 2010 Methods for composite index building An alternative methodology: MPI The penalty function The target is to penalize the geographical areas that present an “unbalanced” set of indicators (for example, an indicator shows good result and another a bad one). The “horizontal variability” can be measured by the coefficient of variation (CV). In this way, it is possible to penalize the “score” of each area (the mean of the standardized values) by a directly proportional quantity to the CV. The “penalty” can be add or subtract depending on the phenomenon nature (development or poverty, wealth or social inequality). Wien, february 24-26 2010

11. Conference on Indicators and Survey Methodology 2010 Methods for composite index building Steps for computing MPI: Normalization Being X={xij} the original data matrix, we denote and the mean and the standard deviation of the j-th indicator, where: ; . The standardized matrix Z={zij} is computed as follows: if the j-th indicator is concordant; if the j-th indicator is discordant . Wien, february 24-26 2010

12. Conference on Indicators and Survey Methodology 2010 Methods for composite index building • Steps for computing MPI: aggregation • Let cvi be the coefficient of variation for the i-th unit: • where • The generalized form of MPI is given by: • where the sign ± depends on the direction of the indicators. Wien, february 24-26 2010

13. Conference on Indicators and Survey Methodology 2010 Social inequality in Europe ec.europa.eu/eurostat Wien, february 24-26 2010

14. Conference on Indicators and Survey Methodology 2010 The dimensions of social inequality Earlyschoolleavers Ginicoefficient Long termunemployment rate Social inequality At riskofpoverty rate Projected total public social expenditure Selfreportedunmetneedformedical care Wien, february 24-26 2010

15. The dimensions

16. Conference on Indicators and Survey Methodology 2010 The matrix of the individual indicators Wien, february 24-26 2010

17. Conference on Indicators and Survey Methodology 2010 Cograduation Spearman’s index Wien, february 24-26 2010

18. Conference on Indicators and Survey Methodology 2010 Why using MPI? • Independence from the variability and measurement unit of the indicators • Independence from the “ideal unit”, since it is subjective, it is not univocal and it can vary during the time • Non substitutability of the indicators • This methodology is not conditioned by the “versus” and by the “range” of the elementary indicators • Easy computation • Easy interpretation (it is easy to individuate the geographical areas that are over the mean value (values greater than 100) and the geographical areas that are under the mean value (values smaller than 100) Wien, february 24-26 2010

19. Conference on Indicators and Survey Methodology 2010 Level of social inequality Wien, february 24-26 2010

20. Conference on Indicators and Survey Methodology 2010 The map of social inequality Wien, february 24-26 2010

21. Conference on Indicators and Survey Methodology 2010 Concluding remarks The MPI is an alternative composite index based on the property of “non-substitutability” of indicators that wants, in the scientific outline, both to respect the desirable characteristics of a composite index and to be validly applied to different scientific contexts In fact, this methodology is not conditioned by the “versus” and by the “range” of the elementary indicators Therefore, the MPI can be a useful “tool” to synthesize multidimensional phenomena (positive like development and negative like social inequality) The combination of the 6 individual indicators and the MPI represents a new tool called SINCI (Social Inequality Composite index) SINCI is a robust measure of social inequality in Europe Wien, february 24-26 2010

22. Conference on Indicators and Survey Methodology 2010 References Mazziotta M., Pareto A. (2007) “Un indicatore sintetico di dotazione infrastrutturale: il metodo delle penalità per coefficiente di variazione”, in: Atti della XXVIII Conferenza Italiana di Scienze Regionali, AISRe, Bolzano. De Muro P., Mazziotta M., Pareto A. (2009), “Composite Indices for Multidimensional Development and Poverty: An Application to MDG Indicators”, Wye City Group, FAO, Roma. http://www.fao.org/es/ess/rural/wye_city_group/2009/ OECD (2008) Handbook on Constructing Composite Indicators. Methodology and user guide, OECD Publications, Paris. Sen A., 1999, Development as Freedom, Oxford University Press, Oxford mazziott@istat.it pareto@istat.it valentina.talucci@uniroma1.it Wien, february 24-26 2010