Matteo Mazziotta and Adriano Pareto Istat - Methodological Office Valentina Talucci

Matteo Mazziotta and Adriano ParetoIstat - Methodological Office

Valentina TalucciUniversity of Rome “La Sapienza”

Composite Indices to Measure Poverty and Social Inequality in Europe

Wien, february 24-26 2010

IntroductionConference on Indicators and Survey Methodology

2010

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


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”

Conference on Indicators and Survey Methodology

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Multidimensional phenomenaConference on Indicators and Survey Methodology

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• 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?

Measuring social inequality and poverty - 1Conference on Indicators and Survey Methodology

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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

Measuring social inequality and poverty - 2Conference on Indicators and Survey Methodology

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Working with many dimensions:Theoretical and methodological problems

1. Choice of dimensions or of the “informational basis” (Sen, 1999) concept of justice or ethics– Choice of indicators

2. Use of the included information– Standardization/normalization– Space/time comparisons

• Using “profiles”: pro and cons• Using composite indices: pro and cons

Composite index: general aspects

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

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)


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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:(i) normalization of the individual indicators by “standardization”;(ii) 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.


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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).


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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).


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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 .

jxMjxS

n

xn

iij

x j

1M

n

xn

ixij

x

j

j

1

2)M(

S

10S

)M(100

j

j

x

xijij

xz

10S

)M(100

j

j

x

xijij

xz


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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.

i

i

z

zi M

Scv

m

z

M

m

1jij

z .i

m

)Mz(

S

m

1j

2zij

z

i

i

izz2

iz/

i cvSMcv1MMPIiii


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Social inequality in EuropeConference on Indicators and Survey Methodology

2010

ec.europa.eu/eurostat


The dimensions of social inequalityConference on Indicators and Survey Methodology

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The dimensions

SUBJ ECT INDICATOR DEFINITION

Social InclusionAt risk of poverty rate

Share of persons with an equivalised disposable income below 60% of the national equivalised median income.Equivalised median income is defined as the household's total disposable income divided by its "equivalent size", to take account of the size and composition of the household, and is attributed to each household member.

Income Gini coefficient

Summary measure of the cumulative share of equivalised income accounted for by the cumulative percentages of the number of individuals.I ts value ranges from 0% (complete equality) to 100% (complete inequality).

Education and training

Early school leavers

Share of persons aged 18 to 24 who have only lower secondary education (their highest level of education or training attained is 0, 1 or 2 according to the 1997 International Standard Classification of Education – ISCED 97) and have not received education or training in the four weeks preceding the survey.

Labour market (including LFS - Labour Force Survey)

Long term unemployment rate

Total long-term unemployed population (?12 months; ILO definition) as a proportion of total active population aged 15 years or more.

Social ProtectionProjected Total Public Social expenditures

Age-related projections of total public social expenditures (e.g. pensions, health care, long-term care, education and unemployment transfers), current level (% of GDP) and projected change in share of GDP (in percentage points) (2010-20-30-40-50)Specific assumptions agreed in the AWG/EPC. See "The 2005 EPC projections of age-related expenditures (2004-2050) for EU-25: underlying assumptions and projection methodologies"

Health CareSelf reported unmet need for medical care

Total self-reported unmet need for medical care in terms of number of people who reported that at least once in the previous 12 months they felt they needed medical care and did not receive it either because they had to wait, or it was too expensive, or it was too far away.

The matrix of the individual indicatorsConference on Indicators and Survey Methodology

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CountryAt risk of

poverty rate Gini coefficient

Early school leavers

Projected Total Public Social expenditures

Long term unemployment

rate

Self reported unmet need for

medical care

at Austria 13 25 19,7 3507 1,2 1,0be Belgium 15 28 33,4 3421 3,8 1,8bg Bulgaria 14 24 74,1 734 4,0 28,9cy Cyprus 16 29 30,9 1550 0,7 6,6cz Czech Republic 10 25 9,8 1447 2,8 1,4de Germany 13 27 16,7 3251 4,7 4,1dk Denmark 12 24 18,3 3169 0,6 0,2ee Estonia 18 33 11,5 846 2,3 14,4es Spain 20 31 51,8 2260 1,7 0,9fi Finland 13 26 20,4 2523 1,6 4,7fr France 13 27 33,5 3306 3,3 4,3gr Greece 21 34 41,3 2283 4,1 7,9hu Hungary 16 33 22,0 1440 3,4 3,9ie Ireland 18 32 35,0 3126 1,4 2,7it Italy 20 32 48,9 2496 2,9 9,2lt Lithuania 20 35 11,6 862 1,4 13,6lu Luxembourg 14 28 34,8 4153 1,3 0,8lv Latvia 23 39 15,5 860 1,6 28,9mt Malta 14 28 74,1 1733 2,6 3,4nl Netherlands 10 26 27,7 3192 1,3 0,9pl Poland 19 33 14,3 843 4,9 13,3pt Portugal 18 38 72,9 2029 3,8 9,6ro Romania 19 33 74,1 507 3,2 28,9se Sweden 12 24 16,0 3012 0,8 4,1si Slovenia 12 24 18,6 1959 2,2 0,3sk Slovakia 12 28 11,4 1130 8,3 6,4uk United Kingdom 19 32 27,5 2580 1,3 2,6


Cograduation Spearman’s indexConference on Indicators and Survey Methodology

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Arithmetic mean

MPIGeometric

meanWroclaw's

method

First principal

component

Rizzi's method

Weighted mean of

factors

Arithmetic mean 1 0,994 0,998 0,979 0,983 0,915 0,985

MPI 1 0,992 0,990 0,968 0,915 0,979

Geometric mean 1 0,976 0,983 0,921 0,983

Wroclaw's method 1 0,954 0,910 0,974

First principal component 1 0,920 0,971

Rizzi's method 1 0,897Weighted mean of factors 1

Why using MPI?Conference on Indicators and Survey Methodology

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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)


Level of social inequalityConference on Indicators and Survey Methodology

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COUNTRY MPI GROUPLEVEL OF

SOCIAL INEQUALITY

Denmark 89,90 1Sweden 90,97 1Austria 91,09 1Netherlands 91,44 1Luxembourg 93,35 1Slovenia 93,73 2Finland 94,24 2Czech Republic 94,50 2France 96,28 2Germany 96,69 2Belgium 97,52 2Ireland 98,90 2Cyprus 98,95 2United Kingdom 99,52 2Hungary 102,14 3Spain 102,29 3Malta 102,62 3Estonia 104,43 3Italy 104,59 3Lithuania 105,39 3Slovakia 105,40 3Greece 106,58 3Poland 107,48 3Bulgaria 109,95 4Portugal 109,98 4Latvia 112,59 4Romania 114,19 4

LOW

MEDIUM- LOW

MEDIUM- HIGH

HIGH


The map of social inequalityConference on Indicators and Survey Methodology

2010


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

Concluding remarks



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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

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2010

Documents

Matteo Mazziotta and Adriano Pareto Istat - Methodological Office Valentina Talucci