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Composite Indicator of Social Inclusion for European Countries

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Abstract

Social inclusion is one of the key challenges of the European Union (EU) Sustainable Development Strategy. We use four indicators from EU policies to measure social inclusion for the 27 member countries of Europe. In particular, we aggregate the four indicators in a multiplicative composite indicator via a DEA-BoD approach with weights determined endogenously with proportion constraints. We obtain a score of social inclusion that allows us to grade the 27 EU countries from 2006 to 2010. In this way, we highlight the specific role played by the four indicators in determining improvements and deteriorations of social inclusion during the European phase of the financial and economic crisis.

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Notes

  1. The 27 member countries of the European Union are: Austria (AT), Belgium (BE), Bulgaria (BG), Cyprus (CY), Czech Republic (CZ), Germany (DE), Denmark (DK), Estonia (EE), Greece (EL), Spain (ES), Finland (FI), France (FR), Hungary (HU), Ireland (IE), Italy (IT), Lithuania (LT), Luxembourg (LU), Latvia (LV), Malta (MT), Netherlands (NL), Poland (PL), Portugal (PT), Romania (RO), Sweden (SE), Slovenia (SI), Slovakia (SK) and United Kingdom (UK).

  2. Because in the paper we refer to social inclusion, positive concept specular and contrary to the negative concept of exclusion, it would be more intuitive to change the direction of the indicators, though this transformation is irrelevant from the point of view of substance. However, for maximum comparability, at this stage we prefer to maintain the data as made available by Eurostat without changing direction and interpretation of the raw data.

  3. We see immediately that correlations among the four indicators are moderate; in fact, there is no risk of double-counting: ideal condition in the construction of a composite indicator. In 2010, the highest correlation is between “severely materially deprived people” and “people at risk-of-poverty after social transfers”: 0.59. It follows 0.44 between “people at risk-of-poverty after social transfers” and “early school leavers”. The value is 0.12 between “people living in households with very low work intensity” and “people at risk-of-poverty after social transfers”, and it is 0.08 between “people living in households with very low work intensity” and “early school leavers”. Finally, the correlation between “severely materially deprived people” and “early school leavers” is 0.02. Values are similar in other years.

  4. Many composite indicators exist in literature with varying degrees of methodological complexity. For example, the “Corruption Perceptions Index” by Transparency International (2011), the “Human Development Index” by UN (2011), the “Composite Leading Indicators” by OECD (2012) and so on. A good starting point on the issue is OECD (2008).

  5. Geometric aggregation is a good compromise between methods with full compensability and non-compensatory approaches, for example MCDA (Munda and Nardo 2003). In addition, in many cases, geometric aggregation is preferable to approaches MCDA because it can lead to the minimum information loss (Zhou and Ang 2009). Furthermore, using the social choice theory, Ebert and Welsch (2004) found that geometric aggregation is particularly relevant in composite indicator construction when the ordinal information is involved.

  6. Obviously, with multiplicative aggregation, basic indicators must always be larger than 1, and this forces us to normalize and to shift the scale of the data used in this paper. Of course, data must be processed without altering the relationship between them and without that this may affect the final results of the composite indicators. In particular, we use a min–max transformation in a continuous scale from 2 (minimum) to 10 (maximum) where higher values correspond to better social inclusion. In other words, we apply the transformation: (max(y)-y)/(max(y)-min(y)) 8 + 2. In this way, the direction of the indicators is changed allowing a direct reading of the values in more intuitive terms of social inclusion rather than social exclusion. Furthermore, the values move from a scale 0–1 to a scale 2–10. Given the techniques used in this paper, as it will be clear later, these data transformations do not distort the final results.

  7. Here, the Benefit-of-the-Doubt (BoD) logic assumes a favourable judgement in the absence of full evidence using a model similar to Data Envelopment Analysis (DEA) (Coelli et al. 2005). In fact, we are not sure about the appropriate weights, rather we look for BoD weights such that the country’s performance of social inclusion is as high as possible (Melyn and Moesen 1991; Despotis 2005; Zhou et al. 2007; Cherchye et al. Cherchye et al. 2007a, b, 2008; Mohamad 2007; Murias et al. 2008; Zhou and Ang 2008; Zhou et al. 2008). In brief, model (2) is like an output-oriented DEA model where indicators y are outputs whereas a variable always equal to one is the only input: it is the Koopmans “helmsman”, by which countries have an apparatus responsible for the conduct of their social policies (Koopmans 1951). Therefore, the social inclusion performance is evaluated in terms of the ability of the helmsman in each country to maximize the levels of the four basic indicators (Knox Lovell et al. 1995).

  8. It should be noted that DEA typically does not require normalization of the data, made here for the unique needs of presentation and analysis of the four indicators; it is not even mandatory that the unit of measurement is identical: in fact, the weights will be determined accordingly and their sum is not necessarily equal to 1 (Knox Lovell et al. 1995).

  9. This means a preference for an internal benchmark as the best practice country, rather than an external benchmark that could not be realistically achievable in the specific local context.

  10. Without constraints on the weights, the DEA model could cancel the contribution of the under-performing dimensions to find the best solution. Thus, results could depend even on a single indicator and, consequently, we could have a large number of insignificant benchmarks. This event occurs more likely when the sample is not large as in our case. Specific constraints on the weights and use of a few indicators avoid this “curse of dimensionality” (Coelli et al. 2005). Here, in particular, we use proportion constraints which offer a very intuitive interpretation that we consider preferable to the available alternatives.

  11. Table A1 lists the original estimates obtained from the multiplicative DEA model and it highlights the role of the four basic indicators in construction of the composite indicator. This table, in particular, shows the multiplication factors (or contributions) assigned to the four indicators that, in fact, multiplied together determine the composite indicator of social inclusion.

  12. Of course, these measures should be read in relative and not absolute way. Unfortunately, at the time of writing, we do not have complete data for 2011.

  13. This indicator HI, usually expressed in percentage of total population, corresponds to the sum of persons who are: at risk of poverty or severely materially deprived or living in households with very low work intensity. Persons are only counted once even if they are present in several sub-indicators. We remember that at risk-of-poverty are persons with an equivalised disposable income below the risk-of-poverty threshold, which is set at 60 % of the national median equivalised disposable income (after social transfers). Material deprivation covers indicators relating to economic strain and durables. Severely materially deprived persons have living conditions severely constrained by a lack of resources, they experience at least 4 out of 9 following deprivations items: cannot afford (i) to pay rent or utility bills, (ii) keep home adequately warm, (iii) face unexpected expenses, (iv) eat meat, fish or a protein equivalent every second day, (v) a week holiday away from home, (vi) a car, (vii) a washing machine, (viii) a colour TV, or (ix) a telephone. Finally, people living in households with very low work intensity are those aged 0–59 living in households where the adults (aged 18–59) work less than 20 % of their total work potential during the past year. We note that early leavers from education and training are not included. Also in this case, to simplify comparisons, the headline indicator is normalized by its range.

  14. We remember that SI combines four dimensions differentiating the weights according to the best possible combination for each country with the constraint that the contribution of each pillar, that is the indicator's value to the power of the corresponding weight, is between a minimum and a maximum defined a priori.

  15. For purposes of interpretation, the contributions are more interesting and useful than the weights, the sum of which, conversely, is not necessarily equal to one. Readers can easily calculate the values of the weights. It should be noted that the average contribution is quite stable over time (in general, the variability is low) and, thus, it represents a good summary for all years.

  16. Some specific features of certain countries could determine outliers able to strongly influence the score of SI. To verify this vulnerability of the results, we have repeated m = 27 times the calculation of SI removing each time a different country. The impact of the j-th missing country was measured through sum of m-1 squared differences between the score of the i-th countries (i ≠ j) obtained with and without the j-th country. At the end, we obtain 27 values each attributable to the country from time to time excluded from the calculation of the composite indicator. Differences are very small in many cases and, sometimes, completely negligible, even when they involve the benchmark countries. In brief, the results are robust to outliers.

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Acknowledgments

The Authors wish to thank anonymous referees for the useful comments on an earlier version of the paper. The usual disclaimer applies.

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  1. Dipartimento di Scienze Statistiche e Matematiche “Silvio Vianelli”, Università degli Studi di Palermo, Viale delle Scienze, Edificio 13, Palermo, Italy

    Francesca Giambona & Erasmo Vassallo

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  1. Francesca Giambona
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  2. Erasmo Vassallo
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Correspondence to Erasmo Vassallo.

Appendix

Appendix

See Tables 3 and 4.

Table 3 Multiplicative composite indicator (2006–2010)
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Table 4 Average contribution over time (2006–2010) of the four pillars on the composite indicator
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Giambona, F., Vassallo, E. Composite Indicator of Social Inclusion for European Countries. Soc Indic Res 116, 269–293 (2014). https://doi.org/10.1007/s11205-013-0274-2

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