Abstract
Social inclusion is one of the key challenges of the European Union Sustainable Development Strategy (EU SDS). We use the main indicators identified by Eurostat within the operational objectives of the specific European policies to measure social inclusion for the 27 member countries of the European Union. In particular, we aggregate four basic 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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- 1.
We note that although the multidimensional nature of social inclusion is widely shared, some dimensions are neglected in the time of measurement. In effect, EU social indicators are much better developed for poverty, material deprivation, labour market and level of education than for political or cultural dimensions [9]. However, the use of the same four basic indicators selected by Eurostat allows us to maintain a strong connection with the objectives set by the European strategies and allows us an easy comparability of the results.
- 2.
Many composite indicators exist in literature with varying degrees of methodological complexity. For example, the “Corruption Perceptions Index” by Transparency International [11], the “Human Development Index” by UN [12], the “Composite Leading Indicators” by OECD [13] and so on. A good starting point on the issue is OECD [10].
- 3.
Geometric aggregation is a good compromise between methods with full compensability and non-compensatory approaches, for example, MCDA (Multiple-Criteria Decision Analysis) [14]. In general terms, geometric aggregation is preferable to approaches MCDA because it can lead to the minimum information loss [15]. Furthermore, using the social choice theory, Ebert and Welsch [16] found that geometric aggregation is particularly relevant in composite indicator construction when the ordinal information is involved.
- 4.
With multiplicative aggregation, the sub-indicators must be larger than 1 otherwise the logarithmic transformation obtains negative values. Therefore, it is necessary to normalize the data of the four basic indicators extracted from Eurostat. 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: \( \left( \max (y)-y\right)/\left( \max (y)- \min (y)\right)\cdot 8+2 \). Furthermore, we note that in this way the direction of the sub-indicators is reversed so that higher values represent, in more intuitive terms, greater social inclusion and not greater social exclusion as in the original scale of the Eurostat indicators. For our purposes, given the techniques used here, this does not distort the final result as it will be clear later. Finally, it should be noted immediately that correlations among the four sub-indicators are moderate; in fact, there is no risk of double-counting: this is an ideal condition in the construction of a composite indicator.
- 5.
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) [20]. 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 [21, 22, 18, 17, 23, 24, 25, 26, 27, 28]. In brief, model (2) is like an output-oriented DEA model where indicators y are outputs and 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 [29]. 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 (obviously normalized in terms of social inclusion) [30].
- 6.
It should be noted that DEA typically does not require normalization of the data, made here for the unique needs of greater convenience of analysis. It is not even mandatory that the unit of measurement is identical, since the weights take into account the unit of measurement of the sub-indicators [30].
- 7.
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 specific local contexts.
- 8.
Without constraints on the weights, the DEA model could reset the contribution of the underperforming dimensions to find the best solution. Thus, the 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, compared to the number of countries, avoid this “curse of dimensionality” [20]. Here, in particular, we use proportion constraints which offer a very intuitive interpretation that we consider preferable to the available alternatives such as absolute, relative or ordinal restrictions.
- 9.
For example, if in a given country three indicators reach the minimum contribution of 20 %, the contribution of the fourth indicator will necessarily have an upper bound of 40 %. In fact, the specification of the upper bound is not necessary since the sum of the contributions of the four indicators must be 100 %.
- 10.
It is appropriate to make a final comment about the robustness of the results. Some countries may be outliers and 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 the sum of the m − 1 squared differences between the score of the i-th countries (i ≠ j) computed including the j-th country and that one computed excluding the j-th country. So, we obtain 27 values each representing the influence on the SI score of the country from time to time excluded from the calculation. The differences are very small in many cases and, sometimes, completely negligible, even when they involve the benchmark countries.
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Giambona, F., Vassallo, E. (2016). Composite Indicator of Social Inclusion for the EU Countries. In: Alleva, G., Giommi, A. (eds) Topics in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-27274-0_21
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