EU MECI: A Network-Structured Indicator for a Union of Equality

How are the Member States performing in their challenge toward a fairer and more equal Europe? Based on the data measured by the EU Multidimensional Inequality Monitoring Framework (EU MIMF), we introduce the Multidimensional Equality Complexity Index, EU MECI, derived by structuring the EU MIMF data as a bipartite network of countries and indicators. EU MECI is defined upon the economic complexity methodology, exploiting the network’s centrality metrics to calculate aggregate scores of the capacity of Member States to ‘build a Union of equality’.


Introduction
I will not rest when it comes to building a Union of equality.
-President von der Leyen, The State of the European Union 2020 Building a Union of equality requires extensive knowledge of prevailing inequalities across multiple life domains, from material living conditions to health and from environmental conditions to political participation, social life, knowledge and education. Inequalities pose a major threat to social cohesion and the COVID-19 pandemic has inflated these by 1 3 attacking the global society at its core (UN, 2020). The global health crisis calls for immediate political action to avoid a further deepening of poverty and inequalities, and in turn, political action calls for information, evidence and policy research.
Although inequality has been the focus of a vast amount of research aiming to identify policy recommendations and solutions, the consensus regarding goals, priorities and methods is often limited (Alberti et al., 2021). Different measures and methodological approaches serve as sources of possible inconsistencies that often lead to incomparable, mixed or even strikingly different results (OECD, 2017). Inequality has been measured through the use of vertical inequality metrics (Atkinson & Brandolini, 2010;Niño-Zarazúa et al., 2017;Ravallion et al., 2004), horizontal inequality measures (OECD, 2018), the equality of opportunity approach (Ferreira & Peragine, 2016), the capability approach (Sen, 1985(Sen, , 1999Nussbaum, 2001), the social mobility approach (OECD, 2017) and the discriminatory norms, attitudes and practices approach (Williamson, 2000). Despite the valuable and valid conclusions that the received literature extracts, it becomes evident that such a complex and multifaceted issue, requires a more comprehensive methodological approach, capable of synthesizing inter-related and complementary elements captured through the different approaches.
Following a request from the European Parliament, the European Commission (EC)'s Joint Research Centre (JRC) has undertaken a pilot research project to develop a Multidimensional Inequality Monitoring Framework for the EU (EU MIMF) that provides a novel and comprehensive dashboard of 346 indicators for the 28 Member States. 1 The JRC researchers refrain from computing a composite inequality index leading to a single EU inequality ranking, due to the correlation structure of the indicators used. They offer instead an analysis based on the set of 346 indicators, recognizing though, the importance of a country-ranking methodology and providing a way to compare countries' performances based on a double-sorting algorithm (Copeland method (Copeland, 1951)). Hence, the EU MIMF captures information from a great spectrum of dimensions with regard to inequality, arguably more informative than traditional indexes, such as the IHDI, the Gini, the OECD inequality framework, the Measurement Framework for Equality developed by the Equality and Human Rights Commission (EHRC), the Multidimensional Inequality Framework (MIF) by the London School of Economics (LSE)'s Centre for Analysis and Social Exclusion (CASE), the Sustainable Society Index by the TH Köln, among others (Alberti et al., 2021).
The EU MIMF methodology produces a ranking, able to identify "winners" and "losers" across the inequality indicators, based on pairwise comparisons between the Member States. Furthermore, the application of equal weights across Member States and indicators, results in a ranking that fails to account for the complex interconnections of the countriesindicators system. Sciarra et al., (2020) introduce a novel mathematical approach, the GENeralized Economic comPlexitY (GENEPY), based on linear-algebra tools within a bipartite-networks framework to measure economic complexity, reconciling the established methodologies of Economic Complexity Index (Hidalgo & Hausmann, 2009) and Fitness (Tacchella et al., 2012;Sciarra et al., 2021) apply this methodology to assess the Sustainable Development Goals (SDGs). The advantage of the recommended methodology lies in considering all available information on network dynamics, in both trade and SDG data, while exploiting the non-linearities inherent in such systems.
In this paper, we apply the GENEPY methodological approach on the inequality indicators used in the EU MIMF. Through the use of this methodology, we devise and suggest the EU Multidimensional Equality Complexity Index, EU MECI, that quantifies the overall structure of the hidden bipartite network of countries and equality indicators, beyond oneto-one comparisons, to emphasize and disentangle the intrinsic complexity of this system. To the best of our knowledge, this is the first attempt to introduce a new index, that ranks the EU Member States using network science and data-driven weights, to unveil the policy areas in which countries struggle to make progress in their efforts to tackle inequalities.
Our ranking of indicators and the EU MECI allow for a geographical prioritization of the corresponding policy interventions, pointing towards the directions in which EU and Member State strategies should align. The high correlation structure between the EU MECI, on one hand, and per capita GDP, HDI and Life Satisfaction, on the other, enforces the reliability of our proposed tool. The emerging disparities between the EU MECI and the aforementioned traditional indicators, raises questions regarding the comprehensiveness of the latter, mainly due to the data-driven weights revealed through our method, which highlight the indicators in which countries trail behind and/or struggle to improve.
The identification of obstacles to the EC president's call for action towards a more equitable, fair and inclusive EU is the cornerstone of the 2019-2024 priority of 'An economy that works for people' for 'a deeper and fairer economic and monetary union'. 2

Data
Information on equality measures comes from the EU MIMF, which is a comprehensive dashboard of inequality-related indicators covering different dimensions of well-being and conceptual approaches for measuring inequality. 3 The 346 indicators of the EU MIMF are calculated for the most recent year available at the time of the preparation of the framework (2021) and cover the (then) 28 EU Member States. The EU MIMF spans 10 key life dimensions: (1) Knowledge and skills, (2) Health, (3) Material living conditions, (4) Natural and environmental conditions, (5) Working life, (6) Cultural life and recreation, (7) Political participation and voice, (8) Social and family life, (9) Bodily integrity and safety, and (10) Overall life experience. Each domain covers indicators from up to five different approaches for measuring inequalities: horizontal inequality metrics, vertical inequality metrics, inequality of opportunity metrics, intergenerational mobility metrics, and metrics related to the presence of discriminatory norms, attitudes and practices (a detailed discussion of each of the different methodological approaches applied in the EU MIMF can be found in Chapter 1 of the report (Alberti et al., 2021). The full list of EU MIMF indicators is shown in the Annex of the report).
The aim of the EU MIMF project is to 'provide independent scientific advice on the measurement, monitoring and analysis of a wide range of different aspects of inequality, 1 3 from unacceptable disparities in life outcomes to inequalities of opportunity and obstacles to social mobility' ((Alberti et al., 2021), p. 8). In practical terms, the EU MIMF addresses the different aspects of inequality at the EU level by bringing together relevant indicators from different measurement approaches, constructed upon ten key life dimensions.
For the analysis, all 346 listed indicators have been transformed and normalised according to a maximum (100 indicating the best performance in terms of equality) and a minimum value (0 indicating the poorest performance) to ensure comparability and enable the aggregation of measurements. Then, indicators with missing values are dropped. The final list of 177 indicators considered in the computation of the EU MECI is shown in Table 4 of the Appendix A. Figure 8 in the Appendix A. shows the distribution of indicators per measuring approach and key life dimensions in comparison to the initial EU MIMF set. Careful observation of the different colouring, blue and orange, representing the EU MECI and EU MIMF sets respectively, reveals that the reduction of indicators in the EU MECI is proportionally distributed across dimensions and measuring approaches, with no substantial biases. In addition, we argue that our approach, being indicator and not dimension driven, leaves the informative content of the EU MECI at dimensions' level, qualitatively intact. The main implication of the reduced set of indicators considered in the computation of the EU MECI, as compared to the EU MIMF, is the inability of deriving valuable conclusions in the remaining missing inequality areas. Last, we note that our set of 177 indicators includes 15 out of the 16 social and labour market inequality indicators selected by the JRC researchers in their country ranking ( Figure 3.2 of the EU MIMF report (Alberti et al., 2021)) as having the stronger conceptual link to the variables included in the Social Scoreboard for the European Pillar of Social Rights. 4

The Bipartite Network of Member States and Equality Measures
A central role in our analysis is played by the bipartite network of Member States and equality indicators. Several examples of bipartite or bi-modal networks appear in the scientific literature (Allesina & Tang, 2012;Bascompte et al., 2003;Sbardella et al., 2017). In this analysis, we use the data for the 177 indicators described above to generate a 28 × 177 Member States-indicators matrix M , where the matrix element M ci represents country c's achievement in equality indicator i (a value ranging from 0 to 100, indicating worst and best performance, respectively).
The matrix M allows for the construction of an undirected network of Member States and equality goals by linking each of the Member States to the equality indicators. Figure 1a shows the bipartite network of countries and equality measures aggregated (averages) at the 10 key life dimensions discussed above. We connect the equality indicators with each country via the performance values M ci , according to the EU MIMF data: the denser the links, the better the (average) performance of the Member States in a given equality indicator. Figure 1b shows the respective adjacency matrix: darker squares indicate higher average values, i.e. a higher overall performance. The main equality dimensions showing high performance, on average, are 'Bodily integrity and safety', 'Natural and environmental conditions' and 'Social and family life'. The dimension for which countries appear to experience most difficulty in improving their position (on average) is 'Knowledge and skills' Figure 2 presents the adjacency matrix using the equality indicators. For ease of visualisation, we only consider the indicators with average values above the median. The adjacency matrix depicts the existence of a group of Member States that performs very well in many equality indicators (the countries listed at the top of the matrix) and other Member States that perform well only in a small set of equality goals (at the bottom of the matrix). The economic complexity methodology that we discuss below assigns a higher index score to the former. With respect to the indicators, the matrix shows that code 151, 'Relative gap in average hours of of full-time employment worked per week (female over male)' in the 'Working life' dimension, followed by code 199, 'Odds ratio of practising artistic activities as a hobby (young adult over middle-aged adult, adjusted)' in the 'Cultural life and recreation' dimension and code 105, 'Odds ratio of household not being able to afford an unexpected expense (elderly over middle-aged adult, adjusted)' in the 'Material living conditions' dimension are relatively 'easy to accomplish' equality goals at the EU level. On the other hand, equality measures such as the 'Odds ratio of people rating their satisfaction with leisure time as high (female over male, adjusted)' (code 190) in the 'Cultural life and recreation' dimension and the 'Odds ratio of feeling depressed (senior over middle-aged adult, adjusted)' in the 'Health' dimension, seem to require more effort and better strategies from the policy side.

The Economic Complexity Methodology
To rank the equality performance of Member States based on their equality indicator scores, we rely on complex network science and, more specifically, on the GENEPY methodology described in Sciarra et al. (2020) and Sciarra et al. (2021), which reconciles the commonly used methodologies to measure economic complexity, i.e. the method of reflections developed by Hidalgo and Hausmann (2009) and, the fitness and complexity algorithm developed by Tacchella et al. (2012). Economic complexity methodologies quantify the international trade network, using dimensionality reduction techniques on data capturing economic activities, without imposing the factors of production, but rather through discovering the combinations of such factors, that best explain the geography of exported goods directly from the data (Hidalgo, 2021). Sciarra et al. (2021) take the method of Sciarra et al. (2020) one step further, by applying it on the Sustainable Development Goals (SDGs). In this case, the bipartite system consists of countries and Goals instead of countries and exports, while the achievements are eventually ranked -by Goal and by country-after allowing for complex interplays between the two. According to the authors, the GENEPY framework represents an appropriate methodology to assess country achievements in SDGs by (a) accounting for the relative performance of countries and the synergies and trade-offs across Goals, and (b) providing useful insights of the policy actions required to be undertaken by the countries to achieve sustainable development. It does so by assigning higher GENEPY scores to the few countries that have relatively more capabilities in implementing policy interventions towards achieving the Goals within the Agenda 2030.
In the same vein, we argue that the GENEPY methodology can be directly applicable to equality indicators. The system of 28 countries and 346 indicators within the EU MIMF is complex and characterised by high heterogeneity and disordered interactions, and any attempt to assess multidimensional equalities is not compatible with the absence of a complex networks approach (Sciarra et al., 2021;Le Blanc, 2015;Ladyman et al., 2013). In particular, equality indicators are linked through the country specific knowledge embedded in the political and economic institutions (Acemoglu et al., 2005), culture and history (Tabellini, 2008), while countries' achievements across indicators exhibit significant heterogeneity. Thus, the double-sorting algorithm (Copeland method (Copeland, 1951)) adopted in the EU MIMF, based on one-to-one comparisons between the Member States, is unable to capture the overall structure of the bipartite network, and only considers the local information of node connections (Sciarra et al., 2021;Bonacich, 1987). In addition, even in the case of an application of the Copeland method with non-neutral weights, the GENEPY framework, is still arguably more comprehensive, since the weights are not imposed arbitrarily but rather are data driven.
To consolidate the multidimensional information available for the Member States into a single composite equality indicator, we devise and introduce the EU MECI, defined upon the GENEPY methodology, exploiting the network's centrality metrics, to introduce an innovative way to measure and address inequalities. The advantage of this approach is that it accounts for (a) the complex interconnections between the equality indicators and (b) the high heterogeneity of Member States performance across the equality goals.
The GENEPY framework is set in a linear algebra framework and embeds the interplay between Member States and equality indicators (Sciarra et al., 2021(Sciarra et al., , 2020 by defining the following system of S c and Y i centrality properties for countries and equality indicators, respectively:

3
where k c = ∑ i M ci is the degree of the countries and k � i = ∑ c M ci ∕K c is the level of equality indicator i accounting for the relative performance of countries in this equality goal. Note that computing the EU MECI ≡ S c requires the calculation of the Y i values and the indicator-specific weights, w i = Y i ∕k � i . The Y i (and w i ) values are functional to the computation of the EU MECI and vice versa. The data-driven weight w i can be interpreted as a measure of difficulty of improving equality indicator i at the EU level. Table 1 lists the indicators with the five highest and lowest weighting scores (the complete list is available upon request). The GENEPY approach suggests that the equality indicator 'P90/P10 ratio of PISA scores in mathematics' (code 5) in the 'Knowledge and skills' dimension is the measure with the biggest limitations in terms of improvement when chasing a more equitable Union. On the other end of the spectrum is 'Relative gap in average hours of full-time employment worked per week (female over male)' (code 151) in the 'Working life' dimension, which reflects a (generally) good performance by all Member States.
These findings are of high importance in guiding policy making both at the EU and the national level. More effort through policy interventions is needed in improving the EU's performance in PISA scores and this effort should be initiated and focused on the Member States with low EU MECI scores (see next Section).  Table 3 in Appendix A. shows the ranking and values.

A Snapshot of EU Member States Responses to the President's Call
Sweden appears at the top of the ranking of the most equal countries, followed by Denmark, Finland and the Netherlands. These top four Member States show relatively good performance on the indicators with the top three weights (5, 209 and 166) compared to the low EU MECI countries: Portugal, Bulgaria, Croatia and Slovakia (Table 2). This might imply that the relatively 'good performers' in equality goals that are challenging have invested more effort towards the improvement and achievement of equitable development compared to the other Member States. On the other hand, the relatively 'poor performers' tend to do well only on the indicators with the lowest limitations of improvement at the EU level, such as the indicators with codes 105, 199 and 151. Figure 4 plots the EU MECI ranking positions of countries and their degree rankings. This figure reveals the differences in the rankings when instead of using more classical approaches based on the countries' degrees, k c (i.e., the sum of all indicators' performances assuming equal weights), one follows the complex network approach proposed here. The figure visually reveals the two-tier Europe, with "low" and "high" performers. The "geography curse" of the east and the south, differentiates the group located in the bottom left corner of the figure, from the rest of the EU. At the same time, the traditionally high achievers of the strong core of the Union remain at the top of the rankings. The geographical segregation or the EU's internal East-West divide is a well established finding in various areas    (Ulceluse & Bender, 2022). In fact, a strand of this literature warns against the implicit hierarchical structure of the EU predating its formation (Ulceluse & Bender, 2022;Antonucci & Varriale, 2020), built on strong trade-offs benefiting the core countries at the expense of the periphery (Underdeveloped Europe, 1979). The verification of such geographical segregation through the EU MECI should raise a more boisterous alarm to those in charge of public policies in the Union.
To shed some further light on our findings, in Figs. 5, 6 and 7 we compare the computed EU MECI rankings vs the GDP per capita and well being indicators not included in the MIMF, such as the HDI and Life Satisfaction respectively. The astonishingly high similarity level in all figures lies in the replication of the segregation of the two tiers of countries on one hand, and the clearly positive correlation between equality performance, GDP per capita, HDI and Life Satisfaction.
The differences between the EU MECI and GDP per capita exhibited in Fig. 5, reflect that, despite the high correlation between their rankings, there is valuable information captured by the novel and comprehensive GENEPY approach, able to partially shake the traditional and deep-rooted per capita GDP country ranking. This finding might imply the need for adjustments in the prioritization of areas and/or countries towards which EC policies are directed.  Roser (2013) Furthermore, a closer observation of the dispersion of countries around an imaginary 45 degree line reveals that countries lying on the right of the line exhibit a higher ranking in terms of GDP per capita versus the EU MECI, stressing the significant limitation of a single indicator in informing country performance when it comes to equality. Figures 6 and 7 verify the geographical segregation and the positive correlation discussed above, however exhibit less dispersion, verifying that both indicators, namely the HDI and Life Satisfaction, capture information more comparable to the EU MECI. All in all, we conclude that the EU MECI performs at least as well as the standard socio-economic indicators used in the literature, while being able to encompass rich information hidden in its structure, offering new insights.

Conclusions
The study of a complex system, such as the multifaceted phenomenon of equality at the EU level, which percolates through various dimensions of citizens' well-being from material living conditions to health, education and culture, requires a complex systems approach. In this work, based on the data measured by the EU MIMF, we devise the EU MECI, derived by structuring the EU MIMF data as a bipartite network of countries and indicators. The EU MECI introduces an innovative way to measure and address inequalities by applying the economic complexity methodology on the countries-indicators network's centrality metrics and exploring (a) the interactions across the equality indicators and (b) the interplay between Member States and equality measures, while the corresponding weights of countries and indicators are determined endogenously by the data. Our ranking of indicators, based on the data-driven weights, reveals the equality goals, and implicitly the key life dimensions, that policy makers should concentrate their efforts on in order to devise action plans towards a more equitable European society. What is more, the EU MECI, offers a comprehensive tool for monitoring and analysing multidimensional inequalities in the EU, that allows for a geographical prioritization of the corresponding policy interventions, where EU and Member State strategies should align and collaborate. Our aggregate ranking captured by the EU MECI verifies the geographical two-tier segregation of EU countries, while highlights the advantages, in terms of actionable insights, that the network science offers as compared to traditional approaches with neutral weights.
From a policy perspective, the proposed analysis complements the EU MIMF by introducing an additional arrow into the policymaker's quiver of effective policies to tackle unfair social inequalities. It does so by identifying-through data-driven techniques-the areas in which Member States find it more difficult to reduce existing inequalities.
Building a Union of equality is a core topic in the von der Leyen Commission's policy debate, and the analysis presented in this work can play an important role in the formulation of evidence-based policy responses to rising social disparities.

Disclaimer
The information and views set out in this paper are those of the authors and do not necessarily state or reflect the official opinion of the European Commission. The scientific output expressed does not imply a policy position of the European Commission. Neither the European Union institutions and bodies nor any person acting on their behalf may be held responsible for the use, which may be made of the information contained therein.

Appendix A
See Fig. 8.
See Tables 3 and 4.

Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
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