Multidimensional Well-Being and Inequality Across the European Regions with Alternative Interactions Between the Well-Being Dimensions

We use the nine dimensions considered in the OECD regional well-being index (OECD 2016) and compiled them into three categories of well-being (i.e., material, personal and community) to track the progress in three general categories of well-being in the regions of Europe.

Table 1 offers the dimensions and categories of well-being and indicators used in each dimension, and the details of how each indicator is measured. Material well-being category consists of achievements of the regions in income (measured by the average household disposable income per capita), jobs (measured by the employment and unemployment rates), and housing (number of rooms available per person) dimensions. Personal well-being category consists of education (measured by the share of the labor force with at least secondary education), health (measured by the life expectancy and mortality rates), and access to services (which measures the share of households with broadband access) dimensions. Finally, community well-being category includes the civic engagement (measured by voter turnout), environmental quality (measured by air pollution levels) and safety (measured by homicide rates) dimensions. For potential policy implications of the proposed index, we only consider achievements of European regions in these dimensions in 2000 and 2014.⁶

Since the indicators are measured in different units, we need to normalize the indicators prior to the aggregation. There are numerous methods of normalization such as standardization (or z-scores), rescaling (or min–max), and distance to reference points, and one can choose a specific normalization procedure depending on the problem at hand [see OECD (2008) for further discussion on the benefits and disadvantages of various normalization procedures]. In this paper, we follow the OECD approach to normalize the indicators in order to have comparisons across space and time. To avoid the effects of large outliers in each indicator, indicators are censored in the lower and upper limits (i.e., 4th and 96th percentile of the distribution).⁷ Then min–max formula is used to normalize all indicators between 0 and 1:where \(z_{ij}^{t}\) and \(X_{ij}^{t}\) are normalized and actual outcomes in region i for a given indicator j at a given time t, respectively. \(\hbox{max} (X_{j} )\) and \({ \hbox{min} }(X_{j} )\) represent the maximum and minimum value for a given indicator j during the period of the comparison.⁸ It should be noted that the higher normalized values represent higher welfare levels.⁹ Once the indicators are normalized, we then have normalized scores in nine dimensions.¹⁰

Table 2 presents the Spearman and Kendall rank correlation matrices for the nine well-being dimensions across the European regions where the first and second rows between pairs of dimensions represent the Spearman and Kendall rank correlation coefficients between pairs of dimensions, respectively. Even though most of the well-being dimensions are positively correlated, some well-being dimensions are either negatively correlated with each other or some of them have no significant rank correlation coefficients. If all well-being dimensions were highly and positively correlated, any index constructed from these well-being dimensions would hardly provide additional information or would have been redundant [see e.g., McGillivray (2005), Cahill (2005), Berenger and Verdier-Chouchane (2007), Permanyer (2011), Foster et al. (2013) among many others that examine the redundancy of composite indices based on correlation analysis]. Hence, the existence of negative and insignificant correlation coefficients (and in some cases low positive correlation coefficients) between well-being dimensions is reassuring to construct multidimensional well-being indices as the index would provide additional set of information. In the next subsection, we propose the generalized mean aggregation methodology, which we use to obtain multidimensional well-being indices.

As discussed before, we offer a generalized mean aggregation method which is flexible enough to take into account various value judgments of the decision maker (individuals and/or policymakers): a weighting vector for the dimensions and a parameter that express the degree of substitution (complementarity) between the dimensions. To capture the degree of substitution (complementarity) between the well-being dimensions, normalized achievement levels can be aggregated by taking a generalized weighted mean of order β to obtain a multidimensional well-being index as follows:where \(w_{j}\) is the weight attached to well-being dimension j, \(z_{ij}^{t}\) is the normalized achievement level of a region i in dimension j at time t. The parameter β is the main parameter of interest in this paper which captures the value judgment of the decision maker with respect to the degree of substitution (complementarity) between the dimensions.¹¹

Clearly, when β = 1, the aggregation pins down to arithmetic mean aggregation where there is a perfect substitutability between the dimensions. In this case, a lower achievement in one dimension can be compensated by the higher achievement in another dimension. In this case, the regions can concentrate on some dimensions which can be easily manipulated (or less costly to achieve) to increase their regional well-being given the compensation across dimensions, which might lead to unbalanced achievement across the well-being dimensions. For instance, one of the criticisms of the arithmetic mean aggregation of the dimensions of the HDI was that perfect substitutability between dimensions led to uneven achievements where some research papers suggested a lower degree of substitutability (or some level of complementarity) between dimensions [e.g. Herrero et al. (2010) suggested the use of geometric mean to aggregate the dimensions of the HDI].¹²

Another popular use with the above case is obtained when β is set to 0 where the aggregation function becomes a geometric mean. This is referred as the Cobb–Douglas utility function (see the recent use of this aggregation by the UNDP’s HDI).¹³ In this case, trade-offs across the well-being dimensions depend on both relative weights and level of achievements across well-being dimensions. A percentage decrease in one dimension can be compensated by the percent increase in other dimensions. In this case, the aggregation would penalize regions with unbalanced achievements in the well-being dimensions, hence reflecting some degree of complementarity between the dimensions rather than perfect substitutability.¹⁴

Beyond these two special cases, when parameter β decreases, this makes it increasing difficult to compensate a decrease in one dimension by an increase in another. In particular, when β is set to \(- \infty\), multidimensional well-being of a region is determined by the worst outcome across all dimensions of well-being. In other words, change in any other dimension which is not the worst achieved dimension does not affect the composite well-being outcome. For the case when β is set to \(- \infty\), a region that wants to improve the composite well-being is implied to focus on the dimension in which the achievement level is the worst one. This choice clearly favors a case requiring regions to promote perfectly balanced achievements between the well-being dimensions.

In the evaluation of complex multidimensional well-being (sustainability) regional (country) performances, the choice of various parameters in the aggregation procedure conveys the preferences of decision makers (e.g., policymakers and the general public). Given the complexity of aggregation procedure for the decision makers, there is a stream of literature that elicit decision makers’ preferences through questionnaire to obtain necessary parameters for the aggregation to increase the acceptability and applicability of these aggregation methods in policy-making [see e.g., Guh et al. (2008) for discussion generalized mean aggregation]. For the derivation of questionnaires to obtain decision-maker preferences on interactions between the well-being (sustainability) indicators, interested readers are referred to Meyer and Ponthiere (2011), Garmendia and Gamboa (2012), Rowley et al. (2012), Carraro et al. (2013), Merad et al. (2013), Pinar et al. (2014), Bertin et al. (2018) among many others. In this paper, we obtain overall regional well-being outcomes in three categories (i.e., material, personal and community) by allowing different degrees of complementarity (substitution) between well-being dimensions by choosing specific β parameters while keeping the weights between the dimensions equal. There is an extensive literature concerning the effects of choice of weights on both the ranking and composite achievement levels (see e.g., Chowdhury and Squire 2006; Cherchye et al. 2008; Permanyer 2011; Foster et al. 2013; Pinar et al. 2013, 2015, 2017; Tofallis 2013; Athanassoglou 2015). However, in this paper, our main focus is to allow different degrees of substitutability (complementarity) between the dimensions when obtaining composite well-being indices and to examine whether this normative preference has any effect on the composite scores and allocation of resources across the European regions. Hence, when obtaining the overall, material, personal and community multidimensional well-being index, we keep the allocation of the weights between the dimensions equal.¹⁵ For instance, the BLI allows its users to choose relative weight allocation across well-being dimensions in its interactive web application, however, this feature does not allow individuals to reflect their preferences on whether they consider the well-being dimensions as substitutes and/or complements of each other.¹⁶ In this paper, we will examine the effect of this choice on the multidimensional well-being achievements of the European regions and also examine how this choice affects the multidimensional inequality across the European regions in the next section.

In this subsection, we examine the average achievements in income, overall, material, personal, and community composite well-being outcomes among European countries in 2014. We also look at within- and cross-country multidimensional well-being inequality in the European regions. Table 4 summarizes the average achievement levels of European countries in income, overall, material, personal, and community composite well-being outcomes (with different \(\beta\) parameters), and within- and cross-country inequality in income dimension and composite indices in 2014. This table is quite heavy to follow but let us provide the details of the general patterns of achievements and inequality measures across the European countries. We can see that the within-country income inequality is small in relatively rich countries and large for the relatively poor countries suggesting a negative correlation between average income of a country and within-country income inequality (see Fig. 1 which plots the average income and within-country income inequality in the European countries).²⁵ Similar pattern is observed in overall, material, and community well-being when well-being dimensions are considered to be complements at some degree (i.e., cases when \(\beta \le 0\)). Countries that have a composite achievement level of 0.5–0.6 or above (below) have relatively low (high) levels of within-country inequality in overall, material and community well-being indices. With the exception of Portugal, both within- and cross-country inequality levels in personal well-being are relatively lower compared to other multidimensional well-being categories suggesting relatively balanced achievements between the education, health and access to services dimensions.²⁶ Finally, when \(\beta\) parameter is decreased from 0 to − 1 (i.e., higher degree of complementarity between the dimensions), we observe that within- and cross-country inequality increases and the increase in within-country inequality is relatively higher for the countries that have lower multidimensional well-being scores.²⁷

When well-being dimensions are considered to be perfect substitutes (i.e., when β = 1), by definition, overall, material, personal, and community well-being increases (or at most remains unchanged) compared to the cases when β ≤ 0. In particular, increases in the average achievement levels in each multidimensional well-being category are relatively higher for the set of countries that have unbalanced achievements between the dimensions (i.e., set of countries that have multidimensional achievement levels in each category that are less than 0.5–0.6 when β = 0). For instance, when β parameter is increased to 1 from 0 (i.e., when well-being dimensions are aggregated with arithmetic mean rather than geometric mean), overall well-being scores of Estonia, Greece, Slovak Republic, Portugal, Poland, and Italy increased by 0.36, 0.27, 0.26, 0.20, 0.16, and 0.14, respectively. On the other hand, there have been limited increments in the multidimensional well-being scores of the regions that belong to countries that are relatively wealthier and have balanced achievements between the dimensions when β parameter is increased from 0 to 1.²⁸ Finally, there is smaller within-country inequality when there is perfect substitution between the dimensions, which then leads to a smaller cross-country inequality in multidimensional well-being categories.²⁹

Overall, there are distinctive differences in multidimensional well-being scores, and within- and cross-country inequality measures when dimensions are considered to be perfect substitutes (i.e., β = 1) or have some degree of complementarity between them (i.e., \(\beta \le 0)\). In this subsection, we analyzed the average achievement scores and within- and cross-country inequality in different multidimensional well-being categories. In the next subsection, we analyze the sensitivity of composite scores and rankings to the choice of β parameters.

In this subsection, we analyze composite well-being scores and rankings of European regions in each well-being category when different β parameters are used in the aggregation procedure. In particular, we will examine how sensitive composite scores and rankings are to the choice of β parameter (i.e., how composite scores and rankings vary when dimensions are considered to be perfect substitutes or complements).

First of all, we examine the rank correlation coefficients when multidimensional well-being composite indices are obtained with different β parameters in 2014.³⁰ We find that the composite well-being index rankings are positively and significantly correlated with each other even though we allow the dimensions to be perfect complements or complementary at some degree. In the lines with the literature that analyzed the redundancy of composite indices, one might argue that the composite well-being indices obtained with alternative β parameters are redundant and an index with a single β parameter would be sufficient to rank regions since the rankings are positively and significantly correlated with each other. However, we argue that even though rankings are highly and positively correlated with each other when different β parameters are used, they convey distinctively different outcomes for two reasons. First, rankings obtained with different β parameters can be very similar, but they produce very different multidimensional well-being scores, within- and cross-country inequality measures. For instance, depending on whether well-being dimensions are considered to be perfect substitutes or complements at some degree, composite well-being scores and inequality measures do vary dramatically (see Table 4 for average multidimensional well-being scores in different categories, and within- and cross-country inequality measures with different β parameters). When well-being dimensions are considered as perfect substitutes (complements at some degree), there is a lower (higher) within- and cross-country inequality and higher (lower) multidimensional well-being across the European regions. As some of the most important goals and policy decisions of the EU are based on tracking the multidimensional well-being (e.g., the European Commission’s “Going beyond GDP” initiative) and decreasing regional inequality (e.g., the main objective of the EU structural funds is to reduce the income inequality), composite indices that are obtained with different β parameters gives distinctively different signals to policymakers.

The plots in Fig. 2 compare overall, material, personal and community well-being scores obtained when the sub-dimensions are considered as perfect substitutes (i.e., when β = 1 or arithmetic mean of dimensions) with the composite well-being scores obtained when the sub-dimensions are considered as complements at some degree (i.e., when β = − 1). This figure clearly shows that there is a major variation in composite scores achieved by the most European regions when different β parameters are used. It can be seen in this figure that regions that achieved a higher composite score (i.e., high performers) are located close to the 45-line degree which suggests that their composite scores in different well-being categories are less sensitive to the choice of β parameter. These regions have relatively balanced achievements across the sub-dimensions. On the other hand, composite scores of regions with unbalanced achievements across the sub-dimensions are more sensitive to the choice of β parameter and these regions are the ones that are located far away from the 45-line degree. For instance, Table 5 presents some regions whose composite scores are extremely sensitive to the choice of β parameter and that these regions would have had very different overall, personal, material, and community well-being scores when the dimensions are considered as perfect substitutes (β = 1) or complements at some degree (β = − 1). The variation in composite scores for these regions are quite high when β increased from − 1 to + 1. For instance, overall well-being score of Lombardy would have been 0.692 lower if one were consider dimensions to be complements at some degree (i.e., β = − 1) rather than them being perfect substitutes (i.e., β = 1). Most of these regions that see major changes in their composite well-being scores when two different β parameters used are located at the southern Europe (e.g., regions of Italy, Spain, Greece, and Portugal) and eastern Europe (e.g., regions of Estonia, Czech Republic, and Hungary). Common characteristic of these regions is that they have relatively unbalanced performances in sub-dimensions. In one hand (when β = 1), relatively poor performances in some sub-dimensions are compensated by good performances in other sub-dimensions and on the other hand (when β = − 1), poor performances in some sub-dimensions are reflected in lower composite well-being scores.³¹

We furthermore show that there are major rank reversals when different β parameters are used to obtain composite scores even though the rankings obtained with different β parameters are positively and significantly correlated with each other.³² The plots in Fig. 3 compare overall, material, personal and community composite well-being ranks in 2014 when β is set to − 1 and + 1. This figure reveals that the high performing regions are less sensitive to the choice of β parameter as they are located near the 45-line degree. On the other hand, rankings of some regions are extremely sensitive to the choice of β parameter as they are far off from the 45-line degree. For instance, some regions are ranked higher when sub-dimensions are considered as complements (i.e., plots that are located at the upper left of the 45-line degree) and some others are ranked in relatively higher positions if one were to consider sub-dimensions as substitutes of each other (i.e., plots that are located at the lower right of the 45-line degree). Table 6 provides some of the regions that would experience major rank reversals in composite well-being indices when β = 1 and β = − 1 are used to obtain composite well-being indices. Panel A (B) of Table 6 represents some set of regions that would have been ranked in higher positions when sub-dimensions are considered to be complements at some degree (perfect substitutes) compared to the case when the dimensions are considered as perfect substitutes (complement at some degree). For instance, Zurich and Åland rank at the 88th and 39th positions based on their overall well-being achievement when the dimensions are considered to be perfect substitutes (i.e., when β = 1), whereas, these two regions would have been ranked at the 155th and 102nd positions when dimensions are more seen as complements (i.e., β = − 1), respectively. The reason why these regions rank in lower positions when β = − 1 is used to obtain overall well-being index is that their achievements in civic engagement dimension are relatively low. On the other hand, East Macedonia of Greece ranks at the 177th (213th) position when β = − 1 (β = 1) is used to obtain overall well-being score. Even though East Macedonia region of Greece have low achievements in some well-being dimensions, neither of its achievements in well-being dimensions are at the lowest possible levels allowing this region to achieve relatively higher position when dimensions are considered to be complements. Most of the regions that East Macedonia region of Greece surpass when the dimensions have some complementarity are the ones that have the lowest achievement score in one or more dimensions moving them to lower ranking positions when dimensions are considered as complements. Similar patterns are observed for the remaining set of regions that moved to higher positions when dimensions are seen more of complements compared to the case where they are considered to be perfect substitutes.

Overall, even though the rankings are positively and significantly correlated with each other, there are also major differences between two rankings when the dimensions are more seen as substitutes or complements, respectively (i.e., β = 1 and β = − 1, respectively). Regions that have relatively balanced (unbalanced) achievements between the dimensions move to higher rankings when dimensions are considered to be complementary (perfect substitutes).

In the previous sections, we analyzed the multidimensional well-being and inequality across the European regions depending on the β parameter choice and in this subsection, we will examine the well-being improvements and changes in inequality measures between 2000 and 2014.³³ Table 7 offers average achievement and inequality measures in income dimension and composite indices in 2000 and 2014 when different β parameters are used to aggregate dimensions. Panel A of Table 7 offers the average achievement in income and composite well-being outcomes and multidimensional inequality (i.e., Gini measures) in 2000 and 2014 for 103 regions that have overlapping information for all well-being dimensions in both years. Whereas, Panel B of Table 7 offers the same information for different number of regions where we have information for all dimensions that are used each respective composite well-being category, respectively.

Since both panels of Table offer roughly similar outcomes, we discuss the results from the panel A of Table 7. Irrespective of the β measure, average overall well-being index increased and multidimensional inequality across the European regions are decreased between 2000 and 2014. However, the increase in average overall well-being index is relatively higher when dimensions are considered to have some degree of complementarity compared to the case when dimensions are perfect substitutes (e.g., average overall well-being index increased by 0.206, 0.202, and 0.165 between 2000 and 2014 when β is set to be − 1, 0, and 1, respectively). This suggests that the improvements in well-being dimensions across the European regions between 2000 and 2014 were towards rounded achievements across well-being dimensions. Similarly, Gini coefficients in 2014 were smaller than the ones in 2000 suggesting that the inequality in overall well-being across European regions declined between 2000 and 2014. Similarly, decrease in Gini coefficient is relatively higher when dimensions are considered to have some complementarity (i.e., \(\beta \le 0)\). When we move to composite well-being categories, average achievement and inequality levels in material well-being across the European regions roughly remained to be the same irrespective of the β parameter choice.³⁴ The composite well-being category in which European regions experienced the largest improvement during the period is personal well-being one. Average achievement in this category roughly doubled between 2000 and 2014, and there is distinctive decrease in inequality measures when well-being dimensions are considered to have some degree of complementarity (i.e., Gini coefficients dropped from 0.423 and 0.377 to 0.165 and 0.130 when β is set to − 1 and 0, respectively). This suggests that well-being improvements in this category across the European regions were towards rounded achievements across the well-being dimensions in this category (i.e., health, education, access to services). Community well-being index also improved between 2000 and 2014, and these improvements were roughly similar irrespective of the β parameter choice (i.e., average improvements in community composite index were 0.143, 0.137, and 0.128 when β is equal to − 1, 0, and 1, respectively). Finally, average achievement in income dimension increased from 0.488 to 0.582 and the Gini coefficient dropped from 0.308 to 0.276 between 2000 and 2014, respectively. Comparing income dimension with other composite well-being indices, we observe that improvements in overall, personal and community well-being categories between 2000 and 2014 were higher than the improvement in the income dimension over the same period irrespective of the β parameter choice. Similarly, decreases in overall, personal, and community well-being inequality were relatively higher than the decrease in income inequality between 2000 and 2014. On the other hand, achievements in material well-being (which also includes income dimension) is higher than income dimension when well-being dimensions are considered to be perfect substitutes (i.e., β = 1). Overall, given the changes in composite well-being categories and income dimension, we can suggest that multidimensional well-being improvements were relatively higher compared to the improvements in income dimension, which also led to a lower degree of multidimensional inequality across the European regions.

To analyze the effects of β parameter choice on the changes in the regional well-being outcomes, Panels A, B, and C of Table 8 offer achievements of some regions in well-being dimensions in material, personal, community categories, and composite well-being outcomes with different β parameters in 2000 and 2014, respectively. Each panel consists of two regions that experienced changes in well-being outcomes that were towards balanced (uneven) composition of development across the well-being dimensions.³⁵ Furthermore, to assess whether the changes in well-being achievements between 2000 and 2014 were towards balanced (uneven) composition of development across the well-being dimensions, we obtain a “deviation” measure which calculates the level of evenness of achievements across well-being categories.³⁶ The lower (higher) this score, the more rounded (unbalanced) the achievements across the well-being dimensions in each category are.

Panel A of Table 8 offers two regions that experienced changes in income, jobs and housing dimensions that were towards balanced (unbalanced) achievements across the well-being dimensions in material well-being category. Standard of living and job conditions (income and jobs dimensions) in Vienna deteriorated between 2000 and 2014 but the region experienced major improvement in housing, which led to a more rounded composition of development in this category (e.g., “deviation” measure dropped from 1.23 to 0.61 between 2000 and 2014). Even though the aggregate improvement across the three dimensions is limited (i.e., aggregate change in achievements in the three dimensions was 0.015), achievements across the dimensions were more rounded in 2014 than in 2000, which can also be seen by looking at the changes in composite scores when β = 0 and β = − 1 are used in the aggregation (i.e., composite index outcomes for Vienna increased by 0.042 and 0.083 when respective β parameters are used). Similar case is observed for Saxony-Anhalt region of Germany. This region experienced improvements in all dimensions, however, the major improvement had been in the dimension that was the least achieved one in 2000 (i.e., jobs dimension). Improvements in this region were towards rounded achievements across the three dimensions, which are also reflected in the composite score improvements when β = 0 and β = − 1 are used in aggregation since the changes in composite scores are higher than the change in the index that is obtained with arithmetic mean. On the other hand, over-time improvements in central Estonia and Wallonia region of Belgium were towards unrounded achievements across the three dimensions. Wallonia region experienced a deterioration in jobs dimension (which was the least achieved dimension in 2000) and an improvement in housing dimension (which was the most achieved dimension in 2000), which led to a divergence in achievements across the well-being dimensions (i.e., deviation measure increased by 0.56 between 2000 and 2014). Whereas, even though there had been an improvement in all dimensions in the central Estonia, the major increase was observed in jobs dimension (which was the highest achieved dimension in 2000). Even though, equally-weighted index (i.e., when β = 1) does not differentiate whether the improvements were towards even (unbalanced) composition of development across the three dimensions, improvements in composite scores are relatively lower when dimensions allowed to have some degree of complementarity (i.e., when composite indices are obtained with β = 0 and β = − 1). Panels B and C of Table 8 also offer two regions that experienced changes in well-being dimensions in personal and community well-being categories that were towards rounded (unbalanced) achievements across the three dimensions, respectively (see respective panels in Table 8 for the details).

Overall, in this section, we showed that the over-time improvements in composite scores are different when dimensions are considered to be complementary at some degree when the over-time changes in achievement levels in dimensions are towards balanced (or unbalanced) composition of development across the dimensions or not. Even (uneven) composition of the development across the dimensions are reflected in the composite indices that are obtained with β ≤ 0 by having relatively higher (lower) changes in composite well-being scores than the changes in the composite index obtained with arithmetic mean. This feature of aggregation is particularly important since the choice of β parameter for aggregation (i.e., whether policymakers are sensitive to the even composition of development across the dimensions or not) would lead to different approaches by the regional policymakers to improve regional composite well-being outcomes. For instance, if a composite index is obtained with the arithmetic mean aggregation method (i.e., when β is set to be 1), regional policymakers can choose to improve any dimension they wish irrespective of whether this dimension is the least or most achieved dimension. In this case, regions may choose to improve “easy” dimensions (i.e., well-being dimensions that are relatively easier to improve or less costly to manipulate) since any aggregate improvement in these dimensions would be reflected similarly in the composite score irrespective of whether this dimension is the least or most achieved one. However, if aggregation procedure prioritizes balanced composition of development or penalizes uneven composition of development (i.e., the cases when β ≤ 0), regions would prioritize improvements in dimensions in which their achievements are relatively weak since this would lead to a higher improvement in their composite scores (see the cases in Table 8). Therefore, if the aim is to promote balanced composition of development across well-being dimensions, policymakers should integrate this feature in their aggregation procedure to give the right signals to the policymakers.