Quality of Life in the European Union: A Multidimensional Analysis

Frisch (1998) computes the life satisfaction score as the sum of satisfaction ratings on the different life domains.

The comparative advantage of no (perfect) substitutability/constant trade-offs between the different sub-indicators also holds for other non-compensating methods (Mazziotta and Pareto 2012; Munda and Nardo 2005) even to those not based on geometric aggregations. However, given the appeal of using BoD-weighting in the sensitive setting of measuring and benchmarking subjective quality of life in EU countries, we opt for a geometric version of the BoD-method.

An alternative approach to introduce non-compensability in the construction of BoD-weighted CIs was recently proposed by Vidoli and Mazziotta (2013) and Vidoli et al. (2015).

As to the task of comparing and ranking countries on complex, multi-faceted concepts such as well-being and quality of life, the well-known problem is that one cannot rank them unless one aggregates the country values on the multiple indicators measuring the multidimensional concept. Of course, all reasonable CIs would return the same logical ordering in the trivial case where a multidimensional dominance relation at the level of the indicators existed. But settings in which a complete ordering can be achieved in such an uncontested manner are rare, if they exist at all. The present case study with people’s satisfaction data on multiple life domains for the EU countries is not different, with people of some countries appreciating their satisfaction with one life domain with a higher rating than the people of other countries and vice versa. Note, however, that the use of CIs and the approach of just looking at the people satisfaction data in the single life domains are not mutually exclusive.

For theoretical studies exploring the issue of measuring and/or comparing quality of life using welfare-theoretic foundations, we refer the interested reader to Nussbaum and Sen (1993), Diener (2000), Diener and Suh (1997), Costanza et al. (2007), and Robeyns (2005).

Another popular multidimensional measure is the Satisfaction With Life Scale (SWLS) developed by Diener et al. (1985) which involves five questions, all rated on a 7-point Likert scale.

As nicely reminded to us by an anonymous referee, in the setting of construction of CIs, Munda and Nardo (2005) pointed out that linearity of aggregation can be positively accepted only by following the theorem of Krantz et al. (1971): "given the set of M variables y₁, y₂,…, y_M, an additive aggregation function exists if and only if these variables are mutually preferentially independent". Clearly, in the present case study, as demonstrated by the correlational analysis, life domains are not are mutually preferentially independent.

The BoD-approach has by now also become an established method to construct CIs in various contexts. As an example, BoD-based versions of the HDI have been presented in the literature by, amongst others, Mahlberg and Obersteiner (2001), Despotis (2005a, b), Despotis et al. (2009), Blancard and Hoarau (2013), Mariano et al. (2015). In the context of evaluating quality of life, Guardiola and Picazo-Tadeo (2014) proposed a BoD-MCDM (Multi Criteria Decision Making) approach to evaluate the quality of life of a sample of 178 people living in a rural community in Yucatan (Mexico).

As to the applicability of the BoD-method to frequency data, note that there are some papers in the literature that have applied a BoD-method in the construction of a CI using frequency data deriving from a Likert scale. An example is Verschelde and Rogge (2012) which used citizen satisfaction data to measure the effectiveness of local police forces.

As a robustness check we computed the BoD-model as in (1) with lower weight bound values set equal to 10% and upper weight bound values set equal to 40%. Overall, this implied only minor differences in the majority of resulting importance weights (detailed results available from the author upon request). For the interested reader, note that robustness of outcomes in BoD-models to different weight bound values can be easily verified using the interactive website https://​fvidoli.​shinyapps.​io/​compind_​app/​.

Applying such extended versions of the BoD-model with this (rather low) number of observations risks considerably deteriorating the discriminatory power of the BoD-analysis, with a lot of countries being evaluation as outstanding performers in terms of promoting subjective quality of life among its citizens.