Social and Economic Wellbeing in Europe and the Mediterranean Basin: Building an Enlarged Human Development Indicator

Abstract

This paper calculates a human Wellbeing Composite Index (WCI) for 42 countries, belonging to the European Economic Space, North Africa and the Middle East, as an alternative to the shortcomings of other well-known measures of socio-economic development (i.e. Gross Domestic Product per head and Human Development Index). To attain this goal, different data envelopment analysis (DEA) models are used as an aggregation tool for seven selected socio-economic variables which correspond to the following wellbeing dimensions: income per capita, environmental burden of disease, income inequality, gender gap, education, life expectancy at birth and government effectiveness. The use of DEA allows avoiding the subjectivity that would be involved in the exogenous determination of weights for the variables included in WCI. The aim is to establish a complete ranking of all countries in the sample, using a three-step process, with the last step consisting in the use of a model that combines DEA and compromise programming, and permits to obtain a set of common weights for all countries in the analysis. The results highlight the distance that still separates Southern Mediterranean countries from the benchmark levels established by some European countries, and also point to the main weaknesses in individual countries’ performance. Nordic countries, plus Switzerland, top the list of best performers, while Mauritania, Libya and Syria appear at the bottom.

Appendix

1.1 Step (i) Model

For DMU _o , the decisional unit under analysis (or any individual country in this case), the following model can be computed:

$$ \begin{array}{lll} {{\text{Max}}_{{\mu_{ro} }} } \hfill & {h_{o} = \sum\nolimits_{r = 1}^{R} {\mu_{ro} I_{ro} } } \hfill & {} \hfill \\ {{\text{Subject}}\;{\text{to:}}} \hfill & {\sum\nolimits_{r = 1}^{R} {\mu_{ro} I_{rk} } \le 1} \hfill & {k = 1, \ldots ,K} \hfill \\ {} \hfill & {\mu_{ro} \ge 0} \hfill & {r = 1, \ldots ,R} \hfill \\ \end{array} $$

(2)

where I _rk stands for the value of indicator r for unit k, and μ _ro is the weight attached to indicator r in the assessment of the efficiency of DMU _o . This model represents a linearization of model (1) and also the assumption of a single virtual input for each decisional unit, with value equal to one. Notice also that we use I as a substitute for y as a reminder that we are no longer using outputs in our objective function, but partial indexes corresponding to measurable attributes of the decisional units.

The problem with model (2) is that the measure of efficiency obtained represents the maximum achievable radial expansion of outputs (attributes) and does not include additional expansions that can only be achieved for some outputs (attributes), but not for all of them in the same proportion. For that reason we use another model that summarizes in a single measure the effect of radial expansions and differences among DMUs concerning the existence of slacks for some attributes in the projection onto the frontier [see Cooper et al. (2007) for technical details]. To overcome this problem we use the Slacks Based Measure (SBM) of efficiency, introduced by Tone (2001), which is computed according to the following model (output-oriented SBM model):

$$ \begin{aligned} & h_{o}^{*} = {\text{Min}}_{{\lambda_{k} ,s_{r}^{ + } }} \frac{1}{{1 + \frac{1}{R}\sum\nolimits_{r = 1}^{R} {{{s_{r}^{ + } } \mathord{\left/ {\vphantom {{s_{r}^{ + } } {I_{ro} }}} \right. \kern-\nulldelimiterspace} {I_{ro} }}} }}\\ & \begin{array}{lll} { {\text{Subject}}\;{\text{to:}}} \hfill & {x_{o} \ge \sum\nolimits_{k = 1}^{K} {\lambda_{k} x_{k} } } \hfill & {} \hfill \\ {} \hfill & {I_{ro} = \sum\nolimits_{k = 1}^{K} {\lambda_{k} I_{rk} } - s_{r}^{ + } } \hfill & {r = 1, \ldots ,R} \hfill \\ {} \hfill & {\lambda_{k} \ge 0} \hfill & {k = 1, \ldots ,K} \hfill \\ {} \hfill & {s_{r}^{ + } \ge 0} \hfill & {r = 1, \ldots ,R} \hfill \\ \end{array} \end{aligned}$$

(3)

where $s_{r}^{ + }$ is the slack in the socioeconomic indicator or attribute r, and λ _k measures the intensity with which DMU _k enters in the composition of the efficient reference set to which DMU _o is being compared. Furthermore, the parameter $h_{o}^{*}$ is upper bounded to one, with a unity score indicating the best performance.

1.2 Step (ii) Model

The same model (3) as in Step (i) is used, following an iterative procedure that has been described in the main text.

1.3 Step (iii) Model

In the first place, the scores obtained according to model (3) are employed to establish the reference, or ideal, idiosyncratic efficiency scores. Then, the following model is employed to obtain common weights and global efficiency scores:

$$ \begin{aligned} & {\text{Min}}_{{d_{k} ,\mu_{r} ,z}} \;t\frac{1}{K}\sum\nolimits_{k = 1}^{K} {d_{k} + (1 - t)z} \\ & \begin{array}{lll} { {\text{Subject}}\;{\text{to}}:} \hfill & {\sum\nolimits_{r = 1}^{R} {\mu_{r} I_{rk} + d_{k} = h_{k}^{*} } } \hfill & {k = 1, \ldots ,K} \hfill \\ {} \hfill & {(d_{k} - z) \le 0} \hfill & {k = 1, \ldots ,K} \hfill \\ {} \hfill & {d_{k} \ge 0} \hfill & {k = 1, \ldots ,K} \hfill \\ {} \hfill & {\mu_{r} \ge \varepsilon } \hfill & {} \hfill \\ {} \hfill & {z \ge 0} \hfill & {} \hfill \\ \end{array} \\ \end{aligned} $$

(4)

ε being a non-Archimedean small number which assures that all attributes I _r are used in the computation of the scores.

The first term of the objective function represents the mean deviation between the DEA-efficiency scores, or ideal scores, namely $h_{k}^{*}$ and the global efficiency scores for all units, whereas the second term represents, through the non-negative variable z, the maximum deviation between the aforementioned efficiency scores (see Despotis 2002, 2005 for technical details). Different sets of common weights μ _r are generated by varying the parameter t between 0 and 1, thus granting more or less relative importance to the norms respectively implied by the first and second terms of the objective function. Each value of the parameter t may produce a different set of common weights thus generating a different global efficiency pattern. A series of alternative ranks can thus be obtained, according to different t values, and all DMUs can then be ranked with regards to their average global efficiency score.