Working with Non-compensatory Composite Indicators: A Case Study Based on SDG for Mediterranean Countries

In recent years there has been an increasing interest in measuring phenomena through the use of composite indicators. There are at least two main motivations: on the one hand, composite indicators are able to summarize in a single number the many faces of the analyzed phenomena. On the other hand, any composite indicator induces a ranking that allows easy comparisons both over time and space. Here, we propose a two-stage aggregation procedure to construct four overall composite indicators. In the first stage, the aggregation is made at domain level and then domains are aggregated to get the overall indicator. The four methods are based on the idea of mitigating the compensability hypothesis. Starting from the simplest non-compensatory index, computed through the geometric mean, we modify it taking into account the horizontal variability and the vertical variability, obtaining the so-called Penalized Geometric Mean Indicator and Weighted Geometric Mean Indicator, respectively. Then, by combining both horizontal and vertical variability we define the Penalized Weighted Geometric Mean indicator. We apply the above-mentioned methods to measure sustainability according to the 17 targets of the Sustainable Development Goals (SDGs). Thus, for each method, we calculate an overall index and, among the 193 countries we put attention on the results provided by 17 Mediterranean countries.