SDG composite indicators for Mediterranean countries: a new theoretical approach

Composite indicators provide summary picture of multidimensional phenomena, and thecorresponding rankings facilitate evaluations and comparisons over time and space.Standard composite indicators often assume compensability among indicators. We arguethat the compensability hypothesis needs to be restricted especially when analyzingeconomic, social and environmental aspects.Among all the member of the new family of composite indicators made by penalizedversions of the generalized means introduced by Mariani et al (2022), we focus on thepenalized Geometric Mean (pGM). This index is defined by means of a penalty factor thataccounts for the (horizontal) variability of the normalized indicators opportunely scaled andtransformed via the Box-Cox function.To illustrate the appealing of our proposal, we compute penalized Geometric Mean andwe compare it with the Arithmetic Mean and the Geometric Mean. We focus on data referringto the Sustainable Development Goals (SDGs) (Sachs et al., 2021). More in datail, amongthe 17 Goals, analyse Goal 2: “End hunger, achieve food security and improved nutrition andpromote sustainable agriculture”, the so-called “Zero Hunger” and we compute the threeindices for world-wide Countries with a focus on 17 Mediterranean Countries.