An SDG composite index based on Hierarchical DEA and Cooperative Game Theory

Abstract

The aim of this research is to develop a new approach to compute an SDG Composite Index (CI) aggregating the close to one hundred indicators compiled by the Sustainable Development Report (SDR). These indicators have a hierarchical structure based on the 17 SDGs. The proposed approach formulates a Common Weights Hierarchical Data Envelopment Analysis (CWH-DEA) model that allows defining a Transferable Utility (TU) game with a priori unions. The associated game belongs to the class of Airport games, for which the Owen value is used to compute the contribution of each index to the aggregate performance index. Allocating these contributions allows computing an SDG composite index for each country. The proposed approach does not require establishing a priori bounds on the importance of the different indicators or group of indicators and has been applied to 167 countries using the most recent SDR 2024 data with the corresponding results analysed and discussed. Besides, the proposed approach has been able to endogenously determine the contribution of each of the 98 indicators considered, leading to a rather balanced share distribution by SDG group. The proposed SDG CI is highly correlated with the SDG Index, identifying the OECD as the region with the highest SDG performance, followed by Eastern Europe and Central Asia, while the Middle East and North Africa, Oceania and, especially, Sub-Saharan Africa fall below the World average.