Geometric mean approach to measure Composite Index

Abstract

Composite Index (CI) combines measures of indicators on economic, social, environmental variables, government initiatives, wellbeing of health, psychological, satisfaction of basic needs, social/cultural, etc. However, existing measures of CIs suffer from limitations. The paper proposes CI measure as geometric mean (GM), which avoids scaling and choosing of weights. It helps in better comparison of countries across time and space and satisfies desired properties like monotonically increasing continuous function, constant elasticity, identification of key areas, reduction of level of substitutability, formation of chain indices to show growth of CI of a country, and is less affected by outliers. The index with wide applicability can be used for ranking, classification of countries and facilitates computation of mean and variance of a sample of countries. In addition, the index satisfies time-reversal test, helps to identify the critical areas and find contribution of the component indicators, estimation of population parameters and testing statistical hypothesis. Separate indices for domains can be constructed by considering indicators relevant to a domain. Thus, it is an improvement over the existing methods. Future studies suggested.