A Note on Construction of a Composite Index by Optimization of Shapley Value Shares of the Constituent Variables

Sudhanshu K. MISHRA

Abstract


Abstract. This paper proposes a method to construct composite index, which is a linear combination of several variables, by deriving weights on the criterion of Shapley value (from cooperative game theory) that a constituent variable has in making the composite index.  In practice it is found oftentimes that the most common method of principal component analysis has a tendency to ignore (or poorly weigh) those constituent variables that do not have strong correlation with the sister variables. This elitist nature of PCA forces a compromise upon the analyst’s desire and need to incorporate those weakly correlated (but theoretically and practically important) variables into the composite index. In that case, one must construct a composite index that is more inclusive in nature. The Shapley value based composite index meets that requirement.

Keywords. Shapley value, Composite index, Principal Component Analysis, Inclusive indices, Global optimization.

JEL. C43, C63, C71.


Keywords


Shapley value; Composite index; Principal component analysis; Inclusive indices; Global optimization.

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DOI: http://dx.doi.org/10.1453/ter.v3i3.903

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