Multidimensional Indices with Data-driven Dimensional Weights: A Multidimensional Coefficient of Variation

Multidimensional indices require specification of the dimensional weights. There are two broad approaches to the task: the normative and the data-driven. The data-driven approach, however, often yields indices violating economic norms. This article asks whether a normatively acceptable index of inequality of the standard of living in an economy can be obtained from data-driven weights. It gives an affirmative answer by deriving a multidimensional coefficient of variation (MCV) from an endogenous weighting scheme and showing that the index satisfies the various economic norms suggested in the literature. The derived index does not appear in the existing literature and the literature does not seem to contain an MCV satisfying all of the economic norms discussed in the article. JEL: D60, D63