Geometric mean quantity index numbers with Benefit-of-the-Doubt weights

Geometric mean index numbers are a multiplicative aggregation of (price or quantity) ratios with their importance exponents/weights derived from one or more observed budget shares. In the specific context of composite indicator construction, we propose to use the budget shares as naturally generated by the linear Benefit-of-the-Doubt model. This approach is directly inspired by the literature on index number theory. Our basic model is easily extended to provide transitive composite indicator orderings in a multilateral setting. Also, a multi-factor decomposition is proposed to explain the intertemporal evolution of a single entity. We illustrate our results with social inclusion data for the EU-countries.