Output Frontier and Increasing Returns to Scale

Convex output set is common hypothesis in production theory and empirical applications such as the Data Development Analysis. This seems to be taken for granted without any reference to returns to scale. This paper focuses on the relation between returns to scale and the nature of output frontier shapes. Since output sets are non convex if at least one activity has increasing returns to scale, the DEA is showed to be inappropriate to study economic sectors facing increasing returns to scale. The other two methodologies, the Free Disponible Hull and the econometric parametric method, could also imply mistakes if output frontier estimations do not take into account the link between returns to scale and output frontier shapes. This generates a fundamental question : does it make sense to estimate output frontiers without any a priori consideration for returns to scale?