Calculation of scale elasticities in data envelopment analysis models: direct and indirect approaches

The qualitative characterisation of returns to scale in DEA has been a research issue the last decade. However, quantitative information provides the ultimate information. This paper presents two ways of obtaining numerical values of scale elasticity by an indirect approach using efficiency scores and dual variables for radial projections of inefficient points to the frontier, and a direct approach that is more general and powerful and directly evaluates numerically scale elasticity at any point on the DEA surface along intersections with planes. The direct and indirect approaches are compared using real data and a very high correspondence is found.