Partial local and global returns to scale in efficiency analysis with different technologies

Local and global returns to scale are two different characteristics of production frontiers. The former is a marginal characteristic that reflects the elasticity of response of the vector of outputs to small proportional changes of the vector of inputs. In contrast, the latter is indicative of the direction of the movement for the unit under the assessment towards its optimal scale known as the most productive scale size. It is known that, if the technology is convex, the local and global characterizations of returns to scale are identical. However, in a nonconvex technology, the two characterizations are generally different. The purpose of this paper is to extend these results to scenarios in which returns to scale are evaluated only with respect to selected subvectors of inputs and outputs, for example, those that are considered discretionary for the unit under the assessment.