Local and global returns to scale in performance measurement

In data envelopment analysis, the type of local returns to scale (RTS) exhibited by a technically efficient unit indicates whether an increase or reduction of the scale of operations could improve the productivity of the unit. One of the approaches to testing RTS is based on the comparison of the efficiency of the unit in specially constructed reference technologies. It has been suggested that this approach is equally suitable for convex and non-convex, including the free disposal hull, technologies. In this paper, we construct examples that show that this suggestion in the case of non-convex technologies is not correct. We show that the type of RTS obtained by this approach is not a local, but global, characteristic of the technology, as it indicates the direction to the most productive scale size of the unit. In non-convex technologies, the local and global classifications of RTS are generally different.