Maximum incremental (minimum decremental) ratio and one-sided RTS in FDH production technologies

TL;DR

This paper introduces new measures for scale elasticity and one-sided returns to scale in nonconvex FDH production models, addressing limitations of existing methods and providing efficient testing procedures.

Contribution

It defines maximum incremental and minimum decremental ratios for FDH models and develops polynomial-time algorithms for their calculation and for testing one-sided RTS.

Findings

New scale elasticity measures for FDH models.

Polynomial-time algorithms for ratio calculation.

Conditions for identifying one-sided RTS.

Abstract

In very recent decades, Scale Elasticity (SE), as a quantitative characterization of Returns to Scale (RTS), has been an attractive research issue in convex DEA models. However, we show that the existing Scale Elasticity (SE) measure does not work properly under nonconvex FDH technologies. Due to this, we define an SE counterpart in FDH models. To this end, two new quantities, called maximum incremental and minimum decremental ratios are introduced; and a polynomial-time procedure is developed to calculate them. The second part of the paper is devoted to introducing and investigating left- and right-hand RTS notions in FDH models. Some necessary and sufficient conditions are established, leading to a polynomial-time test for identification of the one-sided RTS status of DMUs. Finally, the relationships between one-sided RTS, Global RTS (GRS), and the newly-defined ratios are established.