Estimating directional returns to scale in DEA

Abstract

ABSTRACTData envelopment analysis (DEA) is one of the most commonly used methods to estimate the returns to scale (RTS) of the public sector (e.g. research institutions). Existing studies are all based on the traditional definition of RTS in economics and assume that multiple inputs or outputs change in the same proportion, which is the starting point to determining the qualitative and quantitative features of the RTS of decision-making units (DMUs). However, for more complex products, such as the scientific research in institutes, changes of inputs or outputs are often not in proportion. Therefore, the existing definition of RTS in the framework of DEA may need to be extended to estimate the RTS in such situations. This paper proposes the definitions of directional scale elasticity and directional RTS in the DEA framework and estimates the directional RTS using DEA models. Further in-depth analysis is performed for an illustrative example of 16 basic research institutes in the Chinese Academy of Sciences (CAS) in 2010.