  Data 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 and outputs change in the same
proportion, which is the starting point to determine the qualitative and
quantitative features of RTS of decision making units (DMUs). However, for more
complex products, such as the scientific research in institutes, changes of
various types of inputs or outputs are often not in proportion. Therefore, the
existing definition of RTS in the framework of DEA method may not meet the need
to estimate the RTS of research institutions with multiple inputs and outputs.
This paper proposes a definition of directional RTS in the DEA framework and
estimates the directional RTS of research institutions using DEA models.
Further in-depth analysis is conducted for an illustrative example of 16 basic
research institutes in Chinese Academy of Sciences (CAS) in 2010.
