On the Estimation of Directional Returns to Scale via DEA models

TL;DR

This paper introduces a new concept of directional returns to scale within DEA models, allowing for more accurate estimation of research institutions' productivity when inputs and outputs change non-proportionally.

Contribution

It proposes a novel definition of directional RTS in DEA and demonstrates its application on Chinese research institutes, addressing limitations of traditional RTS assumptions.

Findings

Directional RTS provides more flexible analysis for complex research outputs.

Application to Chinese institutes illustrates the method's practical utility.

Results show differences between traditional and directional RTS estimates.

Abstract

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.