Abstract
Most data envelopment analysis (DEA) studies on scale elasticity (SE) and returns to scale (RTS) of efficient units arise from the traditional definitions of them in economics, which is based on measuring radial changes in outputs caused by the simultaneous change in all inputs. In actual multiple inputs/outputs activities, the goals of expanding inputs are not only to obtain increases in outputs, but also to expect the proportions of such increases consistent with the management preference of decision-makers. However, the management preference is usually not radial changes in outputs. With the latter goal into consideration, this paper proposes the directional SE and RTS in a general formula for multi-output activities, and offers a DEA-based model for the formula of directional SE at any point on the DEA frontier, which is straightforward and requires no simplifying assumptions. Finally, the empirical part employs the data of 16 basic research institutions in Chinese Academy of Sciences (CAS) to illustrate the superiority of the proposed theories and methods.
Highlights
Returns to scale (RTS) is an important issue in the performance analysis of production organizations, which is concerned with the relationship between efficient vectors of inputs and outputs for a given technology production function
We employ the data from 16 basic research institutions in Chinese Academy of Sciences (CAS) as the empirical example to illustrate the advantages of the analyses of directional Scale elasticity (SE) and directional RTS
The most existing approaches for quantitative analysis of RTS follow the concepts of the traditional RTS and SE in economics, i.e., the radial change in outputs resulting from the radial changes of all inputs
Summary
Returns to scale (RTS) is an important issue in the performance analysis of production organizations, which is concerned with the relationship between efficient vectors of inputs and outputs for a given technology production function. Scale elasticity (SE) is a quantitative measure of the strength of RTS characterization [11] It is defined as the ratio of the proportional change in output to the equal-proportional change in inputs at a (frontier function) unit. Within the existing work in DEA, there are two strands of research to providing RTS information of the decision-making units (DMUs), including the qualitative and quantitative approaches. The former is to describe the qualitative characterization of RTS, that is, to distinguish whether DMUs have increasing, constant or decreasing RTS (see, e.g., [4,5,8,9,22,23], among others). The last section contains the conclusion and delineates prospects of further research
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