Objective identification of technological returns to scale for DEA models

One of the most critical issues for setting up a ýýýDEA model is identification of the technological returns to scaleý. We refer to it as the technological returns to scale (TRTS) to completely separate the technology’s RTS from the DMU’s RTS. The only existing objective approaches for the TRTS identification are statistical based approach. While they are supported by strong theories, they might be problematic in practice. In this paper, we introduce a novel and objective non-statistical method for the identification of the data’s TRTS. Our proposed approach is called the Angles method since it utilizes the angles between the hyperplanes to calculate the gap between the constant and variable TRTS assumptions. The gap is calculated for both the increasing and the decreasing sections of the frontier. The larger the gap in the increasing and/or the decreasing sections of the frontier, the more the TRTS approaches the increasing and/or the decreasing assumptions. The novelty of the Angles method is that it determines the TRTS by utilizing only the dataset without any statistical assumptions. Besides, unlike the existing statistical tests that merely accept or reject some hypothesis, the introduced gap represents the rate of increase or decrease of the TRTS. ýTo validate the proposed methodý, ýwe consider six sample with one input/one output and a two inputs/one output sampleý. Moreover, the Angles method is applied on a real world data set of province gas companies.