Objective identification of technological returns to scale for data envelopment analysis models

In this paper, we consider one of the most critical problems for setting up a data envelopment analysis model: the identification of suitable returns to scale (RTS) for the data. 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 statistically based. 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 such gap is, the more the TRTS approaches the increasing and/or decreasing assumptions. The novelty of the Angles method is that it determines the TRTS by using only the dataset without any statistical assumptions. Moreover, the introduced gap in the Angles method represents the rate of increase or decrease of the TRTS. For the validation test of the proposed method, we examine 6 one input/one output cases. Also, we test the method using real world data of a major Canadian Bank.