Measurement of Returns-to-Scale using Interval Data Envelopment Analysis Models

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkThe economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterized by intervals. For instance, the heat losses of the combined production of heat and power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study

Calculating the scale elasticity in DEA models.

In economics scale properties of a production function is charcterised by the value of the scale elasticity. In the field of efficiency studies this is also a valid approach for the frontier production function. It has no good meaning to talk about scale properties of inefficient observations. In the DEA literature a qualitative characterisation is most common. The contribution of the paper is to apply the concept of scale elasticity from multi output production theory in economics to the piecewise linear frontier production function, and to develop formulas for calculating values of the scale elasticity for radial projections of inefficient observations. Illustrations also on real data are provided, showing the differences between scale elasticity values for the input- and output oriented projections and the range of values for efficient observations.Scale elasticity; DEA, production theory; Farrell efficiency measures

Marginal values and returns to scale for nonparametric production frontiers

We present a unifying linear programming approach to the calculation of various directional derivatives for a very large class of production frontiers of data envelopment analysis (DEA). Special cases of this include different marginal rates, the scale elasticity and a spectrum of partial and mixed elasticity measures. Our development applies to any polyhedral production technology including, to name a few, the conventional variable and constant returns-to-scale DEA technologies, their extensions with weight restrictions, technolo gies with weakly disposable undesirable outputs and network DEA models. Furthermore, our development provides a general method for the characterization of returns to scale (RTS) in any polyhedral technology. The new approach effectively removes the need to develop bespoke models for the RTS characterization and calculation of marginal rates and elasticity measures for each particular technology

Using data envelopment analysis for the efficiency and elasticity evaluation of agricultural farms

Data Envelopment Analysis (DEA) is a well-established relative efficiency measurement technique, which has been widely applied to evaluate the technical efficiency of agricultural units in different countries by focusing on different aspects of agricultural production. This research deals with the evaluation of efficiency through DEA in non-homogeneous agricultural production, where units produce a wide range of different outputs. The objectives are threefold. Firstly, we propose a novel methodological approach of integrating the production trade-offs concept of DEA into non-homogeneous agricultural efficiency evaluation to prevent the overstatement of the efficiency of specialist farms and overcome the issue of insufficient discrimination due to large number of outputs in the models. Secondly, we aim to integrate this methodological perspective to the theory of elasticity measurement on DEA frontiers. The efficient frontiers of DEA are not defined in functional forms as in the classical economic theory, therefore obtaining elasticity measures on them require different considerations. We introduce the production trade-offs to the elasticity measurement and derive the necessary models to calculate the elasticities of response in the presence of production trade-offs. As a third objective, before moving to the introduction of the trade-offs in elasticity measurement, for theoretical completeness, we first consider the elasticity measurement on DEA frontiers of constant returns-to-scale (CRS) technologies. Our proposed methodology and all the developed elasticity theory are illustrated in a real world case of Turkish agricultural sectors. We provide extensive empirical applications covering all the proposed theory and methodology. Among the results of this research, we provide an elasticity measurement framework, which enables us to calculate elasticities of response measures in both VRS and CRS technologies, with or without production tradeoffs included. We observe that the integration of production trade-offs provide better discrimination of efficiency scores compared to the models without trade-offs included. We also investigate how changing production trade-offs affect the efficiency and elasticity measures of the evaluated units