Weak Disposability in Nonparametric Production Analysis: Reply to Färe and Grosskopf

Färe and Grosskopf (this issue) claim that a single abatement factor suffices for modeling weak disposability in nonparametric production models, and that the Kuosmanen (2005) technology that uses multiple abatement factors is larger than necessary. This article demonstrates by a numerical example that a single abatement factor does not suffice to capture all feasible production plans, and that its use leads to the violation of convexity, one of the maintained assumptions of the model. We also prove that the Kuosmanen technology is the correct minimum extrapolation technology under the stated axioms.     

Optimal solutions of multiplier DEA models

Journal of Productivity Analysis - Conventional models of data envelopment analysis (DEA) are based on the constant and variable returns-to-scale production technologies. Any optimal input and...     

Symposium Overview

Journal of Productivity Analysis -     

Efficiency and Global Scale Characteristics on the “No Free Lunch” Assumption Only

In a production technology, the type of returns to scale (RTS) associated with an efficient decision making unit (DMU) is indicative of the direction of marginal rescaling that the DMU should undertake in order to improve its productivity. In this paper a concept of global returns to scale (GRS) is developed as an indicator of the direction in which the most productive scale size (MPSS) of an efficient DMU is achieved. The GRS classes are useful in assisting strategic decisions like those involving mergers of units or splitting into smaller firms. The two characterisations, RTS and GRS, are the same in a convex technology but generally different in a non-convex one. It is shown that, in a non-convex technology, the well-known method of testing RTS proposed by Färe et al. is in fact testing for GRS and not RTS. Further, while there are three types of RTS: constant, decreasing and increasing (CRS, DRS and IRS, respectively), the classification according to GRS includes the fourth type of sub-constant GRS, which describes a DMU able to achieve its MPSS by both reducing and increasing the scale of operations. The notion of GRS is applicable to a wide range of technologies, including the free disposal hull (FDH) and all polyhedral technologies used in data envelopment analysis (DEA).     

Improving discrimination in data envelopment analysis: some practical suggestions

In some contexts data envelopment analysis (DEA) gives poor discrimination on the performance of units. While this may reflect genuine uniformity of performance between units, it may also reflect lack of sufficient observations or other factors limiting discrimination on performance between units. In this paper, we present an overview of the main approaches that can be used to improve the discrimination of DEA. This includes simple methods such as the aggregation of inputs or outputs, the use of longitudinal data, more advanced methods such as the use of weight restrictions, production trade-offs and unobserved units, and a relatively new method based on the use of selective proportionality between the inputs and outputs.     

Production technologies based on combined proportionality assumptions

The assumption of full proportionality is incorporated in the constant returns-to-scale (CRS) technology and allows for proportional scaling of inputs and outputs of production units. The assumption of selective proportionality was recently incorporated in the hybrid returns-to-scale (HRS) technology in which only a subset of outputs is proportional to a subset of inputs. In this paper we develop a production technology that exhibits both the full and selective proportionality at the same time. Real examples of such technology are pointed out. Subject to certain conditions, the DEA models based on this technology provide better discrimination than the CRS and HRS models.