Non-convex Technologies and Cost Functions: Definitions,Duality and Nonparametric Tests of Convexity

This contribution is the first systematic attempt to develop a series of nonparametric, deterministic technologies and cost functions without maintaining convexity. Specifically, we introduce returns to scale assumptions into an existing non-convex technology and, dual to these technologies, define non-convex cost functions that are never lower than their convex counterparts. Both non-convex technologies and cost functions (total, ray-average and marginal) are characterized by closed form expressions. Furthermore, a local duality result is established between a local cost function and the input distance function. Finally, nonparametric goodness-of-fit tests for convexity are developed as a first step towards making it a statistically testable hypothesis. An erratum to this article is available at .     

Fuzzy Pair-wise Dominance and Implications for Technical Efficiency Performance Assessment

Classically, the concept of efficiency measurement is based on the definition of a frontier that envelops the observed production plans. The efficiency score itself is based on the distance of an observed production plan from this frontier. The frontier along with the required technological assumptions (such as convexity) needed for its definition may be replaced with the concept of pair-wise dominance. This concept leads to a classification scheme for all production plans instead of a ranking based on efficiency scores. Also, the traditional assumption of deterministic or crisp production plans may be substituted with the weaker assumption of fuzzy production plans as proposed by fuzzy set theory. This paper merges these two concepts and defines a new classification scheme based on fuzzy dominance.     

Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies

Thepurpose of this short article is to simplify goodness-of-fitmethods to obtain qualitative information about returns to scalefor individual observations. Traditional and new goodness-of-fitmethods developed for estimating returns to scale on nonparametricdeterministic reference technologies are reviewed. Using compositionrules for technologies with specific returns to scale assumptions,we show how these goodness-of-fit methods can be simplified inthe case of convex technologies (Data Envelopment Analysis (DEA)models).     

A new criterion for technical efficiency measures: non‐monotonicity across dimensions axioms

Based on non‐parametric deterministic production technologies radial and non‐radial measures of technical efficiency are evaluated using properties guaranteeing insensitivity to the dimensionality of technology. These new axioms are important in empirical research and may especially prevent manipulation of results when implementing these benchmark methodologies in private or public organizations. An empirical example illustrates to which extent a series of radial and non‐radial technical efficiency measures satisfies the proposed axioms. Copyright © 1999 John Wiley & Sons, Ltd.