Combining two approaches to efficiency assessment
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Combining two approaches to efficiency assessment C Tofallis University of Hertfordshire Business School, Hertford The advent of data envelopment analysis (DEA) enabled the measurement of efficiency to be extended to the case of multiple outputs. Prior to DEA we had the parametric approach based on multiple regression. We highlight some difficulties associated with these two approaches and present a hybrid which overcomes them whilst maintaining the respective advantages of each. This hybrid models the efficient frontier using an algebraic expression; the resulting smooth representation allows all units to be naturally enveloped and hence slacks to be avoided. (Slacks are potential improvements for inefficient units which are not accounted for in the DEA (radial) score, and so have been problematic for DEA.) The approach identifies the DEA-efficient units and fits a smooth model to them using maximum correlation modelling. This new technique extends the method of multiple regression to the case where there are multiple variables on each side of the model equation (eg outputs and inputs). The resulting expression for the frontier permits managers to estimate the effect on their efficiency score of adjustments in one or more input or output levels. Keywords: data envelopment analysis; econometrics; performance measurement; regression; statistics
Introduction Given a set of decision making units (DMUs: departments, branches, firms, etc) to be compared, there are two main approaches for the construction of an efficient frontier upon which efficiency scores can be based. One is the parametric approach, often used by economists, the other is the nonparametric approach known as data envelopment analysis (DEA). We shall outline these and point out their drawbacks. The purpose of this paper is to propose a hybrid approach which not only brings together the useful aspects of these two methods but also avoids their limitations. In both of the standard approaches mentioned above the efficiency of an organisational unit is measured by reference to a frontier. There are two types of parametric frontier: deterministic and stochastic. In the former a given functional form which relates output to the various inputs (eg a Cobb– Douglas function) is fitted using regression constrained so that all points lie on one side of the (production) frontier. This is achieved by restricting the residuals to be one-sided, ie all of the same sign. This means that no unit can produce more output than that calculated from this frontier production function for its given levels of inputs. With stochastic frontiers we have both unrestricted residuals as well as onesided ones within the same model, the idea being that the former will represent random effects such as the weather and equipment failures, while the latter indicate inefficiency. *Correspondence: C Tofallis, Department of Statistics, Economics, Accounting and Management Systems, Un
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