Rolf Färe

Measuring the technical efficiency of production

Production technology is commonly modelled by means of a production function, which in the scalar output case specifies the maximum output obtainable from an input vector. The degree to which the actual output of a production unit approaches its maximum is called the technical efficiency of production. A technically efficient unit must operate on its production function, although this condition is not sufficient; a technically inefficient unit may operate beneath its production function, although this condition is not necessary. If the notion of technical efficiency is to have empirical content, it must be based on a proper measure, or index, of the technical efficiency of a production unit. It is the purpose of this paper to specify a set of properties such an efficiency measure should satisfy, to show that the widely used measure proposed by Farrell [4] does not satisfy these properties, and to introduce a new measure that does satisfy these properties. The pioneering work on technical efficiency is that of Farrell. Inspired by the work of Debreu [2] and Koopmans [7], Farrell suggested a measure of technical efficiency that can be interpreted, somewhat loosely for the moment, in either of two ways: as the ratio of technically minimal to actual inputs, given output and the input mix, or as the ratio of actual to technically

Profit, directional distance functions, and Nerlovian efficiency

The directional technology distance function is introduced, given an interpretation as a min-max, and compared with other functional representations of the technology including the Shephard input and output distance functions and the McFadden gauge function. A dual correspondence is developed between the directional technology distance function and the profit function, and it is shown that all previous dual correspondences are special cases of this correspondence. We then show how Nerlovian (profit-based) efficiency measures can be computed using the directional technology distance function.

Productivity Developments in Swedish Hospitals: A Malmquist Output Index Approach

The purpose of this chapter is to study productivity change in Swedish hospitals during the time period from 1970 to 1985. By comparing annual changes in the productivity of individual hospitals, it is possible both to identify general trends in the productivity of the hospital industry as a whole and to identify individual hospitals exhibiting patterns of change in productivity that differ from the rest of the industry. A careful analysis of the results of this exercise should add to our knowledge about the factors determining the pattern of hospital productivity in Sweden.

Derivation of Shadow Prices for Undesirable Outputs: A Distance Function Approach

Many production activities generate undesirable byproducts in conjunction with the desirable outputs they produce. Russell W. Pittman (1983) showed how to adjust productivity calculations, and Rolf Fare et al. (1989) showed how to adjust efficiency measures, in the presence of undesirable outputs. Here the authors show how to estimate output distance functions as frontiers in order to generate shadow values of the undesirable outputs that are required to make both types of adjustment. An empirical application is provided. Coauthors are Shawna Grosskopf, C. A. Knox Lovell, and Suthathip Yaisawarng. Copyright 1993 by MIT Press.

An activity analysis model of the environmental performance of firms - Application to fossil-fuel-fired electric utilities

The productivity of firms when some outputs (pollution) are undesirable has been studied in the literature for some time. In this paper we introduce an environmental performance indicator based on the decomposition of overall factor productivity into a pollution index and an input-output efficiency index. This indicator is compared to the more conventional Jaggi and Freedman (1992) model. Results are given for illustrative purposes, using data from U.S. fossil-fuel-fired electric utilities. The rankings of the utilities obtained with the two models show significant divergence, which is due to the different ways in which the undesirable outputs are dealt with, as well as due to the different possible tradeoffs between the pollutants released into the atmosphere and the resources used as inputs.

Theory and Application of Directional Distance Functions

In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrells technical efficiency measure) are ‘dual’ to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.

Nonparametric Cost Approach to Scale Efficiency

Starting with Farrell & Fieldhouse (1962), a host of notiparametric models have been developed for calculation of scale efficiency. A common property of these models is that they are specified in terms of input/output data. Duality theory has taught us that technological characteristics may be analyzed from either the primal or the dual cost side. The purpose of this paper is to introduce a nonparametric dual method of calculating scale efficiency.

Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach

In this paper, the authors develop measures of plant capacity, plant capacity utilization, and technical change based on observed best practice performance in a given industry. These measures are calculated as solutions to linear programming problems that are closely related to those used to calculate Farrell-type efficiency measures. An example using electric utility data is included. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Malmquist Productivity Indexes: A Survey of Theory and Practice

In 1982, Caves, Chris tensen and Diewert introduced the Malmquist productivity index. Although that paper was extremely influential and widely cited, the Malmquist productivity index itself was rarely computed (Pittman, (1983) and Nishimizu and Page (1982) are exceptions), until Fare, Grosskopf, Lindgren and Roos (1989), showed how it could be calculated using a nonparametric linear programming method. In this paper we review the theoretical development and empirical applications of (some of) the various Malmquist productivity indexes. Other surveys of productivity which include the Malmquist indexes are Diewert (1992:a,1993), Hjalmarsson (1991) in Swedish, Roos (1993) and Sudit (1995).

Directional distance functions and slacks-based measures of efficiency

In this paper we introduce a SBM (slacks-based measure) of efficiency based on directional distance functions. This measure is contrasted with the SBM due to Professor Tone [Tone, K., 2001. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 130, 498-509].