1、中文 3950 字， 2250 单词， 1.3 万英文字符 外文翻译之二 The Measurement of Productive Efficiency: A Reconsideration Author(s)： RAYMOND J. Kopp Nationality： USA Source： The Quarterly Journal of Economics, Vol. 96, No. 3 (Aug., 1981), pp. 477-503 Abstract The purpose of this paper is to generalize the Farrell indexes of
2、 productive efficiency to nonhomothetic production technologies, and at the same time maintain the cost interpretation of the Farrell measures. Since the generalized indexes rely heavily on recent developments in the estimation of frontier cost and production functions, several frontier models are r
3、eviewed. In addition to generalized indexes of technical, allocative, and overall productive efficiency, a variety of single-factor efficiency measures are discussed. The applicability of the proposed efficiency measures is illustrated with a numerical example of electric power generation. Introduct
4、ion The pioneering work of Michael Farrell 1957 focused attention on the concept of productive efficiency and the consequences of its recognition for the modeling of production processes. This paper reviews the elements of the original Farrell approach to efficiencymeasurement and contemporary effor
5、ts utilizing frontier functions.It provides the foundation for a synthesis of Farrell efficiency measures and frontier efficiency standards. The resultant approach to efficiency measurement ameliorates many of the weaknesses associated with both the Farrell and frontier methods while capitalizing on
6、 their combined strengths. To be clear at the outset, productive efficiency isdefined as the ability of a production organization to produce a well-specified output at minimum cost. To be more precise, the output and factor inputs must be clearly specified by vectors of measurable attributes that un
7、ambiguously define their characteristics. Further, for the sake of exposition, it is assumed that the production organization has adopted a specific technology； i.e., the exante production decisions have been made, and what we observe is the operation of the expost technology. The body of this paper
8、 is in four sections. The first section reviews the original contribution by Farrell, focusing onthe choice ofanefficiency standard. Contemporary efficiency standards derived from frontier functions are discussed in the second section. The third section proposes a series of Farrell-type efficiency m
9、easures utilizingfrontier functions, and the fourth section illustrates the empirical application of the measures with a numerical example of electricpower generation. I. THE FARRELL APPROACH In a paper read before the Royal Statistical Society, Farrell presented an ingenious method for measuring tw
10、o forms of productive efficiency. He hypothesized thatefficiencycould be dichotomized into two subcomponents reflecting the physical efficiency of the input-output production transformation (the technical component) and the economic efficiency of optimal factor allocation (price efficiency).It can b
11、e argued that the decisions of economic agents involved in production are joint； that is, decisionsthat affect allocative (technical) efficiency might also have technical (allocative) ramifications. This clearly is a possibility that Farrell did not reject. What he did assume is the ability to disag
12、gregate the effect of these joint decisions into two subcomponents, and to measure empirically their individual effects. To follow Farrells exposition, consider a linear homogeneous production process employing two factors, capital ( K ) and fuel ( F ) to produce a single output, electricity (Q ). S
13、ummarizing the technology by a unit isoquant allows one to measure productive efficiency relative to the standard set by the isoquant. Figure 1 depicts a unit isoquant denoted SS . Points to the southwest of SS are infeasible, while those to the northeast are inefficient. Given an input combination
14、such as R, Farrell defined the degree of Rs technical efficiency (TE ) as the ratio 0 /0BR. The technical efficiency index(bounded between zero and one) is an input-based measure that is the ratio of best practice input usage to actual usage, output held constant. Figure 1 Farrell defined and provid
15、ed a measure for the allocative efficiency ( AE ) of a production organization, which is independent of technical efficiency. Allocative efficiency involves the selection of aninput mix that allocates factors to their highest valued uses and thus introduces the opportunity cost of factor inputs to t
16、he measurement of productive efficiency. Returning to the model depicted in Figure 1 and assuming competitive markets for the purchase of factor inputs, we see that the relative factor prices can be embodied in the isocostline PP . The input set corresponding to pointE minimizes the cost of producin
17、g the unit output. Measuring the extent of Rs allocative inefficiency independent of its technical inefficiency, we utilize Rs technically efficient projection pointB and evaluate the ratio 0 / 0DB. Farrell combined physical (TE ) and economic (AE ) efficiency into a single index termed overall prod
18、uctive efficiency ( OPE ). Overall productive efficiency is measured by evaluating the ratio 0 / 0DR, which is the product of the TE and AE indexes and thus is a composite of the two. All of the Farrell measures are made along a ray from the origin through the inefficient input set, thus preserving
19、the inefficient factor proportions. Under the assumption of continuity and strict monotonicity, measurement along the ray ensures the distinction between technical and allocative efficiency, and enables the indexes to be interpreted in terms of total factor cost. A unit isoquant specifying the locus
20、 of minimum unit-output-input requirements was chosen by Farrell as his efficiency standard. There are three features of this standard that deserve discussion.First, the isoquant is derived from the primal production functionrelating physical units of input to physical output. The choice of the prim
21、al function rather than its dual, the cost function, is necessary if the distinction between technical and allocative efficiency is to be maintained. A cost function would supply information onOPE , but not on its constituent elements. The second feature deals with the relative nature of the standar
22、d. Discussing his choice, Farrell states: Although there are many possibilities, two at once suggest themselves-a theoretical function specified by engineers and an empirical function based on the best resultsobserved in practice. The former would be a very natural concept to choose-after all, shoul
23、d not a postulated standard of perfect efficiency represent the best that istheoretically obtainable? Certainly it is a concept used by engineers themselves when they discuss the efficiency of a machine or process. However, although it is a reasonable and perhaps the best concept for the efficiency
24、of a single production process, there areconsiderable objections to its application to anything so complex as a typical manufacturing firm, let alone an industry. Thus, although the theoretical standard is perfectly valid and has its own uses, this paper will be concerned with the observed standard
25、1957, p. 255. The observed standard is determined by those production organizations sharing acommon technology that produce the greatest output from a given input set. Efficiency measures based on the observed standard are relative in the sense that individual production organizations are compared with the performance of their peer groups. As the performance of the peer group changes, so will measured efficiency. Finally, the adoption of a unit isoquant necessarily implies that the
