外文翻譯--再議生產(chǎn)效率的測度

1、<p>　　中文3950字，2250單詞，1.3萬英文字符</p><p><b>　　外文翻譯之二</b></p><p>　　The Measurement of Productive Efficiency: A Reconsideration</p><p>　　Author(s)：RAYMOND J. Kopp </

2、p><p>　　Nationality：USA</p><p>　　Source：The Quarterly Journal of Economics, Vol. 96, No. 3 (Aug., 1981), pp. 477-503</p><p><b>　　Abstract </b></p><p>　　The pur

3、pose of this paper is to generalize the Farrell indexes of productive efficiency to nonhomothetic production technologies, and at the same time maintain the cost interpretation of the Farrell measures. Since the generali

4、zed indexes rely heavily on recent developments in the estimation of frontier cost and production functions, several frontier models are reviewed. In addition to generalized indexes of technical, allocative, and overall

5、productive efficiency, a variety of single-factor eff</p><p>　　Introduction</p><p>　　The pioneering work of Michael Farrell [1957] focused attention on the concept of productive efficiency and t

6、he consequences of its recognition for the modeling of production processes. This paper reviews the elements of the original Farrell approach to efficiency measurement and contemporary efforts utilizing frontier function

7、s. It provides the foundation for a synthesis of Farrell efficiency measures and frontier efficiency standards. The resultant approach to efficiency measurement ameliorate</p><p>　　To be clear at the outset,

8、 productive efficiency is defined 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 m

9、easurable attributes that unambiguously define their characteristics. Further, for the sake of exposition, it is assumed that the production organization has adopted a specific technology; i.e., the ex ante production de

10、cisions have been made, and what w</p><p>　　The body of this paper is in four sections. The first section reviews the original contribution by Farrell, focusing on the choice of an efficiency standard. Conte

11、mporary efficiency standards derived from frontier functions are discussed in the second section. The third section proposes a series of Farrell-type efficiency measures utilizing frontier functions, and the fourth secti

12、on illustrates the empirical application of the measures with a numerical example of electric power generation.</p><p>　　I. THE FARRELL APPROACH</p><p>　　In a paper read before the Royal Statist

13、ical Society, Farrell presented an ingenious method for measuring two forms of productive efficiency. He hypothesized that efficiency could be dichotomized into two subcomponents reflecting the physical efficiency of the

14、 input-output production transformation (the technical component) and the economic efficiency of optimal factor allocation (price efficiency). It can be argued that the decisions of economic agents involved in production

15、 are joint; that is,</p><p>　　To follow Farrell's exposition, consider a linear homogeneous production process employing two factors, capital () and fuel () to produce a single output, electricity (). Su

16、mmarizing 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 . Points to the southwest of are infeasible,

17、 while those to the northeast are inefficient. Given an input combination such as R, Farrell defined the de</p><p><b>　　Figure 1</b></p><p>　　Farrell defined and provided a measure f

18、or the allocative efficiency () of a production organization, which is independent of technical efficiency. Allocative efficiency involves the selection of an input mix that allocates factors to their highest valued uses

19、 and thus introduces the opportunity cost of factor inputs to the measurement of productive efficiency. Returning to the model depicted in Figure 1 and assuming competitive markets for the purchase of factor inputs, we s

20、ee that the relative</p><p>　　Farrell combined physical () and economic () efficiency into a single index termed overall productive efficiency (). Overall productive efficiency is measured by evaluating the

21、ratio , which is the product of the and 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 the inefficient fa

22、ctor proportions. Under the assumption of continuity and strict monotonicity, measurement along the ra</p><p>　　A unit isoquant specifying the locus of minimum unit-output-input requirements was chosen by F

23、arrell as his efficiency standard. There are three features of this standard that deserve discussion. First, the isoquant is derived from the primal production function relating physical units of input to physical output

24、. The choice of the primal function rather than its dual, the cost function, is necessary if the distinction between technical and allocative efficiency is to be maintained. A cost funct</p><p>　　Although th

25、ere are many possibilities, two at once suggest themselves-a theoretical function specified by engineers and an empirical function based on the best results observed in practice. The former would be a very natural concep

26、t to choose-after all, should not a postulated standard of perfect efficiency represent the best that is theoretically obtainable? Certainly it is a concept used by engineers themselves when they discuss the efficiency o

27、f a machine or process. However, although it is a</p><p>　　Thus, although the theoretical standard is perfectly valid and has its own uses, this paper will be concerned with the observed standard [1957, p. 2

28、55].</p><p>　　The observed standard is determined by those production organizations sharing a common technology that produce the greatest output from a given input set. Efficiency measures based on the obser

29、ved 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,

30、the adoption of a unit isoquant necessarily implies that the technology employed by the</p><p>　　II. FRONTIER FUNCTIONS AS EFFICIENCY STANDARDS</p><p>　　Farrell's efficient unit isoquant was

31、 the precursor of the frontier production functions of today. While Farrell's sole intent was to evaluate the performance of production organizations, frontier production and cost functions can serve as efficiency st

32、andards and provide information on the features of the best practice technology as well. Motivated by the theoretical definitions of production and cost functions, empirical frontier functions specify maximal output from

33、 given inputs or minimum co</p><p>　　Consider the primal production relation given in equation (1):</p><p><b>　　(1)</b></p><p>　　where is a vector of observations on ou

34、tput, is a matrix of observations on productive factors, is a vector of unknown production parameters, and is a vector of random disturbances. Traditional average production function estimation would specify to be d

35、istributed independently and identically and would apply OLS to estimate the parameter vector . The frontier estimators, on the other hand, generally specify to have a nonzero expectation reflecting the presence of te

36、chnical inefficiency</p><p>　　Table 1 summarizes eight of the most recent frontier function estimators by detailing the type of function estimated, the assumptions made concerning the stochastic disturbance,

37、 the constraints on the error, the estimation method employed, and the corresponding measures of productive efficiency. The specified disturbances fall into one of three general categories: (1) an unspecified random shoc

38、k constrained to be everywhere less than or equal to zero, (2) a random disturbance specified to follow</p><p>　　Measures of productive efficiency derived from frontier production functions are directly rela

39、ted to the assumed causes of output variation. The approach of Aigner and Chu [1968] and Timmer [1971] assumes all variation to be the result of technical inefficiency and thereby constrains the residuals to be of one si

40、gn. Their measures of technical efficiency can be specified as output actually produced divided by maximum output technically feasible. Afriat [1972] and Richmond [1974], on the other ha</p><p>　　An extensio

41、n to the Aigner, Lovell, and Schmidt [1977] frontier has been recently proposed by Schmidt and Lovell [1979]. Recognizing that departures from minimum cost are the result of both technical and allocative inefficiency and

42、 further, that a frontier cost function standard alone cannot define the two components, Schmidt and Lovell employ a stochastic frontier production function and the necessary conditions for a cost minimum to identify b

43、oth technical and allocative inefficiency. Variat</p><p>　　Several features distinguish the frontier functions from the Farrell efficient isoquant. The most notable difference is the assumption of a specifi

44、c functional form. Whereas the Farrell isoquant is merely a series of connected hyperplanes convex to the origin in input space, frontier functions are parametric production or cost surfaces in input-output or price-outp

45、ut-cost space. The adoption of a specific functional form by Aigner and Chu eliminated the need for the linear homogeneity assumptio</p><p>　　The most recent frontier function models differ from both the Aig

46、ner and Chu approach and that of Farrell by adopting a full stochastic representation of production. These models assume specific structures for the disturbance mechanisms affecting variation in output or cost, estimate

47、 production and efficiency parameters jointly, and provide an ability to test statistical hypotheses concerning those parameters. The most recent work of Schmidt and Lovell [1979] has further extended the usefulness</

48、p><p>　　Stochastic frontier functions are clearly superior to the Farrell isoquant in several respects, most notably their statistical properties. However, by the very fact that efficiency measures are estimate

49、d parameters, measures of productive efficiency at the production unit level are generally impossible. For some forms of analysis, a sample-based efficiency measure is sufficient, but in the majority of analyses where pr

50、oductive efficiency is an issue, efficiency comparisons between productive org</p><p><b>　　再議生產(chǎn)效率的測度</b></p><p><b>　　作者：雷蒙德·庫珀</b></p><p><b>　　國籍：

51、美國</b></p><p>　　出處：經(jīng)濟(jì)學(xué)季刊，96卷，第3期(8月8日，1981)，477-503頁</p><p><b>　　摘要</b></p><p>　　本文的目的是概括非同位相似生產(chǎn)技術(shù)的法瑞爾生產(chǎn)效率指數(shù)，同時(shí)保持法瑞爾測度成本的解釋。由于一般的指標(biāo)在近期的發(fā)展中很大程度上依賴于在前沿面成本和生產(chǎn)函數(shù)的估計(jì)，因此

52、我們綜述了幾種前沿面模型。除了技術(shù)效率，配置效率和整體生產(chǎn)效率的一般指標(biāo)，我們還討論了測度效率的各種單因子指標(biāo)。所提出的效率測度的適用性我們用一個(gè)數(shù)值模擬發(fā)電的例子來檢驗(yàn)。</p><p><b>　　簡介</b></p><p>　　本文主體分為四部分。第一部分回顧了法瑞爾獨(dú)創(chuàng)性的貢獻(xiàn)，側(cè)重于效率標(biāo)準(zhǔn)的選擇。來自前沿面函數(shù)當(dāng)代的效率標(biāo)準(zhǔn)在第二部分討論。第三部分提出了

53、一系列利用前沿面函數(shù)的法瑞爾式效率的測度，第四部分闡述了一個(gè)數(shù)值模擬發(fā)電例子的實(shí)證研究。</p><p>　　首先要明確，生產(chǎn)效率的定義是生產(chǎn)單位以最低的成本生產(chǎn)一個(gè)指定產(chǎn)量的能力。更精確的說。必須明確規(guī)定輸出和輸入因素通過可測量向量明確界定的特征。進(jìn)一步，由于論述的原因，它假定生產(chǎn)單位使用了特定的技術(shù)；比如，事前已經(jīng)做出的生產(chǎn)決定和我們所觀察到的事后的操作技術(shù)。</p><p>　　邁克

54、爾法瑞爾(1957)開創(chuàng)性的研究主要關(guān)注的是生產(chǎn)效率的概念和對生產(chǎn)過程建模識(shí)別的結(jié)果。本文綜述了原來的法瑞爾測量效率方法的元素和當(dāng)代利用前沿面函數(shù)的研究。這為綜合法瑞爾效率的測度和前沿面效率的準(zhǔn)則提供了基礎(chǔ)。綜合后的效率測度的方法改善了與法瑞爾和前沿面兩種方法有關(guān)的許多缺點(diǎn)，同時(shí)又充分利用了他們的優(yōu)勢。</p><p><b>　　I. 法瑞爾的方法</b></p><p

55、>　　在閱讀一篇英國皇家統(tǒng)計(jì)學(xué)會(huì)的文章之前，法瑞爾提出了一個(gè)巧妙的方法衡量生產(chǎn)效率的兩種形式。他推測，效率可以分為兩個(gè)子反映，一是投入產(chǎn)出生產(chǎn)變換的物質(zhì)效率(技術(shù)部分)和優(yōu)化要素配置的經(jīng)濟(jì)效率(價(jià)格效率)?？梢哉f，經(jīng)濟(jì)主體參與生產(chǎn)的決策是相連的；那就是，決策影響資源配置(技術(shù))效率，可能也對技術(shù)(配置)有影響。這顯然是一個(gè)法瑞爾沒有拒絕的可能性。他所做的假設(shè)是把這些聯(lián)合決策的影響分為兩個(gè)子部分的能力，并測量它們各自影響的實(shí)證研究。

56、</p><p>　　按照法瑞爾的論述，考慮一個(gè)齊次線性生產(chǎn)過程采用的兩個(gè)因素，資本()和材料()去產(chǎn)生一個(gè)輸出：電()?？偨Y(jié)技術(shù)通過單位等產(chǎn)量曲線允許一個(gè)相對于標(biāo)準(zhǔn)等產(chǎn)量曲線的生產(chǎn)效率的測量。圖1描述了單位等產(chǎn)量曲線，記作。西南方向的點(diǎn)是不可行的，同時(shí)其東北方向的點(diǎn)是無效的。給定一個(gè)輸入組合，如R，法瑞爾定義比率為R的技術(shù)能力()的程度。技術(shù)效率指數(shù)(0和1之間有界實(shí)數(shù))是一個(gè)基于輸入的，在實(shí)際使用中的最佳實(shí)踐

57、的比率，且輸出保持不變的測度。</p><p><b>　　圖1</b></p><p>　　法瑞爾定義并提供了一種一個(gè)生產(chǎn)單位的配置效率()測量方法，它與技術(shù)效率相獨(dú)立。配置效率涉及到輸入組合的選擇，即，他們最高價(jià)值用途的分配因素，從而引入了要素投入機(jī)會(huì)成本的生產(chǎn)效率的測量?；氐綀D1所描述的模型，假定投入要素的購買是在完全競爭市場中，我們可以看到要素相對價(jià)格能體現(xiàn)在

58、等成本線上。輸入集對應(yīng)的點(diǎn)是生產(chǎn)單位產(chǎn)量的最小成本。測度R的配置無效程度與其技術(shù)無效相獨(dú)立，我們利用R的技術(shù)有效投影點(diǎn)和比率評(píng)估。</p><p>　　法瑞爾把物質(zhì)效率()和經(jīng)濟(jì)效率()結(jié)合成一個(gè)單一的指數(shù)稱為整體生產(chǎn)效率()。整體生產(chǎn)效率的測度通過比率來評(píng)估，它是和兩個(gè)指標(biāo)的復(fù)合產(chǎn)物。所有的法瑞爾測度都是沿著從原點(diǎn)發(fā)出的射線，通過無效的輸入集，從而保持低效率的要素比例。在連續(xù)性及嚴(yán)格單調(diào)性的假設(shè)下，沿射線測量保

59、證了技術(shù)效率與資源配置效率之間的區(qū)別，使指標(biāo)可由全要素成本來解釋。</p><p>　　單位等產(chǎn)量曲線指定了單位輸出輸入要求最小的軌跡，選擇法瑞爾作為他的效率標(biāo)準(zhǔn)。此標(biāo)準(zhǔn)有三大特點(diǎn)值得討論。第一，等產(chǎn)量線是從原始的與生產(chǎn)函數(shù)有關(guān)的物質(zhì)單位輸入派生出來的物質(zhì)輸出。初始函數(shù)的選擇而不是它的對偶，成本函數(shù)，是必要的如果技術(shù)效率和資源配置效率之間的區(qū)別能保持的話。成本函數(shù)將會(huì)對提供信息，但不會(huì)影響其構(gòu)成的要素。第二個(gè)特點(diǎn)

60、是標(biāo)準(zhǔn)的相對性。討論他的選擇，法瑞爾說道：</p><p>　　雖然有很多的可能性，但一再建議自己的理論函數(shù)要通過工程師和實(shí)踐中觀察到最好的結(jié)果實(shí)證功能的基礎(chǔ)上確定。前者將是選擇一個(gè)很自然的概念，應(yīng)不應(yīng)該假定理論上可獲得的，帶來最后表現(xiàn)的完美效率的標(biāo)準(zhǔn)？當(dāng)然這是工程師自己在討論機(jī)器或過程的效率時(shí)用的概念。然而，盡管對于一個(gè)單一生產(chǎn)過程的效率來說是合理的，或是最好的概念，但是它在應(yīng)用于一個(gè)復(fù)雜的典型制造企業(yè)時(shí)不成立

61、，更不用說一個(gè)行業(yè)了。</p><p>　　因此，雖然理論的標(biāo)準(zhǔn)是完全有效的，有它自己的使用范圍，但本文將關(guān)注觀察到的標(biāo)準(zhǔn)(1957年，255頁)。</p><p>　　觀察到的標(biāo)準(zhǔn)是由共同使用一項(xiàng)能從給定輸入集中得到最大輸出的技術(shù)確定的。效率測度基于觀察的標(biāo)準(zhǔn)，即個(gè)人生產(chǎn)單位與他們的同儕團(tuán)體的表現(xiàn)相比，在這種意義上是相對的。作為同儕團(tuán)體的表現(xiàn)發(fā)生了變化，那么將影響效率的測量。最后，使用單

62、位產(chǎn)量曲線必然意味著技術(shù)的應(yīng)用通過齊次線性的生產(chǎn)單位。正是規(guī)模報(bào)酬不變這個(gè)假設(shè)使在第三部分中沒有了限制。</p><p>　　II. 前沿面函數(shù)的效率準(zhǔn)則</p><p>　　法瑞爾的有效單元等產(chǎn)量曲線是今天的前沿面生產(chǎn)函數(shù)的前身。而法瑞爾的唯一目的是評(píng)估生產(chǎn)單位的表現(xiàn)，前沿面生產(chǎn)函數(shù)和成本函數(shù)可以作為效率標(biāo)準(zhǔn)并提供的最佳技術(shù)實(shí)踐的特點(diǎn)的信息。利用生產(chǎn)函數(shù)和成本函數(shù)的理論定義，前沿面函數(shù)的

63、實(shí)證研究指定了在給定輸入時(shí)的最大輸出或在給定輸出和要素價(jià)格時(shí)的最小費(fèi)用。這些前沿面的產(chǎn)出或成本偏差可以作為生產(chǎn)效率的測度。然而，這些測度與法瑞爾的有所不同，因?yàn)樗闹笜?biāo)要保持輸出恒定不變并將注意力放在不同的輸入水平上。最近幾年的前沿面估計(jì)(源自于阿弗里亞(1972))顯示了參數(shù)化的生產(chǎn)效率估計(jì)量的測度。這些前沿面模型同時(shí)處理該生產(chǎn)函數(shù)的技術(shù)參數(shù)和效率參數(shù)。一般來說，這些效率參數(shù)被認(rèn)為與造成效率低下的原因有關(guān)，是由各種隨機(jī)干擾因素構(gòu)建的模

64、型。</p><p>　　考慮方程(1)中初始的生產(chǎn)關(guān)系：</p><p><b>　　(1)</b></p><p>　　其中，是輸出的一個(gè)觀測向量，是生產(chǎn)要素的一個(gè)觀測矩陣，是未知生產(chǎn)參數(shù)的一個(gè)向量，是一個(gè)隨機(jī)擾動(dòng)的向量。傳統(tǒng)平均生產(chǎn)函數(shù)的估計(jì)會(huì)指定是獨(dú)立分布的且都服從于，利用最小二乘法對參數(shù)向量進(jìn)行估計(jì)。另一方面，前沿面的估計(jì)量通常指定有

65、一個(gè)非零的期望值來反映在生產(chǎn)中技術(shù)無效的存在。</p><p>　　表1總結(jié)了最新的八種前沿面函數(shù)的估計(jì)量，通過利用不同類型的細(xì)化函數(shù)進(jìn)行估計(jì)，作出與隨機(jī)干擾有關(guān)的假設(shè)，對測量誤差的限制，使用的估計(jì)方法和對應(yīng)的生產(chǎn)效率的測度。其中所指定的干擾可以分為三大類：(1)一個(gè)未指定的隨機(jī)震蕩的約束條件是各處都小于或等于零，(2)隨機(jī)擾動(dòng)指定遵循單一分布(例如，截尾正態(tài)分布，指數(shù)分布，伽馬分布等)，和(3)復(fù)合誤差的合并，

66、兩者均為對稱或單一分布。前兩種類別是“充分”的前沿面和其輸出的變化與存在技術(shù)效率低下有關(guān)，而第三種類別承認(rèn)除了技術(shù)無效以外的對稱誤差的存在。</p><p>　　利用前沿面生產(chǎn)函數(shù)的生產(chǎn)效率的測度是與假設(shè)引起的輸出變化直接相關(guān)的。愛格納和朱(1968)的方法與蒂默(1971)的方法假設(shè)所有的變化都技術(shù)效率低下的結(jié)果，因此要把殘差約束到一個(gè)值。他們技術(shù)效率的測度可以被指定為實(shí)際輸出產(chǎn)量除以可行的最大技術(shù)輸出。另一方

67、面，阿弗里亞(1972)和里奇滿(1974)選擇指定一個(gè)特定的無約束條件的殘差的單一的概率分布。因?yàn)樗麄冇昧藛我环植紒頊y度其技術(shù)效率的期望值，所以每次觀察得到的觀測值都不是獨(dú)立的，但是只能被定義在整個(gè)樣本空間。同樣地，愛格納，雨宮和波里爾(1976)效率的測度；梅夫森和范登伯洛克(1977)效率的測度；和愛格納，洛弗爾和施密特(1977)效率的測度的本質(zhì)都是平均，并不能應(yīng)用到各個(gè)生產(chǎn)單元。格林(1980)提出的前沿面利用有約束條件的伽馬

68、分布把伽馬分布的參數(shù)放在一個(gè)“充分”的隨機(jī)前沿面上，通過極大似然的方法估計(jì)得到。的期望值和偏度系數(shù)都能在測度生產(chǎn)效率時(shí)使用。再次，這些效率的測度是參數(shù)估計(jì)的轉(zhuǎn)換，因此不能從每個(gè)觀測值中獲得。</p><p>　　最近由施密特和洛弗爾(1979)提出的前沿面對愛格納，洛弗爾和施密特(1977)的進(jìn)行了延伸。認(rèn)識(shí)到最小成本的偏差是技術(shù)效率和資源配置效率低下共同作用的結(jié)果，進(jìn)一步的，這一前沿面成本函數(shù)的標(biāo)準(zhǔn)不能單獨(dú)定義

69、的這兩個(gè)組成部分，施密特和洛弗爾采用隨機(jī)前沿面生產(chǎn)函數(shù)和成本最低的必要條件去確定技術(shù)無效和資源配置無效。愛格納，洛弗爾，和施密特(1977)指出，輸出的變化歸因于技術(shù)效率低下和遵循復(fù)合隨機(jī)擾動(dòng)結(jié)構(gòu)。違反必要條件通過一個(gè)對稱的干擾而建立的模型導(dǎo)致了資源配置效率低下。從本質(zhì)上講，生產(chǎn)函數(shù)和技術(shù)效率的參數(shù)是用極大似然法估計(jì)得到的。生產(chǎn)參數(shù)估計(jì)后代入必要的條件方程，并利用這些方程的殘差估計(jì)配置效率。這種方法的獨(dú)特之處是有能力估計(jì)技術(shù)效率與資源配

70、置效率并且估計(jì)每個(gè)數(shù)據(jù)點(diǎn)的配置效率。只可惜技術(shù)效率的估計(jì)只能對一個(gè)有限樣本進(jìn)行測度。</p><p>　　從法瑞爾效率的等產(chǎn)量曲線中區(qū)分前沿面函數(shù)的幾個(gè)特征。最明顯的差異是具體函數(shù)形式的假設(shè)。而法瑞爾等產(chǎn)量曲線僅僅是與輸入空間原點(diǎn)連接的一系列凸平面，前沿面函數(shù)輸出或輸出成本價(jià)格空間參數(shù)生產(chǎn)或成本面。前沿面函數(shù)是投入產(chǎn)出或輸出成本價(jià)格空間的參數(shù)化生產(chǎn)或成本曲面。通過采用愛格納和朱的特定函數(shù)形式消除了線性同質(zhì)性假設(shè)的

71、需要，并且提供了最佳實(shí)踐技術(shù)的估計(jì)。</p><p>　　最新的前沿面函數(shù)模型不同于愛格納和朱兩個(gè)人的方法，而是法瑞爾采用一個(gè)充分的隨機(jī)過程表示生產(chǎn)。這些模型假定特定結(jié)構(gòu)影響產(chǎn)出或成本變化的干擾機(jī)制，生產(chǎn)效率參數(shù)的聯(lián)合估計(jì)，并提供測試有關(guān)參數(shù)的統(tǒng)計(jì)假設(shè)的能力。施密特和洛弗爾(1979)最近的研究通過提供技術(shù)效率和資源配置效率的估計(jì)，進(jìn)一步擴(kuò)展前沿面函數(shù)實(shí)用性。</p><p>　　隨機(jī)前沿

72、面函數(shù)在某幾個(gè)方面明顯優(yōu)于法瑞爾等產(chǎn)量曲線，尤其是它們的統(tǒng)計(jì)特性。然而，事實(shí)上通過效率測度來估計(jì)參數(shù)，對生產(chǎn)單位進(jìn)行生產(chǎn)效率的測度一般是不可行的。對于一些分析形式來說，基于樣本的效率測度便足夠了，但是在生產(chǎn)效率這個(gè)問題的大多數(shù)分析中，生產(chǎn)單位之間效率的比較是必要的。在下一部分中，法瑞爾型的效率測度將與前沿面生產(chǎn)函數(shù)相結(jié)合對生產(chǎn)單位水平的技術(shù)效率，配置效率和整體生產(chǎn)效率進(jìn)行估計(jì)。還提供了個(gè)人因素的效率等幾個(gè)輔助測度。</p>