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新英格兰大学效率与生产力分析中心(CEPA)工作报告DEAP 2.1版本指南:数据包络分析（计算）程序Coelli T.JNo.8/96澳大利亚，NSW2351，阿米代尔新英格兰大学，计量经济学系CEPA工作报告.au/econometrics/cepawp.htmISSN1327-435XISBN 1 86389 4969目 录摘 要31.INTRODUCTION说明42.EFFICIENCY MEASUREMENT CONCEPTS效率测度的概念。52.1 Input-Orientated Measures投入主导型的测度62.2 Output-Orientated Measures 产出主导型测量方法93.Data Envelopment Analysis(DEA)数据包络分析123.1 The Constant Returns to Scale Model(CRS) 规模报酬不变模型13Slacks 松弛变量15Example 1 例子1193.2 The Variable Returns to Scale Model (VRS)and Scale Efficiencies 规模收益变化模型（VRS）和规模效率22Calculation of Scale Efficiencies 规模效率的计算23Example 2例子2253.3 Input and Output Orientations 投入和产出主导型263.4 Price Information and Allocative Efficiency 价格信息和配置效率29Example 3 例子3303.5 Panel Data,DEA and the Malmquist Index 面板数据，DEA和Malmquist指数31Scale Efficiency 规模效率34Example 4 例子4344.The DEAP Computer Program DEAP计算机程序35Data file 数据文件36Instruction file 向导文件37Output file 输出文件385.Examples 例子385.1 Example 1:An Input-orientated CRS DEA Example 例子1：一个CRS投入主导型DEA例子395.2 Example 2:An Input-orientated VRS DEA Example 例子2：一个VRS投入主导型的DEA模型例子435.3 Example 3:A Cost Efficiency DEA Example 例子3：成本效率DEA例子475.4 Example 4:A Malmquist DEA Example 例子4：Malmquist DEA例子496.Concluding Comments 结束语53REFERENCES 参考文献：53APPENDIX 附录55Tips on using DEAP in File Manager in Windows 3.1: 在Windows 3.1的File Manager使用DEAP的小贴士：56DEAP 2.1版本指南:数据包络分析(计算)程序澳大利亚， 威尔士，2351，阿米代尔新英格兰大学，计量经济学系效率和生产力分析中心Tim CoelliEmail:.auWeb:.au/econometrics/cepa.htmCEPA 工作报告 96/08摘 要This paper describes a computer program which has been written to conduct data envelopment analyses(DEA)for the purpose of calculating efficiencies in production. The methods implemented in the program are based upon the work of Rolf Fare, Shawna Grosskopf and their associates. Three principal options are available in the computer program. The first involves the standard CRS and VRS DEA models(that involve the calculation of technical and scale efficiencies)which are outlined in Fare, Grosskopf and Lovell(1994). The second option considers the extension of these models to account for cost and allocative efficiencies.These methods are also outlined in Fare et al(1994). The third option considers the application of Malmquist DEA methods to panel data to calculate indices of total factor productivity (TFP) change; technological change;technical efficiency change and scale efficiency change. These latter methods are discussed in Fare,Grosskopf,Norris and Zhang(1994). All methods are available in either an input or an output orientation(with the exception of the cost efficiencies option).这篇论文描述了一个程序，这个程序是用来实施数据包络分析（DEA），以此来计算生产中的效率。程序中实施的方法是基于Rolf Fare，Shawna Grosskopf和他的同事的工作。计算程序中有三个主要的选择。第一个包括标准的CRS和VRS两个DEA模型（这包括了技术效率和规模效率的计算），这两个模型是Fare, Grosskopf and Lovell(1994)设计的。第二个选择考虑了这些模型的延伸，即说明成本和配置效率。这些模型也是Fare et al(1994)设计的。第三个选择考虑到了Malmquist DEA模型的使用，这个模型是用面板数据来计算全要素生产率变化（TFP）、技术进步、技术效率变化和规模效率变化的指数。后面所说的模型Fare,Grosskopf,Norris and Zhang(1994)曾经讨论过。所有的模型无论在投入主导型还是产出主导型（除了成本效率）都能够获得。1.INTRODUCTION说明This guide describes a computer program which has been written to conduct data envelopment analyses(DEA). DEA involves the use of linear programming methods to construct a non-parametric piecewise surface(or frontier)over the data,so as to be able to calculate efficiencies relative to this surface. The computer program can consider a variety of models.The three principal options are:这个指南描述了一个实施数据包络技术的计算机程序。DEA模型是运用线性规划的方法通过建造一个非参数分段的面（前沿），然后相对这个面计算效率。计算机程序能够考虑模型的多样性。三个主要的选择是：1.Standard CRS and VRS DEA models that involve the calculation of technical and scale efficiencies(where applicable).These methods are outlined in Fare, Grosskopf and Lovell(1994).2.The extension of the above models to account for cost and allocative efficiencies. These methods are also outlined in Fare et al(1994).3.The application of Malmquist DEA methods to panel data to calculate indices of total factor productivity(TFP)change;technological change;technical efficiency change and scale efficiency change.These methods are discussed in Fare, Grosskopf,Norris and Zhang(1994). 1.标准CRS 和VRS的数据包络分析模型，它们包括技术效率和规模效率的计算（当规模效率适合）。这些模型是Fare,Grosskopf and Lovell(1994)构造的。2.上述模型的延伸，考虑了成本和配置效率。这些模型也是Fare et al(1994)构造的。3. 第三个选择考虑到了Malmquist DEA模型的使用，这个模型是用面板数据来计算全要素生产率变化（TFP）、技术进步、技术效率变化和规模效率变化的指数。这些方法Fare,Grosskopf,Norris and Zhang(1994)曾经讨论过。All methods are available in either an input or an output orientation(with the exception of the cost efficiencies option). The output from the program includes,where applicable,technical,scale,allocative and cost efficiency estimates;residual slacks;peers;TFP and technological change indices.这些方法无论是在投入主导型还是在产出主导型（除了成本效率）都是能够获得的。当合适的时候，程序的结果可以包括技术、规模、配置、成本效率的估计值；还有松弛变量的残值；对应点；全要素生产率和技术进步变化指数。 The paper is divided into sections.Section 2 provides a brief introduction to efficiency measurement concepts developed by Farrell(1957);Fare,Grosskopf and Lovell(1985, 1994)and others. Section 3 outlines how these ideas may be empirically implemented using linear programming methods(DEA). Section 4 describes the computer program,DEAP,and section 5 provides some illustrations of how to use the program.Final concluding points are made in Section 6. An appendix is added which summarises important technical aspects of program use 文章可以分为以下几章。第二章给出了Farrell(1957);Fare,Grosskopf and Lovell(1985,1994)等关于效率测度概念的简短的介绍。第三章概述了这些思想是怎样通过DEA方法实现实证研究的。第四部分描述了计算程序，DEAP。第五章给了一些运用程序的例子。最后，在第六章，总结了要点。附录里面包含了程序所用的重要技术方面的概述。2.EFFICIENCY MEASUREMENT CONCEPTS效率测度的概念。The primary purpose of this section is to outline a number of commonly used efficiency measures and to discuss how they may be calculated relative to an efficient technology, which is generally represented by some form of frontier function. Frontiers have been estimated using many different methods over the past 40 years.The two principal methods are:这章的主要目的是概述一些常用的测度效率的方法，并且讨论了相对于技术有效（通常由某种形式的前沿机构所代表）怎样计算出他们。过去的40年里，我们运用了很多不同的方法估计前沿效率。两个有代表性的方法是：1.data envelopment analysis(DEA)and2.stochastic frontiers,1.数据包络分析2.随机前沿法which involve mathematical programming and econometric methods, respectively.This paper and the DEAP computer program are concerned with the use of DEA methods. The computer program FRONTIER can be used to estimate frontiers using stochastic frontier methods.For more information on FRONTIER see Coelli(1992, 1994).他们分别包含了数学规划和计量经济学的方法。这篇论文和DEAP计算机程序是关于DEA 方法的。计算机程序FRONTIER可以通过随即前沿法估计前沿效率，想得到更多关于FRONTIER请看Coelli(1992,1994)的研究。The discussion in this section provides a very brief introduction to modern efficiency measurement. A more detailed treatment is provided by Fare,Grosskopf and Lovell (1985,1994)and Lovell(1993). Modern efficiency measurement begins with Farrell (1957)who drew upon the work of Debreu(1951)and Koopmans(1951)to define a simple measure of firm efficiency which could account for multiple inputs. He proposed that the efficiency of a firm consists of two components:technical efficiency,which reflects the ability of a firm to obtain maximal output from a given set of inputs,and allocative efficiency,which reflects the ability of a firm to use the inputs in optimal proportions,given their respective prices. These two measures are then combined to provide a measure of total economic efficiency. Some of Farrells terminology differed from that which is used here. He used the term priceefficiency instead of allocative efficiency and the term overall efficiency instead of economicefficiency.The terminology used in the present document conforms with that which has been usedmost often in recent literature.一些Farrell的经济效率和这里使用是不同的。他使用价格效率代替这里的配置效率，使用总体效率代替这里的经济效率。这篇文献里面的术语同最近大部分文献的术语是一致的。这章对现代的效率测度给了一个简短的介绍。更详细的方法请参考Fare, Grosskopf and Lovell (1985,1994)and Lovell(1993)的研究。现代效率测量是与Farrell (1957)，他在Debreu(1951)and Koopmans(1951)的工作的基础上定一个一个简单的测度公司效率的方法，这个方法考虑了多投入。他认为公司的效率可以分为两个部分：技术效率，反映了公司在给定投入的情况下所能获得的最大的产出的能力。另一个是配置效率。它反映了给定各自投入价格的情况下使用最优比例的能力。两个测量结合起来给出了总经济效率的测度。The following discussion begins with Farrells original ideas which were illustrated in input/input space and hence had an input-reducing focus.These are usually termed input-orientated measures.接下来的讨论从Farrell最初的想法开始，这个想法产生于投入，然后关注于投入的减少。这通常被称为投入主导型。2.1 Input-Orientated Measures投入主导型的测度Farrell illustrated his ideas using a simple example involving firms which use two inputs (x1 and x2)to produce a single output(y),under the assumption of constant returns to scale. The constant returns to scale assumption allows one to represent the technology using a unitisoquant.Furthermore,Farrell also discussed the extension of his method so as to accommodate morethan two inputs,multiple outputs,and non-constant returns to scale.规模报酬不变的假设允许我们使用单位等产量曲线代表效率。进一步讲，Farrell也讨论了他方法的进一步延伸，以使他的方法适应比两个个多的投入和多产出以及规模报酬变化的情形。 Knowledge of the unit isoquant of the fully efficient firm The production function of the fully efficient firm is not known in practice,and thus must beestimated from observations on a sample of firms in the industry concerned.In this paper we useDEA to estimate this frontier.在现实中，全效率公司是不知道的，所以在工业中必须在相关的一些公司观测样本里面估计它。在这篇论文里，我们用DEA方法估计它。, represented by SSin Figure 1,permits the measurement of technical efficiency. If a given firm uses quantities of inputs,defined by the point P,to produce a unit of output,the technical inefficiency of that firm could be represented by the distance QP,which is the amount by which all inputs could be proportionally reduced without a reduction in output .This is usually expressed in percentage terms by the ratio QP/0P,which represents the percentage by which all inputs could be reduced. The technical efficiency(TE) of a firm is most commonly measured by the ratioTEI=0Q/0P, (1)which is equal to one minus QP/0P. It will take a value between zero and one,and hence provides an indicator of the degree of technical inefficiency of the firm. A value of one indicates the firm is fully technically efficient.For example,the point Q is technically efficient because it lies on the efficient isoquant.Farrell通过一个简单的例子阐述了他的观点。这个例子假设一个公司的规模报酬不变，使用了两个投入（x1和x2）生产单一的产出（y）已知全效率公司的单位等产量曲线，由数据1的SS代表，允许技术效率的度量。如果给定的公司用一定数量的投入，由P点所定义，去生产一单位的产出，公司的技术无效可以有QP的距离所表示，它就是在不减少产出的情况下，所有的投入按比例减少的数量。这通常由百分数QP/OP的比率表示，它代表了所有投入减少的百分比。公司的技术效率通常由TEI=OQ/OP （1）也就是1减去QP/OP The subscript“I”is used on the TE measure to show that it is an input-orientated measure.Output-orientated measures will be defined shortly.脚注“I”用于技术效率测量，表示是投入主导型方法。产出主导型定义的就比较简洁。它取值01，因此提供了公司技术无效的指标。1代表完全的技术有效，例如，Q点就是技术有效的，因为他在效率曲线上。数据 1技术和配置效率If the input price ratio,represented by the line AAin Figure 1,is also known,allocative efficiency may also be calculated.The allocative efficiency(AE)of the firmoperating at P is defined to be the ratioAEI=0R/0Q, (2) since the distance RQ represents the reduction in production costs that would occur if production were to occur at the allocatively(and technically)efficient point Q,instead of at the technically efficient,but allocatively inefficient,point Q. One could illustrate this by drawing two isocost lines through Q and Q.Irrespective of the slope ofthese two parallel lines(which is determined by the input price ratio)the ratio RQ/0Q would representthe percentage reduction in costs associated with movement from Q to Q.我们可以通过画一条通过点Q和点Q的等成本曲线来阐述这个问题。不考虑两条平行线（由投入的价格比率决定）的斜率，RQ/0Q的比率就代表了从Q点到Q点成本下降的百分比。如果投入的价格的比率由数据1的AA表示，那么配置效率也就算出来了。P点运作的公司的配置效率由下面的比率给出定义。AEI=OR/OQ （2）因为RQ的距离代表如果生产发生在配置有效的点Q,而不是技术有效但是配置无效的Q点，那么就可以降低生产成本。The total economic efficiency(EE)is defined to be the ratioEEI=0R/0P, (3)where the distance RP can also be interpreted in terms of a cost reduction.Note that the product of technical and allocative efficiency provides the overall economic efficiencyTEIAEI=(0Q/0P)(0R/0Q)=(0R/0P)=EEI. (4)Note that all three measures are bounded by zero and one.总经济效率（EE）可以由下面的比率EEI=OR/OP （3）RP的距离可以解释为成本降低。注意，技术和配置的效率给出了总的经济效率，TEI*AEI=（OQ/OP）*（OR/OQ）=（OR/OP）=EEI （4）数据 2分段线性等量曲线（Piecewise Linear Convex Isoquant）These efficiency measures assume the production function of the fully efficient firm is known.In practice this is not the case,and the efficient isoquant must be estimated from the sample data. Farrell suggested the use of either(a)a non-parametric piecewise-linear convex isoquant constructed such that no observed point should lie to the left or below it(refer to Figure 2),or(b)a parametric function,such as the Cobb- Douglas form,fitted to the data,again such that no observed point should lie to the left or below it.Farrell provided an illustration of his methods using agricultural data for the 48 continental states of the US.这些效率测量假设完全有效率的公司是已知的。在实践中，这并不是问题，效率等量曲线是从样本数据中估计出的。Farrell认为无论是使用非参数分段线性等量曲线（没有观测的点在它的左边或下边）（参考数据2），还是参数形式，比如柯布道格拉斯形式，相对应的数据也都没有在它左边或者下边的。Farrell用美国48个洲的农业数据给出了他的方法的一个例子。2.2 Output-Orientated Measures 产出主导型测量方法The above input-orientated technical efficiency measure addresses the question:“By how much can input quantities be proportionally reduced without changing the output quantities produced?”. One could alternatively ask the question“:“By how much can output quantities be proportionally expanded without altering the input quantities used?”. This is an output-orientated measure as opposed to the input-oriented measure discussed above. The difference between the output-and input-orientated measures can be illustrated using a simple example involving one input and one output. This is depicted in Figure 3(a)where we have a decreasing returns to scale technology represented by f(x),and an inefficient firm operating at the point P. The Farrell input-orientated measure of TE would be equal to the ratio AB/AP,while the output-orientated measure of TE would be CP/CD. The output-and input-orientated measures will only provide equivalent measures of technical efficiency when constant returns to scale exist,but will be unequal when increasing or decreasing returns to scale are present(Fare and Lovell 1978). The constant returns to scale case is depicted in Figure 3(b)where we observe that AB/AP=CP/CD,for any inefficient point P we care to choose.上述投入主导型技术效率测量方法提出了一个问题：在不减少产出数量的同时，能按比例减少多少的投入？人们也可以问这样的问题：不改变投入数量的同时，产出数量可以按比例增加多少呢？这是一个与上面阐述的投入主导型测量方法相反的产出主导型测量方法。投入主导型测度方法和产出主导型测度方法可以用仅包含一个投入还让一个产出的简单例子进行阐述。数据3（a）描述了这一问题。我们有一个规模收益递减的函数f（x），和一个在P点运行的无效率的公司。Farrell的投入主导型测量方法中的TE与图中的AB/AP是相同的，然而产出主导型测度方法的TE是CP/CD。仅当规模收益不变的时候，产出主导型和投入主导型测度方法的技术效率是相等的。但是存在规模报酬递增还是递减的时候就不相等。数据3（b）描述了规模报酬不变。我们可以看到AB/AP=CP/CD，对于任意无效率的P,我们都可以选择。One can consider output-orientated measures further by considering the case where production involves two outputs(y1 and y2)and a single input(x1). Again , if we assume constant returns to scale,we can represent the technology by a unit production possibility curve in two dimensions. This example is depicted in Figure 4 where the line ZZis the unit production possibility curve and the point A corresponds to an inefficient firm. Note that the inefficient point,A,lies below the curve in this case because ZZrepresents the upper bound of production possibilities.我们可已通过考虑包括两产出（y1和y2）和一投入（x1）来进一步考虑产出主导型测度方法。再一次，我们假设规模报酬不变，我们可以用一单位产品可能曲线（产品等量曲线）的两个方面来表示技术。数据4描述了这个例子，ZZ就是单位产品可能曲线，点A是无效率的公司。注意，无效率的点A，在曲线下方，因为ZZ代表最高的生产可能线。数据3投入和产出主导型技术效率测度方法和规模收益Input-and Output-Orientated Technical Efficiency Measuresand Returns to Scale数据 4产出主导型的技术和配置效率The Farrell output-orientated efficiency measures would be defined as follows.In Figure 4 the distance AB represents technical inefficiency. That is,the amount by which outputs could be increased without requiring extra inputs.Hence a measure of output-orientated technical efficiency is the ratioTEO=0A/0B. (7)Farrell的产出主导型测度模型可以如下定义。在数据4中，AB的距离代表技术无效。这就是，在不增加额外的投入的基础上，可以增加多少产出。因此，产出主导型的技术效率就是这个比率。TE0=OA/OB （7）If we have price information then we can draw the isorevenue line DD,and define the allocative efficiency to be AEO=0B/0C (8)如果我们有价格的信息，我们就可以画等产量曲线DD，并定义配置效率为AE0=OB/OC （8）which has a revenue increasing interpretation(similar to the cost reducing interpretation of allocative inefficiency in the input-orientated case). Furthermore,one can define overall economic efficiency as the product of these two measuresEEO=(0A/0C)=(0A/0B)(0B/0C)=TEOAEO. (9)他有一个使收益增加的定义（类似于投入主导型的减少成本的配置无效的定义）。进一步，我们可以定义总体经济效率为两个测度的综合：EE0=（OA/OC）=（OA/OB）*（OB/OC）=TE0*AE0 （9）Again,all of these three measures are bounded by zero and one.这三个测量也都在01之间。Before we conclude this section,two quick points should be made regarding the six efficiency measures that we have defined:在总结这章之前，关于我们定义的六个效率测度的两点我们需要说明。1)All of them are measured along a ray from the origin to the observed production point.Hence they hold the relative proportions of inputs(or outputs)constant. One advantage of these radial efficiency measures is that they are units invariant.That is,changing the units of measurement (e.g. measuring quantity of labour in person hours instead of person years)will not change the value of the efficiency measure. A non-radial measure,such as the shortest distance from the production point to the production surface,may be argued for,but this measure will not be invariant to the units of measure