A structure for classifying and characterizing efficiency and inefficiency in Data Envelopment Analysis

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is obtained for each DMU from the observed magnitudes of its multiple inputs and outputs without requiring use of a priori weights or relative value assumptions and, in addition, sources and amounts of inefficiency are estimated for each input and each output for every DMU. Earlier theory is extended so that DEA can deal with zero inputs and outputs and zero virtual multipliers (shadow prices). This is accomplished by partitioning DMUs into six classes via primal and dual representation theorems by means of which restrictions to positive observed values for all inputs and outputs are eliminated along with positivity conditions imposed on the variables which are usually accomplished by recourse to nonarchimedian concepts. Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (zero waste) efficient.The refereeing process of this paper was handled through R. Banker. This paper was prepared as part of the research supported by National Science Foundation grant SES-8722504 and by the IC² Institute of The University of Texas and was initially submitted in May 1985.     

Using data envelopment analysis to evaluate efficiency in the economic performance of Chinese cities

This paper studies the use of DEA (data envelopment analysis) as a tool for possible use in evaluating and planning the economic performance of China's cities (28 in all) which play a critical role in the government's program of economic development. DEA promises advantages which include the absence of any need for the assignment of weights on an a priori basis (to reflect the supposed relative importance of various outputs or inputs) when evaluating technical efficiency. It is also unnecessary to explicitly specify underlying functions that are intended to prescribe the analytical form of the relations between inputs and outputs. Finally, as is illustrated in the paper, DEA can be used to identify sources, and estimate amounts of inefficiencies in each city's performance as well as to identify returns-to-scale possibilities in ways that seem well-suited to the mixture of centralized and decentralized planning and performance that China is currently trying to use.     

Inefficiency Spillovers in Five OECD Countries: An Interindustry Analysis

Empirical studies have widely demonstrated that real-world activities are rarely on their production frontier. Hence, an obvious concern arises towards the detection of inefficiencies affecting sectoral performances. The current literature and practice have widely explored the sources of inefficiency internal to decision-making units. This paper argues that a major role is played by external effects due to inefficiency spillovers propagating through interindustry transactions. In order to take this mechanism into account, the paper suggests assessing sectoral performances by a system approach that makes use of shadow prices of intermediate inputs. Our approach is able to disentangle sectoral inefficiencies into internal sectoral inefficiencies and inefficiencies imported from other sectors. The latter component is due to inefficiency spillovers that appear to be empirically relevant in all sectors of five OECD countries.     

Adjusting for cultural differences,a new DEA model applied to a merged bank

The usefulness and application of Data Envelopment Analysis (DEA) efficiency measurements is usually limited by the requirement of consistent operating circumstances. However, in many real world situations this is not the case, so to overcome this problem, this paper reports on a new strategy by inventing a Culturally Adjusted DEA model to benchmark business units that operate under different cultural (business) environments. This is especially useful when these environmental factors are partial causes of inefficiency and can not be simply incorporated into a DEA model as inputs or outputs. A simulation analysis is conducted to examine the effectiveness of the CA-DEA model for controlling these environmental effects. This model is applied to a real life efficiency study of two major financial firms in Canada in 2000, when the two entities started to consolidate and merge their branch networks. Two cultural indices are identified to represent a firm’s unique operating environment, one to capture the nature of a firm’s corporate strategies (Corporate Index), and the other to estimate the effectiveness of a firm’s operational systems (Service Index). The results show that a firm’s corporate culture has a significant influence on its branches’ efficiency and this, we found, is often neglected in such studies. This paper also makes a contribution to the bank merger literature by providing an internal view of the potential benefits that may result from sharing cultural advantages while identifying the true managerial inefficiencies.     

Two-Stage DEA: An Application to Major League Baseball

We show how to use DEA to model DMUs that produce in two stages, with output from the first stage becoming input to the second stage. Our model allows for any orientation or scale assumption. We apply the model to Major League Baseball, demonstrating its advantages over a standard DEA model. Our model detects inefficiencies that standard DEA models miss, and it can allow for resource consumption that the standard DEA model counts towards inefficiency. Additionally, our model distinguishes inefficiency in the first stage from that in the second stage, allowing managers to target inefficient stages of the production process.     

Using DEA to improve the management of congestion in Chinese industries (1981–1997)

Congestion is said to be present when increases in inputs result in output reductions. An “iron rice bowl” policy instituted in China shortly after the revolution led by Mao Tze Tung resulted in congestion that ultimately led to bankruptcy in the textile industry, and near bankruptcy in other industries. A major policy shift away from the “iron rice bowl policy” in 1990 led to massive layoffs and increasing social tensions. Were these massive layoffs necessary? Extensions of data envelopment analysis models effected in the present paper identified inefficiencies in the management of congestion. Using textiles and automobiles for illustration, it is shown how elimination of such managerial inefficiencies could have led to output augmentation without reducing employment. Thus, even in the presence of congestion, it proved to be possible to identify additional (managerial) inefficiencies that provided opportunities for improvement. In the heavily congested textile industry, these output augmentations could have been accompanied by reductions in the amounts of capital used (as an added bonus). In any case, we show how to identify and evaluate new types of efficiency—viz., the efficiency with which needed (or desired) inefficiencies are managed.     

Efficiency measurement with multiple outputs and multiple inputs

This paper discusses modeling technical and allocative inefficiencies in both cost minimizing and profit maximizing frameworks with special emphasis on multiple inputs and multiple outputs. Both primal and dual models are considered for this purpose. In the primal approach we use a separable output and input function (the constant elasticity of transformation output function and Cobb-Douglas input function). The dual models assume translog cost or profit functions. Technical inefficiency is assumed to be random in the cross-sectional models, and fixed firm-specific parameter in the panel data models. Allocative inefficiencies are always treated as input-specific parameters. We derive exact relations linking technical inefficiency and allocative inefficiencies to cost and profit when the underlying technology is represented by a flexible functional form such as the translog. It is shown that appending a one-sided homoscedastic error term to model technical inefficiency, or neglecting technical inefficiency altogether in a translog profit tunciton results in model misspecification and inconsistent parameter estimates.     

Congestion, ownership, region of operation, and scale: Their impact on bus operator performance in Norway

The goal of this paper is to determine the impact that inputs such as fuel consumption and total number of workers employed have on operators’ efficiency in the Norwegian bus industry. Further, we investigate operations characteristics that are associated with the inefficient use of inputs in bus operations. This information is highly relevant for the subsidizers (decision-makers) since resource inefficiency leads to greater costs (ceteris paribus). We use Data Envelopment Analysis (DEA) to explore these issues. The results suggest that there is, in general, a potential for input saving in the sector of about 21%. No significant differences were found between urban and bus rural operators with respect to efficiency scores; neither were there any performance differences with respect to ownership. This latter result deviates from previous international studies, and can likely be explained by the lack of competition in the Norwegian bus industry. A particularly interesting result suggests a formidable degree of input congestion in the Norwegian bus industry, which is in contrast to previous international studies on such congestion.     

Measures in DEA with an Application to the Malmquist Index

This paper shows the importance of goal vectors G in measuring and dealing with DEA inefficiencies. It emphasizes the advantages of the family of additive relative to the traditional oriented DEA models and shifts the primary emphasis to measuring inefficiency rather than efficiency. This new (raw) inefficiency measure RIN incorporates both the traditional DEA efficiency and the DEA slacks and provides the background for a new approach to the Malmquist Index. The final section points out some deficiencies in existing computational procedures for selecting G and calls for continued research on the selection process, as well as showing a role for G in returns to scale studies.     

Using data envelopment analysis to measure the efficiency of not-for-profit organizations: A critical evaluation—comment

This note responds to Nunamaker (1985) who supposedly deals with deficiencies in Data Envelopment Analysis (DEA) as an approach for (1) measuring efficiencies of not-for-profit entities identified as Decision Making Units (DMUs) and (2) locating sources and amounts of inefficiencies in each of the inputs used and in each of the outputs produced by each DMU. Corrections and comments are offered with references supplied for interested readers who wish to examine more detailed treatments of the topics covered.     

Efficiency in fundraising and distributions to cause-related social profit enterprises

Managerial efficiency is as important in social profit enterprises (SPEs) as it is for more traditional financial-profit organizations. In this regard, both donors and SPE executives use efficiency information in making decisions. Here, we suggest a linked, two-stage Data Envelopment Analysis (DEA) methodology for assessing efficiency in both charitable fundraising and cause delivery, while empirically investigating results for international aid organizations. The model allows efficiency assessment for both the fundraising and utilization of generated funds when directed for cause-related purposes. This, in particular, allows for measurement of the organization’s managerial efficiency relative to both multiple phased goals and peer organizations. Additionally, the approach provides benchmarks for identifying sources of improved performance in fundraising and program/cause service delivery. It can also project the results of changes in inputs on the amount of resources available for the charitable organization’s cause.The proposed model(s) allow the examiner to assess performance while, at the same time, identifying those instances wherein the simple ratio measures commonly used in non-profit assessment are (1) deficient, and/or (2) misleading because of the use of ‘incorrect’ variables, or the ‘hiding’ of inefficiency if/when tax form categories are filed by an SPE. Importantly, the suggested two-stage DEA methodology can be useful for any organization with multiple-linked goals.     

中国分省区FDI的引进效率评价与解析

本文用非参数DEA方法评价和分析了中国各省区1998～2000年和2001-2003年两个时期FDI的引进效率。研究发现，在1998-2000年优势充分发挥的省区是：福建、广东、广西和海南，优势发挥严重不足的地区是青海和新疆；在2001-2003年优势充分发挥的省区是：江苏、江西和海南，优势发挥严重不足的地区是宁夏和新疆。效率分解的结果使我们发现新疆效率低下的主要原因是规模效率低下，宁夏效率低下的主要原因是拥挤测度太低，而青海效率低下的原因则是来自规模效率和拥挤测度两方面。     

Accounting for Environmental Effects and Statistical Noise in Data Envelopment Analysis

In this paper we propose a new technique for incorporating environmental effects and statistical noise into a producer performance evaluation based on data envelopment analysis (DEA). The technique involves a three-stage analysis. In the first stage, DEA is applied to outputs and inputs only, to obtain initial measures of producer performance. In the second stage, stochastic frontier analysis (SFA) is used to regress first stage performance measures against a set of environmental variables. This provides, for each input or output (depending on the orientation of the first stage DEA model), a three-way decomposition of the variation in performance into a part attributable to environmental effects, a part attributable to managerial inefficiency, and a part attributable to statistical noise. In the third stage, either inputs or outputs (again depending on the orientation of the first stage DEA model) are adjusted to account for the impact of the environmental effects and the statistical noise uncovered in the second stage, and DEA is used to re-evaluate producer performance. Throughout the analysis emphasis is placed on slacks, rather than on radial efficiency scores, as appropriate measures of producer performance. An application to nursing homes is provided to illustrate the power of the three-stage methodology.     

A Simulation Study of Joint Uses of Data Envelopment Analysis and Statistical Regressions for Production Function Estimation and Efficiency Evaluation

A previous paper by Arnold, Bardhan, Cooper and Kumbhakar (1996) introduced a very simple method to estimate a production frontier by proceeding in two stages as follows: Data Envelopment Analysis (DEA) is used in the first stage to identify efficient and inefficient decision-making units (DMUs). In the second stage the thus identified DMUs are incorporated as dummy variables in OLS (ordinary least squares) regressions. This gave very satisfactory results for both the efficient and inefficient DMUs. Here a simulation study provides additional evidence. Using this same two-stage approach with Cobb-Douglas and CES (constant elasticity-of-substitution) production functions, the estimated values for the coefficients associated with efficient DMUs are found to be not significantly different from the true parameter values for the (known) production functions whereas the parameter estimates for the inefficient DMUs are significantly different. A separate section of the present paper is devoted to explanations of these results. Other sections describe methods for estimating input-specific inefficiencies from the first stage use of DEA in the two-stage approaches. A concluding section provides further directions for research and use.     

我国大陆主要集装箱港口相对有效性评价

以数据包络分析(DEA)的BC2模型为基础,选取泊位长度、堆场面积和桥吊数量为输入项,吞吐量为输出项,从定量角度对我国大陆主要集装箱港口的相对有效性进行了评价。结合评价结果,对各港口的有效和无效原因做了初步的分析。     

The impact of corporate governance on state-owned and non-state-owned firms efficiency in China

The purpose of this paper is to expand the literature on the corporate governance of transition economies by analyzing the relationship between corporate governance and productive efficiency in China's publicly listed manufacturing industry firms. We use the principal component analysis and the hybrid meta-frontier DEA model, separating inputs into radial inputs that change proportionally and non-radial inputs that change non-proportionally to measure the technical efficiency and technology gap ratios of publicly listed Chinese firms in different manufacturing industries during 2010–2013. The input variables are the net value of fixed assets, staff number, and the characteristics of the corporate governance system, while the output variables are gross revenue and total profit. The empirical result shows that inefficiency due to corporate governance is the main reason for lower efficiency in most manufacturing firms. For the technology gap ratio (TGR), the metal and mineral and the machinery, equipment and instrument are the two highest efficient sectors, whereas the paper and allied products sub-industry has the lowest efficiency during 2010–2013. In addition, the ratio of state-owned firms whose inefficiency is mainly caused by corporate governance to total state-owned firms is greater than that of non-state-owned firms in each year. The TGR analysis shows that the efficiency performance of non-state-owned firms is greater than state-owned firms.     

Mix Efficiency in a Multi-species Fishery

A feature of fisheries that distinguishes them from most other industries is the level of control imposed on the production process. Previous studies have identified inefficiency in fisheries that is directly related to the management restrictions. The development of Slack-based measure (SBM) models allows the effects of management distortions to be further investigated through consideration of input and output mix efficiency. In this paper, the mix efficiency of a fleet operating in a multispecies fishery is examined. The results indicate that inefficiencies exist in the mix of inputs, which have developed as a consequence of the management restrictions imposed.     

Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.     

Categorical and continuous non-discretionary variables in data envelopment analysis: a comparison of two single-stage models

Non-discretionary or environmental variables are regarded as important in the evaluation of efficiency in Data Envelopment Analysis (DEA), but there is no consensus on the correct treatment of these variables. This paper compares the performance of the standard BCC model as a base case with two single-stage models: the Banker and Morey (1986a) model, which incorporates continuous environmental variables and the Banker and Morey (1986b) model, which incorporates categorical environmental variables. Simulation analyses are conducted using a shifted Cobb-Douglas function, with one output, one non-discretionary input, and two discretionary inputs. The production function is constructed to separate environmental impact from managerial inefficiency, while providing measures of both for comparative purposes. Tests are performed to evaluate the accuracy of each model. The distribution of the inputs, the sample size and the number of categories for the categorical model are varied in the simulations to determine their impact on the performance of each model. The results show that the Banker and Morey models should be used in preference to the standard BCC model when the environmental impact is moderate to high. Both the continuous and categorical models perform equally well but the latter may be better suited to some applications with larger sample sizes. Even when the environmental impact is slight, the use of a simple two-way split of the sample data can produce significantly better results under the Categorical model in comparison to the BCC model.     

Marginal Rates and Elasticities of Substitution with Additive Models in DEA

Marginal rates and elasticities of substitution are derived from the optimal slack values obtained from modified versions of additive DEA models. Projection formulas are used to ensure that all points are on the efficient frontier as required for conformance with assumptions in micro-economics. The models used differ from standard versions in that slack values are allowed to be negative as well as positive in these additive models. This makes movement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is therefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includes, but is not restricted to, the case in which all slacks must be zero for full attainment of efficiency—as in standard versions of additive models.