The economic meaning of Data Envelopment Analysis: A ‘behavioral’ perspective

We reconsider the motivation of Data Envelopment Analysis (DEA), the non-parametric technique that is widely employed for analyzing productive efficiency in academia, the private sector and the public sector. We first argue that the conventional engineering motivation of DEA can be problematic since it often builds on unverifiable production axioms. We then provide a dual viewpoint and highlight the ‘behavioral’ interpretation of DEA models. We start from a specification of the production objectives while imposing minimal structure on the production possibilities, and construct tools to meaningfully quantify deviations of observed producer behavior from optimizing behavior. This brings to light the economic meaning of DEA, provides guidelines for selecting the appropriate model in practical research settings, and prepares the ground for instituting new DEA models. We also provide an empirical application that demonstrates the practical relevance of our arguments. We hope that our insights will contribute to the further dissemination of DEA, and stimulate public sector applications of DEA that build on its behavioral interpretation.     

An insight into the specification of the input-output set for DEA-based bank efficiency measurement

Data envelopment analysis (DEA) has become one of the most widely used instruments for measuring bank efficiency. However, its application encounters many problems, which is evidenced by continuous evolvements in the DEA method so far. Our paper addresses the pitfalls of DEA in the context of measuring bank efficiency, with focus on the specification of performance factors. We aim at examining whether the input-output specification for banks in DEA applications is in consistence with the criteria upon which banks make decisions. Four bank behaviour models which are most popularly employed to determine input and output factors in DEA studies—the intermediation approach, production approach, user cost approach and value added approach—are comprehensively discussed and reviewed. The comparative reflection on the bank behaviour models and the standard DEA models shows that the input-output related pitfalls of a DEA application are associated with its implicitly fixed preference structure, flexible weight determination and limited explanatory power. Due to the pitfalls, the conventional DEA models may fail to capture bank behaviours. In such cases, DEA results can hardly reflect the performance in its true sense, i.e. how banks perform against the goals that they decide to pursue. The findings suggest focusing on (DEA-based) performance measurement from a goal-oriented perspective, i.e. from the point of view of multi criteria decision making.     

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.     

Technical Efficiency of the Brazilian Municipalities: Correcting Nonparametric Frontier Measurements for Outliers

In this paper we estimate the DEA technical efficiency for 4796 Brazilian municipalities, by applying a recently proposed “Jackstrap” method, which combines Bootstrap and Jackknife resampling techniques, to reduce the effect of outliers and possible errors in the data set. We perform calculations to identify and eliminate high leverage municipalities, using different variants of Data Envelopment Analysis (DEA), as well as Free Disposal Hull (FDH). Corroborating previous results, efficiency results for the Brazilian municipalities show a clear relationship between the size of the municipality and its efficiency scores. Indeed, under both DEA variants, smaller cities tend to be less efficient than larger ones hence indicating that the quality of the frontier adjustment improves significantly as the size of the municipality increases. We present arguments that may explain to some extent these findings, such as economies of scale and the excess spending due to revenue from royalties. However, such effects require further, more careful examination.     

Advances in physician profiling: the use of DEA

Insurers, health plans, and individual physicians in the United States are facing increasing pressures to reduce costs while maintaining quality. In this study, motivated by our work with a large managed care organization, we use readily available data from its claims database with data envelopment analysis (DEA) to examine physician practices within this organization. Currently the organization evaluates primary care physicians using a profile of 16 disparate ratios involving cost, utilization, and quality. We employed these same factors along with indicators of severity to develop a single, comprehensive measure of physician efficiency through DEA. DEA enabled us to identify a reference set of “best practice” physicians tailored to each inefficient physician. This paper presents a discussion of the selection of model inputs and outputs, the development of the DEA model using a “stepwise” approach, and a sensitivity analysis using superefficiency scores. The stepwise and superefficiency analyses required little extra computation and yielded useful insights into the reasons as to why certain physicians were found to be efficient. This paper demonstrates that DEA has advantages for physician profiling and usefully augments the current ratio-based reports.     

A cross-national comparison and taxonomy of DEA-based hospital efficiency studies

This paper provides the first taxonomy of hospital efficiency studies that uses data envelopment analysis (DEA) and related techniques. We provide a systematic review of 79 such studies published from 1984–2004 that represent 12 countries. Only studies written in English are considered. A cross-national comparison reveals significant differences with respect to important study characteristics such as type of DEA model selected and choice of input and output categories. Compared with US studies, European efforts are more likely to measure allocative rather than technical efficiency, use longitudinal data, and use fewer observations. We take a longitudinal perspective that illustrates the life cycle of this research, as well as its diffusion across disciplines. Our taxonomy can be used by policy makers and researchers to review past, and assemble new, DEA models.     

DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea—Ratio Analysis. Our model, called DEA-R, treats all possible ratios “output/input” as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts’ opinions via flexible restrictive conditions on individual “output/input” pairs.     

A PCA–DEA approach to measure the quality of life in Estonian counties

This paper investigates the application of a PCA–DEA model to assess the quality of life (QOL) scores in Estonian counties and analyses the model's results. The dataset is a balanced panel of 15 Estonian counties covering the period from 2000 to 2011. We consider a PCA–DEA model as an alternative method to estimate and predict QOL scores and rankings of Estonian counties. The method consists of a two-stage analysis that begins with a principal component analysis. In the second stage, the standard DEA is used. The results from the conventional DEA model and the PCA–DEA model are compared and discussed. A comparison of the methodologies demonstrates that a PCA–DEA model provides a powerful tool for performance ranking. The rankings of Estonian counties using QOL scores for different model specifications are presented. Finally, the QOL ranking of Estonian counties is revised using PCA–DEA.     

Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank

The interest in Data Envelopment Analysis (DEA) as a method for analyzing the productivity of homogeneous Decision Making Units (DMUs) has significantly increased in recent years. One of the main goals of DEA is to measure for each DMU its production efficiency relative to the other DMUs under analysis. Apart from a relative efficiency score, DEA also provides reference DMUs for inefficient DMUs. An inefficient DMU has, in general, more than one reference DMU, and an efficient DMU may be a reference unit for a large number of inefficient DMUs. These reference and efficiency relations describe a net which connects efficient and inefficient DMUs. We visualize this net by applying Sammons mapping. Such a visualization provides a very compact representation of the respective reference and efficiency relations and it helps to identify for an inefficient DMU efficient DMUs respectively DMUs with a high efficiency score which have a similar structure and can therefore be used as models. Furthermore, it can also be applied to visualize potential outliers in a very efficient way.JEL Classification: C14, C61, D24, M2     

A novel method for computing single output for DEA with application in hospital efficiency

There are two main methods for measuring the efficiency of decision-making units (DMUs): data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Each of these methods has advantages and disadvantages. DEA is more popular in the literature due to its simplicity, as it does not require any pre-assumption and can be used for measuring the efficiency of DMUs with multiple inputs and multiple outputs, whereas SFA is a parametric approach that is applicable to multiple inputs and a single output. Since many applied studies feature multiple output variables, SFA cannot be used in such cases. In this research, a unique method to transform multiple outputs to a virtual single output is proposed. We are thus able to obtain efficiency scores from calculated virtual single output by the proposed method that are close (or even the same depending on targeted parameters at the expense of computation time and resources) to the efficiency scores obtained from multiple outputs of DEA. This will enable us to use SFA with a virtual single output. The proposed method is validated using a simulation study, and its usefulness is demonstrated with real application by using a hospital dataset from Turkey.     

The appreciative democratic voice of DEA: A case of faculty academic performance evaluation

Data envelopment analysis (DEA) is in fact more than just being an instrument for measuring the relative efficiencies of a group of decision making units (DMU). DEA models are also means of expressing appreciative democratic voices of DMUs. This paper proposes a methodology for allocating premium points to a group of professors using three models sequentially: (1) a DEA model for appreciative academic self-evaluation, (2) a DEA model for appreciative academic cross-evaluation, and (3) a Non-DEA model for academic rating of professors for the purpose of premium allocations. The premium results, called DEA results, are then compared with the premium points “nurtured” by the Dean, called N bonus points. After comparing DEA results and N bonus points, the Dean reassessed his initial bonus points and provided new ones – called DEA-N decisions. The experience indicates that judgmental decisions (Dean's evaluations) can be enhanced by making use of formal models (DEA and Non-DEA models). Moreover, the appreciative and democratic voices of professors are virtually embedded in the DEA models.     

中国省际高技术产业效率测度与分解——基于共享投入关联DEA模型

本文基于高技术产业科技成果产出和科技成果转化为生产力两阶段视角,考虑"中间产品产出再投入"和"初始投入在两个子系统间的分配结构",构建共享投入关联DEA模型,利用1999～2010年我国29个省份的面板数据,测算高技术产业系统效率和子系统的纯技术效率,并与关联DEA模型、BCC模型的结果进行比较。结果表明,共享投入关联DEA模型在计算效率水平的同时,还可得到中间产品的转化信息和初始投入的配置信息。     

A DEA-centric decision support system for evaluating Ciclovía-Recreativa programs in the Americas

Ciclovía-Recreativa (CR) is a community-based program with health and social benefits including physical activity promotion, social capital development, improvement in the population's quality of life, and reduction of air pollution and street noise. It is critical that these programs are evaluated through their operational performance and efficient use of resources. In this paper, we develop a DEA methodology that measures each CR efficiency relative to its peer programs, compares its performance to a benchmark system, identifies its sources of inefficiencies and offers recommendations for improvement. We examine the proposed methodology on programs in the region of the Americas as a case study and demonstrate the results and the recommendations. Finally, we present a spreadsheet-based DEA-centric Decision Support System (DSS) that facilitates the evaluation of the CR programs. Based on this study, an award called “Bicis de Calidad” (in English “Bikes of Quality”) was created to be granted to the best CR programs reaching full efficiency according to the DEA outcomes.     

Pushing the DEA research envelope

This brief article first investigates key dimensions underlying the progress realized by data envelopment analysis (DEA) methodologies. The resulting perspective is then used to encourage reflection on future paths for the field. Borrowing from the social sciences literature, we distinguish between problematization and gap identification in suggesting strategies to push the DEA research envelope. Emerging evidence of a declining number of influential methodological (theory)-based publications, and a flattening diffusion of applications imply an unfolding maturity of the field. Such findings suggest that focusing on known limitations of DEA, and/or of its applications, while searching for synergistic partnerships with other methodologies, can create new and fertile grounds for research. Possible future directions might thus include ‘DEA in practice’, ‘opening the black-box of production,’ ‘rationalizing inefficiency,’ and ‘the productivity dilemma.’ What we are therefore proposing is a strengthening of the methodology's contribution to fields of endeavor both including, and beyond, those considered in the past.     

Cross redundancy and sensitivity in DEA models

Data envelopment analysis (DEA) measures the efficiency of each decision making unit (DMU) by maximizing the ratio of virtual output to virtual input with the constraint that the ratio does not exceed one for each DMU. In the case that one output variable has a linear dependence (conic dependence, to be precise) with the other output variables, it can be hypothesized that the addition or deletion of such an output variable would not change the efficiency estimates. This is also the case for input variables. However, in the case that a certain set of input and output variables is linearly dependent, the effect of such a dependency on DEA is not clear. In this paper, we call such a dependency a cross redundancy and examine the effect of a cross redundancy on DEA. We prove that the addition or deletion of a cross-redundant variable does not affect the efficiency estimates yielded by the CCR or BCC models. Furthermore, we present a sensitivity analysis to examine the effect of an imperfect cross redundancy on DEA by using accounting data obtained from United States exchange-listed companies.     

银行效率DEA分析的可信度检验

近年来涌现出大量基于DEA方法的银行效率这一热点问题的研究成果,但是由于DEA方法自身的局限性,诸如对效率值的估计偏低且离散程度较大,以及不能方便地检验结果的显著性等等问题,使其研究的结果受到影响;而Bootstrap技术是基于对经验数据及其相关估计的重复抽样来提高估计置信区间和临界值精度的统计技术,可有效地克服DEA方法结果可信度的这种内在依赖性。本文给出了基于Boot-strap技术的DEA方法来计量银行效率的手段,提高了效率分析结果的可信度,并对我国四大国有商业银行的效率进行了对比性实证分析。     

Measuring efficiency under fixed proportion technologies

Data Envelopment Analysis (DEA) applications frequently involve nonsubstitutable inputs and nonsubstitutable outputs (that is, fixed proportion technologies). However, DEA theory requires substitutability. In this paper, we illustrate the consequences of nonsubstitutability on DEA efficiency estimates, and we develop new efficiency indicators that are similar to those of conventional DEA models except that they require nonsubstitutability. Then, using simulated and real-world datasets that encompass fixed proportion technologies, we compare DEA efficiency estimates with those of the new indicators. The examples demonstrate that DEA efficiency estimates are biased when inputs and outputs are nonsubstitutable. The degree of bias varies considerably among Decision Making Units, resulting in substantial differences in efficiency rankings between DEA and the new measures. And, over 90% of the units that DEA identifies as efficient are, in truth, not efficient. We conclude that when inputs and outputs are not substituted for either technological or other reasons, conventional DEA models should be replaced with models that account for nonsubstitutability.     

A multistage method to measure efficiency and its application to Japanese banking industry

When measuring technical efficiency with existing data envelopment analysis (DEA) techniques, mean efficiency scores generally exhibit volatile patterns over time. This appears to be at odds with the general perception of learning-by-doing management, due to Arrow [The economic implications of learning by doing. Review of Economic Studies 1964; 154–73]. Further, this phenomenon is largely attributable to the fundamental assumption of deterministic data maintained in DEA models, and to the difficulty such models have in incorporating environmental influences. This paper proposes a three-stage method to measure DEA efficiency while controlling for the impacts of both statistical noise and environmental factors. Using panel data on Japanese banking over the period 1997–2001, we demonstrate that the proposed approach greatly mitigates these weaknesses of DEA models. We find a stable upward trend in mean measured efficiency, indicating that, on average, the bankers were learning over the sample period. Therefore, we conclude that this new method is a significant improvement relative to those DEA models currently used by researchers, corporate management, and industrial regulatory bodies to evaluate performance of their respective interests.     

How to improve the performances of DEA/FDH estimators in the presence of noise?

In frontier analysis, most nonparametric approaches (DEA, FDH) are based on envelopment ideas which assume that with probability one, all observed units belong to the attainable set. In these “deterministic” frontier models, statistical inference is now possible, by using bootstrap procedures. In the presence of noise, envelopment estimators could behave dramatically since they are very sensitive to extreme observations that might result only from noise. DEA/FDH techniques would provide estimators with an error of the order of the standard deviation of the noise. This paper adapts some recent results on detecting change points [Hall P, Simar L (2002) J Am Stat Assoc 97:523–534] to improve the performances of the classical DEA/FDH estimators in the presence of noise. We show by simulated examples that the procedure works well, and better than the standard DEA/FDH estimators, when the noise is of moderate size in term of signal to noise ratio. It turns out that the procedure is also robust to outliers. The paper can be seen as a first attempt to formalize stochastic DEA/FDH estimators.      

Axiomatic foundations of efficiency measurement on data-generated technologies

We assess the ability of three well-known technical efficiency indexes, the Debreu-Farrell index, the Färe–Lovell index, and the Zieschang index, to satisfy the Färe–Lovell axioms and continuity axioms (for technologies as well as input quantities) on the class of technologies generated by standard mathematical-programming methods of measuring efficiency: data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Färe–Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu–Farrell index), but (b) none of the indexes satisfies all Färe–Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.