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.     

The Effect of Sample Size on the Mean Efficiency in DEA: Comment

Zhang and Bartels (1998) show formallyhow DEA efficiency scores are affected by sample size. They demonstratethat comparing measures of structural inefficiency between samplesof different sizes leads to biased results. This note arguesthat this type of sample size bias has much wider implicationsthan suggested by their example. Models which implicitly restrictthe comparison set like some models for non-discretionary variableslead to biased efficiency scores as well. A reanalysis of theBanker and Morey (1986b) data shows that the efficiency scoresderived there are significantly influenced by the variation insample size implicit in their model.     

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.     

Assessment and budget allocation of Iranian natural gas distribution company- A CSW DEA based model

Regarding the importance of budgeting in organizations, this research proposes an empirical approach to budget allocation problems. The methodological instrument utilized is data envelopment analysis (DEA) which is a nonparametric mathematical programming technique. In the DEA methodology a standard DEA model should be independently solved to evaluate each decision making unit (DMU). Consequently, it is hard to find the magnitude of budget for each DMU by applying a budget allocation model based on standard DEA models because identifying the DMU under evaluation is problematic. Also, to overcome problems of evaluation using standard DEA models, common set of weights (CSW) DEA models were suggested. These models can be developed for use in budget allocation DEA models that lead to finding a single magnitude of budget for each DMU. Moreover, the opinion of the decision maker can be incorporated into the model using budgetary constraints. As a result, a restricted linear budget allocation CSW DEA model is proposed in which the central authority would like to plan for improving the total efficiency scores of all DMUs. In essence, the proposed model is used to reallocate the available budget and, thus, the results obtained will be a suggestion for budget allocation in subsequent periods. Finally, the proposed model is applied to budget allocation in the Iranian gas industry in which the available budget is reallocated to increase the total efficiency scores of Iranian gas distribution branches.     

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.     

Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification

The appearance of strictly positive slack variables in DEA solutions causes well known computational and analytical problems studied by Olesen and Petersen (1996) and Green et al. (1996) under constant returns to scale. This paper discusses variable returns to scale and suggests the use of efficient facets (EFs) in the reference technology. It is found to give a lower bound of the efficiency scores. Most importantly, efficiency measured with respect to EFs—the EF based efficiency index—may decrease if additional variables are introduced but are disposed in production. Thus, units are penalized for disposal of incoming variables, and the EF based efficiency index captures the net efficiency of a unit. EF is found to be a useful tool also to search a suitable set of variables for efficiency measurement. Its use is demonstrated with Finnish university data and it is found to change the measured performance of the university sector quite significantly.     

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.     

Determination of the efficiency of the world railway companies by method of DEA and comparison of their efficiency by Tobit analysis

This paper attempts to measure the performance of railway companies that produce passenger and freight services around the world. The data covering 10 years from 2000 to 2009 is analyzed first via the data envelopment analysis method in order to obtain technical efficiency and allocative efficiency scores of 31 railway companies for the purpose of the study. In the analysis conducted by use of the CCR model, while total 17 firms were efficient in the first year, this figure reaches to 18 companies for the last year with one more addition. While only two companies seem efficient in the first year, this figure goes down to one for the last year. With input oriented and variable return analysis conducted by use of the BCC model, the firms having technical efficiency at the beginning of the period were 20 in number. At the end of the period, the figure reaches to 24. Next, the outputs of DEA are correlated by Tobit regression and tried to determine decisiveness of the outputs on the efficiency. It has been seen that the same output composition used with Tobit analysis gives more compliant results with the allocative efficiency scores rather than with the technical efficiency scores.     

Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis (DEA). In this study, we focus on a “big data” problem related to the considerably large dimensions of the input-output data. The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation, including principal component analysis (PCA-DEA), which is based on the idea of aggregating input and output, efficiency contribution measurement (ECM), average efficiency measure (AEC), and regression-based detection (RB), which is based on the idea of variable selection. We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test. In addition, we discuss the effect of initial variable selection in RB for the first time. Based on the results, we offer guidelines that are more reliable on how to choose an appropriate method.     

Economic development and growth in Colombia: An empirical analysis with super-efficiency DEA and panel data models

In this paper, we analyse economic development and growth through traditional measures (gross domestic product and human development index) and Data Envelopment Analysis (DEA) in Colombian departments over the period 1993–2007. We use a DEA model to measure and rank economic development and growth from different approaches such as poverty, equality and security. The results show considerable variation in efficiency scores across departments. A second-stage panel data analysis with fixed effects reveals that higher levels of economic activity, quality life, employment and security are associated with a higher efficiency score based on the standards of living, poverty, equality and security. All findings of this analysis should demonstrate that economic development and growth could be achieved most effectively through a decrease in poverty, an increase in equality, a reduction in violence, and improved security. This indicates the need to generate effective policies that guarantee the achievement of these elements in the interest of all members of society.     

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.     

Short and long-run cost efficiency in Indian public bus companies using Data Envelopment Analysis

State Transport Undertakings (STUs) are key players in providing mass road transport in India. Given that they operate under high levels of government imposed regulatory constraints, it is imperative to study their efficiency levels. Given that capital is a relatively scarce resource in developing countries like India, it is important to obtain efficiency in the short-run where some inputs are fixed as well as over the long run, where all inputs are variable. The technique used for capturing efficiency is Data Envelopment Analysis (DEA). A key possible limitation of DEA models based on physical inputs and outputs is that for an inefficient firm, reduction in some or all inputs may be recommended. It may often be desirable for an inefficient firm to increase some less expensive inputs while reducing the use of relatively expensive ones. Hence, when market price data is available, it is advisable to use the cost variant of DEA. Also, it is possible to determine variable cost efficiency in the short run when some inputs cannot be varied. Such inputs are referred to as “quasi-fixed” inputs. In this paper, we examine short and long term efficiencies of select bus companies in India known as State Transport Undertakings (STUs) over a period of 10 years. Fleet strength has been used as the quasi-fixed input. It is possible to ascertain, through a comparison of shadow price of the quasi-fixed input, vis-à-vis its market price, as to whether the quantity of this input is sub-optimally small or large. It is found that by adopting efficiency enhancing practices, STUs can cumulatively reduce their operating costs to the extent of 9123.35 million dollars. Also the tendency to minimize costs is found to be declining over time. In the short run some STUs are found to operate with a sub optimally low fleet size.     

Qualitative data envelopment analysis by affinity set: a survey of subjective opinions for NPOs

Measuring the performance of Non-Profit Organizations (NPOs) is a complicated issue: data envelopment analysis (DEA) is a popular quantitative tool in the past literature. However, the subjective opinions of NPOs could disturb their actual performance, and this problem is seldom considered. In this study, we use the qualitative DEA as a tool to find the emphasized inputs and outputs for these NPOs. Most DEA models are established by the basis of quantitative data, they are difficult to describe the qualitative performance of NPOs. This paper proposes a new perspective for computing the efficiency of a Decision Making Unit based on qualitative data by affinity Set. The DEA model for qualitative data could be traced back to the work of Cook et al. early in 1993. Our contribution prevents the identical efficiency scores from the model of Cook et al., and a combinatorial optimization technique is used to solve the new problem. Finally, we found most NPOs would like to get more resources from outside; but interestingly, they don’t like to be officially monitored. Therefore, we should use the quantitative DEA on NPOs very carefully.     

Reverse efficiency measures for environmental assessment in data envelopment analysis

Environmental issues are becoming more and more important in our everyday life. Data Envelopment Analysis (DEA) is a tool developed for measuring relative operational efficiency. DEA can also be employed to estimate environmental efficiency where undesirable outputs like greenhouse gases exist. The classical DEA method identifies best practices among a given empirical data set. In many situations, however, it is advantageous to determine the worst practices and perform efficiency evaluation by comparing DMUs with the full-inefficient frontier. This strategy requires that the conventional production possibility set is defined from a reverse perspective. In this paper, presence of both desirable and undesirable outputs is assumed and a methodological framework for performing an unbiased efficiency analysis is proposed. The reverse production possibility set is defined and new models are presented regarding the full-inefficient frontier. The operational, environmental and overall reverse efficiencies are studied. The important notion of weak disposability is discussed and the effects of this assumption on the proposed models are investigated. The capability of the proposed method is examined using data from a real-world application about paper production.     

The operating efficiency of financial holding and nonfinancial holding banks—Epsilou‐based measure metafrontier data envelopment analysis model

Previous bank efficiency studies assumed that the same efficient frontier system exists in different types of banks, but the conventional radial data envelopment analysis (DEA) model slacks are not counted in efficiency scores, and nonradial DEA models do not consider radial features. This paper develops an Epsilou‐based measure meta‐DEA approach for measuring the efficiencies and technology gaps of different bank types. The results are as the follows: The average efficiency and technology gaps of nonfinancial holding banks are better than those of financial holding banks. The nonfinancial holding banks are more efficient than financial holding banks in investment and other income.     

Productivity drivers and market dynamics in the Spanish first division football league

This paper analyses efficiency drivers of a representative sample of Spanish football clubs by means of the two-stage data envelopment analysis (DEA) procedure proposed by Simar and Wilson (J Econ, 136:31–64, 2007). In the first stage, the technical efficiency of football clubs is estimated using a bootstrapped DEA model in order to establish which of them are the most efficient; the ranking is based on total productivity in the period 1996–2004. In the second stage, the Simar and Wilson (J Econ, 136:31–64, 2007) procedure is used to bootstrap the DEA scores with a truncated bootstrapped regression. Policy implications of the main findings are also considered.     

EXPLAINING DIFFERENCES IN EFFICIENCY: A META‐STUDY ON LOCAL GOVERNMENT LITERATURE

This paper reviews the literature on local government efficiency by meta‐reviewing 360 observations retrieved from 54 papers published from 1993 to 2016. The meta‐regression is based on a random‐effects model estimated with the two‐step random‐effects maximum likelihood (REML) technique proposed by Gallet and Doucouliagos. Results indicate that the study design matters when estimating a frontier in local government. We find that studies focusing on technical efficiency provide higher efficiency scores than works evaluating cost efficiency. The same applies when using panel data instead of cross‐section data. Interestingly, studies that use the Free Disposal Hull (FDH) approach yield, on average, higher efficiency scores than papers employing the data envelopment analysis (DEA) method, thereby suggesting that in this literature the convexity hypothesis of the production set is a matter. Finally, the efficiency of local government increases with the level of development of the analysed countries and is positively related to the national integrity of the legal system. The opposite holds when considering the corruption.     

Statistical evaluation of Data Envelopment Analysis versus COLS Cobb–Douglas benchmarking models for the 2011 Brazilian tariff revision

In 2011, the Brazilian Electricity Regulator (ANEEL) implemented a benchmarking model to evaluate the operational efficiency of power distribution utilities. The model is based on two benchmarking methods: Data Envelopment Analysis (DEA) and Corrected Ordinary Least Squares (COLS) with a Cobb Douglas production function. Although the estimated scores are highly correlated, differences between the scores are as high as 41%. For some companies differences between the efficiency scores result in substantial reduction in regulatory operational costs. We provide a detailed statistical comparison which indicates that the COLS Cobb Douglas model has major deficiencies in terms of estimating efficiency scores.     

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.