A MONTE CARLO EVALUATION OF SEVERAL TESTS FOR THE SELECTION OF VARIABLES IN DEA MODELS

Data Envelopment Analysis (DEA) is a recently developed methodology that is widely used for estimating relative efficiency scores of Decision Making Units (DMUs) that use several inputs to produce several outputs. Model specification in DEA includes aspects such as the choice of inputs and outputs or the adoption of a returns to scale assumption. As pointed out by many authors, it is obvious that the specification of a model is the key to having reliable efficiency scores. In this paper, we are particularly concerned with the selection of variables in DEA models. To be specific, we investigate the performance of several statistical tests existing in the literature that can be used for the selection of variables. In particular, the behaviour of the well-known tests proposed by Banker2 and the nonparametric tests recently developed by Pastor et al.13 is analyzed in relation to several factors such as sample size, model size, the specification of returns to scale and the type and level of inefficiency. We have drawn some conclusions that will be of help for practical uses, since the observed behaviour of the tests in the different scenarios determined by the specifications of the mentioned factors may provide some useful insight into the choice of an adequate statistical test in the particular context of a given DEA application.

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A Comparison of Ensemble and Dimensionality Reduction DEA Models Based on Entropy Criterion

Algorithms ◽

10.3390/a13090232 ◽

2020 ◽

Vol 13 (9) ◽

pp. 232

Author(s):

Parag C. Pendharkar

Keyword(s):

Dimensionality Reduction ◽

Returns To Scale ◽

Data Envelopment ◽

Objective Functions ◽

High Entropy ◽

Selection Of Variables ◽

Dea Models ◽

Entropy Criterion ◽

Selection Of ◽

Normally Distributed

Dimensionality reduction research in data envelopment analysis (DEA) has focused on subjective approaches to reduce dimensionality. Such approaches are less useful or attractive in practice because a subjective selection of variables introduces bias. A competing unbiased approach would be to use ensemble DEA scores. This paper illustrates that in addition to unbiased evaluations, the ensemble DEA scores result in unique rankings that have high entropy. Under restrictive assumptions, it is also shown that the ensemble DEA scores are normally distributed. Ensemble models do not require any new modifications to existing DEA objective functions or constraints, and when ensemble scores are normally distributed, returns-to-scale hypothesis testing can be carried out using traditional parametric statistical techniques.

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The Efficiency of Waste Sector in Italy: An Application by Data Envelopment Analysis

Environmental and Climate Technologies ◽

10.2478/rtuect-2020-0099 ◽

2020 ◽

Vol 24 (3) ◽

pp. 225-238

Author(s):

Massimo Gastaldi ◽

Ginevra Virginia Lombardi ◽

Agnese Rapposelli ◽

Giulia Romano

Keyword(s):

Data Envelopment Analysis ◽

Environmental Performance ◽

Returns To Scale ◽

Sustainable Growth ◽

Waste Reduction ◽

Data Envelopment ◽

Environmental Legislation ◽

Dea Models ◽

Developed Nations ◽

Variable Returns To Scale

AbstractWith growing environmental legislation and mounting popular concern for the need to pursuing a sustainable growth, there has been an increasing recognition in developed nations of the importance of waste reduction, recycling and reuse maximization. This empirical study investigates both ecological and economic performances of urban waste systems in 78 major Italian towns for the years 2015 and 2016. To this purpose the study employs the non-parametric approach to efficiency measurement, represented by Data Envelopment Analysis (DEA) technique. More specifically, in the context of environmental performance we implement two output-oriented DEA models in order to consider both constant and variable returns to scale. In addition, we include an undesirable output – the total amount of waste collected – in the two models considered. The results show that there is variability among the municipalities analysed: Northern and Central major towns show higher efficiency scores than Southern and Islands ones.

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A review of the literature on DEA models under common set of weights

Journal of Modelling in Management ◽

10.1108/jm2-02-2019-0043 ◽

2020 ◽

Vol 15 (4) ◽

pp. 1277-1300

Author(s):

Ignacio Contreras

Keyword(s):

Future Research ◽

Data Envelopment ◽

Systematic Revision ◽

Systematic Classification ◽

Content Type ◽

Dea Models ◽

Common Set Of Weights ◽

The Individual ◽

Selection Of

Purpose Data envelopment analysis (DEA) is a mathematical method for the evaluation of the relative efficiency of a set of alternatives, which produces multiple outputs by consuming multiple inputs. Each unit is evaluated on the basis of the weighted output over the weighted input ratio with a free selection of weights and is allowed to select its own weighting scheme for both inputs and outputs so that the individual evaluation is optimized. However, several situations can be found in which the variability between weighting profiles is unsuitable. In those cases, it seems more appropriate to consider a common vector of weights. The purpose of this paper is to include a systematic revision of the existing literature regarding the procedures to determine a common set of weights (CSW) in the DEA context. The contributions are classified with respect to the methodology and to the main aim of the procedure. The discussion and findings of this paper provide insights into future research on the topic. Design/methodology/approach This paper includes a systematic revision of the existing literature about the procedures to determine a CSW in the DEA context. The contributions are classified with respect to the methodology and to the main aim of the procedure. Findings The discussion and findings of the literature review might insights into future research on the topic. Originality/value This papers revise the state of the art on the topic of models with CSW in DEA methodology and propose a systematic classification of the contributions with respect to several criteria. The paper would be useful for both theoretical and practical future research on the topic.

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Analyzing technical and super efficiency of aluminium firms in India

Benchmarking An International Journal ◽

10.1108/bij-03-2015-0026 ◽

2017 ◽

Vol 24 (6) ◽

pp. 1729-1741 ◽

Cited By ~ 1

Author(s):

Mini Kundi ◽

Seema Sharma

Keyword(s):

Large Scale ◽

Returns To Scale ◽

Foreign Firms ◽

Data Envelopment ◽

Content Type ◽

Super Efficiency ◽

Young Firms ◽

Dea Models ◽

Dea Analysis ◽

Practical Implications

Purpose The purpose of this paper is to evaluate the efficiency of aluminium firms in India. Design/methodology/approach Different data envelopment analysis (DEA) models have been employed to calculate the various efficiency scores of aluminium firms in India. Findings The major findings of the DEA analysis suggest that 62 per cent firms are found to be technically efficient. Overall, the industry shows good performance with mean technical efficiency levels of 0.936 and 0.911 for VRS and CRS frameworks, respectively. Further, five firms show decreasing returns to scale, signifying the overutilization of plant capacities. Six firms exhibit increasing returns to scale implying underutilization of plants. The results show that domestic firms are more efficient than the foreign firms, young firms are more efficient than young firms and small- and medium-scale firms are more efficient than large-scale firms. Practical implications The results of this study would help the aluminium firms to formulate an appropriate strategy to cautiously use their resources to increase their efficiency levels. Originality/value To the best of authors’ knowledge, no earlier studies seem to have ranked the aluminium firms based on their super-efficiency scores. Further, no previous studies seem to have examined the efficiency differences among aluminium firms across different size, age and ownership groups.

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Measuring the financial efficiencies and performances of Turkish funds

Acta Oeconomica ◽

10.1556/aoecon.60.2010.3.4 ◽

2010 ◽

Vol 60 (3) ◽

pp. 295-320 ◽

Cited By ~ 7

Author(s):

F. Gökgöz

Keyword(s):

Mutual Funds ◽

Returns To Scale ◽

Scale Efficiency ◽

Portfolio Performance ◽

Data Envelopment ◽

Performance Indices ◽

Programming Technique ◽

Dea Models ◽

Constant Returns To Scale ◽

Variable Returns To Scale

Measuring the financial efficiencies of mutual funds in emerging markets has played an important role in finance literature. Charnes et al. (1978) advocated Data Envelopment Analysis (DEA), a valuable mathematical programming technique, which is used to measure the technical, pure and scale efficiencies of decision making units. The general form of DEA is the CCR model that depends on the assumption of constant returns to scale. Subsequently, Banker et al. (1984) developed an alternative DEA model which includes a variable returns to scale approach. The aim of this study is to measure and compare the financial efficiencies of Turkish securities and pension funds in the 2006–2007 period. In this respect, 36 securities mutual funds (SMFs) and 41 pension mutual funds (PMFs) have been evaluated comparatively according to classical portfolio performance measures and DEA models. Results from performance indices and DEA models reveal that PMFs have higher portfolio performances and financial efficiencies than SMFs in the 2006–2007 period. However, SMFs and PMFs have shown considerable increases in efficiency in the 2006–2007 period according to CCR and BCC models. Of the 77 funds studied, 23 funds in 2007 and 20 funds in 2006 demonstrated scale efficiency. Furthermore, the input ratios should be considerably improved for 2006 and 2007. But, mostly the output values of the funds were found to have remained unchanged in the case of PMFs and SMFs in 2007. The output ratios for 2006 should be considerably improved, especially in the case of SMFs. Finally, the DEA method is evaluated as a substantial quantitative tool for investors in analysing the financial efficiencies of funds in the capital markets.

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Selection of Variables in Data Envelopment Analysis for Evaluation of Stock Performance

Management and Labour Studies ◽

10.1177/0258042x211002511 ◽

2021 ◽

pp. 0258042X2110025

Author(s):

B. Senthil Arasu ◽

Desti Kannaiah ◽

Nancy Christina J. ◽

Malik Shahzad Shabbir

Keyword(s):

Data Envelopment Analysis ◽

Stock Exchange ◽

Secondary Market ◽

Data Envelopment ◽

Stock Performance ◽

The Past ◽

Financial Strength ◽

Selection Of Variables ◽

Selection Of ◽

Past Price

Data envelopment analysis (DEA) is a relative measurement technique used to evaluate the efficiencies of a homogeneous group of samples with multiple inputs and/or outputs. DEA can be highly effective when right variables are chosen. The objective of this study is to identify the most appropriate variables for DEA to evaluate stock performance and find the efficient ones from a pool of stocks. Evaluation of stocks are carried out either by assessing their financial strength or by assessing their past price behaviour in the secondary market or both. In any case, it is imperative to use suitable variables to evaluate the performance of stocks. For this purpose, three different combinations of variables were tested on 69 non-financial stocks listed in the National Stock Exchange (NSE), which were selected based on their market capitalization. The results obtained suggest that all the three sets of variables taken for the study help in the identification of efficient stocks. The average returns of the stocks selected in all the three cases are higher than the market return. Among the three sets, stocks identified using the past price behaviour give a higher return when compared to the other two sets. The study can help academicians and investors to percolate efficient stocks from a large pool of stocks. The selected stocks can be further analysed to construct an effective portfolio.

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Appraising healthcare systems’ efficiency in facing COVID-19 through data envelopment analysis

Decision Science Letters ◽

10.5267/j.dsl.2021.2.007 ◽

2021 ◽

Vol 10 (3) ◽

pp. 301-310

Author(s):

Nahia Mourad ◽

Ahmed Mohamed Habib ◽

Assem Tharwat

Keyword(s):

Relative Efficiency ◽

Statistical Tests ◽

Internal Validity ◽

Healthcare Systems ◽

Data Envelopment ◽

Tobit Regression ◽

Medical Practitioners ◽

Tobit Analysis ◽

Dea Models ◽

Tobit Regression Analysis

The healthcare system is a vital element for any community, as it extremely affects the socio-economic development of any country. The current study aims to assess the performance of the healthcare systems of the countries above fifty million citizens in facing the spread of the COVID-19 pandemic since late December 2019. For this purpose, seven scenarios were adopted via the DEA methodology with six variables, which are the number of medical practitioners (doctors and nurses), hospital beds, Conducted Covid-19 tests, affected cases, recovered cases, and death cases. To shed light on the relative efficiency of drivers, the Tobit analysis was used. Besides, the study carried out various statistical tests for the DEA models' findings to validate the choice of the variables and the obtained scores. The DEA results reveal that less than half of the considered countries are relatively efficient. Moreover, the Tobit regression analysis showed that the main impact on the efficiency scores was due to the number of affected and recovered cases. Finally, the results of the tests of Spearman, Mann-Whitney U, and Kruskal-Wallis H indicate the internal validity and robustness of the chosen DEA models. The current study findings raise important implications, which can be helpful for decision makers regarding continuous improvement of performance, in which the findings assert the importance of achieving the best practices regarding relative efficiency through the linkage between the healthcare systems’ resources, and the needed outputs.

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An Entropy-Based Cross-Efficiency under Variable Returns to Scale

Entropy ◽

10.3390/e21121205 ◽

2019 ◽

Vol 21 (12) ◽

pp. 1205

Author(s):

Chun-Hsiung Su ◽

Tim Lu

Keyword(s):

Evaluation Method ◽

Returns To Scale ◽

Peer Evaluation ◽

Data Envelopment ◽

Efficiency Evaluation ◽

Dea Models ◽

Constant Returns To Scale ◽

Numerical Index ◽

Variable Returns To Scale ◽

Decision Making Units

Cross-efficiency evaluation is an effective methodology for discriminating among a set of decision-making units (DMUs) through both self- and peer-evaluation methods. This evaluation technique is usually used for data envelopment analysis (DEA) models with constant returns to scale due to the fact that negative efficiencies never happen in this case. For cases of variable returns to scale (VRSs), the evaluation may generate negative cross-efficiencies. However, when the production technology is known to be VRS, a VRS model must be used. In this case, negative efficiencies may occur. Negative efficiencies are unreasonable and cause difficulties in calculating the final cross-efficiency. In this paper, we propose a cross-efficiency evaluation method, with the technology of VRS. The cross-efficiency intervals of DMUs were derived from the associated aggressive and benevolent formulations. More importantly, the proposed approach does not produce negative efficiencies. For comparison of DMUs with their cross-efficiency intervals, a numerical index is required. Since the concept of entropy is an effective tool to measure the uncertainty, this concept was employed to build an index for ranking DMUs with cross efficiency intervals. A real-case example was used to illustrate the approach proposed in this paper.

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A USE OF NONPARAMETRIC TESTS FOR DEA-DISCRIMINANT ANALYSIS: A METHODOLOGICAL COMPARISON

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595904000126 ◽

2004 ◽

Vol 21 (02) ◽

pp. 179-195 ◽

Cited By ~ 18

Author(s):

TOSHIYUKI SUEYOSHI ◽

SHIUH-NAN HWANG

Keyword(s):

Discriminant Analysis ◽

Group Membership ◽

Financial Analysis ◽

Statistical Tests ◽

Nonparametric Tests ◽

Systems Science ◽

Data Envelopment ◽

Statistical Tool ◽

Linear Discriminant ◽

New Type

Discriminant Analysis (DA) is a statistical tool that can predict the group membership of a newly sampled observation. Sueyoshi (European Journal of Operational Research, 115 (1999) 564; 131 (2001) 324; 152 (2004) 45) and Sueyoshi and Kirihara (International Journal of Systems Science, 29 (1998) 1249) have recently proposed a new type of nonparametric DA approach that provides a set of weights of a linear discriminant function, consequently yielding an evaluation score for the determination of group membership. The nonparametric DA is referred to as "Data Envelopment Analysis-Discriminant Analysis (DEA-DA)," because it maintains its discriminant capabilities by incorporating the nonparametric feature of DEA into DA. In this study, a use of two statistical tests is proposed for DEA-DA and its discriminant capability is compared with DEA from a perspective of financial analysis.

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An Extension of Cross Redundancy of Interval Scale Outputs and Inputs in DEA

Journal of Applied Mathematics ◽

10.1155/2013/658635 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Farhad Hosseinzadeh-Lotfi ◽

Gholam-Reza Jahanshahloo ◽

Mansour Mohammadpour

Keyword(s):

Decision Making ◽

Linear Combination ◽

Data Envelopment ◽

Ratio Scale ◽

Interval Scale ◽

Output Variable ◽

Input And Output ◽

Dea Models ◽

Decision Making Units ◽

Selection Of

It is well known that data envelopment analysis (DEA) models are sensitive to selection of input and output variables. As the number of variables increases, the ability to discriminate between the decision making units (DMUs) decreases. Thus, to preserve the discriminatory power of a DEA model, the number of inputs and outputs should be kept at a reasonable level. There are many cases in which an interval scale output in the sample is derived from the subtraction of nonnegative linear combination of ratio scale outputs and nonnegative linear combination of ratio scale inputs. There are also cases in which an interval scale input is derived from the subtraction of nonnegative linear combination of ratio scale inputs and nonnegative linear combination of ratio scale outputs. Lee and Choi (2010) called such interval scale output and input a cross redundancy. They proved that the addition or deletion of a cross-redundant output variable does not affect the efficiency estimates yielded by the CCR or BCC models. In this paper, we present an extension of cross redundancy of interval scale outputs and inputs in DEA models. We prove that the addition or deletion of a cross-redundant output and input variable does not affect the efficiency estimates yielded by the CCR or BCC models.

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