DEA/AR profit ratios and sensitivity of 100 large U.S. banks

Several important DEA/AR concepts were applied here to banking for the first time. This application includes classification, sensitivity, uniqueness, linked cones (LCs), and profit ratios. Notably, large bank behavior seems to be explained better by profit ratios than by relative efficiency. Measures of DEA efficiency, AR efficiency, and LC profit ratios were made for a bank panel of the U.S.'s 100 largest banks in asset size from 1986 to 1991. High levels of inefficiency were found, as in previous studies. Classification of the DEA efficiency measures identified the inefficient DMUs with some positive primal slacks. Sensitivity analysis of the DEA efficiency measures showed that the extreme-efficient classification was generally relatively insensitive to errors in the data. The ARs eliminated (i) 44% to 60% of the DEA-extreme-efficient DMUs and (ii) all of the banks with unprofitable actual profit ratios. Some statistical analyses highlight the superiority of the LC profit ratios, relative to the AR efficiency measures.     

Computing DEA/AR efficiency and profit ratio measures with an illustrative bank application

This paper describes how the recent, published DEA/AR theory, in conjunction with software, provides measures of radial efficiency and profit ratios, This new DEA theory does not require use of the non-Archimedean principle, i.e., positive infinitesimals, and it allows for analysis of zero data entries. Further, this theory provides a comprehensive classification of the measures for both the efficient and inefficient decision-making units (DMUs). As programmed in the software, the efficiency principles are relative to the Charnes-Cooper-Rhodes ratio model and the Banker-Charnes-Cooper convex model, and the profitability principles are relative to the Thompson-Thrall profit ratio model. An illustrative application to 48 large U.S. banks illustrates some of the most fundamental computations, which are developed for a base option. Additional options may be exercised by the user to more fully utilize the theory. Additions to the software are being made to computer analytic centers and to make multiplier sensitivity analyses. Software utility updates and new DEA theory contributions continue to complement this computational capability.DEA is an advanced operations research method called Data Envelopment Analysis, and AR is an assurance region method used to bound the multipliers in the DEA model. Underlying data have been deposited with the editors.     

A ranked voting system using a DEA/AR exclusion model: A note

This paper addresses ranked voting systems to determine an ordering of candidates in terms of the aggregate vote by rank for each candidate. It is shown that specifying nothing arbitrary, we can obtain a total ordering of candidates by using a DEA/AR (Data Envelopment Analysis/Assurance Region) exclusion model. Explaining the evaluation criterion used to rank candidates, it is concluded that we may consider the system proposed at least as an alternative to determine an ordering of candidates.     

A game theoretical model of DEA efficiency

Motivated by the inherent competitive nature of the DEA efficiency assessment process, some effort has been made to relate DEA models to game theory. Game theory is considered not only a more natural source of representing competitive situations, but also beneficial in revealing additional insights into practical efficiency analysis. Past studies are limited to connecting efficiency games to some particular versions of DEA models. The generalised DEA model considered in this study unifies various important DEA models and presents a basic formulation for the DEA family. By introducing a generalised convex cone constrained efficiency game model in assembling the generalised DEA model, a rigorous connection between game theory and the DEA family is established. We prove the existence of optimal strategies in the generalised efficiency game. We show the equivalence between game efficiency and DEA efficiency. We also provide convex programming models for determination of the optimal strategies of the proposed games, and show that the game efficiency unit corresponds to the non-dominated solution in its corresponding multi-objective programming problem. Our study largely extends the latest developments in this area. The significance of such an extension is for research and applications of both game theory and DEA.     

Unveiling endogeneity between competition and efficiency in Chinese banks: a two-stage network DEA and regression analysis

Although there is a growing number of research articles investigating the performance in the banking industry, research on Chinese banking efficiency is rather focused on discussing rankings to the detriment of unveiling its productive structure in light of banking competition. This issue is of utmost importance considering the relevant transformations in the Chinese economy over the last decades. This is a development of a two-stage network production process (production and intermediation approaches in banking, respectively) to evaluate the efficiency level of Chinese commercial banks. In the second stage regression analysis, an integrated Multi-Layer Perceptron/Hidden Markov model is used for the first time to unveil endogeneity among banking competition, contextual variables, and efficiency levels of the production and intermediation approaches in banking. The competitive condition in the Chinese banking industry is measured by Panar–Rosse H-statistic and Lerner index under the Ordinary Least Square regression. Findings reveal that productive efficiency appears to be positively impacted by competition and market power. Second, credit risk analysis in older local banks, which focus the province level, would possibly be the fact that jeopardizes the productive efficiency levels of the entire banking industry in China. Thirdly, it is found that a perfect banking competition structure at the province level and a reduced market power of local banks are drivers of a sound banking system. Finally, our findings suggest that concentration of credit in a few banks leads to an increase in bank productivity.

     

DEA model with shared resources and efficiency decomposition

Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.     

Bootstrapped efficiency estimates for a model for groups and hierarchies in DEA

We apply some recently introduced bootstrap techniques to derive bias corrected efficiency scores for a model for groups and hierarchies in DEA. The use of the bootstrap makes it possible to overcome some deficiencies of the original formulation of this model, which rests on rescaling individual efficiency scores using average efficiencies calculated from different subsets of the data. These average or structural efficiencies are differently biased and bias varies with sample size when standard DEA techniques are used. Bias correction makes it possible to identify the true differences in efficiency and thus to compare DMUs belonging to different groups via their rescaled individual efficiency scores on one common basis. Moreover, this type of bias problem is present in other DEA applications. Therefore, the method proposed to deal with it has many potential applications beyond the groups and hierarchies model.     

具有偏好锥的面向输出的超效率DEA模型分析

鉴于传统DEA模型无法区分有效决策单元,超效率DEA模型未考虑决策者的偏好,现提出面向输出的权重受限的综合超效率DEA模型及其投影概念,并讨论该模型与其他超效率DEA模型之间的关系.接着,分析模型的最优目标函数值与决策单元有效性之间的关系,并讨论面向输出的权重受限的综合超效投影与多目标规划问题的非支配解之间的关系.最后,通过对中国西部12个地区工业企业科技创新效率综合评价,并与原有方法进行比较研究,得出本文方法更具优势和合理性.     

A simplified version of the DEA cost efficiency model

This short paper deals with a current cost efficiency model and decreases the number of its constraints as well as its variables, which leads to a strong reduction in the computational requirements.     

A DEA game model approach to supply chain efficiency

Data envelopment analysis (DEA) is a useful method to evaluate the relative efficiency of peer decision making units (DMUs). Based upon the definitions of supply chain efficiency, we investigate the efficiency game between two supply chain members. It is shown that there exist numerous Nash equilibriums efficiency plans for the supplier and the manufacturer with respect to their efficiency functions. A bargaining model is then proposed to analyze the supplier and manufacturer's decision process and to determine the best efficiency plan strategy. DEA efficiency for supply chain operations is studied for the central control and the decentralized control cases. The current study is illustrated with a numerical example.     

An enhanced DEA model for decomposition of technical efficiency in banking

Past studies about the application of data envelopment analysis (DEA) to banking performance often follow the concept of technical efficiency (TE) and/or the productivity defined by the TE. In this paper, we propose an enhanced DEA model, based on a modification of the directional distance function by simultaneously but disproportionately seeking the maximum expansion of each desirable output and contraction of each undesirable output for efficiency measurement, which allows us to decompose the TE into operating efficiency (OPE) and risk management efficiency (RME). The OPE characterizes the ability of a bank to expand the room for profits through its regular business activities, while the RME describes a bank’s ability in risk management activities for sustaining operations. To illustrate the usefulness of the proposed model, a case study of Taiwan’s domestic commercial banks is presented. The major findings are that operating inefficiency is the main source of technical inefficiency, although banks with a higher OPE generally also have a higher RME. Banks subordinate to financial holding companies are more efficient in both OPE and RME than stand-alone banks.     

Hyperbolic frontier model: a parametric DEA approach for the distribution of a total fixed output

This paper addresses the problem of assigning shares of a new total fixed output to a group of decision making units (DMUs) using data envelopment analysis (DEA), by assuming the existence of a predefined hyperbolic locus of points that characterizes the DEA frontier. The problem of redistributing an already existing output is then addressed, where the total value of this output may vary, so that no DMU is required to decrease its current output value in the new distribution.     

Cone dominance and efficiency in DEA

This paper incorporates cones on virtual multipliers of inputs and outputs into DEA analysis. Cone DEA models are developed to generalize the dual of the BCC models as well as congestion models. Input-output data and/or numbers of DMUs for BCC models are inadequate to capture many aspects where judgments, expert opinions, and other external information should be taken into analysis. Cone DEA models, on the other hand, offer improved definitions of efficiency over general cone and polyhedral cone structures. The relationships between cone models and BCC models as well as those between cone models and congestion models are discussed in the development. Two numerical examples are provided to illustrate our findings.     

Developing a decomposable measure of profit efficiency using DEA

In for-profit organizations efficiency measurement with reference to the potential for profit augmentation is particularly important as is its decomposition into technical, and allocative components. Different profit efficiency approaches can be found in the literature to measure and decompose overall profit efficiency. In this paper, we highlight some problems within existing approaches and propose a new measure of profit efficiency based on a geometric mean of input/output adjustments needed for maximizing profits. Overall profit efficiency is calculated through this efficiency measure and is decomposed into its technical and allocative components. Technical efficiency is calculated based on a non-oriented geometric distance function (GDF) that is able to incorporate all the sources of inefficiency, while allocative efficiency is retrieved residually. We also define a measure of profitability efficiency which complements profit efficiency in that it makes it possible to retrieve the scale efficiency of a unit as a component of its profitability efficiency. In addition, the measure of profitability efficiency allows for a dual profitability interpretation of the GDF measure of technical efficiency. The concepts introduced in the paper are illustrated using a numerical example.     

Measuring overall efficiency and effectiveness using DEA

This paper presents a framework where data envelopment analysis (DEA) is used to measure overall efficiency and show how to apply this framework to assess effectiveness for more general behavioral goals. The relationships between various cone-ratio DEA models and models to measure overall efficiency are clarified. Specifically it is shown that as multiplier cones tighten, the cone-ratio DEA models converge to measures of overall efficiency. Furthermore, it is argued that multiplier cone and cone-ratio model selection must be consistent with the behavioral goals assigned or assumed for purposes of analysis. Consistent with this reasoning, two new models are introduced to measure effectiveness when value measures are represented by separable or linked cones, where the latter can be used to analyze profit-maximizing effectiveness.     

基于熵权法的DEA/AR交叉效率知识化制造模式评价

用模糊DEA/AR交叉效率方法,解决制造模式的评价与排序问题.首先,构建了四种不同的DEA/AR交叉效率模型—任意型、对抗型、友好型和博弈型.然后,应用熵权法确定每一种交叉效率模型的最终交叉效率值,目的是用保证域来避免传统模型的权重偏差,从而实现了决策单元的相对有效评价和精确排序.同时,引入奇异指数的概念来衡量最终交叉效率的合理性及可靠性.最后,通过实例验证本文模型和方法的可行性及有效性:与采用简单DEA效率模型进行评价比较,我们的方法会使得效率更加精准、排序更加合理.     

Regional concentration and efficiency in Mexican manufacturing

This paper explores the link between industrial location, concentration, and economic efficiency in Mexican manufacturing. Using a linear programming approach, the authors calculate indices of overall, technical, allocative, and scale efficiency for Mexican manufacturing industries by state to test whether, in 1985, those regions with high levels of industrial concentration were suffering from the costs of congestion. The evidence suggests that, at least at the aggregate level, there continued to be a positive relationship between industry concentration and efficiency in production. There is also evidence that overall efficiency was related to scale efficiency, although highly industrialized regions on the production frontier often operated at inefficient scales. In particular, the most concentrated regions (the Federal District, the state of Mexico, Jalisco, and Nuevo León) consistently display decreasing returns to scale, indicating that the process of industrial concentration may be leading to diseconomies of scale. Finally, an econometric analysis suggests that scale, urbanization, and agglomeration economies are positively related to overall and technical efficiency at the regional level, while foreign ownership is negatively related. Agglomeration economies at the industry level were not significant. The paper also makes a methodological contribution. It is the first application of a distance-function production methodology to measuring regional efficiency in a developing country. It demonstrates how to conduct distance-function efficiency analysis using the newly developed GAMS mathematical programming environment. These tools should be of considerable interest to applied microeconomists.     

The LeChatelier principle in a DEA model

This paper aims to relate the LeChatelier principle, first introduced into economics by Samuelson (1947), with the DEA approach through two propositions. These propositions allow for bridging the principle over a DEA model with and without the presence of non-discretionary inputs and enable one to make comparisons for the various efficiency measures under different conditions. The quasi-fixity of some inputs hinders a firm’s capacity from instantly and freely adjusting its input combination in order to minimize its production costs. The assumption that all inputs are discretionary tends to exaggerate managers’ ability to dispense resources and renders invalid information on the adjustment of the current input mix.     

On a risk model with stochastic premiums income and dependence between income and loss

Labbé and Sendova (2009) [9] consider a compound Poisson risk model with stochastic premiums income. In this paper, we extend their model by assuming that there exists a specific dependence structure among the claim sizes, interclaim times and premium sizes. Assume that the distributions of the premium sizes and interclaim times are controlled by the claim sizes. When the individual premium sizes are exponentially distributed, the Laplace transforms and defective renewal equations for the (Gerber-Shiu) discounted penalty functions are obtained. When the individual premium sizes have rational Laplace transforms, we show that the Laplace transforms for the discounted penalty functions can also be obtained.