Multi-output profit efficiency and directional distance functions

We extend a recently developed DEA methodology for cost efficiency analysis towards profit efficiency settings. This establishes a novel DEA toolkit for profit efficiency assessments in situations with multiple inputs and multiple outputs. A distinguishing feature of our methodology is that it assumes output-specific production technologies. In addition, the methodology accounts for the use of joint inputs, and explicitly includes information on the allocation of inputs to individual outputs. We also establish a dual relationship between our multi-output profit inefficiency measure and a technical inefficiency measure that takes the form of a multi-output directional distance function. Finally, we demonstrate the empirical usefulness of our methodology by an empirical application to a large service company.     

基于整体效率的区间DEA方法研究

针对现有的区间DEA方法采用非统一指标数据进行效率评价的不足,本文在分析现有区间DEA方法的基础上,提出一种基于整体效率的区间DEA方法。该方法能够在多决策单元系统整体效率最大化的同时,得到统一的各决策单元投入/产出的精确数据及各指标权重,一次性求解出所有决策单元的效率。最后,采用一个算例分析说明文章所提方法的合理性和优越性。     

Multi-period efficiency measurement in data envelopment analysis: The case of Taiwanese commercial banks

In measuring the overall efficiency of a set of decision making units (DMUs) in a time span covering multiple periods, the conventional approach is to use the aggregate data of the multiple periods via a data envelopment analysis (DEA) technique, ignoring the specific situation of each period. This paper proposes using a relational network model to take the operations of individual periods into account in measuring efficiencies. The overall and period efficiencies of a DMU can be calculated at the same time. Notably, the overall efficiency is a weighted average of the period efficiencies, and the weights are the most favorable ones for the DMU being evaluated. This model, together with two existing ones, is applied to measure the efficiency of 22 Taiwanese commercial banks for the period of 2009–2011. The three-year multi-period analysis shows that the proposed model is more discriminative than the existing ones in ranking the performance of the banks. The period efficiencies for the three years increased steadily, indicating that the performances of the Taiwanese banks examined in this work were improving over this period.     

基于分段参数型DEA前沿面的投入—产出型技术效率

由传统DEA模型可以直接测算投入固定(产出固定)的条件下,面向产出(投入)的技术效率。尽管加型DEA模型同时考虑了投入和产出的松弛,但却不能像传统模型一样直接测算投入—产出型技术效率。为了直接由加性模型测算投入产出型技术效率,本文将利用DEA有效决策单元建立分段参数型DEA生产前沿面,并根据古典技术效率的定义,解决投入产出型技术效率的测算问题。研究发现,这种效率实质上是产出型技术效率与投入配置效率的乘积。由于同时考虑了投入和产出的技术无效性,与其它类型的技术效率相比,这种投入产出型技术效率的可分性更强。     

两阶段DEA前沿面投影问题研究——兼对我国上市银行运营绩效进行评价

DEA方法,即数据包络分析方法,是一种用于评价决策单元(Decision Making Units,DMUs)相对有效性的实证方法。近年来DEA方法已经广泛的应用于各行各业的绩效评价中,并发展出两阶段DEA方法。两阶段DEA方法相对于传统DEA方法的优势在于,它不但可以提供被评价对象的总体效率值,还可以分别生成每一阶段的效率值。但正是由于中间要素的存在,按照传统的DEA方法来调整两阶段DEA投入、产出要素的优化过程已不能成功投影在有效前沿面上。本文基于两阶段DEA方法,通过加入"虚拟中间要素"在两阶段DEA中嵌入一个"虚拟阶段",这样不但完善了两阶段DEA的逻辑结构,而且成功的将被评价单元投影到有效前沿面。最后本文应用以上方法对我国上市银行的运营绩效进行了实证分析。实证结果令我们意外的是,国有商业银行运营绩效优于股份制银行。     

Exploring the efficiency of Mexican universities: Integrating Data Envelopment Analysis and Multidimensional Scaling

National policy initiatives require the expenditure of large amounts of resources over several years. It is common for these initiatives to generate large amounts of data that are needed in order to assess their success. Educational policies are an obvious example. Here we concentrate on Mexico׳s “Educational Modernisation Programme” and try to see how this plan has affected efficiency in teaching and research at Mexico׳s universities. We use a combined approach that includes traditional ratios together with Data Envelopment Analysis models. This mixture allows us to assess changes in efficiency at each individual university and explore if these changes are related to teaching, to research, or to both. Using official statistics for 55 universities over a six year period (2007–2012), we have generated 12 ratios and estimated 21 DEA models under different definitions of efficiency. In order to make the results of the analysis accessible to the non-specialist we use models that visualise the main characteristics of the data, in particular scaling models of multivariate statistical analysis. Scaling models highlight the important aspects of the information contained in the data. Because the data is three-way (variables, universities, and years) we have chosen the Individual Differences Scaling model of Carroll and Chang. We complete the paper with a discussion of efficiency evolution in three universities.     

环保项目有效性评价的数据包络分析方法

利用数据包络分析(DEA)方法评价环保项目有效性时,输入、输出数据中可能同时存在环境因素,不符合传统的DEA模型要求,需要对这些数据进行转换。本文讨论了"不好的"数据平移转换法、输入和输出因素转换法、倒数转换法,建立了三种DEA模型,对建立的DEA模型一致性进行了分析,拓宽了以前DEA模型的应用范围。一个例子验证了这三种方法在评价环保项目有效性时是一致的。     

Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA

Measuring and improving the efficiency of the Chinese commercial banking system has recently attracted increasing interest. Few studies, however, have adopted the two-stage network DEA to explore this issue in the Chinese context. Because the entire operational process of the banking system could be divided into two sub-processes (deposit producing and profit earning), the evaluation of the sub-process efficiencies could be used to assist in identifying the sources of the inefficiency of the entire banking system. In this study, we utilize the network DEA approach to disaggregate, evaluate and test the efficiencies of 16 major Chinese commercial banks during the third round of the Chinese banking reform period (2003–2011) with the variable returns to scale setting and the consideration of undesirable/bad output. The main findings of this study are as follows: (i) the two-stage DEA model is more effective than the conventional black box DEA model in identifying the inefficiency of banking system, and the inefficiency of the Chinese banking system primarily results from the inefficiency of its deposit producing sub-process; (ii) the overall efficiency of the Chinese banking system improves over the study period because of the reform; (iii) the state-owned commercial banks (SOBs) appear to be more overall efficient than the joint-stock commercial banks (JSBs) only in the pre-reform period, and the efficiency difference between the SOBs and the JSBs is reduced over the post-reform period; (iv) the disposal of non-performing loans (NPLs) from the Chinese banking system in general explains its efficiency improvement, and the joint-equity reform of the SOBs specifically increases their efficiencies.     

DEA for non-homogenous parallel networks

In practice, systems are often composed of a group of sub-units. Each sub-unit has a set of performance metrics that are classified as inputs and outputs in data envelopment analysis (DEA). Conventional DEA views such a system as a “black-box”, other DEA-based models are developed to investigate the inner structure, either with a serial structure where components are connected by intermediate products, or with a parallel system under the key assumption that all sub-units are associated with the same type of inputs and outputs (in differing amounts) without the links. In many applications, however, this property of identical input/output factors may not hold. For example, factories may have various manufacturing lines whose inputs and outputs differ from one another. The current paper proposes a series of DEA models to accommodate settings where non-homogenous sub-units operate in parallel network structures with intermediate measures or links. Both the overall performance of the entire parallel network system and efficiency decomposition for each sub-unit can be evaluated through our method.     

Diversification-consistent data envelopment analysis based on directional-distance measures

We propose new diversification-consistent DEA models suitable for assessing efficiency of investment opportunities available on financial markets. The formulations based on directional distance measures enable to use several risk measures as inputs and return measures as outputs, which can take both positive and negative values. We show that various models with different strength can be obtained and strongly, semi-strongly or weakly Pareto–Koopmans efficient investment opportunities can be identified. Moreover, the optimal solutions correspond to efficient investment opportunities and can be used by investors to revise the inefficient ones. If we consider discretely distributed returns, we can prove that under proper choice of the inputs (CVaRs) and outputs (expected return), the strongest model is able to identify efficient investment opportunities with respect to the second-order stochastic dominance. Moreover, the model can be formulated as a linear programming problem. In the numerical study, the proposed DEA models are applied to 48 representative industry portfolios from US stock markets.     

A slack-based measure of efficiency in context-dependent data envelopment analysis

Data envelopment analysis (DEA) has been proven as an excellent data-oriented performance evaluation method when multiple inputs and outputs are present in a set of peer decision-making units (DMUs). In the DEA literature, a context-dependent DEA is developed to provide finer evaluation results by examining the efficiency of DMUs in specific performance levels based upon radial DEA efficiency scores. In DEA, non-zero input and output slacks are very likely to present after the radial efficiency score improvement. Often, these non-zero slack values represent a substantial amount of inefficiency. Therefore, in order to fully measure the inefficiency in DMU's performance, it is very important to also consider the inefficiency represented by the non-zero slacks in the context-dependent DEA. This study proposes a slack-based context-dependent DEA which allows a full evaluation of inefficiency in a DMUs performance. By using slack-based efficiency measure, we obtain different frontier levels and more appropriate performance benchmarks for inefficient DMUs.     

Evaluating the administrative efficiency of courts

In addition to being held accountable for judicial decision, courts, like other public agencies, can and should be evaluated in terms of their administrative efficiency. This paper illustrates how courts can be evaluated in terms of their relative administrative efficiency, using a new approach—data envelopment analysis (DEA)—first proposed by Charnes et al. [1]. The DEA is based upon the economic notion of Pareto optimality which states that a given decision making unit (DMU) is inefficient if some other DMU, or some combination of other DMUs, can produce at least the same amounts of all outputs with less of some resource input and not more of any other resource. Conversely a DMU is said to be efficient if the above is not possible. Charnes et al. [1] generalized the usual input/output ratio measure of efficiency for a given unit in terms of a fractional linear program with fractional constraints. In the case of courts, the efficiency of any particular court is calculated by forming the ratio of a weighted sum of outputs to a weighted sum of inputs, where the weights for both outputs and inputs are to be selected in a manner that calculates the Pareto-Koopmans efficiency of the court. This paper reviews the DEA method and illustrates its application to a data base for 100 criminal superior courts in North Carolina.     

Benchmarking airports from a managerial perspective

Benchmarking airports is currently popular both in the academic literature and in practice but has proved rather problematic due to the heterogeneity inherent in any reasonably sized dataset. Most studies either treat the airport production technology as a black box, or separate the terminal and airside activities, assessing them individually. In this article we analyze airports as a single unit due to the direct complementarities, thus avoiding the artificial separation of inputs. Using data envelopment analysis (DEA), we open the black box in which a network describes the production process, thus demonstrating the sequential effects that separate final from intermediate outputs, including those under partial managerial control and those that are known to be non-discretionary. To further improve the benchmarking process, we identify appropriate peers for a case study of 43 European airports over 10 years, through a restricted reference mechanism according to pre-defined characteristics. Compared to basic DEA models, the results of the proposed structure provide more meaningful benchmarks with comparable peer units and target values that are potentially achievable in the medium term. By identifying each unit's individual reference set, unique outliers influence the performance measurement less severely than occurs under basic DEA. In addition, the formulations produce an implementation path that moves the airport towards the Pareto frontier gradually, taking into account the regulatory and business environment in which the unit is located.     

Dynamic DEA: A slacks-based measure approach

In data envelopment analysis, there are several methods for measuring efficiency changes over time, e.g. the window analysis and the Malmquist index. However, they usually neglect carry-over activities between two consecutive terms and only focus on the separate time period independently aiming local optimization in a single period, even if these models can take into account the time change effect. In the actual business world, a long time planning and investment is a subject of great concern. For these cases, single period optimization model is not suitable for performance evaluation. To cope with long time point of view, the dynamic DEA model incorporates carry-over activities into the model and enables us to measure period specific efficiency based on the long time optimization during the whole period. Dynamic DEA model proposed by Färe and Grosskopf is the first innovative contribution for such purpose. In this paper we develop their model in the slacks-based measure (SBM) framework, called dynamic SBM (DSBM). The SBM model is non-radial and can deal with inputs/outputs individually, contrary to the radial approaches that assume proportional changes in inputs/outputs. Furthermore, according to the characteristics of carry-overs, we classify them into four categories, i.e. desirable, undesirable, free and fixed. Desirable carry-overs correspond, for example, to profit carried forward and net earned surplus carried to the next term, while undesirable carry-overs include, for example, loss carried forward, bad debt and dead stock. Free and fixed carry-overs indicate, respectively, discretionary and non-discretionary ones. We develop dynamic SBM models that can evaluate the overall efficiency of decision making units for the whole terms as well as the term efficiencies.     

Target intermediate products setting in a two-stage system with fairness concern

In a two-stage system with two divisions connected in series, fairly setting the target outputs for the first stage or equivalently the target inputs for the second stage is critical, in order to ensure that the two stages have incentives to collaborate with each other to achieve the best performance of the whole system. Data envelopment analysis (DEA) as a non-parametric approach for efficiency evaluation of multi-input, multi-output systems has drawn a lot of attention. Recently, many two-stage DEA models were developed for studying the internal structures of two-stage systems. However, there was no work studying fair setting of the target intermediate products (or intermediate measures) although unreasonable setting will result in unfairness to the two stages because setting higher (fewer) intermediate measures means that the first (second) stage must make more efforts to achieve the overall production plan. In this paper, a new DEA model taking account of fairness in the setting of the intermediate products is proposed, where the fairness is interpreted based on Nash bargaining game model, in which the two stages negotiate their target efficiencies in the two-stage system based on their individual efficiencies. This approach is illustrated by an empirical application to insurance companies.     

超效率DEA模型的模糊扩展

在输入、输出数据为模糊数而效率值为准确值的模糊DEA模型中,会出现有两个以上有效单元,从而无法对所有决策单元进行全排序的情形。本文利用模糊数的基于α-截集的比较规则,建立了模糊条件下的超效率DEA模型,有效地解决了模糊决策单元的全排序问题。文末给出了一个实例。     

Identifying traffic safety best practice: an application of DEA and Malmquist indices

DEA is used in this paper to investigate target achievements of the operational units of the Norwegian Public Roads Administration (NPRA) charged with traffic safety services. The DEA framework applied corresponds to a BCC model with a unique constant input, or equivalently, with no inputs. This framework is further extended to a DEA-based Malmquist index to measure productivity growth in target achievements. Finally, we use a bootstrapping method to ascertain confidence intervals for efficiency scores derived and to test hypotheses on the extent of productivity growth or regress. The mean efficiency scores by which targets are achieved across the sample years are in the range 0.81–0.93 and significant at the 5% level. Total productivity in target achievements shows progress with significance, on average at 7%. Much of the progress is attributed to technological progress. The results illustrate the usefulness of using a decomposable index for productivity measurement, and the use of bootstrapping for sensitivity tests.     

Dynamic performance assessment of bus transit with the multi-activity network structure

This paper proposes a multi-activity dynamic network data envelopment analysis model that combines the multi-activity, network and dynamic DEA models to assess the performance in terms of individual activities, individual processes, individual periods and overall operation. The main advantage of this model is that the linkages among activities and processes, the shared inputs among activities and processes, and the carry-over items among periods are included in a unified model. It can provide more appropriate performance measures. An empirical application of 20 bus transit firms in Taiwan for the period 2004–2012 is provided. Based on the operational characteristics of bus transit firms, both desirable and undesirable outputs are also incorporated into this model. The results show that none of the bus transit firms was effective in terms of the operational effectiveness, and the sources of operational ineffectiveness among bus transit firms were different. Over the period 2004–2012, the period-operational effectiveness scores maintained stable variance, the period efficiencies of highway and urban bus services appeared to have similar patterns, and transit bus firms performed well in the consumption process.     

Governance Structures,Multidimensional Efficiency and Firm Profitability

Using a panel data set of 361 German corporations for the period 1991–1996 we test the hypothesis that firms with more efficient governance structures have higher profitability. To determine efficiency we compare firms with respect to ownership concentration, the identity of owners, capital structure, investment and firm growth by a multi-input/multi-output Data Envelopment Analysis (DEA). This non-parametric linear programming technique considers both multiple in- and out- puts. Based on the concept of pareto efficiency, it computes an efficiency score where the associated weights of the inputs and outputs are determined endogenously. The DEA efficiency scores are then used as explanatory variables in panel data regressions of profitability. Our main finding is that the efficiency scores indeed contribute significantly to explaining profitability differences between firms, even after controlling for industry effects and unobserved systematic firm effects.     

Reprint of: Dynamic efficiency in the English and Welsh water and sewerage industry

The English and Welsh water and sewerage industry is characterised by indivisible capital which has a long service life. Previous studies of efficiency for the English and Welsh water and sewerage industry take a static framework, assuming all inputs can be adjusted instantaneously. This paper measures dynamic efficiency by incorporating intertemporal links of capital within the production function for the English and Welsh water and sewerage industry for the period 1997–2011. Dynamic Data Envelopment Analysis (DEA) considers capital as a quasi-fixed input and is modelled as a contemporaneous output into current production and an input from past production. The results show that the inadequate intertemporal allocation of quasi-fixed inputs is the largest contributor of inefficiency.