The enhanced Russell-based directional distance measure with undesirable outputs: Numerical example considering CO2 emissions

Following the spirit of the enhanced Russell graph measure, this paper proposes an enhanced Russell-based directional distance measure (ERBDDM) model for dealing with desirable and undesirable outputs in data envelopment analysis (DEA) and allowing some inputs and outputs to be zero. The proposed method is analogous to the output oriented slacks-based measure (OSBM) and directional output distance function approach because it allows the expansion of desirable outputs and the contraction of undesirable outputs. The ERBDDM is superior to the OSBM model and traditional approach since it is not only able to identify all the inefficiency slacks just as the latter, but also avoids the misperception and misspecification of the former, which fails to identify null-jointness production of goods and bads. The paper also imposes a strong complementary slackness condition on the ERBDDM model to deal with the occurrence of multiple projections. Furthermore, we use the Penn Table data to help us explore our new approach in the context of environmental policy evaluations and guidance for performance improvements in 111 countries.     

存在非期望产出的决策单元阻塞问题研究

阻塞是指企业的过量投入引起生产效益下降的经济现象,近年来已经受到实业界与学术界的广泛关注。现有的决策单元阻塞问题研究普遍假设产出均是期望指标,然而,在实际生产中很多产出属于非期望指标。本文构建了同时存在期望产出和非期望产出决策单元的阻塞度量模型,该模型不仅可以判别决策单元是否存在阻塞,而且可以测算各项投入的阻塞程度,并给出了决策单元阻塞和技术无效之间的关系。最后,运用所提出的模型对我国上市商业银行的效率和阻塞情况进行了测算与分析,验证了本文模型的实用性与可行性。     

Estimating two-stage network Slacks-based inefficiency: An application to Bangladesh banking

This paper studies the performance of nineteen private commercial banks and two government-owned banks in Bangladesh during the period 2005–2008 using a slacks-based inefficiency measure and the directional technology distance function. Performance is measured assuming a black-box production structure and then the black-box is opened and examined using a two stage network production structure. Current period performance in maximizing desirable loans and securities investments and minimizing bad loans depends on how efficiently inputs at one stage of production are transformed into intermediate outputs which are used at a subsequent stage of production. In addition, current period production of the intermediate output is constrained by the amount of non-performing loans that were generated in an earlier period.     

Additive slacks-based measure: Computational strategy and extension to network DEA

The current paper visits a set of data envelopment analysis (DEA) models that identify inefficiency by optimizing input and output slacks. These slacks are aggregated either in an additive or ratio form. Only the ratio slacks-based DEA models can be solved as a linear program and generate a DEA score between zero and unity. The additive slacks-based model can be equivalent to the Russell graph measure and converted into a second order cone programming (SOCP) problem whose solving procedure has become a mature technology. As such, the additive slacks-based model can also yield a DEA score between zero and unity. This study shows that the additive slacks-based model can be applied to modelling network DEA where the internal structures of decision making units (DMUs) are of interest. The additive slacks-based network DEA can be solved using SOCP technique and adapted to the preference of the decision maker by choosing the weights for aggregating individual components in the network structures. It is shown that the additive slacks-based approach can yield divisional efficiencies of Pareto optimal equivalences to be selected by the decision maker when compared to the existing ratio slacks-based measure. An example and solving codes are provided in the current study.     

存在非期望输入输出的多阶段系统效率评价模型

现有多阶段DEA模型的研究普遍假设所有输入、输出均为期望指标, 对存在非期望指标的情况研究较少, 尚无对最初投入和中间产出带有非期望指标的研究。为此, 本文首先提出了输入、输出类型的判定方法, 并将其应用于存在非期望输入、输出的两阶段系统。进一步针对存在非期望指标的两阶段生产系统中同种输入、输出, 尤其中间产出类型判定一致与不一致的情况, 构建了相应的生产可能集以及两阶段DEA模型, 最后利用本文方法和模型对我国上市银行效率进行了评价。     

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.     

Returns to scale vs. damages to scale in data envelopment analysis: An impact of U.S. clean air act on coal-fired power plants

This study proposes a use of Data Envelopment Analysis (DEA) to measure Returns to Scale (RTS) of US coal-fired power plants. The power plants produce not only desirable outputs (e.g., electricity) but also undesirable outputs (e.g., CO₂ and NO_x) as a result of their plant operations. Therefore, the proposed use of DEA also measures a new concept, or “DTS: Damages to Scale” (corresponding to RTS for undesirable outputs). Both scale measures discussed in this study are a quick-and-easy approach for assessing RTS and DTS, but not an exact method, because it does not consider a direct linkage between the two measures. This study applies the proposed approach to examine the legal validity of U.S. Clean Air Act (CAA). We find that the CAA has been legally effective and influential on the operation of coal-fired power plants in the United States because their plant operations belong to increasing RTS on a desirable output and increasing DTS on three undesirable outputs. The increasing DTS indicates a need for managerial improvement and/or engineering innovation such as advanced clean coal technology. This empirical result implies that U.S. federal and state governments need to expand the legal scope of CAA to the emission control of CO₂ because the current CAA excludes the regulation on CO₂ emission that is now considered as a main source of the global warming and climate change.     

A new slacks-based measure of Malmquist–Luenberger index in the presence of undesirable outputs

In the majority of production processes, noticeable amounts of bad byproducts or bad outputs are produced. The negative effects of the bad outputs on efficiency cannot be handled by the standard Malmquist index to measure productivity change over time. Toward this end, the Malmquist–Luenberger index (MLI) has been introduced, when undesirable outputs are present. In this paper, we introduce a Data Envelopment Analysis (DEA) model as well as an algorithm, which can successfully eliminate a common infeasibility problem encountered in MLI mixed period problems. This model incorporates the best endogenous direction amongst all other possible directions to increase desirable output and decrease the undesirable outputs at the same time. A simple example used to illustrate the new algorithm and a real application of steam power plants is used to show the applicability of the proposed model.     

Two-stage DEA models with undesirable input-intermediate-outputs

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). Many studies have examined DEA efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Although single-stage DEA models with undesirable input-outputs have been extensively studied, there still lacks of more systematical investigation on two-stage DEA with undesirable variables. For instance, depending on its operating model, even whether an intermediate variable is desirable or undesirable can be questionable for a particular two-stage system. Furthermore, most of the existing studies on two-stage systems focus on the case where only the final outputs are undesirable. In this work, we try to systematically examine two-stage DEA models with undesirable input-intermediate-outputs. Particularly, we utilize the free-disposal axioms to construct the production possibility sets (PPS) and the corresponding DEA models with undesirable variables. The proposed models are then used to illustrate some theoretical perspectives by using the data of China׳s listed banks.     

Eco-efficiency analysis of paper mills along the Huai River: An extended DEA approach

The objective of this paper is to estimate the ecological efficiency of paper mills along the Huai River in China. The main characteristic of the ecological efficiency evaluation problem is that an undesirable output of biochemical oxygen demand (BOD) and a non-discretionary input (BOD emission quota) should be considered simultaneously. By analyzing the impacts of the non-discretionary input on decision-making units’ (DMUs) desirable and undesirable outputs, a non-radial output-oriented DEA model is proposed. In the proposed model, we describe a new approach of defining reference set that requires reference units operate in a similar environment on average. We employ the model to provide efficient inputs/outputs targets for DMU managers to improve DMUs’ efficiencies. Based on the developed model, impacts of the non-discretionary input on DMUs’ returns are also analyzed. We illustrate the proposed model, using real data, for 32 paper mills along the Huai River in China.     

环境规制下的投入产出效率及规制成本研究

现实的生产活动往往同时具有期望和非期望(主要是环境污染物)两种产出.将环境因素纳入到具体的投入产出分析框架,利用环境生产技术建立一组效率评价模型和成本测算模型,并依据不同的效率导向从环境效率、经济效率、综合效率和两阶段效率等多个角度实证研究2001年～2005年中国28个省、自治区、直辖市的投入产出水平和不同环境规制下的成本问题.研究结果表明,中国各地区总体的环境效率和经济效率普遍偏低,差异也较大,经济效率与环境效率的变动并不具有完全的一致性,反映环境污染和经济发展水平的综合效率与环境效率变化趋势基本一致,部分省、自治区、直辖市在期望产出最优后仍有进一步削减非期望产出的可能,严格环境规制下的成本明显高于一般环境规制下的成本,且两者都具有明显的上升趋势.     

Efficiency evaluation of banks in China: A dynamic two-stage slacks-based measure approach

Operational processes of banks in China can be divided into productivity and profitability stages. Within this, non-performing loans can be treated as a carry-over variable, an undesirable output of the profitability stage in the previous period but an input to the profitability stage in the current period. Using this framework, this paper proposes a dynamic two-stage slacks-based measure model to evaluate the efficiencies of Chinese banks. Based on the proposed model, the measures of stage, period and period stage efficiencies are defined. The proposed approach is applied to evaluate the operational efficiency of banks in China during 2008–2012. Key findings are that banks in China show both technical and scale inefficiency during 2008–2012, which results from the inefficiencies of both the productivity stage and profitability stage; city-owned commercial banks are more overall technically efficient than state-owned commercial banks and joint-stock commercial banks although state-owned commercial banks show best practice for pure technical efficiency, and city-owned commercial banks perform better than joint-stock commercial banks for pure technical efficiency.     

Multi-valued measures in DEA in the presence of undesirable outputs

Data envelopment analysis (DEA) evaluates the relative efficiency of a set of comparable decision making units (DMUs) with multiple performance measures (inputs and outputs). Classical DEA models rely on the assumption that each DMU can improve its performance by increasing its current output level and decreasing its current input levels. However, undesirable outputs (like wastes and pollutants) may often be produced together with desirable outputs in final products which have to be minimized. On the other hands, in some real-world situations, we may encounter some specific performance measures with more than one value which are measured by various standards. In this study, we referee such measures as multi-valued measures which only one of their values should be selected. For instance, unemployment rate is a multi-valued measure in economic applications since there are several definitions or standards to measure it. As a result, selecting a suitable value for a multi-valued measure is a challenging issue and is crucial for successful application of DEA. The aim of this study is to accommodate multi-valued measures in the presence of undesirable outputs. In doing so, we formulate two individual and summative selecting directional distance models and develop a pair of multiplier- and envelopment-based selecting approaches. Finally, we elaborate applicability of the proposed method using a real data on 183 NUTS 2 regions in 23 selected EU-28 countries.     

The technical efficiency of the Japanese banks: Non-radial directional performance measurement with undesirable output

The paper analyses technical efficiency of the Japanese banks from 2000 to 2007. The estimation technique is based on the Russell directional distance function that takes into consideration not only desirable outputs but also an undesirable output that is represented by non-performing loans (NPLs). The results indicate that NPLs remain a significant burden as for banks' performance. We show that banks' inputs have to be utilised more efficiently, particularly labour and premises. We also argue that a further restructuring process is needed in the segment of Regional Banks. We conclude that the Japanese banking system is still far away from being fully consolidated and restructured.     

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.     

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。     

Duality of weakly disposable technology

The axiom of weak disposability is frequently imposed in data envelopment analysis (DEA) models involving undesirable outputs such as pollution. This paper sheds new light on the economic interpretation of weak disposability by developing dual formulations of the weakly disposable DEA technology. We find that the economic implications of weak disposability on the multiplier DEA problem are two-fold: (1) the shadow prices of the undesirable outputs can be positive or negative, and (2) the economic loss of the benchmark cannot exceed the suck cost of the inputs. We interpret the second implications as a limited liability condition. The dual formulations developed in this paper enable one to estimate shadow prices of the undesirable outputs using the weakly disposable technology. The insights gained are illustrated by a numerical example and an empirical application to the US power plants.     

A Nerlovian cost inefficiency two-stage DEA model for modeling banks’ production process: Evidence from the Turkish banking system

By developing a two-stage model the paper examines the cost inefficiency levels of Turkish banks during the period from 2007 to 2016. Using the notion of Koopmans input efficiency we deconstruct the estimated Nerlovian cost inefficiency to the sum of slack-based allocative and technical inefficiency levels. Alongside the traditional inputs, intermediates and outputs used to model banks’ performance measure we additionally use their labor education quality factor as a non-discretionary input. This allows us to model how human capital factors affect a bank's revenue generation stage. Our findings suggest that cost inefficiency levels are driven mainly by a bank's ability to control its allocative inefficiency levels. The empirical evidence also shows that foreign banks perform better, suggesting that bank ownership structures matter when measuring cost performance. Finally, it is evident that the Global Financial Crisis (GFC) had a negative effect on banks’ ability to minimize their cost inefficiency levels. However, the post-crisis findings demonstrate that Turkish banks have started to recover from its negative effects, mainly by improving their allocative performance.     

利益相关者关系视角下考虑非期望产出的商业银行效率问题研究

商业银行效率评价及影响因素分析一直是学术界和实务界研究的热点问题,但尚未有文献从利益相关者视角展开研究。本文运用SBM模型对考虑非期望产出的商业银行效率评价问题进行了分析。结合契约理论、商业银行生产函数、期望理论的分析,得出利益相关者关系是影响考虑非期望产出的商业银行效率的关键变量,并构建了分析两者关系的Tobit模型。在此基础上,选取我国2004-2011年14家代表性商业银行为样本,对考虑非期望产出的商业银行效率的评价与影响因素问题进行实证研究,结果表明,利益相关者关系是影响考虑非期望产出的我国商业银行效率的关键因素。     

Opening the black box of efficiency analysis: An illustration with UAE banks

Standard data envelopment analysis (DEA) does not provide adequate detail to identify the specific sources of inefficiency embedded in interacting divisions of an organization. On the other hand, network DEA gives access to this underlying diagnostic information that would otherwise remain undiscovered. As a first study of its kind, the paper illustrates an application of non-oriented network slacks-based measure using simulated profit center data that, in turn, rely on actual aggregate data on domestic commercial banks in the United Arab Emirates (UAE). The study also contributes to a perennial research problem, namely, inability of the outside researcher to access internal data for developing or testing new methods. In addition to these contributions to the Operations Research literature, focusing on UAE contributes to banking literature because this rapidly expanding part of the Middle East seldom appears in frontier efficiency literature.