随机环境下的多投入多产出生产前沿面估计

传统的DEA模型假设观测样本的投入产出都是确定型数据, 这使得DEA在实际应用中受到限制, 本文提出的基于拟似然估计的多投入多产出随机非参数包络数据 (PLE-StoNED) 方法拓展了这个假设, 能够估计随机环境下的生产前沿面.本文证明, 生产可能集假设条件下的前沿面可以用一个有凹凸性和单调性限制的函数来表示.相较之前的StoNED方法, 本文提出的方法可以估计随机环境下多投入多产出决策单元 (DMU) 的前沿面.通过Monte Carlo实验, 多投入多产出PLE-StoNED方法的有效性得到验证, 它可纠正DEA等传统方法产生的偏误.最后, 实证研究部分运用这一新提出的方法估计了中国大陆商业银行的生产前沿面和效率.本文提出的方法弥补了DEA缺乏统计性的不足, 可为决策者在随机环境下对多投入多产出决策单元进行生产力和效率评估提供决策参考.     

基于机会约束随机Index-DEA的投资组合效率评价

传统DEA和分散化DEA是两种常见的非参数评价方法,二者也被广泛应用于投资组合效率评价。已有相关研究通常将风险和期望收益视为投资组合的投入和产出指标,但该投入-产出假设与实际投资过程并不吻合。在实际投资过程中,真实投入应为投资组合的初始财富,产出则是其终端财富。基于新的投入-产出假设,本文对投资组合初始财富进行标准化,将终端财富转化为收益率形式,进而构造随机生产可能集和相应的机会约束随机Index-DEA模型。当投资组合收益率服从联合正态分布时,随机Index-DEA模型被转化为等价的确定性模型,从理论上证明该等价模型的凸凹性,并提出相应的求解算法。最后,利用该随机Index-DEA模型对我国30只开放式基金进行效率评价,验证所提出DEA模型和求解算法的有效性。     

How to better identify the true managerial performance: State of the art using DEA

Our motivation is to detail a potential improvement on the three-stage analysis published by Fried et al. [Accounting for environmental effects and statistical noise in data envelopment analysis. Journal of Productivity Analysis 2002;17:157–74] that can distinguish true performers from those that may be advantaged by favourable environments or measurement errors. The method starts with data envelopment analysis (DEA), and continues with stochastic frontier analysis to explain the variation in organisational performance in terms of the operating environment, statistical noise and managerial efficiency. It concludes with DEA again using adjusted data to reveal a measure of performance based on management efficiency only. Our proposed contributions include (i) a comprehensive approach where total input and output slacks are identified simultaneously for non-radial inefficiencies before levelling the playing field, (ii) identifying percent adjustments attributable to the environment and statistical noise, and (iii) using a fully units-invariant DEA model.     

基于偏好DEA模型的中国纺织业效率评价

基于具有输入输出指标偏好信息的数据包络分析模型评价中国纺织工业的效率,给出了描述规模报酬不变和规模报酬可变假设的DEA模型及其对偶规划的一种形式。模型克服传统DEA模型应用中常见的决策单元权重为零进而高估决策单元效率的不合理现象,有效地测算了中国31个地区纺织工业的经济运行效率,并分析了地区间效率水平差异的原因。利用各决策单元在经验生产前沿面上的投影点,估计了中国纺织工业的随机生产前沿函数,最后用效率弹性线性递减模型分析了销售收入、人均资产、台港澳和外商投资对各地区效率的微观影响关系。     

随机加权交叉效率下的资源分配问题研究

资源在经济发展中的地位变得越来越重要,本文针对资源分配中存在的某些影响因素是随机的,提出利用随机DEA方法,从三方面综合分析研究资源分配问题,即从生产效率、投入产出弹性和生产潜能。提出并建立了新的随机加权交叉效率计算模型,建立了潜在生产能力模型,给出了规模回报计算公式。综合三个影响因素,建立了新的资源分配权重计算模型。经算例验证,其计算结果令人满意。     

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。     

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.     

Turbofan aero-engine efficiency evaluation: An integrated approach using VSBM two-stage network DEA

The application of Data Envelopment Analysis (DEA) has been wide, especially for the purpose of evaluating efficiency among similar production processes within enterprises belonging to particular industries. Although research pertinent to DEA has primarily focused on efficiency of production systems or corporate entities/organizations (e.g., terminals, hospitals, universities/schools, banks), fairly little attention has been given to efficiency evaluation among engineering systems featuring common configurations (e.g., automobiles, power plants). Furthermore, the limited previous literature involving efficiency evaluation of engineering systems has implemented DEA methodologies with limited discriminative power, i.e. there is a quite increased portion of efficient Decision Making Units (DMUs). In the current paper, a methodological framework deploying Variable intermediate measures Slacks-Based Measure (VSBM) Two-Stage Network DEA is implemented, in order to evaluate the efficiency of turbofan aero-engines, currently utilized by active-duty commercial and military aircraft. Apart from exploring the positive correlation of DEA efficiency with engineering efficiency, we also develop a methodology evaluating the features of near-future turbofan designs in terms of DEA efficiency, thus comprising a potential tool for efficiency assessment of any turbofan aero-engine being in the conceptual or preliminary design stage.     

具有独立子系统的DEA模型及其应用

考虑到现有的DEA模型基本都是针对单系统的,而仅有的多系统模型[10]也是在假设决策单元相互独立并且不存在规模收益的条件下给出的,本文首先建立了3个评价具有独立子系统的决策单元相对有效性的DEA模型,即假设存在规模收益的模型(1),允许存在组内合作的模型(2),组内与组间都可以进行合作的模型(3),并通过分析3个模型之间的关系得到了决策单元通过组内或者组间合作带来的收益,同时证明了模型的一些性质以及决策单元相对有效与子系统相对有效之间的关系,进而应用这3个模型对1997年我国制造业的东、西、中三个区域的域内以及域间合作问题作了研究.结果表明:本文建立的模型不仅可以得到不同省市制造业的整体效率,而且还可以得到各省市制造业的不同行业的效率以及通过域内或域间合作带来的收益,从而得到运作和管理效率低下的根本原因.     

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.     

Estimation of portfolio efficiency via DEA

Traditional DEA models and nonlinear (diversification) DEA models are often used in performance evaluation of portfolios. However, the diversification models are usually very complicated to compute except the very basic models. And the classic DEA models still need to be further justified and tested, since it is not clear whether they are over-linearised according to the diversification models. The existing studies on performance evaluation via the classic DEA models generally focus on the selection of inputs and outputs. In this work, we investigate theoretical foundation of DEA models for portfolios from a perspective of sampling portfolio. We show the classic DEA provides an effective and practical way to approximate the portfolio efficiency (PE). We further verify this approach through different portfolio models with various frictions and bounds on the market. Through the comprehensive simulations carried out in this study, we show that with adequate data sets, the classic DEA models can effectively sample portfolios to take into account sufficient diversification, and thus can be used as an effective tool in computing the PE for their performance assessments. This study can be viewed as a justification of the classic DEA performance assessments and the way to introduce other efficiency notions (like allocation efficiency, scale efficiency, etc) into assessment of portfolios.     

部分中间产出作为最终产品的两阶段合作效率

网络DEA模型研究多个进程和多个子系统的复杂系统的效率度量.针对中间产出无法为第2阶段完全消耗的情形,传统DEA模型对系统效率的评价偏高,已有网络DEA模型则对系统效率的评价偏低.本文提出部分中间产出作为最终产品,进入流通渠道的两阶段效率模型,用来测度两阶段生产过程的真实效率.采用乘积形式描述两阶段合作的特征,给出不同...     

矩阵型网络DEA模型及其实证检验

针对传统DEA模型无法有效的评价矩阵型网络系统的效率,本文构建了矩阵型网络决策单元的生产可能集,建立了矩阵型网络DEA模型。在此基础上证明了决策单元在矩阵型网络DEA模型下为弱DEA有效的充分必要条件为其每个子系统均为弱DEA有效。最后,选用美国的十个电力公司作为决策单元对模型进行实证检验,得出结论:矩阵型网络DEA模型弥补了传统DEA模型无法反映内部有效性从而可能得到错误结果的缺陷,并能精确地计算出各个子过程的效率,辨识出具体需要改进的子过程。同时新模型为评价复杂系统的效率提供了新的思路。     

Pitfalls of decomposition weights in the additive multi-stage DEA model

This paper examines limitations of the multi-stage DEA (data envelopment analysis) model in the literature. We focus on the DEA model with additive efficiency decomposition. We create taxonomy for the multi-stage DEA models and show when the decomposition weights can be non-increasing. When the decomposition weight for a stage is deemed reflective of the stage׳s relative importance, this property then implies that upstream stages (regardless the stage efficiency scores) in the model will obtain higher priority in efficiency decomposition. We also find that the non-increasing weights can affect the evaluation of overall and stage efficiency scores. We illustrate our findings through an empirical data set.     

DEA博弈模型的分析与发展

数据包络分析(Data Envelopment Analysis,DEA)与博弈论之间关系密切.传统DEA模型忽略了决策单元(Decision Making Units,DMUs)之间的竞合关系,对权重的限制过于宽松,难以合理评价DMU效率值.为此,将博弈论方法引入至DEA模型,开展DEA的博弈研究,既是对DEA理论的重大发展,也将极大拓宽博弈论的应用研究.本文分三个阶段对现有的DEA博弈研究进行述评:(1)DEA的博弈论解释;(2)DEA Game模型及其应用;(3)DEA效率博弈;在深入分析重点模型基础上,总结其发展脉络,促进DEA理论与实践的发展.     

A fair evaluation of certain stage in a two-stage structure: revisiting the typical two-stage DEA approaches

The efficiency of decision processes with a two-stage structure has been studied by some modified versions of Data Envelopment Analysis (DEA) methodology, such as the relational or centralized model, and the non-cooperative model. After revisiting the rationale of the centralized model provided by the literature, we find that some unfairness exist in its efficiency evaluation of certain stage. This unfairness leads to the usual underestimation of the overall efficiency by the centralized model. Furthermore, because the independent DEA model for one stage ignores its relation and coordination with the other stage and the two-stage system, externalities between these members may arise and lead to the seeming contradiction in efficiencies derived by independent DEA models for the stages and the black box system. Therefore, we argue that the efficiency of certain stage in the context of a two-stage structure should be reevaluated instead of simply using the independent DEA model. A sequence of leader-follower procedures, with data adjustment on intermediates, is proposed to eliminate the externalities and to ensure a fair evaluation. We find that, after this data adjustment, the reevaluation of the second stage for a given Decision Making Unit (DMU) yields the same result as obtained by the standard DEA model regarding the two-stage as a black box. Moreover, some explicit relations are established between the black box model, the centralized model, and the non-cooperative model. Two typical examples taken from the literature illustrate our main results. Our findings also imply that more emphasis should be placed on the game theoretic DEA approach to model the efficiency evaluation of two-stage processes.     

基于决策者满意度的区间DEA的求解

定义了一种反映决策者满意度的区间数序关系,基于此将区间DEA中的区间不等式约束转化为确定型约束。研究了区间DEA模型向确定型DEA模型转化过程中的数据一致性问题。在保持数据一致性的前提下,根据决策者给出的满意度水平,将区间DEA转化为确定型DEA并进行求解。最后给出算例,并总结和分析了决策单元的DEA效率值随满意度水平变化的规律。     

基于修正Russell方法的模糊决策单元的排序

文章首先建立基于修正Russell方法的超效率DEA模型,然后基于模糊数的比较,建立并求解模糊环境下的基于修正Russell方法的超效率DEA模型,从而解决了模糊决策单元的全排序问题。文末的算例将基于修正Russell方法的模糊超效率DEA模型,与基于CCR模型的模糊超效率DEA模型的结果进行了比较分析。     

Association of DEA super-efficiency estimates with financial ratios: Investigating the case for Chinese banks

The great majority of applications of the popular frontier technique data envelopment analysis (DEA) do not test for the association of efficiency estimates with key performance indicators used by industry observers. Nevertheless, identifying efficiency estimates’ associations with commonly accepted financial measures of performance could guide benchmarking activities, pricing decisions, and regulatory monitoring. Thus, the current paper investigates to what extent bank DEA super-efficiency estimates are associated with key financial ratios. A low correlation may present an opportunity to address inefficiencies that were not obvious in financial ratio analysis, thus enabling an update of inferences drawn from ratios. Regressing ratios on efficiency estimates may also help predict financial ratios. Where an input–output specification is comprised of key financial ratios, DEA can also be used to objectively identify benchmarks for ratio analysis based on actual observed data collected from peers. Nine super-efficiency DEA formulations across two profitability models are systematically tested. The slacks-based measure of DEA with a parsimonious profitability efficiency model emerges as the most significant combination explaining the variation in the two industry ratios, post-tax profit/average total assets and return on average equity.     

一个新的考虑非期望产出的非径向-双目标DEA模型

如何实现对环境效率更准确的定量评价,是国际上从事DEA研究的学者们当前关注的问题之一。在传统DEA效率模型的基础上,综合考虑评价过程中期望产出与非期望产出之间的差异以及实际生产过程中人们追求期望产出最大化和非期望产出最小化的双重目标,构建非期望产出的非径向-双目标DEA环境效率评价模型,通过线性加权和法转化为一个求最大值的单目标线性规划问题。研究结果表明,这种新模型不仅可以分析DEA有效性与Pa-reto最优之间的关系,还利用决策单元的投影获得投入和产出的可调整量,从而提高考虑非期望产出的环境效率评价的精度。实证分析结果与现实情况的高度吻合,说明这种新的非径向-双目标DEA环境效率模型是有效的。